## Actuarial Science Questions

### CM1 Actuarial Mathematics

WHY DO WE PAY INTEREST?

Since, lenders provide borrowers with money for a specified period of time, lender will not be able to use that money during that time, so to make up for this inconvenience along with protecting lenders from the risk of default by the borrower, lender demands interest which may either be fixed in monetary terms or in percentage with respect to the principal amount.

WHAT IS FORCE OF INTEREST?

If we consider a nominal interest rate convertible very frequently (e.g. every second), we are no longer thinking of a fund that suddenly acquires an interest payment at the end of each interval, but of a fund that steadily accumulates over the period as interest is earned and added. In the limiting case, the amount of the fund can be considered to be subject to a constant ‘force’ causing it to grow which is known as force of interest.

WHAT DO YOU MEAN BY DISCOUNTING?

When we are interested in finding out the present value of any amount by pulling it back to the present time at a given rate of interest, it is known as discounting of the cash flows.

WHAT IS A TREASURY BILL? WHO ISSUES IT?

Treasury bills are short-term loans made by the government, these are generally issued at discount and redeemed at par value.

STATE THE EQUATIONS OF VALUE?

An equation of value equates the present value of money received to the present value of money paid out: ‘PV income = PV outgo’

HOW DO WE CALCULATE PROSPECTIVE LOAN OUTSTANDING?

Calculating the loan prospectively involves looking forward and calculating the present value at the current point in time of future cash flows, the loan outstanding at time t is the present (or discounted) value at time t of the future repayment instalments.

HOW DO WE CALCULATE RETROSPECTIVE LOAN OUTSTANDING?

Calculating the loan retrospectively involves looking backwards and calculating the accumulated value of past cash flows, the loan outstanding at time t is the accumulated value at time t of the original loan less the accumulated value at time t of the repayments to date.

WHAT IS DISCOUNTED PAYBACK PERIOD?

The DPP tells us how long it takes for the project to move into a position of profit. Other things being equal, a project with a shorter discounted payback period is preferable to a project with a longer discounted payback period because it will start producing profits earlier.

WHAT DO YOU UNDERSTAND BY INTERNAL RATE OF RETURN?

In economics and accountancy terms, the yield per annum is often referred to as the ‘internal rate of return’ (IRR) or the ‘yield to redemption’. The internal rate of return for an investment project is the effective rate of interest that equates the present value of income and outgo, i.e. it makes the net present value of the cash flows equal to zero.

WHAT IS NET PRESENT VALUE OF A PROJECT?

Net present value is defined as the difference between the value of the positive cash flow and the value of the negative cash flow. The net present value is similar to the accumulated profit, the only difference being that we are now looking at the value at the outset (which, by definition, is a fixed date), rather than the value at the end of the project. A higher net present value indicates a more profitable project.

WHAT IS PAYBACK PERIOD?

Payback period refers to the amount of time it takes to recover the cost of an investment. It is calculated by dividing the initial investment by the average cash flows.

WHICH IS BETTER: PAYBACK PERIOD OR DISCOUNTED PAYBACK PERIOD?

Since the discounted payback period factors in the time value of money, it shows how long it will take to recoup an investment based on observing the present value of the project’s projected cash flows. Thus, DPP is better than PP.

IS TREASURY BILL A PART OF MONEY MARKET OR CAPITAL MARKET?

Treasury bills or T-bills, which are money market instruments, are short term debt instruments issued by the Government of India and are presently issued in three tenors, namely, 91 day, 182 day and 364 day. Treasury bills are zero coupon securities and pay no interest.

WHERE EQUATIONS OF VALUE IS USED?

Equations of value are used throughout actuarial work. For example:  the ‘fair price’ to pay for an investment such as a fixed-interest security or an equity (ie PV outgo) equals the present value of the proceeds from the investment, discounted at the rate of interest required by the investor.  Also, the premium for an insurance policy is calculated by equating the present value of the expected amounts received in premiums to the present value of the expected benefits and other outgo.

WHAT ARE THE MAIN COMPONENTS OF LOAN SCHEDULE?

The loan schedule usually consists of original loan amount, the loan balance at each payment, the interest rate, the amortisation period, the total payment amount, and the proportion of each payment that is made up of interest vs. principal.

HOW IRR IS CALCULATED?

IRR is calculated as a discount rate where NPV is equal to zero.

STATE THE BENEFITS OF USING NPV FOR PROJECT APPRAISAL?

The most important advantage of NPV is that it takes into account time value of money. Along with this, it makes adjustment for cost of capital the risk inherent in making projections about the future. Also, NPV is easy to calculate with its additive nature where multiple projects’ NPV can be added up to get the actual view of wealth creation.

WHAT DO YOU MEAN BY CONVEXITY OF A BOND?

Convexity gives a measure of the change in duration of a bond when the interest rate changes. Thus, ‘Convexity’ refers to the shape of the graph of the present value as a function of the interest rate.  For a series of cash flows with the same discounted mean term, a series consisting of payments paid close together will have a low convexity, whereas a series that is more spread out over time will have a higher convexity.

HOW VOLATILITY OF BOND IS DETERMINED?

The effects of changes in interest rates on the cash flows generated by an asset or required by a liability can be quantified by calculating the volatility. Both the volatility and the discounted mean term provide a measure of the average ‘life’ of an investment. This is important when considering the effect of changes in interest rates on investment portfolios since an investment with a longer term will in general be more affected by a change in interest rates than an investment with a shorter term.

WHAT IS DISCOUNTED MEAN TERM OF AN INVESTMENT?

One measure of interest rate sensitivity is the duration, also called Macaulay duration or discounted mean term (DMT). This is the mean term of the cash flows weighted by present value.

WHAT IS IMMUNISATION OF A PORTFOLIO?

Immunisation refers to the selection of an asset portfolio that will protect this surplus against small changes in the interest rate.

WHAT ARE THE CONDITIONS IN REDINGTON THEORY OF IMMUNISATION?

In the 1950s, the actuary Frank Redington derived the three conditions that are required to achieve immunisation. The conditions for Redington’s immunisation may be summarised as follows: 1. the value of the assets at the starting rate of interest is equal to the value of the liabilities. 2. The volatilities of the asset and liability cash flow series are equal. 3. The convexity of the asset cash flow series is greater than the convexity of the liability cash flow series.

An index-linked bond is a bond which has payment of interest income on the principal that is related to a specific price index, usually the Consumer Price Index (CPI) or Wholesale Price Index (WPI).

EXPLAIN RUNNING YIELD OF A BOND?

The running yield of a bond is the yield generated by the payment of the coupons alone ignoring the redemption payment.

HOW RUNNING YIELD IS DIFFERENT FROM GROSS REDEMPTION YIELD OF A BOND?

A redemption yield is the yield obtained by an investor who holds the bond until redemption whereas the running yield is the yield generated by the payment of the coupons alone (ignoring the redemption payment).

WHAT IS PAR YIELD? IS IT ALWAYS POSITIVE?

Par yield, also referred to as the par rate, is when the coupon rate and the yield of a bond are equal and the bond price will be the same as its nominal value, also called its par value.A par yield is the coupon rate at which bond prices are zero. A par yield curve represents bonds that are trading at par.

WHAT IS ANNUITY IN PERPETUITY?

‘In perpetuity’ means that the payments continue forever.

WHAT IS SPOT RATE? HOW IS IT DIFFERENT FROM FORWARD RATE?

The n-year spot rate is a measure of the average interest rate over the period from now until n years’ time whereas the discrete-time forward rate is the annual interest rate agreed at time 0 for an investment made at time t for a period of r years.

CAN FORWARD RATE BE NEGATIVE?

Forward interest rates are negative whenever the yield curve is negatively sloped.

WHAT IS TERM STRUCTURE OF INTEREST RATE?

Term structure of interest rates refers to the relationship between interest rates and different terms or maturities of bonds.

WHY I IS GREATER THAN I12?

Due to the effects of accumulation, i is greater than i12.

WHY D IS LESS THAN D12?

Due to the effects of compounding,  we are ‘annualising’ a pthly effective discount rate i.e. d12.  For example, to ‘annualise’ an effective discount rate of 0.5% per month, we would make it twelve times it to get 6% pa. This is not the correct annual effective discount rate. The 6% we have obtained is referred to as a nominal discount rate convertible monthly.

WHAT IS TIME VALUE OF MONEY?

The time value of money is the concept of recognising the earning potential of money over time where a sum of money is worth more now than the same sum will be at a future date. The time value of money is also referred to as the present discounted value.

DESCRIBE THE PROCESS OF DATA ANALYSIS?

The key steps in a data analysis process can be described as follows:

1. Develop a well-defined set of objectives which need to be met by the results of the

data analysis.

1. Identify the data items required for the analysis.
2. Collection of the data from appropriate sources.
3. Processing and formatting data for analysis, eg inputting into a spreadsheet,

database or other model.

1. Cleaning data, eg addressing unusual, missing or inconsistent values.
2. Exploratory data analysis, which may include:

(a) Descriptive analysis; producing summary statistics on central tendency and

(b) Inferential analysis; estimating summary parameters of the wider population

of data, testing hypotheses.

(c) Predictive analysis; analysing data to make predictions about future events

or other data sets.

1. Modelling the data.
2. Communicating the results.
3. Monitoring the process; updating the data and repeating the process if required.

DIFFERENCE BETWEEN REPRODUCIBILITY AND REPLICATION.

Reproducibility is linked to the concept of replication which refers to someone repeating an experiment and obtaining the same (or at least consistent) results. Due to the possible difficulties of replication, reproducibility of the statistical analysis is often a reasonable alternative standard.

DIFFERENCE BETWEEN CENSORING AND TRUNCATED DATA.

Censored data occurs when the value of a variable is only partially known. Truncated data occurs when measurements on some variables are not recorded so are completely unknown.

WHY MODELS ARE USED?

A model is an imitation of a real-world system or process. Models of many activities can be developed, for example:  the economy of a country, the workings of the human heart, and  the future cash flows of the broker distribution channel of a life insurance company.

DIFFERENCE BETWEEN DETERMINISTIC AND STOCHASTIC MODELS.

A stochastic model is one that recognises the random nature of the input components. A model that does not contain any random component is deterministic in nature. In a deterministic model, the output is determined once the set of fixed inputs and the relationships between them have been defined. By contrast, in a stochastic model the output is random in nature like the inputs, which are random variables. The output is only a snapshot or an estimate of the characteristics of the model for a given set of inputs. Several independent runs are required for each set of inputs so that statistical theory can be used to help in the study of the implications of the set of inputs. A deterministic model is really just a special (simplified) case of a stochastic model.

WHAT IS SCENARIO BASED TESTING? HOW IS IT DIFFERENT FROM SENSITIVITY TESTING?

A scenario-based model would take into consideration a particular scenario; that is a series of input parameters based on this scenario. Different scenarios would be useful in decision analysis as one can evaluate the expected impact of a course of action. Whereas, sensitivity testing refers to the approach of using a deterministic model with changes in one or more of the assumptions to see the range of possible outcomes that might occur.

WHAT IS ANNUITY CERTAIN?

An annuity-certain provides a series of regular payments in return for a single premium (i.e. a lump sum) paid at the outset.

WHAT IS A PURE ENDOWMENT PLAN?

A pure endowment is an insurance policy which provides a lump sum benefit on survival to the end of a specified term usually in return for a series of regular premiums. For example, a payment of £50,000 is made if a life now aged 30 survives to age 60, but no payment is made if this life dies before age 60.

WHAT ARE VARIOUS ASSURANCE PRODUCTS?

whole life assurance, term assurance, pure endowment & endowment assurance.

WHAT ARE SOME FEATURES OF ANNUITIES?

An annuity is a regular series of payments. An annuity-certain is an annuity payable for a definite period of time: the payments do not depend on some factor, such as whether a person is alive or not. If payments are made at the end of each time period, they are paid in arrears. If they are made at the beginning of each time period, they are paid in advance. An annuity paid in advance is also known as an annuity-due. Where the first payment is made during the first time period, this is an immediate annuity. Where no payments are made during the first time period, this is a deferred annuity. If each payment is for the same amount, this is a level annuity. If payments increase (decrease) each time by the same amount, this is a simple increasing (decreasing) annuity.

RATE ON BASIS OF PREMIUM: TERM ASSURANCE, ENDOWMENT POLICY AND WHOLE LIFE ASSURANCE?

Endowment>whole life>term assurance

HOW NOMINAL RATE OF INTEREST IS DIFFERENT FROM EFFECTIVE RATE OF INTEREST?

Effective rates have interest paid once per measurement period whereas nominal rates are paid more frequently than once per measurement period.

WHAT IS ACCUMULATED PROFIT?

Accumulated profit is the accumulated value of the net cash flows as at the time of the last payment.

WHAT IS SELECT MORTALITY?

Policyholders with a duration of one year, say, will have recently satisfied the company about their state of health. We would therefore expect their mortality to be better than that of policyholders of the same age with duration of, say, 3 years who passed the medical underwriting hurdle several years ago. Thus, the mortality of the recently joined policyholders is called select mortality, and we expect it to be better than that of longer duration policyholders, whose mortality we call ultimate mortality.

HOW UDD IS DIFFERENT FROM CFM?

Under uniform distribution of deaths(UDD) assumption, for an individual aged exactly x , the probability of dying on one particular day over the next year is the same as that of dying on any other day over the next year whereas under constant force of mortality(CFM), for integer ages, we suppose that the force of mortality is constant.

The gross premium is the premium required to meet all the costs under an insurance contract, and is the premium that the policyholder pays.  It is also sometimes referred to as the office premium which contains impact for loaded profits, cost of capital, adjustments for competition and other loadings.

WHEN PROSPECTIVE AND RETROSPECTIVE RESERVES ARE EQUAL?

If the retrospective and prospective reserves are calculated on the same basis, and this basis is the same as the basis used to calculate the premiums used in the reserve calculation, then the retrospective reserve will be equal to the prospective reserve.

WHAT IS JOINT LIFE ANNUITY?

A joint life annuity covers two lives, where the regular payments are contingent on the survival of one or both of those lives.

WHEN LAST SURVIVOR POLICY BEGINS PAYMENT?

Two common types of policy are: an annuity payable to a couple while at least one of them is alive, and  an assurance payable on the second death of a couple. These are both examples of last survivor policies, where the payment is contingent on what happens to the second life to die, rather than the first.

WHAT IS MORTALITY PROFIT?

The mortality profit is defined as the difference between Expected Death Strain & Actual Death Strain where EDS is the amount the company expects to pay out, in addition to the year-end reserve for a policy and ADS is the amount it actually pays out, in addition to the year-end reserve.

HOW MULTIPLE STATE MODELS IS DIFFERENT MULTIPLE DECREMENTS MODEL?

Multiple state models are well suited to valuing cash flows that are dependent on multiple transitions, such as of health insurance contracts. A multiple decrement model is a multiple state model which has:  one active state, and  one or more absorbing exit states.

WHAT IS UNIT FUND?

Unit fund is the total value of the units in respect of the policy at any time.

HOW ULIP WORKS?

With unit-linked contracts the policyholders are entitled units, which represent a portion of a fund or funds of investments managed by the life insurer referred to as the unit fund of the policy. The unit fund value moves in line with the performance of the backing investments. The non-unit fund represents the accumulation of all cash flows paid in that are not used to buy units, less all cash flows paid out that have not arisen from the cancellation of units. As such it represents the accumulation of the company’s profits from the policy at any time.

WHAT ARE THE VARIOUS CONSTITUTES OF NON-UNIT FUND?

Non-unit fund includes unallocated premiums, bid/offer spread and unit fund charges. Non-unit benefits include, for instance, any sum insured payable on death in excess of the value of the units, or any guaranteed maturity value in excess of the value of the units.

The bid price is the cash-in value of each unit and the offer price is the price that has to be paid to purchase a unit in the fund. The difference between the two (with the offer price being greater than the bid price) is called the bid-offer spread.

WHAT ARE THE STEPS OF PROFIT TESTING?

The steps in profit testing starts with deciding on the structure of the product, building a model to project cash flows for the product then deciding on a risk discount rate and profit criterion then decide on some ‘first draft’ premiums (conventional product) / charges (unit-linked product), vary the premiums / charges until our profit criterion is met, keep varying premiums until we have a product that meets the profitability criterion, is marketable, and is resilient to adverse future experience.

HOW PROFIT MARGIN IS CALCULATED?

Profit margin is the NPV expressed as a percentage of the EPV of the premium income where the risk discount rate is used to do the discounting in both the numerator and the denominator.

### CM2 Financial Engineering & Loss Reserving

WHAT ARE THE DIFFERENT FORMS OF EFFICIENT MARKETS?

Efficient market consists of: weak form market where market prices reflect all of the information contained in historical price data, semi-strong form is one where market prices reflect all publicly available information & strong form is where market prices reflect all information, whether or not it is publicly available.

WHAT IS MEANT BY UTILITY?

In economics, ‘utility’ is the satisfaction that an individual obtains from a particular course of action.

WHAT IS THE SHAPE OF UTILITY CURVE FOR A RISK-AVERSE INVESTOR?

for a risk-averse investor, utility is a (strictly) concave function of wealth which reflects that the marginal utility of wealth (strictly) decreases with the level of wealth and consequently each additional dollar, say, adds less satisfaction to the investor than the previous one.

WHAT IS ABSOLUTE AND RELATIVE RISK AVERSION?

if the absolute value of the certainty equivalent decreases (increases) with increasing (decreasing) wealth, the investor is said to exhibit declining absolute risk aversion. If the absolute value of the certainty equivalent decreases (increases) as a proportion of total wealth as wealth increases the investor is said to exhibit declining (increasing) relative risk aversion.

WHAT IS VARIANCE OF RETURN?

Variance of return refers to change in the market value of the asset about the mean value.

WHAT IS DOWN-SIDE VARIANCE? WHY IS IT IMPORTANT?

Downside semi variance helps to calculate the possibility of low returns. It is the risk of actual values being less than expected values.

WHAT DO YOU UNDERSTAND BY VALUE AT RISK?

VaR represents the maximum potential loss on a portfolio over a given future time period with a given degree of confidence. It calculates the likelihood of underperforming.

WHAT IS PORTFOLIO THEORY?

Mean-variance portfolio theory leads to optimum portfolios where investors can be assumed to have quadratic utility functions & if returns are assumed to be normally distributed.

DESCRIBE DIFFERENT TYPES OF MULTI-FACTOR MODELS?

macroeconomic, fundamental and statistical factor models.

WHAT ARE THE BASIC ASSUMPTIONS OF CAPITAL ASSET PRICING METHOD?

The basic assumptions of CAPM are investors are risk-averse and non-satiated, no transaction costs, there is a fixed single-step time period, investors make their decisions purely on the basis of expected return and variance which can be known.

WHAT DOES CAPM DEPICT?

The capital asset pricing model (CAPM) tells us about the relationship between risk and return for security markets as a whole.

WHAT IS A MARTINGALE?

A martingale is a process whose current value is the best estimate of its future values. So, the expected future value is the current value or that the process has ‘no drift’.

STATE SOME PROPERTIES OF A STANDARD BROWNIAN MOTION.

A Wiener process is a stochastic process with independent and stationary increments, also  it has normally distributed increments, along with continuous sample paths.

ARE STOCHASTIC PROCESSES GOOD MODELS FOR ASSET PRICES?

No, since asset prices do not start at zero, are not continuous and they certainly don’t exhibit normally distributed increments.

STATE WHAT IS MEANT BY ARBITRAGE?

An arbitrage opportunity is a situation where we can make a certain profit with no risk.

OUTLINE THE FACTORS THAT AFFECT OPTION PRICES.

There are usually 5 factors affecting option prices: the underlying share price, the strike price, the time to expiry, the volatility of the underlying share and the risk-free interest rate.

EXPLAIN WHAT IS MEANT BY PUT-CALL PARITY.

In an arbitrage free market, two portfolios which  have the same value at expiry, for example, A: consisting of a European call plus cash, B: consisting of the underlying share plus a European put with the same expiry date and exercise price as the call, and since the options cannot be exercised before then they should have the same value at any time.

NAME DIFFERENT TYPES OF OPTION GREEKS.

The Greeks are a group of mathematical derivatives that can be used to help us to manage or understand the risks in our portfolio. Greeks are: delta, gamma, theta, rho and vega.

IS THERE ANY DIFFERENCE BETWEEN EUROPEAN AND AMERICAN OPTION?

A European option is an option that can only be exercised at expiry. An American option is one that can be exercised on any date before its expiry.

EXPLAIN THE DIFFERENCE BETWEEN THE REAL-WORLD MEASURE AND THE RISK-NEUTRAL MEASURE.

Risk-neutral measure is the probability measure with respect to which any asset, whether risky or risk-free, offers the same expected return to investors, namely, the risk-free rate of return. However, in the real-world, investors do need extra return for the amount of risk undertaken.

WHAT ARE RUN-OFF TRIANGLES?

Run-off triangles are two-dimensional matrices that help in estimating the ultimate cost of claims under general insurance business.

STATE HOW RUN-OFF TRIANGLES ARE USED FOR RESERVE CALCULATIONS?

The method is based on an accident-year basis where claims development is clustered by the year an accident has occurred. The task is to decide the amounts yet to be paid in respect of the given accident years by calculating respective development factors and accumulating the claims already paid and finally, finding the incremental claims to be paid.

### CS1 Actuarial Statistics

DIFFERENTIATE BETWEEN CONTINUOUS RANDOM VARIABLE & DISCRETE RANDOM VARIABLE?

Discrete random variables are random variables that take a finite number of values. For example, the outcome of rolling a die. Continuous random variables, on the other hand, can take on any value in a given interval.

WHAT IS LAW OF LARGE NUMBERS?

Law of large number states that as there is greater exposure to losses, the expected value of loss equals the actual value of loss. It basically helps in predicting the losses in a better manner.

WHAT DO YOU MEAN BY POISSON PROCESS?

This distribution models the number of events that occur in a specified interval of time, when the events occur one after another in time in a well-defined manner.

HOW MONTE CARLO SIMULATION TAKES PLACE?

A Monte Carlo simulation is used to predict the probability of a variety of outcomes when there are random variables present. Monte Carlo simulations help to explain the impact of risk and uncertainty in prediction and forecasting models.

WHAT IS THE SIGNIFICANCE OF P-VALUE?

The p-value, also called probability value, is the lowest level at which H0 (null hypothesis) can be rejected.

GIVE AN EXAMPLE OF APPLICATION OF BINOMIAL DISTRIBUTION.

Rolling a die, Tossing a coin, Number of Spam Emails per Day and Number of Fraudulent Transactions.

WHAT IS CENTRAL LIMIT THEOREM?

Central Limit Theorem gives us an approximate distribution of the sample mean when the population distribution is unknown and more importantly does not need to be known. It provides useful normal approximations to the distributions of particular functions.

WHAT DOES LEVEL OF SIGNIFICANCE DEPICT?

It is the probability of rejecting H0 when it is in fact true.

WHAT IS POSTERIOR DISTRIBUTION? HOW IS IT RELATED TO PRIOR DISTRIBUTION?

The conditional distribution given the observed data is called the posterior distribution of theta. If the prior distribution is continuous, then the posterior distribution is also continuous. Similarly, if the prior distribution is discrete, then the posterior distribution is also discrete.

WHAT IS CREDIBILITY FACTOR?

The credibility premium formula for this risk is Z*X_BAR+(1-Z)*MU where Z is a number between zero and one and is known as the credibility factor.

WHAT IS MEANT BY CAUSATION EFFECT?

Spurious correlations refers to correlation does not equal causation which means  that a change in one variable causes a change in the other — is a common misinterpretation of correlation coefficients.

WHAT IS SENSITIVITY AND SPECIFICITY?

Sensitivity refers to the true positive rate whereas specificity refers to the true negative rate. For example,the ability of a test to correctly identify patients with a disease is  sensitivity whereas specificity is the ability of a test to correctly identify people without the disease

WHAT IS R SQUARED AND ADJUSTED R SQUARE? HOW ARE THEY RELATED?

the proportion of the total variation of the responses ‘explained’ by a model, called the coefficient of determination, denoted R-square whereas adjusted r-square gives a measure of how much variability is explained by the regression model. It takes account of the undesirability of increased complexity by the r-square method.

NAME SOME DISTRIBUTIONS BELONGING TO EXPONENTIAL FAMILY.

Normal, poisson, binomial, gamma, lognormal.

DIFFERENCE BETWEEN SAMPLE VARIANCE AND POPULATION VARIANCE.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data. Sample variance is an unbiased estimator of the population variance.

WHAT IS PRINCIPAL COMPONENT ANALYSIS? WHAT IS ITS OBJECTIVE?

Principal components analysis (PCA) is used  to identify the most important variables for multivariate data sets. It is also called factor analysis, and provides a method for reducing the dimensionality of the data set.

WHAT IS A SATURATED MODEL?

A saturated model is defined to be a model in which there are as many parameters as observations, so that the fitted values are equal to the observed values.

WHAT DOES CONTINGENCY TABLE SIGNIFY?

A contingency table consists of rows and columns containing counts of sample items (people, claims etc) that are classified according to two category variables.

WHAT IS CONDITIONAL EXPECTATION?

The conditional expectation of Y given X =x is the mean of the conditional distribution of Y given X= x.

DIFFERENCE BETWEEN COVARIANCE AND CORRELATION.

Covariance refers to the relationship between two random variables in which a change in the other reflects a change in one variable which can range from -∞ to +∞. Correlation determines the degree to which two or more random variables move in sequence. Its value ranges from -1 to 1.

### CS2 Risk Modelling & Survival Analysis

WHAT IS A COUNTING PROCESS?

A counting process is a stochastic process, X , in discrete or continuous time, whose state space is the collection of natural numbers {0,1,2,…}.

WHAT IS MEANT BY SAMPLE PATH OF A PROCESS?

A sample path is the sequence of outcomes of a particular set of experiments i.e. THEIR JOIN REALISATION.

STATE HOW MARKOV CHAIN IS USEFUL?

When a Markov process has a discrete state space and a discrete time set it is called a Markov chain.it is mainly used in general and life insurance companies to decide on a no-claim discount system.

HOW MARKOV CHAIN PROCESS IS DIFFERENT FROM MARKOV JUMP?

When a Markov process has a discrete state space and a discrete time set it is called a Markov chain but when the time set is continuous, it is known as the Markov jump process.

The curtate future lifetime k_x of a life aged exactly x, is the whole number of years lived after age x i.e. it takes only discrete values where the expected future lifetime after age x which is continuous is complete future lifetime.

WHAT IS MEANT BY FORCE OF MORTALITY? HOW IS IT USEFUL?

Force of mortality is the instantaneous rate of mortality acting on a certain age, also known as hazard rate. It is useful in calculating the survival functions such as expected future lifetime, death rates, etc

WHAT ARE COVARIATES?

different factors that are used to split the population into subgroups are called covariates such as age, sex, gender, etc

HOW PROPORTIONAL HAZARD MODELS ARE DEVELOPED?

proportional hazards models inculcates calculating hazard rates where the formula incorporates an adjustment to reflect the characteristics of each particular individual of the population.

STATE DIFFERENT TYPES OF PARAMETRIC MODELS?

Most common parametric models are developed by distributions such as the exponential (constant hazard), Weibull (monotonic hazard), Gompertz-Makeham (exponential hazard) and log-logistic (‘humped’ hazard).

STATE SOME FACTORS BY WHICH LIFE INSURANCE MORTALITY IS GROUPED INTO?

(a) Sex (b) Age (c) Type of policy (which often reflects the reason for insuring) (d) Smoker/non-smoker status (e) Level of underwriting (e.g have they undergone a medical examination?) (f) Duration in force.

The crude estimates usually progress erratically from age to age. We therefore  smooth the crude estimates, to produce a set of graduated estimates that do progress smoothly with age. This is done because smoothing reduces the sampling errors at each age.

WHAT ARE DIFFERENT TYPES OF CENSORING? GIVE FEW EXAMPLES.

Censoring is present when we do not observe the exact length of a lifetime, but observe only that its length falls within some interval.

Right Censoring- ending of a mortality investigation before all the lives being observed have died.

Left censoring- In medical studies patients are subject to regular examinations. Discovery of a condition tells us only that the onset fell in the period since the previous examination; the time elapsed since onset has been left censored.

Interval censoring- In actuarial investigations, where we might know only the calendar year of death.

Random censoring- life insurance withdrawals

Type I censoring- Lives censored at the end of an investigation period

Type II censoring -When a medical trial is ended after 100 lives on a particular course of treatment have died.

WHAT IS PURELY IN-DETERMINISTIC TIME SERIES?

A process X is called purely indeterministic if knowledge of the previous values is progressively less useful at predicting the value of future events as N tends to infinity.

WHAT ARE INTEGRATED TIME SERIES?

X is said to be  ‘integrated of order 0’ if it is a stationary time series process, X is I(1) if X itself is not stationary but the increments X_t-X_(t-1) form a stationary process,

HOW COPULAS ARE USED IN INSURANCE INDUSTRY?

A copula is a function that takes as inputs marginal CDFs and outputs a joint CDF. For example, suppose an insurer wants to work out the joint probability that annual losses on its household portfolio will be less than or equal to £5m and that annual losses on its motor portfolio will be less than or equal to £3m. For simplicity of calculation, we assume that the two portfolios give rise to losses independently, then using copula their joint CDF can be calculated as a product of marginal CDFs.

WHY REINSURANCE IS NECESSARY FOR AN INSURANCE COMPANY?

The claims on an insurance company must be met in full, but, to protect itself from large claims, the company itself may take out an insurance policy; such a policy is called a reinsurance policy.

WHAT IS MACHINE LEARNING?

Machine learning is a method of training computers where computer algorithms are developed and applied to data to generate information. This information can consist simply of hidden patterns in the data, but often the information is applied to solve a specific problem.

WHAT ARE VARIOUS MACHINE LEARNING METHODS?

Supervised, Unsupervised, Semi-supervised and reinforcement learning methods.

ARE DECISION TREES AND RANDOM FOREST SAME?

Decision trees are used to make a prediction where each root node on a tree represents a single input variable and the leaf nodes of the tree contain an output variable. Random forests apply a method based on averaging a number of randomly generated decision trees.

WHAT IS MEANT BY PRUNING OF DECISION TREES?

Pruning refers to the stopping criteria which influences the performance of the tree such as using hold-out tests where only key leaf nodes are kept.

HOW PRECISION AND ACCURACY ARE DIFFERENT?

Accuracy measures how close the result is to the actual value required whereas precision measures how close results are to one another. While accuracy can be used in one instance, precision will be measured over time.

HOW DATA IS DIVIDED INTO TRAINING AND TEST DATA? WHY IS IT NECESSARY?

In machine learning, the ‘training’ data is often split into a part used to estimate the parameters of the model, and a part used to validate the model. Also, a test data set is created where the sample of data used to provide an unbiased evaluation of the final model fit.

WHY GENERALISED LINEAR MODELS IMPORTANT IN PRICING INSURANCE PRODUCTS?

WHAT IS OVER AND UNDER GRADUATION?

If the graduation process results in rates that are smooth but show little adherence to the data, then we say that the rates are over graduated. However if they adhere to the data but progress erratically, then they seem to be under-graduated.

HOW IS GINI INDEX A USEFUL TOOL IN MACHINE LEARNING?

Gini index measures the purity of the decision tree in such a way that it depicts an indication of how ‘pure’ the leaf nodes are. For each node, Gini index is weighted by the total number of instances in the parent node.

HOW FUTURES ARE DIFFERENT FROM FORWARDS?

A forward is an agreement between two parties to trade a specified asset at a set date in the future at a set price whereas futures are standardised and exchange-tradeable.

WHAT ARE DERIVATIVES?

A derivative is a financial instrument that derives its value from the value of some other asset. Some types of derivatives are swaps, options, futures and forwards.

STATE THE RELATION BETWEEN EPS AND DPS?

Dividend per share is the actual EPS that is paid out to the shareholders in the form of dividends.

HOW CROWDFUNDING TAKES PLACE?

Crowdfunding is the way through which a large number of participants, individuals or businesses, support a business, project, campaign or an individual by often building a crowdfunding website which will typically charge a fee, eg a percentage of the money raised.

WHAT DO YOU UNDERSTAND BY DOUBLE TAXATION RELIEF? WHEN DOES IT OCCUR?

Double taxation relief (DTR) means that the local tax authority allows companies with overseas income or capital gains to offset tax paid overseas against their liability to domestic tax on that income or capital gains.

WHAT IS NIL PAID RIGHTS?

In case of rights issue, when the shareholders acquire these shares without paying immediately, such issue is known as nil-paid rights.

WHAT IS THE USE OF DELPHI TECHNIQUE?

The Delphi technique involves gathering the thoughts of a number of experts in a particular area where the organiser sends questions to experts and maintains the anonymity of the answers to finally reach a common conclusion.

WHAT IS MEANT BY GEARED BETA?

The beta of a company’s shares is affected by the company’s existing gearing. If the gearing were to change, then the volatility of returns would change, and hence the beta would change.

WHAT ARE THE MAIN DECISIONS TAKEN BY A FINANCIAL MANAGER?

A company’s financial managers are responsible for the major investment and financing decisions.

WHY CAPITAL BUDGETING IS IMPORTANT?

The capital budgeting decision considers the choice of projects, and hence real assets, in which the firms should invest. Thus, it helps in deciding the profitable project amongst the alternatives.

STATE SOME CONFLICTING OBJECTIVES OF DIFFERENT STAKEHOLDERS.

The scope for conflict between owners and managers may arise when some managers might wish to pursue projects of interest over more profitable projects but shareholders’ objective will normally be to receive a high return on their investment in the company. Also there may be  differences between the lenders’ short-term desire for security and the shareholders’ long-term interest in the development of the company.

WHAT IS AGENCY PROBLEM?

The managers of a company may have aims which are not in the best interests of the shareholders, this is known as the ‘agency problem’. For example, some managers might wish to pursue projects of interest over more profitable projects but shareholders’ objective will normally be to receive a high return on their investment in the company.

WHAT DO YOU UNDERSTAND BY OPPORTUNITY COST OF CAPITAL?

It is the cost of the next best alternative foregone. Since firms have limited cash, they may wish to invest in one project by sacrificing to invest in some other project. The cash flows arising from the foregone project is then the opportunity cost of capital for the existing project.

WHAT IS CAPITAL GAINS TAX?

Capital gains tax is the difference between the sale price and purchase price of a real asset when the former is greater.

WHAT IS OFFER FOR SALE?

In an offer for sale at a fixed price, a predetermined number of shares is offered to the general public at a specified price.

WHAT IS THE MAIN DIFFERENCE BETWEEN HIRE PURCHASE AND LEASE?

A hire purchase agreement is an agreement to pay regular rental payments for the goods you hire and then to buy them at the end of the agreed period. Legal ownership passes to the buyer only when the final payment is made. A lease is an agreement where the owner of an asset gives the lessee the right to use the asset over a period of time, in return for a regular series of payments. Legal ownership does not change hands.

WHEN ARE DERIVATIVES MOST USEFUL?

The uses of derivatives vary widely: risk management, e.g. of interest rates, exchange rates, stock market indices or prices along with borrowing cost reduction.

WHAT ARE THE THREE SECTIONS OF CASH FLOW STATEMENT?

Cash flow from operating activities, cash flows from investing activities and cash flow from financing activities.

WHAT IS WORKING CAPITAL? HOW IS IT CALCULATED?

Working capital is the amount that the business has in cash or near-cash having deducted the claims on that cash in the form of current liabilities. It is calculated as the difference between current assets and current liabilities.

DIFFERENCE BETWEEN A FORECAST AND A BUDGET?

Forecasts are predictions of future events in a passive manner. In contrast, budgets are active. They are plans, expressed in monetary terms, for the future.

HOW IS DIVIDEND POLICY OF A COMPANY DECIDED?

Key factors in the dividend decision are stock market reaction eg adverse reaction to dividend cuts, competitors’ policies cash reserves, tax – investors prefer dividends if they are taxed at a higher rate on capital gains, growth opportunities – if these exist it may be better to retain profits stability and consistency with previous dividend policy and  investor preferences- eg need for cash, better opportunities to invest elsewhere.

HOW PRECISION AND ACCURACY ARE DIFFERENT?

Accuracy measures how close the result is to the actual value required whereas precision measures how close results are to one another. While accuracy can be used in one instance, precision will be measured over time.

HOW DATA IS DIVIDED INTO TRAINING AND TEST DATA? WHY IS IT NECESSARY?

In machine learning, the ‘training’ data is often split into a part used to estimate the parameters of the model, and a part used to validate the model. Also, a test data set is created where the sample of data used to provide an unbiased evaluation of the final model fit.

WHY GENERALISED LINEAR MODELS IMPORTANT IN PRICING INSURANCE PRODUCTS?

WHAT IS OVER AND UNDER GRADUATION?

If the graduation process results in rates that are smooth but show little adherence to the data, then we say that the rates are over graduated. However if they adhere to the data but progress erratically, then they seem to be under-graduated.

HOW IS GINI INDEX A USEFUL TOOL IN MACHINE LEARNING?

Gini index measures the purity of the decision tree in such a way that it depicts an indication of how ‘pure’ the leaf nodes are. For each node, Gini index is weighted by the total number of instances in the parent node.

WHAT HAPPENS WHEN MB > MC?

If MB > MC, then we should increase production of respective good, and decrease the production of other goods, since the value of one more unit of good, MB, is greater than the value of goods we must forego to make it, MC.

WHY IS PPC NOT A STRAIGHT LINE?

The shape of PPC depends on the opportunity cost of additional unit produced. If marginal opportunity cost remains constant then PPC will be a straight line owing to constant slope.

WHAT IS MARKET CLEARING?

The process of balancing or clearing the market by setting prices of goods in such a manner that the quantity supplied is equal to quantity demanded is known as market clearing.

HOW GOODS AND FACTOR MARKET ARE INTERDEPENDENT?

The goods and services market drives the factor market. When consumers demand more goods and services, manufacturers increase their purchases of the resources used to make those goods and services. Factor market producers, in turn, step up production of the raw materials that the manufacturers need. Thus, they are closely related to each other.

STATE THE LAW OF DEMAND.

The law of demand states that there is an inverse relationship between price and quantity demanded i.e. if prices of goods increase, the quantity demanded decreases and vice versa.

SINCE Q = A – BP, WHAT HAPPENS TO THE CURVE IF A CHANGES ALONE AND B CHANGES ALONE?

WHAT IS THE EFFECT ON PRICE WHEN DEMAND & SUPPLY CURVE SHIFT TOGETHER?

If the increase in both demand and supply is equal, the equilibrium price remains the same. In case of increase in demand > increase in supply, both equilibrium price and quantity tend to increase. If the increase in demand < increase in supply, the equilibrium price falls whereas the equilibrium quantity rises.

WHAT IS THE EFFECT OF PRICE ON TR IN CASE OF INELASTIC DEMAND?

If the price for an inelastic good is increased and the demand does not change, the total revenue increases due to the higher price and static quantity demanded.

GIVE A SITUATION WHEN TR REMAINS UNCHANGED.

WHAT IS THE RELATION BETWEEN SLOPE OF DEMAND CURVE AND PED?

STATE ANY 2 IMPACTS OF ADVERTISING?

Advertising campaigns generally intend to increase both demand and brand loyalty for a product.

WHAT DOES IT INDICATE WHEN IED IS POSITIVE AND LESS THAN 1?

GIVE EXAMPLE OF WHERE ACTIONS OF SPECULATORS TEND TO REDUCE PRICE FLUCTUATIONS.

If a speculator believes that an asset is currently overpriced, they sell as much of the asset as possible while prices are higher. This act begins to lower the price of the asset.

GIVE EXAMPLE OF WHERE ACTIONS OF SPECULATORS TENDS TO MAKE PRICE MOVEMENTS LARGER.

If a speculator thinks the value of a certain asset will rise, they can decide to buy as much of the asset as they can. This activity raises the price of the specific asset depending on the projected increase in demand.

WHAT IS THE RELATION BETWEEN TU AND MU?

The total utility rises with a rise in commodity consumption as long as the marginal utility, or MU, is positive. When MU from each succeeding unit starts to decline, TU starts to rise but at a decreasing rate. The MU zeros out at the maximum TU. In this stage, TU stops expanding; this is the so-called “point of safety.” The MU turns negative and TU begins to decline when consumption exceeds the degree of contentment.

STATE THE FORMULA OF MSC.

Marginal Social Cost (MSC) = Marginal Private Cost (MPC) + Marginal External Costs (MEC)

WHEN IS TCS  MAXIMISED?

STATE THE EQUI MARGINAL PRINCIPLE.

The equi-marginal principle states that utility will be maximised if the ratio of the marginal utilities is equal to the ratio of the prices (or alternatively that the marginal utilities per £ spent are equal).

COST = 10, BENEFIT = 20(AFTER 2 MONTHS), DF = 0.9, SHOULD YOU BUY THE PRODUCT OR NOT?

Present value of benefit= 20*0.9^(2/12)= 19.65 approximately which is greater than 10, thus we should buy the product.

IS THE OPTIMUM CONSUMPTION SAME AS EQUI MARGINAL PRINCIPLE?

yes.

WHAT IS THE SUBSTITUTION AND INCOME EFFECT WHEN PRICE OF INFERIOR GOOD RISES?

When an inferior good’s price increases, buyers tend to buy more of it and less of its substitutes because the income effect outweighs the substitution effect for inferior goods.

WHAT IS CERTAINTY EQUIVALENT?

The amount of money that is guaranteed and that someone would deem to have the same level of desirability as a risky asset is known as the certainty equivalent.

WHAT IS THE PROBLEM OF ADVERSE SELECTION?

Adverse selection describes scenarios where an insurance provider offers insurance coverage to a candidate whose actual risk is significantly higher than the candidate’s estimated risk.

STATE THE RELATION BETWEEN TPP AND MPP?

The following is an explanation of the relationship between TPP and MPP: TPP rises at an accelerating rate as long as MPP rises. (ii) TPP rises but at a declining rate when MPP declines but remains positive. (iii) TPP reaches its maximum when MPP falls to zero.

WHY DOES TVC CURVE START FROM ORIGIN BUT NOT TFC CURVE?

It is because when there is zero production, there will still be some fixed or sunk costs related to the factory or workplace.

HOW TO DEAL WITH THE REDUCTION IN SUPPLY DUE TO PRICE CEILING?

The imposed maximum price a seller is permitted to charge for a good or service is known as a price ceiling. The pricing (and profit) controls must be made up for in some way by the producers. They can restrict supply, reduce output or production quality, or tack on new fees for previously free options and features.

WHAT IS SUBSTITUTION EFFECT ON GIFFEN GOODS?

Giffen products are so inferior that the positive substitution effect surpasses the negative income effect. As a result, even as the price drops, less is still being desired. Giffen products have a demand curve that is favourably sloping (which means that as price decreases the quantity demanded also decreases).

WHAT IS RELATION BETWEEN AVC AND APP?

AVC and AP are negatively correlated, meaning that as AP rises, AVC falls. When AP is at its highest, AVC reaches its lowest point, and when AP is at its lowest, AVC rises.

WHAT DO YOU UNDERSTAND BY ECONOMIES OF SCALE?

The phenomenon known as economies of scale occurs when the scale or magnitude of the production produced by a firm increases while the average cost per unit of output decreases.

HOW ECONOMIES OF SCALE IS DIFFERENT FROM ECONOMIES OF SCOPE?

Economies of scope concentrate on the average overall cost of production of a range of items. In contrast, economies of scale concentrate on the cost advantage that results from a higher level of production for a single good.

WHAT IS MEANT BY CONTAINER PRINCIPLE?

Container Principle states that larger capital equipment, such as pipes, containers, and tanks, has a lower cost per unit of output. This is a result of how surface area and volume are related. The materials used to make the outside of a container determine its expenses, but the volume of the container determines its output. A container’s volume increases by a factor of 3 for every unit increase in surface area, hence the larger the container, the less expensive the average production.

WHAT HAPPENS WHEN MPPL/PL > MPPK/PK

WHAT HAPPENS TO CURVES OF LRAC & LRMC WHEN COSTS ARE CONSTANT?

A U-shaped LRAC curve is consistent with the firm facing diseconomies of scale at higher output levels and economies of scale at relatively lower output levels. The LMC curve measures the change in LRTCs as output is raised and is derived from the LRAC curve. When LAC is decreasing, LMC are below the LAC curve, and when LAC is increasing, they are above the LAC curve.

WHEN DOES SHORT RUN SHUTDOWN POINT OCCUR?

If the price of the good is less than the average variable cost in the short run, a firm that cannot recover its fixed costs will decide to temporarily close. In the long run, if the price is less than the average total cost and the company can recover both fixed and variable costs, it will decide to quit.

HOW RETURN ON CAPITAL EMPLOYED IS CALCULATED?

Net operating profit, or earnings before interest and taxes, is used to assess return on capital employed. The difference between total assets and current liabilities can also be used to determine it by dividing earnings before interest and tax by that amount.

CONSTANT COST INDUSTRY?

A sector with constant costs is one in which the addition or exit of new firms has no effect on the costs of any individual firm.

CAN PERFECT COMPETITION EXIST WITH ECONOMIES OF SCALE?

Economies of scale hold that greater production per unit of input will arise from the application of additional resources, such as capital and labour.It also indicates a long-term oligopolistic situation since, if economies of scale are available, the market will be dominated by a small number of very large companies. Perfect competition makes the assumption that all inputs, including labour, can be moved from one activity to another without incurring any costs in order to increase profitability. This frictionless shifting of inputs means that as market conditions change, profit is squeezed out of the market, and suppliers will make no profit over the long term because any markets that generate profit will soon see an infusion of labour and capital until there is no profit left.

HOW EQUILIBRIUM PRICE IS CALCULATED?

The equilibrium price formula is based on amounts of supply and demand; to find the price, put quantity demanded (Qd) equal to quantity supplied (Qs) and find the price (P).

WHAT IS INDIFFERENCE CURVE?

A combination of two items in different quantities that gives a person equal satisfaction (utility) is represented by an indifference curve.

HOW MARGINAL UTILITY IS CALCULATED?

The additional satisfaction that a consumer experiences when they consume an additional unit of a good or service is referred to as marginal utility. It is calculated by subtraction of a unit’s total utility from the unit’s total utility before it.

WHAT IS MEANT LAW OF DIMINISHING RETURNS?

An economic principle known as the law of diminishing returns states that as investment in a certain area increases, the rate of profit from that investment can no longer increase at a certain point assuming other variables remain constant.

WHAT IS LIMIT PRICING OF A PRODUCT?

A limit price, also known as limit pricing, is a pricing strategy in which a supplier sells goods at a price so low as to make it unprofitable for rival suppliers to enter the market.

WHAT ARE THE CONDITIONS NECESSARY FOR PRICE DISCRIMINATION TO OPERATE?

Businesses must inhibit resale, be able to function in an imperfect market, and show demand elasticity for price discrimination to be effective.

WHAT IS FIRST, SECOND AND THIRD DEGREE PRICE DISCRIMINATION?

The business conducts first-degree discrimination by charging the highest price attainable for each consumed unit. Discounts for goods or services purchased in bulk constitute second-degree discrimination, whereas varying rates for various consumer groups constitute third-degree discrimination.

WHAT IS PARETO OPTIMALITY?

When no decision or action can be made makes one individual better off without making another worse off, this is known as Pareto efficiency or Pareto optimality.

WHAT ARE CLUB GOODS?

Club goods are a category of good in economics that are excludable yet non-rivalrous, at least up until a point where congestion arises. They are frequently categorised as a subclass of public goods. These products frequently show great excludability but low consumption rivalry.

WHAT IS THE RELATIONSHIP BETWEEN INFLATION AND UNEMPLOYMENT?

Historically, there has been an inverse correlation between inflation and unemployment. This implies that unemployment decreases as inflation increases. Conversely, higher unemployment results in reduced inflation. When more individuals are employed, they have more disposable income, which raises demand. Inflation in prices then quickly follows. When unemployment increases, the opposite is true.

### Life Insurance

Question 1

AM92 or PFA tables, which one has higher values?

PFA tables have higher values.

Question 2

What is the select mortality table?

A select mortality table is a type of mortality table that displays statistics about the mortality rate for people who have recently purchased life insurance policies. Life insurance companies use these tables to determine the price of their products. The mortality of the recently joined policyholders is called select mortality, and we expect it to be better than that of longer duration policyholders, whose mortality we call ultimate mortality as they have just passed the certain medical exams required to obtain insurance.

Lives who are subject to select mortality are denoted by [x] + r , where x is the age at selection and r is the number of years since the policy inception. A select mortality table has select functions for r = 0,1,…,s-1, where s is the select period. The select period is the number of years since selection during which mortality rates are assumed to be dependent upon the duration since selection as well as on current age.

Question 3

What is the ultimate mortality table?

• Ultimate mortality is based on an assumption of mortality varying by age only.
• An ultimate mortality table lists the percentage of life insurance purchasers expected to still be alive at each given age.
• Typically, the data is based on policyholders from a particular insurance company or group of them, rather than the entire population.
• Ultimate mortality tables exclude data from recently underwritten policies because their owners were probably required to pass a medical exam.
• Insurance companies consult ultimate mortality tables to price their products and determine whether to offer coverage to an applicant.

Question 4

What are life tables and what are its uses?

A life table is a table which shows, for each age, what the probability that a person of that age will die before their next birthday is. Usually it represents the survivorship of people from a certain population.

Use of life table:

•  Life Table provides a measure of the rate of death occurring at specified ages over specified periods of time.
• Life table is used to project the future population on the basis of the present death rate.
• It helps in determining the average expectation of life based on age specific death rates.
• The method of constructing a life table can be followed to estimate the specific death rates, male and female death rates, etc.

Question 5

Explain Uniform Distribution of Death (UDD) and Central Force of Mortality  (CFM)

Uniform Distribution of death – It is based on the assumption that, for integer x and 0<=t<=1 the function, tpx*mu(x+t) is a constant.

Since this is the density(PDF)of the time to death from age x, for an individual aged exactly x, the probability of dying on one particular day over the next year is the same as that of dying on any other day over the next year.

Hence it is called the Uniform Distribution of Deaths(or UDD) assumption.

Constant Force of Mortality (CFM) – constant force of mortality method is based on the assumption of constant force of mortality, which means that for integer x and 0 ≤ t ≤ 1, the function µ(x+t) is a constant i.e. µ(x+t) = µ= constant.

Question 1

What are endowment plans?

Endowment plan is a type of life insurance plan, which is a combination of insurance and saving product which provides both maturity as well as death benefit.

A certain amount is kept for life cover – insurance, while the rest is invested by the life insurance company. In an endowment plan, if the life assured outlives the policy term, the insurance company offers him the maturity benefit. Moreover, Endowment Plans may offer bonuses periodically, which are paid either on maturity or to the nominee under death claim. On death of the policyholder, the death benefit is payable to the nominee.

Endowment plans are also commonly a part of traditional life insurance, even though there is an investment component, but the risk is lower than the other investment products and so are the returns.

It is best suitable for long-term saving plans for people with much lower risk appetite i.e. they prefer safer returns.

Question 2

What are whole life insurance plans?

A whole life insurance policy covers the life assured for the whole life, or in some cases, up to the age of 99 years i.e. the limiting age. The sum assured or the coverage is decided at the time of policy purchase and is paid to the nominee at the time of death claim of the life assured along with bonuses if any.

However, if the life assured outlives the age of 100 years, the insurance company pays the matured endowment coverage to the life insured.

The premiums are higher as compared to term plans. Whole life insurance plans also offer partial withdrawals after completion of premium payment term.Best known for: Life coverage for whole life.

Benefit of Whole Life Plan: Lifelong protection to the insured and an opportunity to leave behind a legacy for heirs.

Question 3

What is term life insurance?

Term insurance is the simplest form of life insurance plan which provides death risk cover for a specified period. In case the policyholder passes away during the policy period, the life insurance company pays the death benefit to the nominee. It is a pure risk cover plan that offers high coverage at low premiums.

There’s an option to add riders to widen up the coverage such as extra payout in case of accidental deaths, critical illness cover, etc.

The death benefit is payable as lump sum, monthly payouts, or a combination of both.

There’s no pay out if the life assured outlives the policy term. However, these days there are companies offering Term Plans with Return of Premiums (TROPS), where insurance companies payback all the paid premium amount in case the life assured outlives the term period. But, such plans are costlier than the vanilla term insurance plan.

Benefit of Term Plan: In case of an untimely death of the breadwinner, the family is supported with an enormous amount of money – sum assured, which helps them to replace the loss of the income caused due to the breadwinner’s death. Moreover, the money could be utilized to pay off loans, monthly household expenses, child’s education, child’s marriage, etc.

Question 4

What is the difference between assurance and insurance?

Insurance is a contract between a company (registered to sell insurance) and the person buying the policy (policyholder) which states that the company will compensate the policyholder in case of a specific loss in exchange for a premium.

Assurance is commonly used with insurance and is related to Life Insurance policies. Here, the policyholder is assured that he/she will receive the compensation upon the occurrence of a certain event, ie, in case of death, survival, surrender, etc.

Question 5

Write the notation for term assurance of 20 years for a 20 year old.

The notation for term assurance of 20 years for a 20-year old is : A_20:<20>

Question 6

What is the cheapest assurance product?

Term assurance is the cheapest assurance product. The most expensive is Endowment Assurance followed by Whole Life Assurance.

Question 7

Is the premium charged more in case of Endowment Assurance or Term assurance and why?

Premium charged in case of Endowment assurance will be more than the premium charged in case of Term Assurance because Endowment Assurance covers both death and maturity benefits, while term assurance covers only death benefits.

Question 8

Arrange in increasing order the price of premium of various life products- term assurance, pure endowment, endowment assurance and whole-life assurance.

• Term Assurance
• Pure Endowment
• Whole-Life Assurance
• Endowment Assurance

Question 9

Which product has more premium and why?

Endowment Assurance and Whole-Life have more premiums than other two types of assurance contracts because of the certainty of receiving claims in both of them unlike others. However, Endowment assurance has even more premiums than Whole-Life Assurance because it offers both death and survival benefits among which survival benefits are much more than death benefits, while Whole-Life Assurance offers just death benefits.

Question 10

What are the disadvantages of term life Insurance?

• No Return on Investment: Unlike other investment plans such as unit-linked, term insurance does not give you any return on investment during your lifetime. Perhaps, the only benefit you can expect is to provide your family financial protection after your life.
• Buying at a later stage: If you buy a term plan at a later stage of your life, you end up paying a high premium for a higher sum assured which is impossible for all people. Some may be in need to go for a high sum assured but unable to pay a higher premium. In such conditions, the individual is either forced to take up an extra burden to pay the premium higher than what he budgeted or compromise the sum assured.
• No financial assistance if you are alive: This is the major con of the term plan. You can never expect financial aid from your term plan if you are alive, especially when you want to withdraw a partial amount or any form of return that another type of insurance plan offers.
• No cash value: You can never expect any cash value from the term plan. The money you pay towards premium is paid, and you can never expect any cash value for it.

Question 11

What is the difference between annuity and assurance?

 Life Insurance Annuities Term life Whole life Deferred annuities Immediate annuities Main reason for buying it Provide income for dependents Provide income for dependents or meet estate planning needs To accumulate money in a tax-deferred product To assure you don’t “outlive your income” Pays out when You die You die, borrow the cash value or surrender the policy You make withdrawals One period after you buy the annuity, stops paying when you die* Typical form of payment Single sum Single sum Single sum or income Lifetime income Buyer’s age when it is typically bought 25-50 30-60 40-65 55-80 Accumulates money tax-deferred? No Yes Yes Yes, but only in the early payout years Pays a death benefit? Yes Yes Yes *payments continue if the annuity has a guaranteed-period option that hasn’t expired at the annuitant’s death Are benefits taxable income when received? No No, unless a cash value withdrawal exceeds the sum of premiums Yes, but only the part derived from investment income Yes, but only the part derived from investment income

Question 12

Tell me the equation to calculate premium if n = 10 years, age = 30 years, expenses = 500, SA = 100000 and the annual premiums are paid in advance.

P*adue:30:<10> = 100000*A:30:<10> + 500*adue:30:<10>, assuming SA is paid at the end of the year of death and 30 is the ultimate age and not select age.

Question 1

What is annuity?

An annuity is a long-term investment agreement between an insurance company and an individual in which the individual makes payments in series or in a lump sum, in exchange for which he gets periodic disbursements or income, either immediately or in the future(deferred annuity). An annuity payment can be in any form: advance, arrear or continuous.

Question 2

Explain the different types of annuity.

• An annuity under which payments are made for the whole of life, with level payments or with increasing/decreasing payments, is called a whole life level annuity or, more commonly, an immediate annuity
• An annuity under which level payments or increasing/decreasing payments are made only during a limited term, is called a temporary annuity.
• An annuity under which the beginning of a series of payments is deferred for a given term, is called a deferred annuity.
• An annuity which pays out for a certain number of years before paying out to a beneficiary or estate once the annuitant dies, is called a guaranteed annuity

Question 3

Explain what is meant by the duration of an annuity.

The period during which an annuitant (the person who owns the annuity) begins to receive payments is known as the annuity period. Payments may be made monthly, quarterly, or annually, and this often occurs in retirement.

Question 4

What is deferred annuity and who gets the major benefit from it, insurance company or policy holder?

Where the first payment is made during the first time period, this is an immediate annuity. Where no payments are made during the first time period, this is a deferred annuity.

A deferred annuity makes sense for people nearing retirement or for younger investors who have maxed out their retirement plans but still want to put money into tax-deferred retirement income. Typically, annuity buyers are in their 60s. They’ve accumulated a significant amount of retirement savings and can roll that money over into an annuity without suffering a financial penalty. A deferred annuity allows you to continue working while money accumulates in the annuity, providing a guaranteed lifetime income stream when you finally retire. At the same time, a deferred annuity limits your ability to repurpose your retirement savings — and can be difficult to reverse if you change your mind. You will have to wait for your annuity income with a deferred annuity. If you want or need the income from your annuity within a year, you may want to consider an immediate annuity instead.

Question 5

Explain annuity, with relation to pension

 Purpose An annuity is an Insurance Product. A Pension is a Retirement Product Meaning An annuity can also be considered as a retirement product, but one may not have to retire to avail of the benefits. The Pension is the benefit received after they have retired from their service or job. Calculation An annuity is based on the amount of investment by an individual towards the scheme. The Pension is calculated based on the sum of the amount earned during the service adjusted for years of service. Advantages An advantage of an annuity is that the individual selects the plan and opens it. The individual has all the right to decide the amount needed to invest and which contract you will sign. If the annuity is funded with post-tax money, then the amount received will not be liable to pay taxes. The advantage of a pension comes when the individual is working since the employer is the one who contributes and handles the payout. Disadvantage The procedure to select the right annuity is complicated. There are various types of annuity, and finding one that fits your needs may be difficult. There are additional fees and commissions incurred. Since the employer takes care of the payment, it gives less transparency to the employees. It may be a disadvantage for some. Guarantee Annuities are not guaranteed. Pensions are backed by the government and are guaranteed. Stability Annuities earnings may be fixed or variable. It may be affected by the interest rate or the stock market. The pension amount is fixed and is divided into monthly payments. Types The annuity has two types – Fixed and Variable. Types of Pension schemes – Defined Contribution plan and Defined benefit plan

Question 1

What does the bonus represent?

An enhancement to the life insurance policy’s accrued value is known as a bonus. When the insurance reaches maturity or the policyholder passes away suddenly, the insurer pays out this sum to the policyholder. The bonus represents the amount of surpluses determined under the With-Profits fund of the company which is allocated to ‘With-Profits’ policies, as well as under the without-profits fund of the company which is incorporated within the company structure itself, and does not need to be mentioned separately.

Question 2

What are the types of Bonuses?

The type of bonus may be simple reversionary, interim or terminal.

Question 3

How is a simple reversionary bonus declared?

The reversionary bonuses are declared as a percentage of the basic sum assured. For products where basic sum assured is increased by a certain percentage after a specified period, the reversionary bonuses are declared as a percentage of the effective sum assured (i.e. increased sum assured). The reversionary bonuses are declared on an annual basis for each policy year during the term of the product, provided the policy is in-force as on the date of bonus declaration (i.e. all due premiums have been paid). Reversionary bonuses once declared and allocated are guaranteed. The future bonuses are, however, not guaranteed and will depend on future experience. If a policy is paid-up (in other words if you stop paying premiums), then the annual bonuses added to date remain credited to that policy, but the policy will receive no further bonuses.

Question 4

How is the interim bonus declared?

Interim bonuses are declared every year as a percentage of the basic sum assured or increased sum assured added to policies, before the declaration of the next reversionary bonus to provide for sudden death of policyholder.

Question 5

How is terminal bonus declared?

Terminal Bonus is paid once, i.e. at the time of maturity of the policy. It is a sort of loyalty bonus given to a policyholder for maintaining the policy till maturity. Its value is not guaranteed and will be disclosed only at the time of policy maturity.

Question 1

Under which scenario, retrospective and prospective reserves are equal?

If:

1. The retrospective and prospective reserves are calculated on the same basis, and
2. This basis is the same as the basis used to calculate the premiums used in the reserve calculation,

Then the retrospective reserve will be equal to the prospective reserve.

Question 2

Difference between Prospective and Retrospective Reserves?

Prospective reserve is the difference between the Expected present value of the future outgo and the Expected present value of the future Income.

The retrospective reserve for a life insurance contract that is in force is defined to be, for a given basis: The accumulated value allowing for interest and survivorship of the premiums received to date less the accumulated value allowing for interest and survivorship of the benefits and expenses paid to date.

Question 3

What are the different types of reserves?

The different types of reserves are: Prospective reserves and Retrospective reserves.

Question 4

How does a company distribute the surplus in a with-profits policy?

The surplus is distributed to the policyholders by way of bonus declaration at the end of each financial year. The policy gets a share of the surplus emerging from the With Profits business in the form of regular reversionary or terminal bonuses.

Question 5

Why is transfer of reserves a negative item in cash flow?

This is money that is currently ‘in the bank’ for a policy that is in force at this point. When we reach the end of the year, we need to account for the fact that the company is required to hold reserves for each policy that is then in force. The increase in reserve between the start and the end of the year represents additional money that the company will have to set aside (i.e. transfer) from other income, i.e. it will be a deduction from the profit earned during the year.

Question 6

What is the need to create reserves?

A reserve represents the amount of money that an insurer sets aside in respect of a policy that is currently in force, in order to meet future payments on that policy. It is important in real life, because an insurer that holds insufficient reserves will ultimately run out of money before all of its policyholders have made their claims, meaning that the company becomes insolvent and policyholders lose money, which can potentially be very large amounts.

Question 7

Explain DSAR.

The death strain at risk (DSAR) for the current policy year is the amount of extra money that the company would need to pay if the policyholder died during that policy year. It is sometimes called the sum at risk.

Question 8

Gross premium reserves are calculated on a prospective basis. They are the present value of future benefits and expenses less the present value of future gross premiums.

Question 1

What is Profit Testing?

This is the process of projecting the income and outgo emerging from a policy, and discounting the results. The results can then be used for various different purposes, such as setting the premium for a life policy that will give us our required level of profitability. We can set the premiums for a product to give a desired level of profitability by projecting cash flows under a certain set of assumptions, deciding on a risk discount rate and profit criterion, and then varying the premium amount until the profit criterion is satisfied.

Question 2

What are the different Decrements?

The different decrements are:

• Healthy
• Sickness
• Critical Illness
• Withdrawal
• Retirement
• Death

Question 3

Difference between Surrender and Lapse.

• Lapse refers to the termination of policies without payout to policyholders, while surrender usually indicates that a surrender value is paid out to the policyholder.
• A life insurance lapse occurs when you stop paying your policy’s premium and the contractual grace period has expired, while surrender refers to the amount that the policyholder will get from the life insurance company if he decides to exit the policy before maturity.

Question 4

What are dependent probabilities and independent probabilities?

The dependent probability is the probability that a life aged x in a particular state will be removed from that state within a year by the decrement alpha, in the presence of all other decrements in the population.

The independent probability xqa is the probability that a life aged x in a particular state will be removed from that state within a year by the decrement alpha, where alpha is the only decrement acting on the population.

Question 5

What is mortality profit? State its formula.

That part of the profit earned during the year due to difference in expected and actual mortality is referred to as mortality profit.

The mortality profit is defined as: Mortality profit = Expected Death Strain – Actual Death Strain. The EDS is the amount the company expects to pay out, in addition to the year-end reserve for a policy. The ADS is the amount it actually pays out, in addition to the year-end reserve. If it actually pays out less than it expected to pay, there will be a profit. If the actual strain is greater than the expected strain, there will be a loss.

Question 1

A unit-linked plan is a comprehensive combination of insurance and investment. The premium paid towards ULIP is partly used as a risk cover (insurance) and is partly invested in funds. One can invest in different funds offered by the insurance company depending on his risk appetite. The insurance company then invests the accumulated amount in the capital market i.e. in bonds, equities, debts, market funds, or a hybrid fund.

Best known for: Long-term investment option with much more flexibility to invest.

Benefit of ULIP: Invest money as per your risk appetite. You have the option to invest either in equity, debt or in hybrid funds through the life insurance company with complete transparency.

Question 2

What are the differences between conventional and ULIP products?

1. Pay-Out Maturity

You get the sum assured only at the time of maturity if you opt for a conventional insurance cover. In case of ULIPs, you can redeem your units at the current unit value prices. Some plans also offer additional units to the policyholder from time to time. This can be on an annual basis or at the time of maturity.

1. Transparency

It is always important to know how your investments are faring at any point in time. However, conventional insurance plans do not offer you this facility. The premium you pay is invested in a common fund and there is no way to track your individual portfolio.

Unlike conventional insurance plans, ULIPs allow you to monitor your portfolio always. You can find out the value of the units you hold at any point in time. You are also informed about the exact percentage of the premium that is invested in different avenues.

1. Partial Withdrawal

Partial withdrawal is a facility where you can withdraw a small portion of your fund before the maturity period. This can be quite useful if you require money in case of an emergency. ULIPs offer you the partial withdrawal option provided that you maintain the minimum fund value. In contrast, conventional insurance plans do not have a partial withdrawal facility.

1. Switching Options

One of the best features of ULIPs is that you have the freedom to switch your investments between different funds. This is an advantage because, as an investor, you have the freedom to switch between different investment options based on market fluctuations. As a result, you can balance your equity-debt portfolio to maximize your returns. The conventional options don’t provide you that freedom. All the investment decisions are taken by the insurer.

Question 3

What are the cash flows of ULIP?

These cash flows arise from the following sources:

1. Premium less cost of allocation, i.e. the difference between the premium paid by the policyholder and the amount invested in the unit fund on the policyholder’s behalf.
2. Expenses incurred by the life office.
3. Interest earned/charged on the non-unit fund.
4. Management charges taken from the unit fund.
5. Extra death or maturity costs (if the benefit payable on death or maturity is greater than the value of the units held at the time of death or maturity).
6. Reserves profit on surrender (if the benefit payable on surrender is lesser than the value of the units held at the time of surrender).

Question 4

Explain ULIP along with concepts of unit fund and non-unit fund.

The most important thing to bear in mind with unit-linked contracts is that we have two worlds to keep track of: the unit world, and a cash (or non-unit) world. The policyholder pays premiums to acquire units, and the eventual benefit is normally denominated in these units, so we will need to keep track of the number of units bought by a policyholder, how they are growing, and what charges we are deducting from them. However, the policyholder pays the life insurance company in real money. So we need to keep track of the cash not used to buy units, because that cash is a source of profit to the life insurance company. Conversely,if the policyholder dies there might be a cash denominated sum insured, and so we need to keep track of the cash outgo on claims. Another very significant cash outgo to consider is the company’s expenses. These include expenses incurred in underwriting and maintaining the policy, as well as commission payments to whoever sold it.

Unit benefits are payable on surrender, death claim or maturity. Non-unit benefits include, for instance, any sum insured payable on death in excess of the value of the units, or any guaranteed maturity value in excess of the value of the units

Unit Fund charges comprise:

•  a fund management charge, for instance 0.5% pa of the unit fund in respect of fund management expenses,
•  a policy fee (paid by cancellation of units) to cover other administration expenses, and
• a charge to cover the cost of providing any additional non-unit benefits, e.g. for any extra money paid out (over and above the unit fund value) when there is a guaranteed minimum death benefit.

There are a number of important things to highlight:

• The unit fund is worth only the bid value of the allocated premium; the rest of the premium goes to the non-unit fund.
• The unit fund charges are made in order to cover the expenses of fund management. However, charges and expenses are different cash flows (charges are part of the company’s income while the expenses are part of its outgo) and are unlikely to be of the same amount.
• The profit or loss to the life company in each year is calculated as the difference between income (charges, unallocated premium, bid/offer spread) and outgo (expenses, non-unit benefits).
• The unit fund is what the policyholder sees for instance, unit growth and all charges are communicated to the policyholder. The non-unit fund is what goes on within the company, and the policyholder does not see anything at this level.

The non-unit fund represents the accumulation of all cash flows paid in that are not used to buy units,less all cash flows paid out that have not arisen from the cancellation of units. As such, it represents the accumulation of the company’s profits from the policy at any time.

Question 5

1. Long term investment: ULIPs are an excellent choice for people looking to invest for the long term. This is because short-term market volatility produces lesser returns, but long-term market investments produce very attractive returns.
2. Tax free returns: ULIPs provide tax-free and tax-advantaged returns. Additionally, the death benefits received from ULIPs are tax-free.
3. Flexibility: ULIPs give investors the ability to switch between investment funds as their goals and needs change. Policyholders can profit from the fluctuation in stock values by switching between equity, debt, and cash.

1. Expensive and Complex: Because ULIPs mix insurance and investing, the premiums  charged for life insurance end up being much higher than term insurance.
2. Higher Beginning costs: ULIPs are more expensive in the first few years due to charges levied on the investor that goes toward policy charges
3. Market Fluctuations: In the early years, investors can expect lesser profits due to market changes. So, if you’re wanting to invest for the short term, ULIPs aren’t the best option.

Question 6

What are the benefits of ULIPs over mutual funds?

 Mutual Funds Unit Linked Products Only Investment, no life cover Used for Investment as well as life cover No guarantee Minimum guarantee offered Tax deductions not necessary Tax deductions on income under Section 80 C of the Income Tax Act Charges – Only managing your money and exit fees Plenty of charges –  Allocation, Life cover

Question 7

Explain the concept of unit fund and non-unit fund?

The unit fund is the amount held in units on behalf of the policyholder at any time.

The amount of money in the non-unit fund is the net result of the life offices (non-unit) cashflows.

These cashflows arise from the following sources:

1. Premium less cost of allocation, i.e. the difference between the premium paid by the policyholder and the amount invested in the unit fund on the policyholder’s behalf.
2. Expenses incurred by the life office.
3. Interest earned/charged on the non-unit fund.
4. Management charges taken from the unit fund.
5. Extra death or maturity costs (if the benefit payable on death or maturity is greater than the value of the units held at the time of death or maturity).
6. Reserves profit on surrender (if the benefit payable on surrender is lesser than the value of the units held at the time of surrender).

Question 8

There are usually two prices of each unit at the same time, the bid price (which is the cash-in value of each unit) and the offer price (which is the price that has to be paid to purchase a unit in the fund). The difference between the two (with the offer price being greater than the bid price) is called the bid-offer spread, and this difference is money that the insurance company makes from each unit purchased and which helps cover its costs and enables it to make profits.

Question 9

What are the Guaranteed benefits offered in Unit Linked policies?

• On death during the policy term, the higher of a fixed sum assured or the value of units might be paid. This ensures that a significant benefit is paid out should the policyholder die early in the term.
• On survival to the maturity date of the policy, a minimum guaranteed sum assured,or a minimum average unit growth rate, may be applied. In either case, the maturity benefit is the higher of the guaranteed amounts (of sum assured or unit fund) and the actual unit fund value at the maturity date. This guarantee is to ensure that the policyholder avoids any difficulties arising from a particularly poor investment performance.
• Death benefit guarantees are generally more common than maturity guarantees. In fact, policies with investment guarantees have proved very costly in the UK in the past.

Question 10

How are ULIPs different from conventional products?

 Description Unit Linked Insurance Plans offered by insurance companies allow policy holders to direct part of their premiums into different types of funds (equity, debt, money market, hybrid etc.). Here the risk of investment is borne by the policyholder. Conventional Plans are traditional life insurance plans. They usually invest in low risk return options and offer guaranteed maturity proceeds along with declared bonuses.

 Flexibility of investment ULIP gives you flexibility to invest as per your risk profile, financial commitments and convenience. You can choose to invest either in equity, or in debt or in a hybrid fund and even change your investment strategy. These plans do not allow you to choose investment avenues. Your funds are invested as per the strategy and discretion of the company.

 Transparency Most Unit Linked Insurance Plans allow you to track your portfolio. They also regularly intimate regarding the percentage of the premium that is invested along with the charges levied. You are also kept informed about the value and number of fund units that you hold. Your premiums are invested in a common ‘with profits’ fund and therefore you cannot track your individual portfolio.

 Maturity benefits payout At the time of maturity you redeem the units collected at the then prevailing unit prices. Some plans also offer you loyalty or additional units annually or at the time of maturity. At the time of maturity you get the sum assured plus bonuses, if applicable in the plan.

 Partial withdrawal Unit Linked Insurance Plans allow you to make withdrawals from your fund, provided the fund does not fall below the minimum fund value and subject to other conditions. Conventional plans do not allow you to withdraw part of your fund. Instead, some policies offer you the facility to take a loan against your investment.

 Switching options You can change your investment fund decision by switching between the funds as being offered by the policy. Not available since the investment decision is taken by the insurance company.

 Charges structure Unit Linked Insurance Plans specify the charges. under various heads. These plans do not specify the charges involved.

Question 1

Elaborate on Money Back Life Insurance Policy.

Money back plan is a unique type of life insurance policy, wherein a percentage of the sum assured is paid back to the insured on periodic intervals as survival benefit.

Money back plans are also eligible to receive the bonuses declared by the company from time to time. This way, policyholders can meet short-term financial goals.

Best known for: Short-term investment product to meet short-term financial goals.

Benefit of Money Back Plan: Short-term financial planning and an opportunity to earn returns on maturity.

Question 2

What are child plans?

Child plans help to build a corpus for a child’s future growth. They help to build funds for the child’s education and marriage. Most of the child plans provide annual installments or one time payout after the age of 18 years.

In case of an unfortunate event like if the insured parent passes away during the policy term – immediate payment is payable by the insurance company. Some child plans waive off the future premiums on death of the life insured and the policy continues till maturity.Best known for: Building funds for your child’s future.

Benefit of Child Plan: Helps in fulfilling your child’s dream.

Question 3

What are Participating Life Insurance Policies?

A participating policy enables you, as a policyholder, to share the profits of the insurance company. These profits are shared in the form of bonuses or dividends. It is also known as a with-profit policy.

Question 4

What is DI and TPD?

The term disability income (DI) insurance refers to an insurance policy that provides income to individuals who can no longer work because of a disability. Disability income insurance helps protect people from financial losses if an accident or illness renders them incapable of working and receiving regular income.

TPD (Total and Permanent Disability) pays a lump sum if you become totally and permanently disabled because of illness or injury.  Each insurer has a different definition of what it means to be totally and permanently disabled.

Question 5

What is the difference between Critical Illness Insurance and Long-Term Care Insurance?

 Long Term Care Insurance Critical Illness Insurance Payments Daily cash benefits that are paid to cover the costs of long term care – this can be through home care, nursing home care, an assisted living facility or an adult day care facility. The daily payments are subject to a maximum benefit. The insured receives a lump sum payment. Control of funds The daily payments are limited to the benefits being covered. The insured has the discretion on how he will use the funds. Duration of payment Payments can last until the person’s lifetime, or until the maximum payment period is reached. This usually involves a one-time payment and the policy will cease to be effective once the payment is made. Basis for payment Payments are based on whether the insured needs long term care – the insured basically is not able to perform daily functions by himself. The disease is not looked upon as a basis. The policy will pay if you cannot do the following functions by yourself: Eating Bathing and dressing Using the toilet Getting in and out of the bed or chair Control of the bladder and bowels Payments are based on diagnosis of a covered critical illness. You can still be able to perform daily activities and still receive the proceeds as long as you are diagnosed with the critical illness. This includes the following critical illnesses: Organ failure necessitating a major organ transplant Stroke Cancer Total blindness or deafness Minimum age You can buy this policy, even if you are past 60 years old. It doesn’t make sense for you to buy this at 60 years old or above, since some critical illnesses are only covered if the disease is diagnosed before the insured turns 60. Reason for getting this cover Desire to protect assets from long-term expenses – you want to preserve the assets to leave as an inheritance. Payment to pay primarily for treatment of the critical illness, although the money can be used for a variety of purposes.

### General Insurance

Question 1

What do you understand about General Insurance?

Insurance contracts that do not come under the ambit of life insurance are called general insurance. The different forms of general insurance are fire, marine, motor, accident and other miscellaneous non-life insurance. A General Insurance policy cover reimburses the insured for a financial loss caused due to certain events as stated in the respective general insurance policy.

Question 2

What do you know about motor insurance?

Vehicle insurance or motor insurance is a type of insurance policy which safeguards you financially in case your vehicle (car or two-wheeler) sustains damages due to natural or man-made calamities such as earthquake, flood, lightning and theft among others. Motor insurance is a unique insurance policy meant for vehicle owners to protect them from incurring any financial losses that may arise due to damage or theft of the vehicle. Whether you have a private car, a commercial vehicle, or a two-wheeler, you can purchase a motor insurance policy.

Question 3

What is Third party motor insurance?

As per The Motor Vehicles Act, third-party car insurance is mandatory while driving a vehicle in India. It reimburses the third-parties for losses/damages caused by the insured four-wheeler. Third-party Car Insurance is the most basic and compulsory insurance plan for your car. It provides financial and legal assistance if you injure a third party or damage their vehicle/property.

Question 4

What is property and casualty insurance?

Property insurance and casualty insurance (also known as P&C insurance) are types of coverage that help protect you and the property you own. Property insurance helps cover stuff you own like your home or your car. Casualty insurance means that the policy includes liability coverage to help protect you if you’re found legally responsible for an accident that causes injuries to another person or damage to another person’s belongings. Property and casualty insurance are typically bundled together into one insurance policy.

Question 5

Elaborate on marine insurance.

Marine insurance refers to a contract of indemnity. It is an assurance that the goods dispatched from the country of origin to the land of destination are insured. Marine insurance covers the loss/damage of ships, cargo, terminals, and includes any other means of transport by which goods are transferred, acquired, or held between the points of origin and the final destination.

Question 6

What are the factors affecting Motor Insurance Premium?

Here is the list of factors affecting motor insurance premium:

1. Brand of the vehicle: A vehicle of a brand which has higher value than another will be charged a higher premium than the latter.
2. Gender and Age: Statistically speaking, young men are more prone to accidents than young women and thus, there are more chances of accidents leading to insurance claims. Hence, insurance is given to young men at a higher premium as compared to young women.
3. Location: Location is one of the primary factors that insurance providers look for while signing a policy to a customer. For instance, if a person lives in an accident prone area, chances are that his premium will be higher in comparison to someone living in a relatively quieter area with a low percentage of such incidents. Moreover, car thefts are common in many areas with high unemployment and low literacy rate that is also a point of consideration.
4. Type of Engine: Does your engine run on diesel? Then you might have to pay a high premium because diesel vehicles are costlier than petrol vehicles which directly impacts the Insured Declared Value. Thus, the higher the price of the vehicle, the higher the IDV will be. This will also lead to an increased premium.
5. Safety Fittings: If you take care of your vehicle, your vehicle will thank you with low premium rates. If your car is fitted with safety amenities like gear lock, GPS, and airbags to name a few safety fittings, the risk of it getting stolen goes down drastically. This instills confidence in the insurance provider that there won’t be frequent insurance claims and will consider these amenities while setting the premium rates.

Question 7

What is home insurance? What are the factors affecting home insurance premiums?

Home insurance is a type of property insurance that provides coverage to the policyholder from the unforeseen loss or damage caused to the house structure as well as its content. Home insurance is popularly known as homeowner’s insurance. It is a sort of property insurance covering private residences. Property insurance policy is the insurance that protects the physical goods and the equipment of the business or home against any loss from theft, fire, and any other perils. It can be an all-risk coverage policy that gives protection against all the risks.

Factors affecting home insurance premium are:

• The extent of coverage – With additional coverage, the extent of protection to your home will also increase along with the premium.
• The location and size of your house – A house that’s located in a safer area is more economical to insure than a house that’s located in a place prone to floods or earthquakes, or where the rate of theft is higher. And, with a bigger carpet area, the premium also tends to rise.
• The value of your belongings – If you’re insuring high-value possessions like expensive jewelry or valuables, then the premium payable also rises correspondingly.
• The security measures in place – A house that has a good deal of safety measures in place costs less to insure than a house that doesn’t come with any security or safeguards. For eg: A house with fire fighting equipment in place will cost less than the others.

Question 8

• Pre-existing medical conditions: The policyholder or applicant will need to provide their own health records to ensure that there aren’t any pre-existing medical conditions. But, if they do have any pre-existing conditions, then the company can either choose to allow those in their policies or can decide not to cover it at all. If the insurance company cannot cover it under the health insurance, then the policyholder will need to bear the costs, thereby, increasing and affecting the premium.
• Gender: Many policies have a difference in premium rates for men and women. The 3 reasons for this, experts say, are – Women are more likely to visit doctors, take prescriptions, and be subject to chronic diseases.
• Age: Most young individuals have premiums at much lower rates since they have fewer identified and unidentified diseases than older individuals. Young policyholders are less likely to have health problems and are more likely not to visit a doctor.
• Choice of profession: Policyholders working in environments with hazardous substances, radiation, chemicals, and jobs with high risk of injuries like constructions have to end up paying higher premiums as per insurance companies since they’re prone to risk of cardiovascular diseases.
• Marital status: It’s still unclear if married people live longer and healthier lives, but the insurance premiums are generally lower in rates. The men generally reap better benefits with this status change.

Question 1

What is the concept of Hypothesis?

A hypothesis is where we make a statement about something; for example the mean lifetime of smokers is less than that of non-smokers. A hypothesis test is where we collect a representative sample and examine it to see if our hypothesis holds true. The standard approach to carrying out a statistical test involves the following steps:

1. Specify the hypothesis to be tested
2. Select a suitable statistical model
3. Design and carry out an experiment/study
4. Calculate a test statistic
5. Calculate the probability value
6. Determine the conclusion of the test.

Question 2

How to handle large datasets?

The steps to handle large data sets are:

1. Develop a well-defined set of objectives which need to be met by the results of the data analysis.
2. Identify the data items required for the analysis.
3. Collection of the data from appropriate sources.
4. Processing and formatting data for analysis, eg inputting into a spreadsheet, database or other model.
5. Cleaning data, eg addressing unusual, missing or inconsistent values.
6. Exploratory data analysis, which may include: (a) Descriptive analysis; producing summary statistics on central tendency and spread of the data. (b) Inferential analysis; estimating summary parameters of the wider population of data, testing hypotheses. (c) Predictive analysis; analyzing data to make predictions about future events or other data sets.
7. Modeling the data.
8. Communicating the results.
9. Monitoring the process; updating the data and repeating the process if required.

Throughout the process, the modeling team needs to ensure that any relevant professional guidance has been complied with. For example, the Financial Reporting Council has issued a Technical Actuarial Standard (TAS) on the principles for Technical Actuarial Work (TAS100) which includes principles for the use of data in technical actuarial work.Further, the modeling team should also remain aware of any legal requirement to be complied with such as Solvency II. Such legal requirements may include aspects around consumer/customer data protection and gender discrimination.

Question 3

What is the meaning of p-value?

A p-value is a statistical measurement used to validate a hypothesis against observed data. A p-value measures the probability of obtaining the observed results, assuming that the null hypothesis is true. The lower the p-value, the greater the statistical significance of the observed difference. A p-value is used in hypothesis testing to help you support or reject the null hypothesis. The p-value is the evidence against a null hypothesis. It is the least probability value in which a null hypothesis can be rejected.

A p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.

Question 4

What does Z-score mean?

A z-score, also known as a standard score, informs you of how far a data point is from the mean. Technically speaking, however, it’s a measurement of how many standard deviations a raw score is from or above the population mean. If a Z-score is 0, it indicates that the data point’s score is identical to the mean score.

Question 5

What is regression analysis? What is the error term in that?

• Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables.It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them.

In order to create predictions about your data, regression analysis will provide you an equation for a graph. For instance, if you’ve gained weight recently, it can estimate how much you’ll weigh in 10 years if you keep gaining weight at the same rate.

• The error term, which refers to the sum of the deviations within the regression line and explains the difference between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.

Question 6

Define Skewness.

Skewness is a measure of the asymmetry of a distribution. A distribution is asymmetrical when its left and right side are not mirror images. A distribution can have right (or positive), left (or negative), or zero skewness. It defines the shape of the distribution.It can be measured as an indicator of how much a distribution deviates from the normal distribution. A lognormal distribution, for instance, would have considerable right skew whereas a normal distribution has zero skew.

Question 7

What is the formula of correlation?

The correlation coefficient(X,Y) (written as corr(X,Y)) or (X,Y) of two random variables X and Y is defined by:

Corr(X,Y)=Cov(X,Y)/[SD(X)*SD(Y)].

Question 8

What is the difference between deterministic and stochastic models?

Deterministic models are the mathematical models in which the outcomes are determined by the relationship between states and events. There is no room for random variation in a deterministic model. The deterministic model helps you make a point estimate of the payments that will need to be made in future but it does not take into consideration any variations that may show up in due course of time, while,

A stochastic model allows room for random variation in one or more inputs overtime and produces a different output every time. The random variation finds its base in historical data. So, the modeler can say with some level of confidence that the payouts in future will fall in that range. On the down-side, the Stochastic models may be computationally very complex to perform.

Question 9

What is Gumbel distribution?

Extreme value distributions (EVDs), which are frequently used to model maximums and minimums, are known as the Gumbel distribution (also known as the Gumbel type). This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur.

Question 10

What is overfitting?

When a statistical model fails to produce reliable predictions on test data, it is said to be overfitted. A model begins to learn from the noise and erroneous data entries in our data set when it is trained with such a large amount of data. And when using test data for testing yields high variance. Due to too many details and noise, the model fails to appropriately identify the data. The non-parametric and non-linear approaches are the root causes of overfitting since these types of machine learning algorithms have more latitude in how they develop the model based on the dataset, making it possible for them to produce highly irrational models.

For example, decision trees are a nonparametric machine learning algorithm that is very flexible and is subject to overfitting training data. This problem can be addressed by pruning (Pruning is a data compression technique in machine learning and search algorithms that reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances) a tree after it has learned in order to remove some of the detail it has picked up.

Question 11

What do you understand about the Markov Chain?

A Markov chain is a representation of an object moving randomly through a discrete number of possible states.The Markov property means that the future value of a process is independent of the past history and only depends on the current value. Markov chains are used in ranking of websites in web searches. Markov chains model the probabilities of linking to a list of sites from other sites on that list; a link represents a transition.

Question 12

Where does the mean, median and mode lie in positively and negatively skewed distributions?

In positively skewed distribution, the mean is greater than the median and the median is greater than the mode (Mean > Median > Mode).

In a negatively skewed distribution,  the mean is always lesser than median and the median is always lesser than the mode. (Mean < Median < Mode).

Question 13

What is correlation?

Linear correlation between a pair of variables looks at the strength of the linear relationship between them. The word correlation is used in everyday life to denote some form of association. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other i.e. it does not imply causation.

Question 14

What is regression?

Regression analysis is a statistical method that helps us to analyze and understand the relationship between two or more variables of interest. The process that is adapted to perform regression analysis helps to understand which factors are important, which factors can be ignored, and how they are influencing each other.

For the regression analysis to be a successful method, we understand the following terms:

• Dependent Variable: This is the variable that we are trying to understand or forecast.
• Independent Variable: These are factors that influence the analysis or target variable and provide us with information regarding the relationship of the variables with the target variable.

Question 15

Briefly explain the various types of distributions.

Binomial distribution – Binomial distribution summarizes the number of trials, or observations when each trial has the same probability of attaining one particular value. The binomial distribution determines the probability of observing a specified number of successful outcomes in a specified number of trials.

Example – The simplest real life example of binomial distribution is the number of students that passed or failed in a college. Here the pass implies success and fail implies failure. Another example is the probability of winning a lottery ticket. Here the winning of reward implies success and not winning implies failure.

Poisson distribution – a Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period.

Example – Call centers use the Poisson distribution to model the number of expected calls per hour that they’ll receive so they know how many call center reps to keep on staff.

Normal Distribution – Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.

Examples: Height of the population, rolling a dice, tossing a coin.

LogNormal distribution – A log-normal distribution is a continuous distribution of random variable whose natural logarithm is normally distributed

Example: One of the most common applications where log-normal distributions are used in finance is in the analysis of stock prices.

Question 16

What is the difference between Poisson and Binomial distribution?

The difference between Poisson and Binomial distributions is as follows:

1. In a Binomial distribution, there is a fixed number of trials. In a Poisson distribution, there could be any number of events that occur during a certain time interval.
2. Poisson distribution is uni-parametric, or characterized by a single parameter m, whereas the binomial distribution is biparametric, or featured by two parameters, n and p.
3. In binomial distribution Mean > Variance while in poisson distribution mean = variance.
4. There are only two outcomes in a binomial distribution: success or failure. On the other hand, the poisson distribution has an infinite number of potential outcomes.
5. Binomial distribution example: flip a coin 3 times, Poisson distribution example: how many customers will arrive at a store in a given hour?

Question 17

What is GLM?

Generalized linear models (GLMs) relate the response variable which we want to predict, to the explanatory variables or factors (called predictors, covariates or independent variables) about which we have information. Thus it (GLM) generalizes linear regression, allows the linear model to be linked to the response variable via a link function and allows the variance of each measurement to be a function of the projected value.

Question 18

How is GLM used in life or general insurance?

They are used to:

• determine which rating factors to use (rating factors are measurable or categorical factors that are used as proxies for risk in setting premiums, eg age or gender)
• estimate an appropriate premium to charge for a particular policy given the level of risk present.

Question 19

Which distribution will two-sample mean follow?

From the Central Limit Theorem, we know that as n gets larger and larger, two-sample mean follows a Normal Distribution. The larger the n gets, the smaller the standard deviation gets. Thus, a two-sample mean will follow a Normal Distribution. If sigma is not known, two-sample mean will follow a t-distribution.

Question 20

What is a multi-state model?

Multi-state models are representations of a process that, at any given time, can be in any one of a number of states, such as one describing the life history of an individual. This might refer to a variety of potential outcomes for a single person or the interdependence of multiple people.

Question 21

What is the difference between multiple state models and multiple risk models?

Multi-state models are models for a process, for example describing a life history of an individual, which at any time occupies one of a few possible states. This can describe several possible events for a single individual, or the dependence between several individuals.

Multiple risk models take into account the effects of various risks within children’s lives and the environments that impact their overall development. The greater the number of risk factors in a child’s life, the more likely that child is to face adversity or experience negative effects developmentally.

Question 22

Suppose you are given a large dataset. How will you decide which distribution applies to it?

First observe the data and determine if it is discrete or continuous. If the data is discrete, then you can apply distributions like Binomial, Negative Binomial and Poisson distribution to the given set of data. If the mean is almost equal to the variance, the distribution can be thought to have come from a Poisson Distribution. If the mean is greater than variance, then the data can be thought to have come from a Binomial Distribution. If the mean is lesser than variance, then we can consider a Negative Binomial Distribution.

If the data is continuous, you can consider distributions like Normal, Cauchy, Exponential, Beta distribution. If the data is symmetric you can consider that the data is taken from a Normal or a Cauchy Distribution. If the tail probability is high, Cauchy Distribution can be considered, else Normal Distribution can be applied to it. If the data appears to be positively skewed, you can consider an Exponential Distribution and a Beta Distribution in case it appears to be negatively skewed.

After you have determined the distribution, you may use Q-Q Plots or determine whether your data fit into a certain distribution may be to use probability plots. The distribution matches your data if they fall along the straight line in the graph. Visually, this procedure is straightforward. This procedure is known as the “fat pencil” test informally.

Question 23

Can you explain the cumulative distribution function to me, and when do we use it in statistics?

The Cumulative Distribution Function (CDF), of a real-valued random variable X, evaluated at x, is the probability function that X will take a value less than or equal to x. It is used to describe the probability distribution of random variables in a table.

In Statistics, the cumulative distribution function is used to describe the probability distribution of random variables. It can be used to describe the probability for a discrete, continuous or mixed variable. It is obtained by summing up the probability density function and getting the cumulative probability for a random variable.

Question 24

What is the degree of confidence?

Degree of confidence represents the probability that the confidence interval captures the true population parameter. So, in statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence intervals that include 95% or 99% of expected observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 – 10.50.

Question 25

How is lognormal distribution used for actuarial science in insurance?

Lognormal distribution is a probability distribution that is used as a model to claim size distribution; and has a range from zero to infinity.  Log-normal distributions are positively skewed with long right tails due to low mean values and high variances in the random variables.It is used to simulate a variety of natural events, including the distribution of revenue, the number of moves in a chess game, how long it takes to fix a maintenance system, and more.

Question 26

What is the difference between exponential and weibull distributions?

The exponential distribution is a special case of the Weibull distribution, the case corresponding to constant failure rate. The Weibull distribution with shape parameter 1 and scale parameter b ∈ ( 0 , infinity ) is the exponential distribution with scale parameter.

Question 27

What is the pdf of exponential distribution?

The pdf of exponential distribution is lambda * e^-(lambda*x).

Question 28

What is the linear regression equation?

The linear regression equation is given by:

Y = alpha + beta*X + e, where,

Y = Response variable.

X = Explanatory variable.

alpha = Intercept parameter.

beta = Slope parameter.

e = Uncorrelated error variables with mean 0 and common variance sigma^2.

Question 1

Explain the concept of Reinsurance.

Reinsurance is a form of insurance purchased by insurance companies in order to mitigate risk. Essentially, reinsurance can limit the amount of loss an insurer can potentially suffer. In other words, it protects insurance companies from financial ruin, thereby protecting the companies’ customers from uncovered losses. The claims on an insurance company must be met in full, but, to protect itself from large claims, the company itself may take out an insurance policy; such a policy is called a Reinsurance policy.

Question 2

State the types of reinsurance and explain them?

There are two types of reinsurance:

1. Proportional reinsurance – Under proportional reinsurance, the insurer and reinsurer split the claim in pre-defined proportions.
2. Excess of loss reinsurance – Under individual excess of loss, the insurer will pay any claim in full up to an amount M, the retention level. Any amount above M will be met by the reinsurer.

Question 1

Explain Run-off.

Run-off triangles are a method used to model claims experience. They’re specifically used to estimate the future claims that will be reported based on those already reported. When a claim event occurs, there will be some time before it is reported or notified to the insurer – this is known as a claim delay. The insurer will incur numerous claims in a calendar year, and each of those claims will have a claim delay. The run off triangles are used to estimate how much or how many claims have been incurred in a reporting period (e.g. financial year), but are not yet reported and a reserve is held for this. It’s called an IBNR – incurred but not reported reserve.

Question 2

Explain Bornheutter – Ferguson method.

The Bornhuetter-Ferguson method combines the estimated loss ratio with a projection method. It, therefore, improves on the crude use of a loss ratio by taking account of the information provided by the latest development pattern of the claims, whilst the addition of the loss ratio to a projection method serves to add some stability against distortions in the development pattern.

Bornhuetter-Ferguson is one of the most widely used loss reserve valuation methods, second only to the chain-ladder method. It combines features of the chain ladder and expected loss ratio methods and assigns weights for the percentage of losses paid and losses incurred.

Question 3

How many methods are there in run-off triangles? What are they?

There are 4 methods in run-off triangles. They are basic chain-ladder method, index chain-ladder method, Bornheutter-Ferguson method and Average Cost Per Claim method.

Question 4

Why would you prefer a simple chain-ladder method over Bornheutter-Fergusson method and vice versa?

We would prefer the basic chain-ladder method over Bornheutter-Fergusson method just because of the simplicity of calculations. Also, We would prefer the Bornheutter-Fergusson method over the basic chain-ladder method because the former accounts for the loss ratio that gives us a more accurate and favorable figure for reserves.

Question 5

Is the loss ratio good? Doesn’t it contradict the principle of prudence? Why?

To account for loss ratio is a very good practice and a very important one too.Loss ratios are useful for evaluating the viability and health of an insurance company. When a company receives more in premiums than it pays out in claims, a high loss ratio may be a sign that it is struggling financially.

It doesn’t contradict with the principle of prudence per se in spite of being a conservative approach because it gives us a realistic figure of reserves and protects us against extremities or anything unforeseen.

### Investment & Finance

Question 1

Reddington’s condition?

There are three conditions:

1. The value of the assets at the given rate of interest is equal to the value of the liabilities.
2. The volatilities of the asset and liability cash flow series are equal
3. The convexity of the asset cash flow series is greater than the convexity of the liability cash flow series.

Question 2

What is immunization?

It is a strategy that ensures that a change in interest rates will not affect the value of a portfolio. In simple cases, it is possible to select an asset portfolio that will protect this surplus against small changes in the interest rate. So, Immunization is a risk-mitigation tool that aims to minimize the long-term impact of interest rates on net worth by matching the duration of assets and liabilities.

Question 3

What is the difference between nominal and effective rate of interest?

Effective rates are compound rates that have interest paid once per unit time either at the end of the period (effective interest) or at the beginning of the period (effective discount).

This distinguishes them from nominal rates where interest is paid more frequently than once per unit time. Bank accounts sometimes use nominal rates of interest. They might quote the annual interest rate (and so the unit time is one year) but interest is actually added at the end of each month (so interest is paid more frequently than once per unit year).

Question 4

What is volatility?

One measure of the sensitivity of a series of cash flows to movements in the interest rates is the effective duration (or volatility). The effective duration is defined to be: -A’/A, where,  A is the present value of the payments at rate (yield to maturity) i. Effective duration is denoted by the Greek letter nu, 𝝼.

Apart from this, Portfolio risk, or the likelihood that a portfolio will depart from its mean return, is quantified by portfolio volatility. Keep in mind that a portfolio consists of various positions, each with its own volatility metrics. When these distinct changes are added together, a single measure of portfolio volatility is produced.

Question 5

What is DMT?

A measure of interest rate sensitivity is the duration, also called Macaulay duration or discounted mean term (DMT). This is the mean term of the cash flows, weighted by present value. That is, at rate i, the duration of the cash flow sequence, compared to effective duration is: τ=(1+i)(i).

Question 6

What happens to PV when the interest rate decreases?

When the interest rate decreases, PV increases due to discounting at a higher rate of interest.

Question 7

How inflation affects Interest rate?

Interest rates are more likely to increase the greater the inflation rate. This happens as a result of the fact that lenders will demand higher interest rates in order to make up for the declining purchasing value of the money they will eventually be paid.

Question 8

What is the difference between nominal and effective rate of interest?

1. The nominal interest rate does not take into account the compounding period.The effective interest rate does take the compounding period into account and thus is a more accurate measure of interest charges.
2. The effective annual rate is normally higher than the nominal rate because the nominal rate quotes a yearly percentage rate regardless of compounding. Increasing the number of compounding periods increases the effective annual rate as compared to the nominal rate.

Question 9

What is meant by the discount rate?

Discount rate, also called the hurdle rate, cost of capital, or required rate of return, is the expected rate of return for an investment.

In other words, this is the interest percentage that a company or investor anticipates receiving over the life of an investment. It is the interest rate used to calculate the present value of future cash flows and can be used in the calculation of future values as well using the Discounted Cash Flow Approach. Investors, bankers and company management use this rate to estimate whether an investment is worth considering or should be discarded.

Question 10

How is the discount rate determined?

There are two different discount rate formulas including – adjusted present value (APV) and the weighted average cost of capital (WACC).

WACC is usually utilized to get the enterprise value of a company by looking into the cost of goods that the company has and that can be sold. These goods can include the bongs, stocks, inventory, and any other debts that the company has on its books. This value combines the after-tax cost of debt and the cost of equity. Then, the cost of each capital source, both equity and debt is multiplied by its relevant weight. All these values are then added together to get the WACC value.

WACC=[Equity/(Equity+Debt)Cost of Equity] +[Debt/(Equity+Debt)

Cost of Debt(1-Tax Rate)].

APV analysis tends to be preferred in highly leveraged transactions since it is not as simple as the NPV valuation. In fact, this formula considers the benefits of raising debts such as the interest tax shield. This formula can also work perfectly when trying to reveal the hidden value of less practical investment possibilities. When there is an investment with a portion of the debt, a few prospects that didn’t look viable with NPV alone suddenly seem more attractive as investment opportunities.

APV=NPV+PV of the impact of Financing.

Question 11

Is Discount rate a financial assumption or an economic assumption?

The discount rate factor is a significant actuarial assumption. It enables us to state expected future cash payments for benefits as a present value on the measurement date. This is referenced to market yield rates, and this does not allow much room to capture specific details by an organization’s policies. A lower discount rate increases the present value of benefit obligations and increases the expense for retirement obligations. Thus, it can be classified as a financial assumption.

Question 12

Limitations of Reddington’s conditions.

Limitations of Reddington’s conditions are as follows:

• The choice of one interest rate for all calculations.
• Only provides protection against small changes in i.
• Yield curves are usually not flat.
• Requires frequent rebalancing of portfolio to keep value of A = value of B.
• Exact cash flows may not be known and may have to be estimated. i.e. callable bonds, prepaid mortgages.
• Assets may not exist in the right maturities to achieve immunization.

Question 13

What will be the DMT of a zero-coupon bond of 10 years?

DMT of a zero-coupon bond of 10 years = 10v^10/v^10 = 10.

Question 1

Briefly explain the concept of Project Appraisal.

Project appraisal is a cost and benefits analysis of different aspects of a proposed project with an objective to adjudge its viability. We consider the following methods to decide between the alternative investment projects which are:

1. Net present value
2. Accumulated Profit
3. Internal Rate of return
4. Payback Period
5. Discounted Payback Period.

Question 2

What is a risk free bond?

A risk-free bond refers to a bond issued by an entity that’s considered absolutely certain to pay back both its principal and interest, with no risk of default.

Question 3

How to check the profitability of a product?

The profitability of a product can be assessed by calculating the accumulated profit:

Accumulated profit = AV income – AV outgo.

The Net Present Value (NPV) of a project can be calculated by subtracting PV of outgo from PV of income. If this NPV is positive, ie., greater than 0, the project is considered to be profitable.

Question 4

What is the difference between Bonds and Equities?

1. Equities (also known as stocks) are shares issued by companies and traded on an exchange. On the other hand, Bonds (also known as fixed income) could be issued by companies or sovereigns and could be traded either publicly, over the counter or privately.
2. When buying equity in a company, the investor becomes a shareholder and can participate in the distribution of profits. When buying a bond, the investor becomes a creditor to the issuer and is entitled to a fixed interest along with the ultimate repayment of the principal.

Typically, equities and bonds have a low correlation and when combined together in a portfolio can offer diversification benefits.

Question 5

Briefly explain the concept of term structure.

The variation by term of interest rates is often referred to as the term structure of interest

rates. The prevailing interest rates in investment markets usually vary depending on the time span of the investments to which they relate. This variation determines the term structure of interest rates. The variation arises because the interest rates that lenders expect to receive and borrowers are prepared to pay are influenced by the following factors, which are not normally constant over time:

1. Supply and demand
2. Base rates
3. Interest rates in other countries
4. Expected future inflation rates
5. Tax rates
6. Risk associated with changes in interest rates

Question 6

Explain Discounted Payback Period.

The discounted payback period for a project is the smallest time t for which the present (or accumulated) value of the income up to time t exceeds the present (or accumulated) value of the outgo up to time t. A discounted payback period gives the number of years it takes to break even from undertaking the initial expenditure, by discounting future cash flows and recognizing the time value of money.

Question 7

What factors do you consider while comparing the profitability of 2 projects?

Suppose that the investor may lend or borrow money at a fixed rate of interest i. Now, let NPV(i) is the present value at rate of interest i of the net cash flows associated with the project, we conclude that the project will be profitable if and only if: NPV(i) > 0.

Now, when comparing the profitability of 2 projects, the following should be kept in mind:

1. NPV(A)>NPV(B), ie, NPV of project A should be greater than NPV of project B.
2. IRR(A)>IRR(B), ie, IRR of project A should be greater than IRR of project B.

In the above cases, project A will be preferable and more profitable.

Question 8

Is it possible to have two IRRs in a single project?

In some cases, it is possible for there to be more than one solution for IRR. In such cases, the smallest positive solution is usually used. Also, if there are only inflows of cash (i.e., no outflow), the internal rate of return will be infinite.

Question 9

Explain internal rate of return.

The internal rate of return for an investment project is the effective rate of interest that equates the present value of income and outgo, ie, it makes the net present value of the cash flows equal to zero. The internal rate of return need not be positive. A zero return implies that the investor receives no return on the investment and if the yield is negative then the investor loses money on the investment. It is difficult, however, to find a practical interpretation for a yield less than 1, and so if there is not a solution to the equation greater than 1, the yield is undefined.

Question 10

What is convexity and volatility?

Convexity demonstrates how the duration of a bond changes as interest rate changes. If a bond’s duration increases as yield’s increases, the bond is said to have negative convexity.

Volatility/effective duration is the sensitivity of a bond‘s price against the benchmark yield curve. One way to assess the risk of a bond is to estimate the percentage change in the price of a bond against a benchmark yield curve such as a government par curve.

Question 11

State the usefulness of Internal rate of return and present value.

Usefulness of internal rate of return:

1. The IRR provides any small business owner with a quick snapshot of the capital projects which would provide the greatest potential cash flow.
2. The IRR provides an easy-to-understand average performance of variable cash flows over the life of an investment.
3. The IRR method does not require the hurdle rate, mitigating the risk of determining a wrong rate. Once the IRR is calculated, projects can be selected where the IRR exceeds the estimated cost of capital.

Usefulness of present value:

1. The primary benefit of using NPV is that it considers the concept of the time value of money, i.e., a dollar today is worth more than a dollar tomorrow owing to its earning capacity. The computation under NPV considers the discounted net cash flows of an investment to determine its viability.
2. The NPV method enables the decision-making process for companies. Not only does it help evaluate projects of the same size, but it also helps in identifying whether a particular investment is profit-making or loss-making.

Question 12

Define NPV.

Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.When comparing similar investments, a higher NPV is better than a lower one.

Question 13

What are the disadvantages of the internal rate of return?

1. A disadvantage of using the IRR method is that it does not account for the project size when comparing projects. Cash flows are simply compared to the amount of capital outlay generating those cash flows. This can be troublesome when two projects require a significantly different amount of capital outlay, but the smaller project returns a higher IRR.
2. The IRR method only concerns itself with the projected cash flows generated by a capital injection and ignores the potential future costs that may affect profit
3. Although the IRR allows you to calculate the value of future cash flows, it makes an implicit assumption that those cash flows can be reinvested at the same rate as the IRR. That assumption is not practical as the IRR is sometimes a very high number and opportunities that yield such a return are generally not available or significantly limited.
4. an investment project may have different and multiple rates of return. Having more than one rate not only increases the complexity of the calculation, but it also creates a dilemma where choosing the best project becomes critical. Therefore, having multiple rates of returns is one of the prominent demerits of IRR.

Question 14

What is the relation between bond price and interest rates?

Bonds have an inverse relationship to interest rates. When the cost of borrowing money rises (when interest rates rise), bond prices usually fall, and vice-versa.

All else being equal, the price of existing bonds will decrease as demand for those bonds decreases if new bonds are issued with an interest rate that is higher than those currently on the market. The price of old bonds will rise in step with demand if new bonds are issued with an interest rate that is lower than bonds already on the market.

Question 15

Explain the concept of time value of money?

The time value of money (TVM) is the concept that a sum of money is worth more now than the same sum will be at a future date due to its earnings potential in the interim. This is a core principle of finance. A sum of money in the hand has greater value than the same sum to be paid in the future.

Question 1

Difference between American and European options?

European Option gives the option holder the right to exercise the Option only at the pre-agreed future date and price. On the other hand, the American Option gives the option holder the right to exercise the Option at any date before the expiration date at the pre-agreed price.

Then we come to premiums. Since the option holder of a European Option has the right to exercise the Option only on expiration date, premiums tend to be lower. The liberty to exercise the Option at any date prior to the expiration date makes the American Option in more demand, which makes it pricey.

In terms of popularity, European options are less popular and hence traded less frequently compared to American options. American options are in high demand since it gives the authority to exercise at any time.

Globally, European options are OTC traded while American options are exchange traded. However, the exception is India where the exchange traded options are all European options only.

While globally, American options are more in vogue, in India, European options are doing a good job overall.

Question 2

Give a basic conceptual understanding of put-call parity.

Consider the argument we used to derive the lower bounds for European call and put options on a non-dividend-paying stock. This used two portfolios:

A: one call plus cash of value K*e^(-r(T-t)).

B: one put plus one share.

Recall that both portfolios included only European options on non-dividend-paying shares. This is an important condition underpinning the arguments that follow.

Both portfolios have the same payoff at the time of expiry of the options of max(K,St).

Since they have the same value at expiry and the options cannot be exercised earlier, then they should have the same value at any time t < T.

i.e, ct + k*e^(-r(T-t)) = pt + St.

This relationship is known as put-call parity.

### Pensions

Question 1

Elaborate on retirement plans.

Retirement plans help to build a corpus for retirement. They help to live independently financially and without worries. Most of the retirement plans provide annual installments or one time payout after the age of 60 years or on /after retirement.

In case of an unfortunate event like if the life assured passes away during the policy term, immediate payment is payable to the nominee by the insurance company. Death benefit will be higher of coverage or fund value or 105% of premiums paid. Vesting Benefit will be payable if the life assured survives the maturity age. In which case, payout will be fund value which has to be utilized for buying an annuity. Best known for: Long-term savings and retirement planning.

Benefit of Retirement Plan: Helps in building corpus for retirement.

This is just a simplified guide to different types of life insurance policies.

Question 2

Why do companies give pensions to their employees?

Your pension helps you to maintain your standard of living in retirement, and savings provides important supplemental income for unforeseen expenses. Group pension plans provide guaranteed monthly income for life, which makes financial security in retirement much more achievable for those who have them.

There are various retirement plan choices available to employers that provide tax benefits for their employees. The results of the survey reflect past studies that found firms often offer retirement benefits to attract and keep talent and to aid employees in saving money.

Question 3

What are the factors that affect the monthly pension payment?

• Your age when you retire, which may result in a reduced pension
• The pension option you choose
• The premiums you pay for health coverage through the post-retirement group benefit plan
• Any legally required deductions, such as income tax

Question 4

What is a provident fund ?

A provident fund​ is an investment fund that is jointly established by the employer and employee to serve as a long-term savings to support an employee upon retirement. It also represents job welfare benefits offered to the employee.

Question 5

What are pensions?

A pension is a retirement plan that provides a monthly income. The employer bears all of the risk and responsibility for funding the plan.

Question 6

What was the recent development made by the Government w.r.t gratuity payments?

An increase in the basic pay of an employee will automatically lead to a higher gratuity payment to the employee. According to the new definition, bonus, pension contributions, provident fund contributions, house rent allowance, conveyance allowance, gratuity and overtime should not be included in the salary.

Question 7

What are the decrements in pension policy other than death?

The decrements in a pension policy other than death are as follows:

• Termination benefits
• Survivor benefits
• Accrued benefits
• Post-retirement benefits
• Pre-retirement death benefits
• Retirement benefits
• Other termination benefits
• Compensation benefits

Question 8

How to calculate pensions?

Pension=Average Salary*Pensionable Service/70, where,

Average Salary = Average of the Basic Salary + Dearness Allowance combined, drawn in the last 12 months, and,

Pensionable Service = the number of years worked in the organized sector after 15th November, 1995.

Question 9

What is a defined benefit pension scheme?

A final salary pension plan is another name for the most popular kind of defined benefit pension plan. According to these plans, employee members are entitled to a certain level of benefit based on their length of service and their retirement wage.

In a defined benefit pension plan, a formula tied to the member’s wages and/or the length of their pensionable service determines the pension payout. The contributions from the company and the employee must be enough to cover the total pension payout, according to those in charge of the programme.

Question 10

What is a defined contribution pension scheme?

A money purchase pension plan is often referred to as a defined contribution pension plan. These pension plans have regular employer contributions that are set as a dollar sum or a percentage of the employee members’ salaries. Additionally, the employee may contribute to the plan. Benefits are calculated based on the following factors: contributions made to the plan, investment returns on those contributions, and the cost of an annuity in retirement.

Regardless of how the assets perform, employers are not required to make any more contributions.

Question 11

What is Financial Reporting Standard 17?

The Accounting Standards Board’s FRS17 accounting standard outlines the financial reporting requirements for organisations, including charities, that manage pension plans. This accounting standard mostly impacts organisations that run defined benefit plans; contribution-based nonprofits are not greatly impacted. Those organisations that have defined benefit plans are required to compute their pension expenditures and make substantial disclosures regarding their plans. FRS 17 doesn’t directly affect a defined benefit scheme’s cash flow, but it does increase transparency in the accounting for retirement payouts and highlights the costs and risks of providing defined benefit pensions.

Question 12

What are the funding requirements for defined benefit pension schemes?

Most defined benefit pension schemes need to meet a statutory funding objective, known as technical provisions, which assesses the required levels of funding a scheme requires to provide benefits for its members. Employers need to work closely with the trustees of the pension scheme to agree what the technical provisions for the scheme should be and set out a schedule of contributions to meet and maintain this level. Regular valuations, at least every three years, are required to check whether the statutory funding objective is met; where it is not, trustees and employers will need to agree on a recovery plan.

Question 13

What is the Pension Protection Fund?

The Pensions Act 2004 introduced the Pension Protection Fund (PPF). The PPF exists to provide compensation to members of schemes where the employer becomes insolvent and the scheme has insufficient funds to provide at least the same levels of benefit as the PPF to its members. The PPF is funded in part by existing pension schemes which pay a yearly levy, part of which depends on their risk profile.

Question 14

What is the role of PFRDA?

As per PFRDA Act 2013, PFRDA is an Authority to promote old age income security by establishing, regulating and developing pension funds to protect the interest of subscribers to schemes of pension funds and for matters connected therewith or incidental thereto.

Question 15

What is the National Pension System?

“National Pension System” (NPS) means the contributory pension system whereby contributions from a subscriber are collected and accumulated in an individual pension account called PRAN using a system of points of presence, a central recordkeeping agency and pension funds as may be specified by regulations.

.

Question 16

Who is covered by the NPS?

NPS is applicable to all employees joining services of the Central Government including Central Autonomous Bodies (except Armed Forces) on or after 1st January 2004. Many State Governments have adopted NPS architecture and implemented NPS mandatorily through Gazette Notifications for their employees joining on or after a cut-off date.

Question 17

What is a PRAN?

PRAN is an acronym for Permanent Retirement Account Number, which is the unique and portable number provided to each subscriber under NPS and remains with him throughout.

Question 18

Are bank details mandatory for opening an NPS account?

Yes. For subscribers, the Bank details are mandatory. In case, Bank details are not available at the time of filling the form, subscribers can provide a declaration for providing the Bank details within six months or on opening of Bank account whichever is earlier.

Question 19

Is NPS applicable to employees of State Autonomous Bodies?

Many State Governments have adopted NPS architecture and implemented NPS for the employees of State Government as well as for the employees of Autonomous bodies, State PSUs, Corporations, Boards, if notified in their respective gazette notifications.

Question 20

Are there any tax benefits on NPS contributions for the central government employees?

Income Tax Act allows benefits under NPS as per the following sections,

• Section 80CCE provides that the aggregate amount of deduction under Section 80CCC and 80CCD shall not exceed Rs 1 lakh. The Finance Act, 2011 provides that contributions made by the Central Government or any other employer to NPS shall be excluded while computing the limit of Rs 1,00,000. The contribution by the employee to the NPS will be subject to the limit of Rs 1,00,000.
• Section CCD (2) provides that deduction in respect of contributions by the Central Government or any other employer to NPS available under Section 80CCD (2) will not be subject to the limit specified in Section 80CCE but it is subject to 10% of Basic + DA maximum.

### Health Insurance

Question 1

Does health insurance policy cover pre-existing illness?

A pre-existing condition is one for which the policyholder is already receiving treatment when they get health insurance. There may be a waiting period before you begin to receive coverage for a pre-existing condition, even though your health insurance company may provide you coverage for it. The waiting period is what it is called. In some circumstances, the waiting time may be up to four years.

Question 2

How are health insurance claims usually settled?

Health insurance claims are either reimbursed or handled without the use of cash. In a cashless setting, your health insurance company will pay your hospital bill on your behalf. You will only be responsible for paying any differences that your health insurance does not cover. However, the cashless facility is only accessible in network hospitals. In the event of reimbursement, you pay your hospital’s outstanding balance before filing a claim with your health insurance company. Your health insurance company reimburses you for the claimed amount, less any applicable exclusions.

Question 3

Can the sum insured be increased on existing health insurance plans?

When your health insurance plan is renewed, you can raise the maximum amount insured. Before purchasing a health insurance plan, be sure to carefully study the policy wordings as this depends on the indemnification policies of the firm.

Question 4

Can someone have more than one health insurance policy?

You are permitted to have multiple health insurance policies, whether they are offered by the same company or different ones. In accordance with your sum covered, you can also divide your claim among the several health insurance policies.

Question 5

What is a cashless facility?

The term “cashless” refers to the benefit when your health insurance company pays your hospital costs immediately. Today, the majority of health insurance providers offer it.

Question 6

What is Family Health Insurance?

A family health insurance plan is a kind of medical insurance that covers all your family members in a single health insurance policy. Under this plan, a fixed sum insured is shared by all family members with an assumption that not everyone will get sick at the same time. Most family health insurance plans offer cashless hospitalisation facilities, maternity benefits and cover pre & post hospitalisation as well.

Question 7

How many people are covered under a family health insurance plan?

Family health insurance plans allow you to cover up to 6 family members under one medi-claim policy. It is a type of health insurance plan for which you pay a single premium amount for a family floater plan and the sum insured splits among all the covered members.

Question 8

What is not covered in a Family Health Insurance Plan?

Following medical expenses are generally not covered by family health insurance plans in India:

• OPD treatments and routine medical check-ups
• Expenses incurred on any aesthetic treatment or plastic surgeries
• Expenses incurred on life-support machines
• Treatment that was taken overseas unless it is included in the plan
• Any illness or injury resulting due to war conditions, nuclear reaction, rebellion, acts of foreign enemies, etc.
• Injury or illness due to participation in unethical or criminal activities
• Pregnancy or childbirth-related complications (unless mentioned in the plan)like voluntary termination of pregnancy, miscarriage or abortion, etc.
• Any pre-existing medical condition is not covered until the completion of the waiting period

Question 9

Which documents are required to raise a reimbursement claim under family health insurance?

The following documents are required to be submitted to raise a family health insurance claim:

• Duly filled health insurance claim form
• Policy document
• Hospital discharge report
• Consultation report and investigation results
• Hospital bills
• Bill payment receipts

Question 10

Is a family health insurance plan better than an individual health plan?

If you need health insurance for your entire family, buying a family health insurance plan is any day better than buying an individual policy. A health insurance policy for a family will cover all the members of your family for a single sum insured and only a single premium needs to be paid to the insurance company.

On the flip side, an individual health plan covers only one person. So, you will need to buy a separate health plan for each family member with a different premium. The combined premium for multiple individual policies will be significantly higher than that of a family health plan.

### HR Questions

Question 1

Good morning, sir or ma’am. I want to start by saying thank you for providing me this chance to introduce myself. I am xxxx, born in Delhi. I completed my schooling from xxxx and am currently pursuing my bachelors’ in xxxx.

In terms of my family, I come from a middle-class background. My mother is a homemaker, and my father has a business.

I am proficient in MS-excel, R programming and I have a keen interest in HTML, Tableau and SQL. My strengths are my self-assurance, optimistic outlook, and diligence. My flaw is that I’m prone to believing anything. My interests include listening to music, playing volleyball, and watching news programmes.

Question 2

Why do you want to work for our company?

I believe that the job requirements for this role are a fantastic fit for me given my existing skill sets and my expertise in the XYZ domain. I could picture myself in that position because it suited my professional goals, abilities, and knowledge. Additionally, after researching your business, I discovered that it had excellent and optimistic prospects, which stoked my excitement about being a part of the exciting future. I would be proud to work for this organisation and felt it to be the ideal setting for leveraging my expertise and the opportunity for personal development.

Question 3

What are your greatest strengths and weaknesses?

I consider my ability to work well in a team to be one of my finest assets. I also have a strong sense of motivation and am a quick learner. Whatever assignment I do, I always do my absolute best to finish it diligently and ahead of schedule. My shortcoming is that I am still developing my people skills while interacting with new people. Talking to new people makes me uncomfortable. I’ve been working on this for a while, and I can state with complete certainty that I’ve made progress.

Question 4

How would you rate yourself on a scale of 1 to 10?

I’d like to give myself an 8. 8 since I recognise that I’m not perfect and that there is always room for growth. The most essential component of both personal and professional development is ongoing learning.

Question 5

What is your biggest achievement so far?

The biggest thing I’ve done is get over my fear of failing. It offers me a fuller sense of life and boosts my self-assurance.

Question 6

Where do you see yourself in 5 years?

If I were chosen for your organisation, I would like to gain experience, additional knowledge, and abilities within the first two to three years before becoming a manager. After that, I would become a senior employee and team leader after completing all my actuarial examinations.

Question 7

Why should we hire you?

Since I’m a fresher, I just have theoretical knowledge; nonetheless, I need a platform where I can put that information to use in the real world. I pledge to make all effort for the organisation’s successful development. I will find it much easier to adapt to the working culture of your company because, as a new employee, I have no preconceived notions about how work should be done in an organisation. Due to my regularity and punctuality, I am able to complete the tasks assigned to me on time and make every effort to meet the needs of the business.

Question 8

How do you get to know about our company?

I got to know about your company from several online websites where I was going through the best companies for actuarial roles and found more about you by visiting and studying your company’s own website.

Question 9

What does success mean to you?

If I believe I am having an impact while working with a group of individuals to create a more successful business. For me, it is the best form of success.

Question 10

How do you handle stress, pressure, and anxiety?

I think it’s important to have a plan for your job and to consistently finish it. I never respond to stress; I always respond to events. I manage the problem and avoid stress in this way.

Question 11

Have you passed all actuarial exams? Can you tell me why or why not?

Different companies and organizations have different needs for their actuaries. To practice in certain settings and industries, you may need to take and pass certain actuarial exams. The hiring manager may ask this question to determine if you are a good fit for the position. To answer the question, be specific about the exams you’ve completed and express your interest in passing more if you haven’t taken them all. To prepare for this question, review the job listing to determine if they specify which exams you need to pass.

Example: “Currently, I have taken and passed seven standard Fellow of the Society of Actuaries exams. I’m very passionate about advancing as an actuary, and am currently studying and preparing to take and pass the fellowship tests.”

### Other Questions

Question 1

What do the shareholders get?

1. Increase in share price

Investors anticipate that the company’s stock price will increase, enabling them to sell their shares for a profit.

The FTSE 100 index of top UK shares has generated an average yearly price return of 6% over the past 35 years, according to trading platform IG. Due to the sharp rise in energy costs over the past year, Shell shareholders have experienced a 40% increase in the value of their shares.

1. Income from dividends

A dividend is a payment made by many businesses to their shareholders. A dividend is paid to shareholders for each share they possess, typically once or twice a year. These funds come from the company’s profits.

1. Pre-emption rights

When new shares are issued, shareholders have a legal pre-emption right, often known as a right of first refusal. A corporation must offer new shares to current shareholders proportionately for at least 14 days if it wants to issue them.

Question 2

State Central Limit Theorem.

It provides the basis for large-sample inference about a population mean when the population distribution is unknown and more importantly does not need to be known. It also provides the basis for large-sample inference about a population proportion, It is one of the reasons for the importance of the normal distribution in statistics.

The Central Limit Theorem can also be used to give approximations to other distributions. This Is useful if we are calculating probabilities that would take too long otherwise. For example, P(X < 30) where X ~ Bin(100,0.3) would require us to work out 30 probabilities and then add them all up. If we use a normal approximation, the calculation of the probability is much simpler, and the loss of accuracy is slight.

Question 3

What is Asymmetric information?

Asymmetric information in insurance refers to a market situation in which one party in a transaction has insufficient information about the other party which leads to market failure. The problem of asymmetric information is common to all insurance markets.

Question 4

How is Attrition rate calculated?

Commonly referred to as a ‘churn rate,’ a company’s attrition rate is the rate at which people leave. If you break it down, it is the number of people who have left the company, divided by the average number of employees over a period of time

Attrition rate = (No. of separations / Avg. No. of employees) x 100.

Question 5

What is the difference between life insurance and general insurance?

The difference between life insurance and general insurance are as follows:

• Life insurance is an insurance contract, which covers the life-risk of the person insured, while general insurance is an insurance that is not covered under Life insurance.
• Life insurance is a form of investment, while general insurance is a contract of indemnity.
• Life insurance is a long term contract. General insurance is a short term contract.
• In life insurance, premium has to be paid over the year. In general insurance, premium has to be paid as a lump sum.
• In life insurance, the insurable amount is paid either on the occurrence of the event, or on maturity. In general insurance, the loss is reimbursed, or liability will be repaid on the occurrence of an uncertain event.
• In life insurance, the insured must be present at the time of contract. In general insurance, the insured must be present, at the time of contract and loss both.
• Life insurance can be done for any value based on the premium policy. In the case of general insurance, the amount payable under life insurance is confined to the actual loss suffered.

Question 6

How is income tax accounted for in the balance sheet?

Income tax payable is found under the current liabilities section of a company’s balance sheet. Income tax payable is one component necessary for calculating an organization’s deferred tax liability. The calculation of income tax liability is dependent on the company’s home country.

Question 7

Name the top 10 companies according to market cap.

The top 10 companies according to market cap are:

• Apple Inc. ( AAPL)
• Saudi Arabian Oil Co. ( 2222.SR)
• Microsoft Corp. ( MSFT)
• Alphabet Inc. ( GOOGL)
• Amazon.com Inc. ( AMZN)
• Tesla Inc. ( TSLA)
• Berkshire Hathaway Inc. ( BRK.A)
• NVIDIA Corp. ( NVDA)
• Taiwan Semiconductor Manufacturing Co. Ltd. (TSM)
• Meta Platforms Inc. (META)

Question 8

What is Bayes’ theorem?

Bayes’ theorem describes the probability of occurrence of an event related to any condition. It is also considered for the case of conditional probability. Bayes’ theorem is also known as the formula for the probability of “causes”. It is a way of finding a probability when we know certain other probabilities.

Question 9

When the government will increase tax on cigarettes of ITC, why will the tax burden be more on consumers?

High taxes affect the lower income families the most. Some economists see taxes on cigarettes as a regressive tax as the higher tax incidence does not take into consideration the standard of living of the cigarette consumers. The lower income group in the society would bear the higher tax burden compared to the higher income group. As the disparity of disposable income between the two groups vary widely, affordability within the lower income group will fall with a price hike, such that cigarettes will be less affordable to these families. However, as cigarettes are quite addictive in nature, depending on the addiction of the smokers they might not be able to cut down on consumption, in which case they may prioritize the purchase of cigarettes over other necessary things. In such scenarios it will be the lower income families that will be affected the most when taxes increase. Therefore, this is why some argue that taxes on tobacco are regressive in nature. Also, ITC is a luxury brand and people consuming ITC cigarettes will show brand loyalty, thus bearing the tax burden more than the producers. However, some consumers belonging to lower income group might shift from ITC to cheaper brands, just to be able to afford cigarettes and other necessities as well. Most of them refuse to simply quit and start a healthier life, continuing to pay higher taxes and compromising on other goods.

Question 10

What does an insurance company do?

Insurance companies can be important for the stability of financial systems mainly because they are large investors in financial markets, because there are growing links between insurers and banks and because insurers are safeguarding the financial stability of households and firms by insuring their risks.Insurance companies assess the risk and charge premiums for various types of insurance coverage. If an insured event occurs and you suffer damages, the insurance company pays you up to the agreed amount of the insurance policy.

Question 11

Explain the Law of large numbers.

The law of large numbers, in probability and statistics, states that as a sample size grows, its mean gets closer to the average of the whole population.

Question 12

State the Principles of  Insurance.

In the insurance world there are six basic principles that must be met, which are:

• Insurable Interest – If you want to purchase a life insurance plan for another person, you should first prove that you have an insurable interest in their life. Insurable Interest means that you will face a substantial, emotional or another type of loss that will negatively affect you upon the demise of the life insured.This interest is evaluated by the life insurer during the application for the plan and before the payment of the death payout.,For example, if you and your spouse live in a two-income household supporting three children, then your spouse would clearly have an insurable interest in your death since it would create a financial hardship to go from two incomes to one income. That’s why life insurance companies generally allow spouses to purchase insurance policies on their partners’ lives.
• Utmost good faith –  It means that both the policyholder and the insurer need to disclose all material and relevant information to each other before commencement of the contract.
• Proximate cause – Proximate cause refers to the first event, or first peril, in a series of events that cause damage in an insurance claim. The proximate cause itself may not do any direct damage. The insurance policy may cover the proximate cause, but not the event that actually causes the damage, so the policy holder will not be reimbursed for his claim.
• Indemnity – The principle of indemnity states that an insurance policy shall not provide compensation to the policyholder that exceeds their economic loss. This limits the benefit to an amount that is sufficient to restore the policyholder to the same financial state they were in prior to the loss. The principle of indemnity ensures that the insured gets made whole from their loss but will not benefit, gain, or profit from an accident or claim.
• Subrogation – subrogation does not apply to life insurance. Definition of Subrogation can be understood as a fair practice of replacing the policyholder’s place with the insurer. In short, by subrogation, you will offer all the legal rights to your insurer to claim money from a third-party, if he/she is found to be guilty of an accident. Subrogation comes under the indemnity clause. Indemnity clause is a contract between a policyholder and an insurer which shows the respective procedures and obligation to compensate the claim amount against damage or losses to your vehicle.
• Contribution – The contribution principle in insurance is a rule that specifies what happens when a person buys insurance from multiple companies to cover the same event, and that event occurs. The principle says that if the policyholder files a claim with one company, that company is entitled to collect a proportional amount of money from the other involved insurance companies.

Question 13

What do you mean by inflation? What are the types of inflation?

Inflation is a quantitative economic measure of a rate of change in prices of selected goods and services over a period of time. Inflation indicates how much the average price has changed for the selected basket of goods and services. It is expressed as a percentage. Increase in inflation indicates a decrease in the purchasing price of the economy.

Types of Inflation are:

• Demand-pull Inflation: It occurs when the demand for goods or services is higher when compared to the production capacity. The difference between demand and supply (shortage) result in price appreciation.
• Cost-push Inflation: It occurs when the cost of production increases. Increase in prices of the inputs (labour, raw materials, etc.) increases the price of the product.
• Built-in Inflation: Expectation of future inflations results in Built-in Inflation. A rise in prices results in higher wages to afford the increased cost of living. Therefore, high wages result in increased cost of production, which in turn has an impact on product pricing. The circle hence continues.

Question 14

What are the main causes of inflation?

Monetary Policy: It determines the supply of currency in the market. Excess supply of money leads to inflation. Hence decreasing the value of the currency.

Fiscal Policy: It monitors the borrowing and spending of the economy. Higher borrowings (debt), result in increased taxes and additional currency printing to repay the debt.

Demand-pull Inflation: Increases in prices due to the gap between the demand (higher) and supply (lower).

Cost-push Inflation: Higher prices of goods and services due to increased cost of production.

Exchange Rates: Exposure to foreign markets are based on the dollar value. Fluctuations in the exchange rate have an impact on the rate of inflation.

Question 15

How do Insurance companies make profit and state the equation?

There are two basic ways that an insurance company can make money. They can earn by underwriting income, investment income, or both. The majority of an insurer’s assets are financial investments, typically government bonds, corporate bonds, listed shares and commercial property. The assets generate investment income and are chosen carefully to reflect the nature and timing of the insurance liabilities that may need to be paid.

So, the equation is : Profit = Premiums + Return on Premiums – Claims – Expenses.

Question 16

Name some of the most common Actuarial softwares used in the industry.

Some of the common Actuarial softwares used in the industry are:

• Milliman Actuarial software solutions
• Moses
• GGY-AXIS
• Poly Systems
• Prophet
• PTS
• RMISWeb
• SAS
• TAS
• Towers Watson

Question 17

Technology and software are important aspects of the work an actuary does. The hiring manager may ask you this question to ensure you are technologically proficient and can use prevalent actuarial programs. To answer, mention at least two programs you’ve used in the past and be specific about what you like or don’t like. To prepare for this question, you can research the company and try to determine which programs they may use.

Example: “I’ve worked with a few different programs, and so far, Moses is my favorite. I like it because it is flexible and detailed, but I know it may be challenging for those who are new to it. That’s why I like to instruct new hires and show them how valuable it can be when you know how to use it. Prophet is another program I’ve used, and I like that it’s simple to obtain and has a clean user interface.”

Question 18

What is the elasticity of price? State its one application in the real world. What are types of elasticity?

Price elasticity measures the responsiveness of the quantity demanded or supplied of a good to a change in its price. It is computed as the percentage change in quantity demanded—or supplied—divided by the percentage change in price.

If a price change for a product causes a substantial change in either its supply or demand, it is considered elastic. Generally, it means that there are acceptable substitutes for the product. Examples would be cookies, luxury, automobiles, and coffee. A                                                                                                                                        Types of elasticity are as follows:

Price Elasticity of Demand (PED):

Price Elasticity of Demand or PED measures the responsiveness of quantity demanded to a change in price. There are two ways to measure PED- arc elasticity that measures over a price range, and point elasticity that measures at one point.

Cross Elasticity of Demand (XED):

Cross Elasticity of Demand (XED) is an economic concept that measures the responsiveness in the quantity demanded of one good when the price of other goods changes. Also called cross-price elasticity of demand, this measurement is calculated by taking the percentage change in the quantity demanded of one good and dividing it by the percentage change in the price of the other good.

Income Elasticity of Demand (YED):

Income Elasticity of Demand measures the responsiveness in the quantity demanded for a good or service when the real income of the consumers is changed, keeping all the other variables constant. The formula for calculating income elasticity of demand is the percent change in quantity demanded divided by the percent change in income. This concept helps us to find whether a good is a necessity or luxury.

Price Elasticity of Supply (PES):

Price Elasticity of supply (PES) measures the responsiveness to the supply of a good or service after a change in its market price. Some basic economic theories explain that when there is a fall in the price of a good its supply is also decreased and when the prices are on a rise the supply is increased.

Question 19

What is double Insurance?

If one person insures some property, such as a home or business, and takes out two policies covering that property, they have purchased double insurance. Individuals are allowed to purchase as much insurance as they please on their property.

Question 20

Brief note on IFRS17 (International Financial Reporting Standard 17)?

IFRS 17 Insurance Contracts establish principles for the recognition, measurement, presentation and disclosure of insurance contracts within the scope of the Standard. The objective of IFRS 17 is to ensure that an entity provides relevant information that faithfully represents those contracts. This information gives a basis for users of financial statements to assess the effect that insurance contracts have on the entity’s financial position, financial performance and cash flows.

Question 21

What is the role of an Actuary?

Actuaries analyze the financial costs of risk and uncertainty. They use mathematics, statistics, and financial theory to assess the risk of potential events, and they help businesses and clients develop policies that minimize the cost of that risk. Actuaries’ work is essential to the insurance industry.

Question 22

Argue IFRS4 vs IFRS17.

• Comparability of Insurers – Since IFRS 4 was put together in a fairly compact timeframe, just ahead of the EU’s adoption of IFRS Standards, it aimed for minimum rather than maximum harmonization. Under IFRS 4, companies could therefore carry on using national standards when accounting for insurance contracts. This made comparability extremely tough, which is never great for investors. IFRS 17 aims to ensure companies across all IFRS jurisdictions apply consistent accounting for all insurance contracts, regardless of product.
• Transparency and quality of investor information – The new standard looks to equip investors with better information about insurance contracts and how each insurer creates value. According to the IASB, IFRS 17 achieves this by:
1. Combining current measurement of future cash flows with the recognition of profit over the period that services are provided under the contract.
2. Presenting insurance service results (including presentation of insurance revenue) separately from insurance finance income or expenses.
3. Requiring an entity to make an accounting policy choice of whether to recognise all insurance finance income or expenses in profit or loss or to recognise some of that income or expenses in other comprehensive income.
• Confidence and cost of capital – Since these will bring greater transparency around insurers’ operations, industry observers believe that the new standard may help to rebuild confidence in the insurance sector and therefore drive M&A activity. Some of the largest insurers may also see their cost of capital reduced as a result.

Question 23

What is SII?

Solvency II is a far-reaching programme of prudential regulations, which vary in severity depending on the riskiness and diversity of an insurer’s business. Similar to the banking industry’s Basel standards, the Solvency II programme is divided into three areas: Pillar 1 lays out quantitative requirements for the amount of capital an insurer should hold; Pillar 2 covers governance and risk management of insurers; and Pillar 3 addresses transparency, reporting and public disclosure.

Question 24

SII vs IFRS17

1. Scope
• Solvency II is a European legal framework that goes far beyond the mere calculation of a solvency capital requirement. It is a full-blown enterprise risk management paradigm, comprising three pillars that deal with quantitative requirements, corporate governance and internal control functions, and transparency and disclosure requirements. Insurers must disclose a Solvency and Financial Condition Report (SFCR) to the public and must submit to the insurance supervisor detailed information about specific attributes of their business, including the Own Risk and Solvency Assessment (ORSA), that is a fundamental component of Solvency II.
• IFRS 17 is a global reporting standard that has as its chief objective the measurement of performance of insurance contracts in a manner that is aligned with economic principles. It does not specifically address corporate governance or operations of insurance companies, and it does not impact only insurance and reinsurance companies, but also any entity that issues insurance contracts.
2. Purpose
• Solvency II attempts to guarantee the solvency of insurance and reinsurance companies. The idea is clearly to force companies to compute a risk-based solvency capital that is commensurate to the exposure to key risks. Solvency II was not designed to measure financial performance.
• IFRS 17, in contrast, is a tool for measuring risk-based financial performance of insurance contracts.
3. Contractual Service Margin (CSM)
• Given that Solvency II does not measure financial performance, the concept of a CSM is not defined.
• IFRS 17 introduces the CSM. The CSM refers to the carrying amount of the asset or liability for a group of insurance contracts representing the unearned profit the entity will recognize as it provides services under the insurance contracts.

Question 25

What is a matrix?

A matrix is a mathematical structure having rows and columns. The element aij of a matrix, say M refers to the element in the i-th row and j-th column.  The matrices are represented as square or rectangular parenthesis or in boxes. The horizontal and vertical lines of the matrix are represented as rows and columns. The numbers in the matrices are called entries or elements. The matrix size is specified in m rows and n columns like m-by-n matrices.

Question 26

How to perform matrix multiplication of two matrices of dimensions  4 x 3 and 4 x 3?

It is not possible to perform matrix multiplication of dimensions 4 x 3 and 4 x 3 since the column size of the first matrix and row size of the second matrix must be equal. Thus, by transposing one of the given matrices, multiplication is possible.

Question 27

What is the difference between financial assumption and demographic assumption?

In order to calculate the pension obligations of a certain company, an actuary must predict the present value of future benefits that will be paid to the plan’s participants. An actuary uses demographic assumptions to evaluate the projected benefits of all the participants in a certain plan. These demographic assumptions include assumptions about mortality, disability, termination of employment, and retirement.

Financial assumptions are the guidelines you give your business plan to follow. They can range from financial forecasts about costs, revenue, return on investment, and operating and startup expenses. Basically, financial assumptions serve as a forecast of what your business will do in the future.

Question 28

Are you aware of the different insurance Sectors?

Yes, I am aware of the different insurance sectors. The Indian Insurance Sector is basically divided into two categories – Life Insurance and Non-life Insurance. The Non-life Insurance sector is also termed as General Insurance. Both the Life Insurance and the Non-life Insurance are governed by the IRDAI (Insurance Regulatory and Development Authority of India).

Question 29

Name some companies which have low beta.

Beta is helpful in understanding the overall price risk level for investors during market downturns in particular. The lower the Beta value, the less volatility the stock or portfolio should exhibit against the benchmark.

Companies which have low beta are outside India are:

• AllState Corporation
• Brown-Forman
• Davita Inc.
• Quest Diagnostics
• Tyson Foods

Companies which have low beta in India are:

• Guj.St.Petronet
• Asian Paints
• Nippon Life Ind.
• Pfizer
• Ajanta Pharma

Question 30

Name the top 10 dividend paying companies.

The top 10 dividend-paying companies are:

• Vedanta ltd
• IOCL
• Power Finance Corporation Ltd.
• Hindustan Petroleum Corporation Ltd
• Coal India Ltd.
• Hindustan Zinc Ltd
• Oracle Financial Services Software Ltd.
• ITC Ltd
• Bharat Petroleum Corporation Ltd.
• Ambuja Cements Ltd.

Question 31

What is the name of the RBI Governor?

Shaktikanta Das is the name of the RBI Governor.

Question 32

What do you mean by pricing in Insurance?

Pricing is one of the most essential components of an insurance company. It is the process by which an insurance company sets up the premium that needs to be charged from the policyholder by considering various risk factors such as age, mortality, gender, location, etc.

Question 33

What are the measures of national income?

The 5 measures of national income are:

• Gross Domestic Product (GDP)
• Net National Product (NNP)
• Gross National Product (GNP)
• Personal income.
• Disposable income.

Question 34

How can an insurance company deal with longevity risk?

An insurance company can focus on selling more annuities than assurances in order to deal with longevity risk. This way, it will have to pay just a proportion of the sum assured if the person dies early and not the whole of it.

Question 35

What is the paradox of thrift?

According to the paradox of thrift, personal savings may actually hinder the expansion of the economy as a whole. It is predicated on an economic cycle in which recent expenditure influences forthcoming spending. In order to increase expenditure during a recession, it suggests cutting interest rates.

### Guesstimate

Question 1

If you have a 5-liter jug and a 3-litre jug, how would you measure exactly 4 litres?

Step 1: Fill 5 litre of water in Jug 1

Step 2: Transfer the water from 5 liters Jug 1 to 3 litres Jug 2.

2 litres remaining in Jug 1.

Step 3: Empty Jug 2.

Step 4: Transfer 2 litres from Jug 1 to Jug 2.

Now, Jug 1 = Empty, Jug 2 = 2 litres.

Step 5: Refill Jug 1 with 5 litres of water.

Step 6: Transfer 1 litre from Jug 1 to Jug 2 (it already has 2 litres from Step 4)

Now, 5 litres – 1 litre = 4 litres in Jug 1

Question 2

If you have 15L data, what will you use Excel or R? And why?

It is preferred to use R for a very large data set as excel could only take data upto 2^20 (1048576).

Question 3

If we throw two dice, what will be the probability of getting 4 in both the dice?

Overall outcomes of throwing 2 dice are:

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Out of these, getting a 4 in both the dice is represented by just 1 outcome, ie, (4,4). So, the probability of getting 4 in both the dice =                                                       Case of getting 4 in both the dice/Total no. of cases=1/36.

Question 4

If there are 730 accidents in a year on a particular road, what is the probability of getting 3 accidents in a day and at least 3 accidents in a day?

If there are 730 accidents in a year on a particular road, there are 730/365=2 accidents in a day on that road. So, this follows Poi(2). Thus, the probability of getting 3 accidents in a day =

P(X = 3) = (e^-2*2^3)/3! = 0.18044.

And, probability of getting at least 3 accidents in a day =

P( X > = 3) = 1 – p(X < = 2) = 1- (P(x = 0) + P(x = 1) + P(x = 2)) = 0.3233.

Question 5

Suppose in a triangle there are 3 ants sitting at each corner . What will be the probability that ants will collide?

Let’s start by reversing the way the riddle is asked and find the probability that there will not be a collision instead. When will this happen?

Well, what if all of the ants are walking in the same direction? Then there will never be a collision between any of the ants because they are all walking in the same direction. And, the only time they will be walking in the same direction is if they are all walking either counter-clockwise around the triangle, or clockwise around the triangle. So, there are only two scenarios in which a collision will not happen between the ants.

Now that we know that there are only two scenarios where the ants will not collide, we have to ask ourselves how many different ways are there for the ants to move on the sides of the triangle? Well, each ant can move in 2 different directions. Because there are 3 ants, this means that there are 23 (which equals eight) possible ways that the ants can move. And since we already know that there are only 2 ways in which the ants can avoid collision entirely, this means that there are 6 scenarios where the ants will collide. And 6 out of 8 possible scenarios, means that the probability of collision is 6/8, which equals 3/4 or .75. Thus, the probability of the ants colliding is 0.75.

Question 6

Guesstimate of the weight of an aircraft.

The total weight W of the aircraft is simply the sum of the weight of all of the individual components.

W = w(fuselage) + w(wing) + w(engines) + w(payload) + w(fuel) + …

To generalize, if we have a total of “n” discrete components, the weight of the aircraft is the sum of the individual i component weights with the index i going from 1 to n.

W=summation of w(i) (i=1 to n).

Question 7

Suppose every day when you travel to the office you take the same route while going and coming back. While going you travel at 40km/hr and while coming back you travel at 60km/hr. What is the average speed in which you travel?

Let us consider distance D. Then, we know, speed = distance/time.

So, 40=(D/T1) and 60=(D/T2).

T1=(D/40) and T2=(D/60).

Total time T=T1+T2.

(D/40)+(D/60)=(D/24).

Total distance = D+D = 2D.

We know, Average speed = Total Distance/Total Time = 2D/(D/24) = 48Km/hour.

Question 8

Suppose in a hole 22metre deep there is an ant and it wants to come out. It climbs up by 5metre before again slipping by 2metre in the hole, how many attempts the ant needed to take before coming out of the well, assuming that it will not get down (slip back)?

The ant would need to make 7 attempts. Everytime the ant climbs 5 meters and slips by 2 meters, in total it would have climbed by 3 metres. In the 6th attempt it would have climbed by (5*3)+5 metres = 20 metres and then slip by 2 metres coming back down to 18 metres. In the 7th attempt, it would have climbed 5 more metres bringing him to 23 metres and thus, out of the well.

Question 9

Suppose a number x, first increases by 25% and then decreases by 25%. After all this adjustment, will the answer be less than x, equal to x or greater than x?

If a number x, first increases by 25% and then decreases by 25%, the resulting answer would be less than x.

Question 10

How many 4 letter words can you make from the word ‘GIFT’?

The number of 4 letter words we can make from the word ‘GIFT’ = 4! = 4*3*2*1 = 24.

Question 11

If you are going to receive Rs 100 after 10 years, what is the present value of it at 3% rate of interest?

If I am going to receive Rs. 100 after 10 years, the present value of it at 3% rate of interest = Rs.100*(1.03)^-10 = Rs.74.41.

Question 12

Suppose you have Rs 200 and you have invested Rs.100 in 2 different banks. One bank offers CI of 12% pa and other bank offers SI of 12%pa. Which bank will give you a higher interest rate by the sixth month?

The bank that offers 12% pa SI will have an amount after 6 months = 100(1+0.5*0.12)=106. This gives us 6% interest at the sixth month. The bank that offers 12% pa CI will have an amount after 6 months = 100(1.12)6/12=105.83. This gives us 5.83% interest at the sixth month. Thus, the bank offering 12% pa SI will give us a higher interest rate.

Question 13

Give a practical example of Binomial Distribution.

Suppose that X is the number of sixes obtained when a fair die is thrown 10 times. Then,

P(X=x)=10Cx*(1/6)^x*(5/6)^(10-x) and the probability of exactly one six in 10 throws is 10C1(1/6)^1*(5/6)^9=0.3230.

Question 14

Suppose you are measuring the rainfall everyday for 365 days. What will be the mode?

If we are measuring rainfall for 365 days, we would have the data for 365 days. The highest rainfall recorded in those 365 days would be the mode of the data.

### Data Analysis

Question 1

What are the various steps involved in any analytics project?

The following are the many steps involved in any typical analytics project:

• Understanding the Problem

Recognize the issue facing the company, specify its objectives, and make plans for a successful resolution.

• Gathering data

Depending on your priorities, get the pertinent information from a variety of sources.

• Cleaning Data

Make the data suitable for analysis by cleaning it to get rid of unnecessary, redundant, and missing values.

• Data exploration and analysis

To evaluate data, employ data mining methods, business intelligence tools, and predictive modelling methodologies.

• Interpreting the results

Analyse the data to uncover underlying trends and patterns and obtain new perspectives.

Question 2

What are the common problems that data analysts encounter during analysis?

Any analytics project will typically involve these phases to solve problems:

-dealing with duplication

-gathering valuable data at the appropriate time and place

-addressing storage and data erasure issues

-securing data and addressing compliance challenges

Question 3

What is the significance of Exploratory Data Analysis (EDA)?

-EDA (exploratory data analysis) aids in better understanding the data.

-It aids in building your data’s confidence to the point where you are prepared to use a machine learning algorithm.

-You can use it to improve the feature variables you choose to include in your model.

Question 4

Explain descriptive, predictive, and prescriptive analytics.

 Descriptive Predictive Prescriptive It provides insights into the past to answer “what has happened” Understands the future to answer “what could happen” Suggest various courses of action to answer “what should you do” Uses data aggregation and data mining techniques Uses statistical models and forecasting techniques Uses simulation algorithms and optimization techniques to advise possible outcomes Example: An ice cream company can analyze how much ice cream was sold, which flavours were sold, and whether more or less ice cream was sold than the day before Example: An ice cream company can analyze how much ice cream was sold, which flavours were sold, and whether more or less ice cream was sold than the day before Example: Lower prices to increase the sale of ice creams, produce more/fewer quantities of a specific flavour of ice cream

Question 5

What are the different types of sampling techniques used by data analysts?

There are majorly five types of sampling methods:

-Simple random sampling

-Systematic sampling

-Cluster sampling

-Stratified sampling

-Judgmental or purposive sampling

Question 6

Describe univariate, bivariate, and multivariate analysis.

Univariate analysis is the simplest and easiest form of data analysis where the data being analysed contains only one variable. Example – Studying the heights of players in the NBA.

Univariate analysis can be described using Central Tendency, Dispersion, Quartiles, Bar charts, Histograms, Pie charts, and Frequency distribution tables.

The bivariate analysis involves the analysis of two variables to find causes, relationships, and correlations between the variables. Example – Analysing the sale of ice creams based on the temperature outside.

The bivariate analysis can be explained using Correlation coefficients, Linear regression, Logistic regression, Scatter plots, and Box plots.

The multivariate analysis involves the analysis of three or more variables to understand the relationship of each variable with the other variables. Example – Analysing Revenue based on expenditure.

Multivariate analysis can be performed using Multiple regression, Factor analysis, Classification & regression trees, Cluster analysis, Principal component analysis, Dual-axis charts, etc.

Question 7

How should missing values be handled in a dataset?

Listwise Removal

If even one value is absent, the listwise deletion approach excludes the entire record from examination.

Average Imputation

Fill up the missing value by using the average of the responses from the other participants.

Regression Substitution

Multiple-regression analyses can be used to guess a missing value.

Multiple Imputations

It then averages the simulated datasets by adding random errors to your predictions, creating believable values based on the correlations for the missing data.

Question 8

How is Overfitting different from Underfitting?

 Overfitting Underfitting The model trains the data well using the training set. Here, the model neither trains the data well nor can generalise to new data. The performance drops considerably over the test set. Performs poorly both on the train and the test set. Happens when the model learns the random fluctuations and noise in the training dataset in detail. This happens when there is less data to build an accurate model and when we try to develop a linear model using non-linear data.

Question 9

How do you treat outliers in a dataset?

The following four techniques can be used to deal with outliers:

-Delete the outlier records.

-Set a new value for your outliers data.

-Try a different transformation.

-Cap the outlier data.

Question 10

What is Data Analysis?

The process of studying, modelling, and interpreting data to derive insights or conclusions is known as data analysis. Decisions can be taken with the information gathered. Every business makes use of it, which explains why data analysts are in high demand. The sole duty of a data analyst is to fiddle with enormous amounts of data and look for undiscovered insights. Data analysts help organisations understand the condition of their businesses by analysing a variety of data.

the aim of factor analysis is to explain the variance between variables.

Question 11

Tell some key skills usually required for a data analyst.

-It is essential to have knowledge of reporting tools (such as Business Objects), programming languages (such XML, JavaScript, and ETL), and databases (such as SQL, SQLite, etc.).

-the capacity to correctly and effectively acquire, organise, and communicate massive data.

-the capacity to create databases, build data models, carry out data mining, and divide data.

-a working knowledge of statistical software for massive dataset analysis (SAS, SPSS, Microsoft Excel, etc.).

-Teamwork, effective problem-solving, and verbal and written communication abilities.

excellent at drafting reports, presentations, and questions.

-knowledge of programmes for data visualisation, such as Tableau and Qlik.

-the capacity to design and use the most precise algorithms on datasets to get answers.

Question 12

What do you mean by data visualisation?

A graphical depiction of information and data is referred to as data visualisation. By using visual elements like charts, graphs, and maps, data visualisation tools let users quickly identify trends, outliers, and patterns in data. With the use of this technology, data may be examined and processed more intelligently and transformed into diagrams and charts.

Question 13

Write the difference between variance and covariance.

Variance: In statistics, variance is defined as the deviation of a data set from its mean value or average value. When the variances are greater, the numbers in the data set are farther from the mean. When the variances are smaller, the numbers are nearer the mean.

Covariance: Covariance is another common concept in statistics, like variance. In statistics, covariance is a measure of how two random variables change when compared with each other.

Question 14

How often should a data model be retained?

A good data analyst would be able to understand the market dynamics and act accordingly to retain a working data model so as to adjust to the new environment.

Question 15

Explain the essential steps in the data validation process.

Data screening and data verification are the two processes that make up the data validation process.

Data screening: Various algorithms are employed in this stage to filter the full data set for any incorrect values. Making sure the data is clear and available for analysis is what it involves.

Data Verification: Before using the data, the correctness and quality of the source data are examined. Every suspected value is assessed against a number of use cases before a final judgement is made regarding whether or not it must be included in the data. Data cleansing also includes data validation.

Question 16

Mention some problems that data analysts face while performing the analysis?

When conducting data analysis, data analysts encounter the following issues:

-Data that is inconsistent and lacking

-Spelling errors and duplicate entries

-A data file with poor formatting

-Inaccurate data classification and various value representations

-Conflicting data

Question 17

What is imputation?

Imputation is the process of replacing the missing data with substituted values.

Question 18

What is the K-means algorithm?

K-means algorithm partitions a data set into clusters such that a cluster formed is homogeneous and the points in each cluster are close to each other. The algorithm tries to maintain enough separation between these clusters. Due to the unsupervised nature, the clusters have no labels

Question 19

What are the most popular statistical methods used when analysing data?

The most popular statistical methods used in data analytics are –

-Linear Regression

-Classification

-Resampling Methods

-Subset Selection

-Dimension Reduction

-Nonlinear Models

-Tree-Based Methods

-Support Vector Machines

-Unsupervised Learning

Question 20

What is the difference between factor analysis and principal component analysis?

The aim of the principal component analysis is to explain the covariance between variables while the aim of factor analysis is to explain the variance between variables.

### CP1 Actuarial Practice

QUESTION 1

What is an actuarial control cycle?

The actuarial control cycle is a fundamental tool of risk management which involves the process of analysing, quantifying, mitigating and monitoring risks.

QUESTION 2

List few applications of actuarial control cycle to actuarial work.

• Asset-liability management
• Model validation
• Monitoring the effect of investment mismatching
• Assessing the need for and calculator of provisions.
• Determining and monitoring mortality, expense and persistency assumptions for use within design of and reserving for contracts or schemes

QUESTION 3

List a few clients to whom actuaries provide advice to.

• Policyholders
• Employers
• Insurance company
• Employees
• Auditors of insurance companies
• Banks
• Members of investment schemes
• Investment fund managers

QUESTION 4

Describe three types of advice given by actuary.

• Indicative advice: giving an opinion without fully investigating the whole issue
• Factual advice: based on research eg legislation
• Recommendation: made consistent with requirements

QUESTION 5

State two forms of insurance that are compulsory in some countries.

Employers’ liability insurance and motor third party insurance.

QUESTION 6

Define information asymmetry.

Information asymmetry is an imbalance between two negotiating parties in their knowledge of relevant factors and details. Typically, that imbalance means that the side with more information enjoys a competitive advantage over the other party.

QUESTION 7

Which five parties are the main providers of benefits?

• The state
• Employers or group of employers
• Individuals
• Financial institutions
• Other organisations

QUESTION 8

Define a defined benefit scheme.

A defined benefit plan, more commonly known as a pension plan, offers guaranteed retirement benefits for employees. Defined benefit plans are largely funded by employers, with retirement payouts based on a set formula that considers an employee’s salary, age and tenure with the company.

QUESTION 9

Define a defined contribution scheme.

Defined contribution (DC) schemes are occupational pension schemes where your own contributions and your employer’s contributions are both invested and the proceeds used to buy a pension and/or other benefits at retirement. The value of the ultimate benefits payable from the DC scheme depends on the amount of contributions paid, the investment return achieved less any fees and charges, and the cost of buying the benefits.

QUESTION 10

Define microinsurance.

Microinsurance products offer coverage to low-income households or to individuals who have little savings. It is tailored specifically for lower valued assets and compensation for illness, injury, or death.

QUESTION 11

What are three types of interest paid on cash deposits?

The three types of interest include simple (regular) interest, accrued interest, and compounding interest.

• Simple (Regular) Interest

Simple or regular interest is the amount of interest due on the loan, based on the principal loan outstanding.

Example:

For example, if an individual borrows \$2,000 with a 3% annual interest rate, the loan would require a \$60 interest payment per year (\$2,000 * 3% = \$60).

• Accrued Interest

Accrued interest is accumulated interest that is unpaid until the end of the period. If a loan requires monthly payments (at the end of each month), interest steadily accumulates throughout the month.

Example:

If \$30 is the interest expense each month, the loan is accruing \$1 of interest each day that requires payment once the end of the month is reached. In this example, by day 15, the loan will have accumulated \$15 in accrued interest (but require payment once \$30 is reached).

• Compound Interest

Compounding interest essentially means “interest on interest.” The interest payments change each period instead of staying fixed. Simple interest is based solely on the principal outstanding, whereas compound interest uses the principal and the previously earned interest.

Example:

If a person borrowed \$1,000 with 2% interest and has \$100 of accrued interest, then that year’s interest would be \$22. It is because the interest is paid on the principal (\$1000) and the accrued interest (\$100), for a total of \$1100. 2% of \$1100 is \$22.

QUESTION 12

What is meant by ‘bond’?

A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically corporate or government).Bond details include the end date when the principal of the loan is due to be paid to the bond owner and usually include the terms for variable or fixed interest payments made by the borrower.

QUESTION 13

What are the main features of an index-linked security?

An index-linked bond is a bond in which payment of interest income on the principal is related to a specific price index, usually the Consumer Price Index (CPI). This feature provides protection to investors by shielding them from changes in the underlying index.

QUESTION 14

What is the relationship between real and nominal yields?

Nominal yield= risk-free real yield+ expected future inflation + inflation risk premium, if inflation risk premium is ignored, the difference between nominal and real yields gives an estimate of the market’s expectations for inflation.

QUESTION 15

What is the purpose of collective investment schemes?

A Collective Investment Scheme is an investment scheme where various individuals come together and pool their money in order to invest their whole fund collection in a particular asset.

QUESTION 16

Why should an investor choose an investment fund scheme?

• Diversification

Funds typically spread their investment across different companies, asset types and geographical regions, providing a benefit known as ‘diversification’. When one investment is down, another might be up, and you’re not taking a chance on the fortunes of one single asset.

• Ease of use

The day-to-day running of your investment is designed to be straightforward. A fund manager invests on your behalf and you’ll receive regular reports on how your money has been invested

• Cost

They spread ﬁxed costs, such as the charges for safekeeping of assets across all investors in the fund.

• Professional investment management

Investment funds allow you to access the expertise of full‑time, dedicated fund managers and their teams of analysts who have access to market information outside the scope of the average investor.

QUESTION 17

What are types of collective investment schemes?

There are two main types of collective investment scheme – unit trusts and investment trusts. As a closed ended fund, investment trusts have a fixed number of shares in an issue. This allows managers to take a longer-term view because they do not have to sell assets when investors sell their shares. Unit trusts are the most common types of collective investment scheme in the UK and are also referred to as open-ended funds, because they will always accept more cash from investors – they just become bigger to accommodate the demand. On the flip side, if there are more sellers than buyers, the fund will become smaller. This is because it is structured as a company that can create shares for new investors and which will buy shares back from an investor if they wish to sell.

QUESTION 18

What factors influence the risk appetite of any organisation?

Risk appetite can vary based on a number of factors, such as:

1) industry,

2) company culture,

3) competitors,

4) the nature of the objectives pursued (e.g. how aggressive they are), and

5) the financial strength and capabilities of the organisation (i.e. the more resources a company has, the more willing it may be to accept risks and the costs associated with them).

QUESTION 19

Give examples of ESG factors affecting risk appetite.