Page 70 - DMGT207_MANAGEMENT_OF_FINANCES

Unit 4: Risk and Return Analysis

Standard deviation of an asset 2.4% Notes
Market Standard deviation 2.0%
Correlation coefficient of portfolio with market 0.9

Solution:
Calculation of Market Sensitivity Index ( )
i
Since, market sensitivity index is not given in the problem, it is calculated by applying the
following formula:


  i  r im
i
 m
Where,  = Market sensitivity index or Beta factor

 = Standard deviation of an asset i.e., 0.024
i
 = Market Standard deviation i.e., 0.02
m
r = Correlation coefficient of portfolio with market i.e., 0.90
im
0.024
 =  0.90  1.08
i
0.02
We can calculate the expected rate of return of a portfolio by applying capital asset pricing
model:
E(R ) = R +  (R – R )
i f i m f
Where,
E(R ) = Expected rate of return of portfolio
i
R = Risk free rate of return i.e., 9%
f
R = Expected return of market portfolio i.e. 15%
m
 = Beta coefficient of investment i.e. 1.08
i
By substituting, we get

E(R ) = 9 + 1.08 (15 – 9) = 9 + 1.08(6) = 15.48 or 15.48%
i
Illustration 2: SCM Portfolio Ltd. has three investments in its portfolio. Its details are given
below:

Investment E(R) Proportion of Invested Funds
Wipro 14% 1.6 50%
SBI 16% 1.2 20%
DCM 12% 0.8 30%

Calculate the weighted average of expected return and Beta factor of the portfolio.
Solution:
Weighted Average of Expected Return of the Total Portfolio:

E(R ) = (14% × 0.5) + (16% × 0.2) + (12% × 0.3) = 7% + 3.2% + 3.6% = 13.8%
p
Weighted Average Market Sensitivity Index of the Total Portfolio:
 = (1.6 × 0.5) + (1.2 × 0.2) + (0.8 × 0.3) = 0.8 + 0.24 + 0.24 = 1.28
p

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