Page 87 - DMGT405_FINANCIAL%20MANAGEMENT

Unit 5: Risk and Return Analysis

Portfolio betas are interpreted in the same way as the betas of individual assets. They indicate Notes
the degree of responsiveness of the portfolio’s return to changes in the market return. For
example, when the market return increases by 10 per cent, a portfolio with a beta of 0.75 will
experience a 7.5 per cent increase in its return (0.75 × 10%).
Again since beta measures the relative volatility of a security’s return, in relation to the market
return, it should be measured in terms of security’s and markets’ covariance and markets variance.
Thus  can be measured by:
1
Cov(K , K ) s s Cor j s Cor j
 = i 2 m = 1 m 2 m = 1 m
1 s s m sm
Where, k = The expected return on indiversifiable security
i
K = The expected return on market portfolio
m
s = Standard deviation of the security
1
s = Standard deviation of the market portfolio
m
Cov = Covariance of security with regard to market portfolio
(kikm)
Cor = Correlation coefficient of the security with the market
jm

Example: An investor is seeking the price to pay for a security whose standard deviation
is 3.00 per cent. The correlation coefficient for the security with the market is 0.8 and the market
standard deviation is 2.2 per cent. The return for government securities is 7.2 per cent and from
the market portfolio 12.8 per cent. The investors know that, by calculating the required return he
can determine the price to pay for the security. What is the required return on the security?
Solution:
´
0.8 0.03
Beta Coefficient = = 1.0909
0.022
Required rate of return = 0.072 + 1.0909 × (0.128 – 0.072)
= 0.072 + 0.061 = 0.133

Task An investor holds two equity shares X and Y in equal proportion with the following
risks and return characteristics:
Return of Security X = 24 %; Return of Security Y = 19 %
Standard Deviation of X = 28% Standard Deviation of Y = 23 %
The return of these securities has a positive correlation of 0.6. You are required to calculate
the portfolio return and risk. Further suppose that the investor wants to reduce the portfolio
risk to 15 per cent. How much should the correlative coefficient be to bring the particular
risk to the desired level?

5.5.3 Limitations of CAPM
1. It is based on unrealistic assumptions that are far from reality. For example, it is very
difficult to find a risk-free security, since inflation causes uncertainty about the real rate of
return. The assumption of the equality of lending and borrowing rate is also not correct.
Further, investors may not hold highly diversified portfolio or the market indices may
not be well-diversified.

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