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8/8/2019 Ch 04 Revised
1/20
RISK AND RETURN:
AN OVERVIEW OF CAPITAL MARKET
THEORY
CHAPTER 4
8/8/2019 Ch 04 Revised
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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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8/8/2019 Ch 04 Revised
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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
!
! !
8/8/2019 Ch 04 Revised
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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
8/8/2019 Ch 04 Revised
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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
8/8/2019 Ch 04 Revised
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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!
! !
8/8/2019 Ch 04 Revised
7/20
7
Investment Worth of Different Portfolios,
1980-81 to 200708
8/8/2019 Ch 04 Revised
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8/8/2019 Ch 04 Revised
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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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8/8/2019 Ch 04 Revised
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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
8/8/2019 Ch 04 Revised
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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
!
! - - -
! -
8/8/2019 Ch 04 Revised
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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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8/8/2019 Ch 04 Revised
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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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8/8/2019 Ch 04 Revised
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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
8/8/2019 Ch 04 Revised
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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
-