Two Risky Portfolios

PART B Two Risky Portfolios

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Suppose that there are many stocks in the security market and that the characteristics of stocks A and B are given as follows:
Stock Expected Return Standard Deviation
A 10% 5%
B 15 10
Correlation =-1

Suppose that it is possible to borrow at the risk-free rate, rf. What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from stocks A and B. )

. A portfolio’s expected return is 12%, its standard deviation is 20%, and the risk-free rate is 4%. Which of the following would make for the greatest increase in the portfolio’s Sharpe ratio? (LO 6-3)
a. An increase of 1% in expected return.
b. A decrease of 1% in the risk-free rate.
c. A decrease of 1% in its standard deviation.

The following data apply to problems 3-7
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are:
Expected Return Standard Deviation
Stock fund (S) 15% 32%
Bond fund (B) 9 23
The correlation between the fund returns is .15.

. Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of 0% to 100% in increments of 20%. What expected return and standard deviation does your graph show for the minimum-variance portfolio? (LO 6-2)

. Draw a tangent from the risk-free rate to the opportunity set. What does your graph show for the expected return and standard deviation of the optimal risky portfolio? (LO 6-3)

. What is the reward-to-volatility ratio of the best feasible CAL? (LO 6-3)

. Suppose now that your portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL. (LO 6-4)
a. What is the standard deviation of your portfolio?
b. What is the proportion invested in the T-bill fund and each of the two risky funds?

.. If you were to use only the two risky funds and still require an expected return of 12%, what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimal portfolio in the previous problem. What do you conclude? (LO 6-4)

. Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, rf. The characteristics of two of the stocks are as follows:

Stock Expected Return Standard Deviation
A 8% 40%
B 13 60
Correlation =-1

Could the equilibrium rf be greater than 10%? ( Hint: Can a particular stock portfolio be substituted for the risk-free asset?) (LO 6-3)