Post on 03-Jun-2018
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RISK AND RETURN: AN OVERVIEW
OF CAPITAL MARKET THEORY
ByVaishnav Kumar
vaishnav@marcbschool.com
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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
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(%)
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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.
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0 29.32
13.52
-