Investment Managemnet

1. RISK AND RETURN: AN OVERVIEW OF
CAPITAL MARKET THEORY
CHAPTER 4

2. 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
2

3. Return on a Single Asset
Total return = Dividend + Capital gain
3
 
1 1 0
1 0
1
1
0 0 0
Rate of return Dividend yield Capital gain yield
DIV
DIV P P
P P
R
P P P
 
 

  

4. Return on a Single Asset
4
Year-to-Year Total Returns on HUL Share

5. 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 R
n n
    


6. 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 R
n


  



7. 7
Investment Worth of Different Portfolios,
1980-81 to 2007–08

8. 8
HISTORICAL CAPITAL MARKET RETURNS
Year-by-
Year
Returns
in India:
1981-2008

9. Averages and Standard Deviations, 1980–81
to 2007–08
9
*Relative to 91-Days T-bills.

10. 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.
10

11. 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

12. 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 n
n
i
i
i
R E R P R E R P R E R P
R E R P


     
      
     
 
 
 


13. Example
13

14. 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.
14

15. Risk preferences
15

16. 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.
16

17. 17
Normal distribution

18. 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.
18

19. Probability of Expected Returns
19

20. 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:
 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.
20