Risk & Return an Overview of Capital Market Theory

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RISK AND RETURN: AN OVERVIEW

OF CAPITAL MARKET THEORY

ByVaishnav Kumar

[email protected]


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LEARNING OBJECTIVES

Discuss the concepts of average and expected rates

return. Define and measure risk for individual assets.

Show the steps in the calculation of standard deviatand variance of returns.

Explain the concept of normal distribution and importance of standard deviation.

Compute historical average return of securities amarket premium.

Determine the relationship between risk and return.

Highlight the difference between relevant airrelevant risks.

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Return on a Single Asset

Total return = Dividend + Capital gain

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1 1 01 011

0 0 0

Rate of return Dividend yield Capital gain yield

DIVDIV

P PP PR

P P P


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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

TotalReturn(%)

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Year-to-Year Total Returns on HUL Share


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Average Rate of Return

The average rate of returnis the sum of the various one-period rates

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 t

tR R R R Rn n


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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

t

t

Variance R Rn


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Investment Worth of Different

Portfolios, 1980-81 to 200708


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HISTORICAL CAPITAL MARKET RETURNS

Year-by-Year

Returns

in India:

1981-2008


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Averages and Standard Deviations,

198081 to 200708

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*Relative to 91-Days T-bills.


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Historical Risk Premium

The 28-year average return on the stock market is higby about 15 per cent in comparison with the averreturn on 91-day T-bills.

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

This excess return is a compensation for the higher of the return on the stock market; it is commoreferred to as risk premium.

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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


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Cont

The following formula can be used to calculate the variance of return

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2 2 2 2

1 1 2 2

2

1

...n

n

ii

i

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

R E R P


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Example

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Expected Risk and Preference

A risk-averse investor will choose among investme

with the equal rates of return, the investment wlowest standard deviation and among investments wequal risk she would prefer the one with higher retu

A risk-neutral investor does not consider risk, awould always prefer investments with higher returns

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

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Risk preferences

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Normal Distribution and Standard Devia

In explaining the risk-return relationship, we assume that returns

normally distributed.

The spread of the normal distribution is characterized by the stan

deviation.

Normal distribution is apopulation-based, theoretical distribution.

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Normal distribution


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Properties of a Normal Distribution

The area under the curve sums to1.

The curve reaches its maximum at the expected va(mean) of the distribution and one-half of the area

on either side of the mean.

Approximately 50 per cent of the area lies withi

0.67 standard deviations of the expected value; ab

68 per cent of the area lies within 1.0 standdeviations of the expected value; 95 per cent of

area lies within 1.96 standard deviation of

expected value and 99 per cent of the area lies wit

3.0 standard deviations of the expected value.

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Probability of Expected Returns

The normal probability table, can be used

determine the area under the normal curve for varistandard deviations.

The distribution tabulated is a normal distribution w

mean zero and standard deviation of 1. Such

distribution is known as a standard norm

distribution.

Any normal distribution can be standardised and he

the table of normal probabilities will serve for

normal distribution. The formula to standardise is:

S=19

( )R E R-

s


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Example

An asset has an expected return of 29.32 per cent and t

standard deviation of the possible returns is 13.52 per cent.

To find the probability that the return of the asset will be zero less, we can divide the difference between zero and the expect

value of the return by standard deviation of possible net prese

value as follows:

S= = 2.17

The probability of being less than 2.17 standard deviations fro

the expected value, according to the normal probabil

distribution table is 0.015. This means that there is 0.015 or 1.

probability that the return of the asset will be zero or less.

20

0 29.32

13.52

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Risk & Return an Overview of Capital Market Theory

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