# Investment & Finance

## Interest Rates

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.

## Project Appraisal

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.

## Stock Market

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.