CHAPTER 4 RISK AND RETURN:

AN OVERVIEW OF CAPITAL MARKET THEORY

Q-1 What is a return? Explain the components of (total) return? Should unrealised capital gain (or loss) be included in the calculations of returns?

A-1 Return can be defined as excess over initial investment earned over a period of time. Return can be calculated in terms of rupee return and/or percentage return. Return can be calculated for both real and financial assets. In case of shares, rate of return would consist of dividend yield and capital gain yield. Note that the unrealised capital gain (or loss) is included in the calculation of return.

Q-2 Illustrate the computation of the expected rate of return of an asset. A-2 The expected rate of return [E (R)] is the sum of the product of each outcome (return) and its associated probability:

Expected rate of return = rate of return under scenario 1 x probability of scenario 1 + rate of return under scenario 2 x probability of scenario 2 +... + rate of return under scenario n x probability of scenario n

Economic Conditions(1)

Rate of Return (%)(2)

Probability(3)

Expected Rate of Return (%)(4) = (2) (4)

Growth 18.5 0.25 4.63Expansion 10.5 0.25 2.62Stagnation 1.0 0.25 0.25Decline - 6.0 0.25 - 1.50

1.00 6.00

Q-3 Define holding-period return. How is it calculated?A-3 Investors may hold their investment in shares for longer periods than for one year.

Suppose you invest Rs 1 today in a company's share for five years. The rates of return are 18 percent, 9 percent, 0 percent, - 10 percent and 14 percent. What is the worth of your shares? You hold the share for five years; hence, you can calculate the worth of your investment assuming that each year dividends from the previous year are reinvested in shares. The worth of your investment after five years is:

Investment worth after five years = (1 + 0.18)x (1 + 0.09)x (1 + 0.0)x (1 - 0.10)x (1 + 14.0)

= 1.18x1.09x1.00x0.90x1.14

= Rs 1.32

Your one rupee investment has grown to Rs 1.32 at the end of five years. Thus your total return is: 1.32 - 1 = 0.32 or 32 percent. Your total return is a five-year holding-period return. The compound annual rate of return is as follows:

Compound annual rate of return = Vl.18xl.09x 1.00x0.90x1.14 -1

= 1.057 -1 = 0.057 or 5.7%

Q-4 What is risk? How can risk of a security be calculated? Explain your answer withthe help of an example. A-4 Risk of returns is the variability in rates of return.

The variability of rates of returnmay be defined as the extent of the deviations (or dispersion) of individual ratesof return from the average rate of return. There are two measures of thisdispersion: variance or standard deviation. Standard deviation is the square root ofvariance.The formulae calculating variance and standard deviation of historical rates ofreturn of a share as follows:

2

The share of Hypothetical Company Limited has the following anticipated returns with associated probabilities:

Return (%) -20 -10 10 15 20 25

Probability 0.05 0.10 0.20 0.25 0.20 0.15

The risk, measured in terms of variance and standard deviation, is:

σ2 = (-20-13)2 x0.05 + (-10-13)2 x0.10 + (10-13)2 x0.20 + (15-13)2 xO.25 +

(20-13)2 x0.20 + (25-13)2 x0.15 + (30-13)2 xO.05 = 156

a = 156=1249.% The expected rate of return is:

= -20x0.05 + -10x0.10 + -10x0.20 + 15x0.25 20x0.20 + 25x0.15 + 30x0.05 =

Q-5 What is a risk-free security? What is risk premium? How can it be estimated from historical data?

A-5 A risk free security is a security which is free from risk of default and the variability on its returns is the lowest. The 28-year average return on the stock market (Sensex) is higher by 8.76 per cent in comparison with the average return on the long-term government bonds for the same period in India. This excess return is a compensation for the higher risk of the return on the stock market; it is commonly referred to as risk premium.

Q-6 What is a normal distribution? How does it help to interpret standard deviation?A-6 The normal distribution is a smooth, symmetric, continuous, bell-shaped curve.

The distribution is neither skewed nor peaked. The spread of the normal distribution is characterised by the standard deviation. It is useful to notice certain properties of a normal distribution.

• The area under the curve sums to 1.• The curve reaches its maximum at the expected value (mean) of the

distribution and one-half of the area lies on either side of the mean.• Approximately 50 percent of the area lies within ± 0.67 standard deviations of

the expected value; about 68 per cent of the area lies within ± 1.0 standarddeviations of the expected value; 95 per cent of the area lies within ± 1.96standard deviation of the expected value and 99 percent of the area lies within+ 3.0 standard deviations of the expected value.