Page 291 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Security Analysis and Portfolio Management

Notes Expected Rate of Return on Market Portfolio
Dividends earned + Capital appreciation 146 145
100 = 100 = 26.33%
Initial investment 1,105

Now we can calculate the expected rate of return on individual portfolio, by applying
CAPM.
E(R) = R + (R – R )
i f i m f
Cement Ltd. = 14 + 0.8 (26.33 – 14) = 23.86%
Steel Ltd. = 14 + 0.7 (26.33 – 14) = 22.63%

Liquor Ltd. = 14 + 0.5 (26.33 – 14) = 20.17%
Govt. of India bonds = 14 + 0.99 (26.33 – 14) = 26.21%

23.86 + 22.63 + 20.17 + 26.21
2. Average Return of the Portfolio = = 23.22%
4
The average return is also calculated by finding out the average of beta factors of all
securities in the portfolio.

0.8 + 0.7 + 0.5 + 0.99
Average of betas = = 0.7475
4
Average return = 14 + 0.7475 (26.33 – 14) = 23.22%

Example: The market portfolio has a historically based expected return of 0.095 and a
standard deviation of 0.035 during a period when risk-free assets yielded 0.025. The 0.06 risk
premium is thought to be constant through time. Riskless investments may now be purchased
to yield 0.08. A security has a standard deviation of 0.07 and a 0.75 correlation with the market
portfolio. The market portfolio is now expected to have a standard deviation of 0.035.
Find out the following:
1. Market’s return-risk trade-off,
2. Security beta,

3. Equilibrium required expected return of the security.
Solution:
1. Calculation of Market’s Return-risk Trade-off

(R m R ) 0.095 0.025
f
= 2
0.035
2. Calculation of Security Beta

i 0.07
= r m = 0.75 1.5
i 0.035
m
3. Calculation of equilibrium required for Expected Rate of Return on the Security
E(R) = R + (R – R )
i f i m f
= 8 + 1.5 (6) – 17%

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