Session 2: Risk Aversion and Capital Allocation

1. Based on the utility formula and the data given below which investment would you select if you were risk averse with A=4? What if you were risk-neutral?

Investment Exp Return

Std Deviation

1 0.12 0.302 0.15 0.503 0.21 0.164 0.24 0.21

2. Consider a portfolio that offers an expected return of 12% and a standard deviation of 18%. T-Bills offer a risk-free 7% return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-Bills?

3. Draw the indifference curve in the expected return-standard deviation plane corresponding to a utility level of 0.05 for an investor with a risk aversion coefficient of 3. Also draw the indifference curve corresponding to utility level of 0.04 for an investor with risk aversion coefficient of A=4. Compare the two. What do you conclude?

4. You manage a risky portfolio with expected return of 18% and standard deviation 28%. T-Bill rate is 8%. Your client wants to invest 70% in your fund and 30% in a T-Bill money market fund. Answer the following:

a. What is the expected return and standard deviation of the return on his portfolio? b. Suppose your risky portfolio includes following investments in the given proportions:

Stock A 25%, Stock B 32% and stock C 43%. What are the investment proportions of the client’s overall portfolio including position in T-Bills?

c. What is the reward-to-volatility ratio of your risky portfolio? Your client’s?d. Suppose the client wants to invest in your fund a proportion y that maximizes expected

return subject to the constraint that complete portfolio’s standard deviation will not exceed 18%. What should be this proportion y? What is the expected return on the complete portfolio?

e. Client’s degree of risk aversion A=3.5. What proportion, y, of the total investment should be made in your fund? What is the expected return and standard deviation of the client’s optimized portfolio?

5. Mr Sheth is the fund manager for Star Equity Mid-cap fund that has an expected return of 11% and a standard deviation of 15%. Treasury bills yield 5% currently.

a. A client wants to invest a proportion of her total investment budget in Star Mid-cap fund so as to provide a return of 8% on her overall portfolio. Find the proportion of to be invested by her in Star Mid-cap fund and in T-Bills.

b. Find the standard deviation of the return on her portfolio

c. Another client wants the highest possible return subject to the constraint that standard deviation of his portfolio is not more than 12%. Which client is more risk-averse?

6. Consider a risky portfolio. End of the year cash flow from the portfolio will be either Rs.70000 or Rs.200000 with a probability of 0.5. Risk-free assets yield 6% pa.

a. If you require a risk premium of 8% how much should you pay for this portfolio?b. If the required risk premium is 12% what should be the price you should be willing to

pay?