RISK AND RETURN: AN OVERVIEW OF CAPITAL MARKET THEORY

CHAPTER 4

LEARNING OBJECTIVES

Discuss the concepts of average and expected rates of return. Define and measure risk for individual assets. Show the steps in the calculation of standard deviation and

variance of returns. Explain the concept of normal distribution and the importance

of standard deviation. Compute historical average return of securities and market

premium. Determine the relationship between risk and return. Highlight the difference between relevant and irrelevant risks.

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Return on a Single Asset

Total return = Dividend + Capital gain

3

1 1 01 011

0 0 0

Rate of return Dividend yield Capital gain yield

DIVDIV

P PP PR

P P P

Return on a Single Asset

21.84

36.99

-6.73

10.81

-16.43

15.65

-27.45

40.94

12.83

2.93

-40

-30

-20

-10

0

10

20

30

40

50

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Year

Tota

l Ret

urn

(%

)

4

Year-to-Year Total Returns on HUL Share

Average Rate of Return

The average rate of return is the sum of the various one-period rates of return divided by the number of period.

Formula for the average rate of return is as follows:

5

1 2=1

1 1 = [ ]

n

n tt

R R R R Rn n

Risk of Rates of Return: Variance and Standard Deviation Formulae for calculating variance and standard

deviation:

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Standard deviation = Variance

2

2

1

1

1

n

tt

Variance R Rn

7

Investment Worth of Different Portfolios, 1980-

81 to 2007–08

8

HISTORICAL CAPITAL MARKET RETURNS

Year-by-Year Returns in India: 1981-2008

Averages and Standard Deviations, 1980–81 to 2007–089

*Relative to 91-Days T-bills.

Historical Risk Premium The 28-year average return on the stock market is higher by

about 15 per cent in comparison with the average return on 91-day T-bills.

The 28-year average return on the stock market is higher by about 12 per cent in comparison with the average return on the long-term government bonds.

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.

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11

The expected rate of return [E (R)] is the sum of the product of each outcome (return) and its associated probability:

Expected Return : Incorporating Probabilities in

Estimates

Rates of Returns Under Various Economic Conditions

Returns and Probabilities

Cont…

The following formula can be used to calculate the variance of returns:

12

2 2 2 21 1 2 2

2

1

... n n

n

iii

R E R P R E R P R E R P

R E R P

Example13

Expected Risk and Preference A risk-averse investor will choose among investments with

the equal rates of return, the investment with lowest standard deviation and among investments with equal risk she would prefer the one with higher return.

A risk-neutral investor does not consider risk, and would always prefer investments with higher returns.

A risk-seeking investor likes investments with higher risk irrespective of the rates of return. In reality, most (if not all) investors are risk-averse.

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Risk preferences15

Normal Distribution and Standard Deviation In explaining the risk-return relationship, we

assume that returns are normally distributed. The spread of the normal distribution is

characterized by the standard deviation. Normal distribution is a population-based,

theoretical distribution.

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17

Normal distribution

Properties of a Normal Distribution The area under the curve sums to1. 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 per cent of the area lies within ± 0.67 standard deviations of the expected value; about 68 per cent of the area lies within ± 1.0 standard deviations of the expected value; 95 per cent of the area lies within ± 1.96 standard deviation of the expected value and 99 per cent of the area lies within ± 3.0 standard deviations of the expected value.

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Probability of Expected Returns The normal probability table, can be used to determine the

area under the normal curve for various standard deviations. The distribution tabulated is a normal distribution with mean

zero and standard deviation of 1. Such a distribution is known as a standard normal distribution.

Any normal distribution can be standardised and hence the table of normal probabilities will serve for any normal distribution. The formula to standardise is:

S =

19

( )R E R-s

Example An asset has an expected return of 29.32 per cent and the standard

deviation of the possible returns is 13.52 per cent. To find the probability that the return of the asset will be zero or less,

we can divide the difference between zero and the expected value of the return by standard deviation of possible net present value as follows:

S = = – 2.17

The probability of being less than 2.17 standard deviations from the expected value, according to the normal probability distribution table is 0.015. This means that there is 0.015 or 1.5% probability that the return of the asset will be zero or less.

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0 29.32

13.52

-