Assume that you manage a risky portfolio with an expected rate of return of 13%
ID: 2787327 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 13% and standard deviation of 22%. The risk-free rate rate on a Treasury-bill is 5%. a. Your client chooses to invest 65% of a portfolio in your fund and 35% in a risk-free T-bill money market fund. What is the expected return and standard deviation of your client’s portfolio? b. Suppose another investor decides to invest in your risky portfolio a proportion (w) of his total investment budget so that his overall portfolio will have an expected rate of return of 10%. What is the proportion w? What is the standard deviation of the rate of return on this client’s portfolio?
Explanation / Answer
a) Expected Returns = w1 x R1 + w2 x R2 = 65% x 13% + 35% x 5% = 10.20%
Std. Deviation of portfolio = weight of risky x SD of risky = 65% x 22% = 14.30%
b) Assume w% is invested in risky portfolio and 1 - w% is invested in risk-free asset
E(R) = 10% = w x 13% + (1 - w) x 5%
=> w = (10 - 5) / (13 - 5) = 62.5% should be invested in risky portfolio
Std. Dev. = w x SD = 62.5% x 22% = 13.75%