Page 92 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 2: Risk and Return

8. You are evaluating an investment in two companies whose past ten years of returns are Notes
shown below:

Companies Percent returns during years
1 2 3 4 5 6 7 8 9 10
FST 37 24 -7 6 18 32 -5 21 18 6
SND 32 29 -12 1 15 30 0 18 27 10

(a) Calculate the standard deviation of each company's returns.

(b) Calculate the correlation coefficient of the company's returns.
(c) If you had placed 50% of your money in each, what would have been the standard
deviation of your portfolio and the average yearly return?
(d) What percentage investment in each would have resulted in the lowest risk?
(e) Assume that a yearly risk-free return of 8% was available and that you had held only
one of the two companies. Which would have been the better to own?
(f) Graph the risk and return of each fund. Given your answer to part (d), what was the
single efficient portfolio of the two?
(g) Use part (f) to determine:

(i) How an average return of 10.8% would have been obtained.
(ii) How an average return of 17.8% would have been obtained.

9. K.S. Bhatt holds a well-diversified portfolio of stocks in the XYZ Group. During the last
five years, returns on these stocks have average 20.0% per year and had a standard deviation
of 15.0%. He is satisfied with the yearly availability of his portfolio and would like to
reduce its risk without affecting overall returns. He approaches you for help in finding an
appropriate diversification medium. After a lengthy review of alternatives, you conclude:
(i) future average returns and volatility of returns on his current portfolio will be the same
as he has historically expected, (ii) to provide a quarter degree of diversification in his
portfolio, investment could be made in stocks of the following groups:

Groups Expected Return Correlation of Returns with Group XYZ Standard Deviation
ABC 20% +1.0 15.0%
KLM 20% -1.0 15.0%
RST 20% +0.0 15.0%

(a) If Bhatt invests 50% of his funds in ABC Group and leaves the remainder in XYZ
Group, how would this affect both his expected return and his risk? Why?
(b) If Bhatt invests 50% of his funds in KLM Group and leaves the remainder in XYZ
Group, how would this affect both his expected return and his risk? Why?
(c) What should he do? Indicate precise portfolio weighting.
10. Consider the two stocks Wipro and TCS with a standard deviation 0.05 and 0.10 respectively.
The correlation coefficient for these two stocks is 0.8.

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