3) Assume that you manage, a risky portfolio with an expected rate of return of

Question

3) 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%. 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 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. (rc) = (0.35×5%) + (0*65×13%) = 10.2% per year expected return

Standard Deviation:

c = 0.65×22% = 14.3% per year

b.

E(rc) = (1 – y)rf+ y E(rP)

= (1-y)5 + 13y = 5 + 8y

if the expected rate of return for the portfolio is 10%, then, solving for y:

10 = 5+ 8y

8y = 5

y =5/8

y =.6250

standard deviation:

P= 0.6250×22% = 13.75% per year

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