ch 04 revised

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RISK AND RETURN:

AN OVERVIEW OF CAPITAL MARKET

THEORY

CHAPTER 4


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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 andvariance of returns.

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

Compute historical average return of securities and marketpremium.

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

!

! !


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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(%)

4

Year-to-YearTotal Returns on HUL Share


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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 t

t

R R R R Rn n

! L


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Risk of Rates of Return: Variance and

Standard Deviation

Formulae for calculating variance and standard

deviation:

6

Standard deviation = Variance

2

2

1

1

1

n

t

t

Variance R Rn

W!

! !


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7

Investment Worth of Different Portfolios,

1980-81 to 200708


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Averages and Standard Deviations, 198081

to 2007089

*Relative to 91-Days T-bills.


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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 ofReturns Under Various Economic Conditions

Returns and Probabilities


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Cont

The following formula can be used to calculate the

variance of returns:

12

2 2 2 2

1 1 2 2

2

1

... n nn

iii

RE

R P RE

R P RE

R P

R E R P

W

!

! - - -

! -


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Example13


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Expected Risk and Preference

A risk-averse investor will choose among investments withthe equal rates of return, the investment with lowest standarddeviation and among investments with equal risk she would

prefer the one with higher return.

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

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

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Risk preferences15


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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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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 of1. Such a distribution is knownas 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 R-

s


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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 theexpected 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.

20

0 29.3 2

13.5 2

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