Question

3) Assume that you manage a risky portfolio with an expected rate of return of 14% and standard deviation of 19%. The risk-free rate rate on a Treasury-bill is 6%. a. Your client chooses to invest 60% of a portfolio in your fund and 40% 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 9%. What is the proportion w? What is the standard deviation of the rate of return on this client's portfolio?

Answer 1

Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)

Standard deviation of portfolio =

(wxox)2 + (wyoy)2 + 2 * 0x *0x *W, * Wy* P1,2

where x and y are the securities

3a)

Expected return = 0.6*0.14+0.4*0.06= 0.108= 10.80%

Standard deviation = ((0.6*0.19)^2 + (0.4*0)^2 + 2*0.6*0.4*0.14*0*0)^0.5 = 0.114

Standard deviation = 11.4%

b)

Expected return = w*0.14+(1-w)*0.06= 0.09

w(0.14-0.06) + 0.06 = 0.09

w = 0.375 = 37.5%

Weight in risk-free = 1-0.375 = 0.625

Standard deviation = ((0.375 *0.19)^2 + (0.625*0)^2 + 2*0.375 *0.625*0.14*0*0)^0.5 = 0.07125

Standard deviation = 7.125%