Inv. Finance Chpt 6

you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 36%. The T-bill rate is 6%. Your client's degree of risk aversion is A = 3.1, assuming a utility function U = E(r) - ½Aσ². a. What proportion, y, of the total investment should be invested in your fund b.What is the expected value and standard deviation of the rate of return on your client's optimized portfolio

27.37 8.97 9.86

You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 38%. The T-bill rate is 6%. 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 17%. a. What is the investment proportion, y?

As the T bill has no risk, so the entire standard deviation will come from the risky asset. So the proportion invested in the risky asset = y y x 38 = 17 y = 0.45 or 45% This implies that 1- y is invested in the T bills so 1-y = 55% Portfolio return = y x return of risky asset + (1-y) x return on Tbill Portfolio return = 0.45 x 17+ (1-0.45) x 6 Portfolio return = y x return of risky asset + (1-y) x return on Tbill Portfolio return = 0.45 x 17+ (1-0.45) x 6 Portfolio return = 10.95%

You manage a risky portfolio with an expected rate of return of 21% and a standard deviation of 32%. The T-bill rate is 8%. Your client chooses to invest 65% of a portfolio in your fund and 35% in a T-bill money market fund. Suppose that your risky portfolio includes the following investments in the given proportions: Stock A27%Stock B36%Stock C37% What are the investment proportions of your client's overall portfolio, including the position in T-bills

T-Bills35.0% Stock A17.6% Stock B23.4s% Stock C24.1%

You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 35%. The T-bill rate is 5%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the reward-to-volatility (Sharpe) ratio (S) of your risky portfolio? Your client's?

Your reward-to-volatility ratio0.3428 Client's reward-to-volatility ratio0.3428

ou manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 29%. The T-bill rate is 8%. Your risky portfolio includes the following investments in the given proportions: Stock A35%Stock B35%Stock C30%

a) let x% be the portfolio portion allocated for risky portfolio then (100-x)% is allocated for T-bill. Expected return is 14%. We can find x by solving the linear equation-> x%*18% + (100-x)% * 8% = 14% we get x=60% b)T-bill= (100-x)%= 40%, A= x*35%= 21%, B=x*35%= 21%, C=x*30%=18% c) We know Variance of a two asset portfolio is given by= (w11) 2 + (w22) 2 + 2w1w212 Now assuming correlation is 0 and for risky and Tbills and w2=0 Std Deviation for Portfolio is (w11) = x1= 17.4% Comment

You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 30%. The T-bill rate is 6%. Your client chooses to invest 65% of a portfolio in your fund and 35% in an essentially risk-free money market fund. What is the expected return and standard deviation of the rate of return on his portfolio

e(r)=13.8% std=19.5%

Consider a portfolio that offers an expected rate of return of 14% and a standard deviation of 27%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills?

max level must be less than 1.92