Investments Ch 6 Questions

You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your client chooses to invest 70% of a portfolio in your fund and 30% in an essentially risk-free money market fund. What is the expected value and standard deviation of the rate of return on his portfolio?

Expected return = (0.7 × 18%) + (0.3 × 8%) = 15% Standard deviation = 0.7 × 28% = 19.6%

You manage an equity fund with an expected risk premium of 10% and an expected standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client's portfolio? What is the reward-to-volatility (Sharpe) ratio for the equity fund?

Expected return for equity fund = T-bill rate + Risk premium = 6% + 10% = 16% Expected rate of return of the client's portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% Expected return of the client's portfolio = 0.12 × $100,000 = $12,000 (which implies expected total wealth at the end of the period = $112,000) Standard deviation of client's overall portfolio = 0.6 × 14% = 8.4% Reward-to-volatility ratio =.10/.14=0.71

You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Suppose that your risky portfolio includes the following investments in the given proportions: Stock A 25% Stock B 32% Stock C 43% What are the investment proportions of your client's overall portfolio, including the position in T-bills?

Investment proportions: 0.7 × 25% = 17.5% in Stock A 0.7 × 32% = 22.4% in Stock B 0.7 × 43% = 30.1% in Stock C 30.0% in T-bills

.The variable (A) in the utility formula represents the:

Investor's aversion to risk.

Utility Formula Data Investment Expected Return, E(r) Standard Deviation, σ 1 0.12 0.30 2 0.15 0.50 3 0.21 0.16 4 0.24 0.21 U = E(r ) - ½ Aσ^2, where A = 4 On the basis of the utility formula above, which investment would you select if you were risk averse with A = 4?

Utility for each investment = E(r) - 0.5 × 4 × σ^2 We choose the investment with the highest utility value, Investment 3.

Utility Formula Data Investment Expected Return, E(r) Standard Deviation, σ 1 0.12 0.30 2 0.15 0.50 3 0.21 0.16 4 0.24 0.21 U = E(r ) - ½ Aσ^2, where A = 4 .On the basis of the utility formula above, which investment would you select if you were risk neutral?

When investors are risk neutral, then A = 0; the investment with the highest utility is Investment 4 because it has the highest expected return.

You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. What is the reward-to-volatility (Sharpe) ratio (S) of your risky portfolio? Your client's?

Your reward-to-volatility (Sharpe) ratio:(.18-.08)/.28=0.3571 Client's reward-to-volatility (Sharpe) ratio:(.15-.08)/.196=0.3571

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $70,000 or $200,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year. a. If you require a risk premium of 8%, how much will you be willing to pay for the portfolio? b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? c. Now suppose that you require a risk premium of 12%. What is the price that you will be willing to pay? d. Comparing your answers to (a) and (c), what do you conclude about the relationship between the required risk premium on a portfolio and the price at which the portfolio will sell?

a. The expected cash flow is: (0.5 × $70,000) + (0.5 × 200,000) = $135,000. With a risk premium of 8% over the risk-free rate of 6%, the required rate of return is 14%. Therefore, the present value of the portfolio is: $135,000/1.14 = $118,421 b. If the portfolio is purchased for $118,421 and provides an expected cash inflow of $135,000, then the expected rate of return [E(r)] is as follows: $118,421 × [1 + E(r)] = $135,000 Therefore, E(r) = 14%. The portfolio price is set to equate the expected rate of return with the required rate of return. c. If the risk premium over T-bills is now 12%, then the required return is: 6% + 12% = 18%

You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio's standard deviation will not exceed 18%. a. What is the investment proportion, y? b. What is the expected rate of return on the complete portfolio?

a. σC = y × 28% If your client prefers a standard deviation of at most 18%, then: y = 18/28 = 0.6429 = 64.29% invested in the risky portfolio. b. E(r)=.08+.1*y =.08+(.6429*.1) =14.429%