Question

Consider the following information about a risky portfolio that you manage and a risk-free asset: E(r_P) = 14%, σ_P = 17%, r_f = 5%.

a. Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 6%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk-free asset? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
RP=

RFA=

b. What will be the standard deviation of the rate of return on her portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
SD=

Answer 1

Part A:

Portfolio Return is the weighted avg return of securities in that portfolio

Let y be the weight of investment in Risky Portfolio.

Stock	Weight	Ret	WTd Ret
Risky Portfolio	y	0.1400	0.14y
Risk Free Asset	1 - y	0.0500	0.05 -0.05y
Portfolio Ret Return		0.0700	0.05 + 0.09y

Given Portfolio ret = 0.06

Thus 0.05 + 0.09y = 0.06

0.09y = 0.06 - 0.05

= 0.01

y = 0.01 / 0.09

= 0.1111

Weight in Risky Portfolio 11.11%

Weight in Risk Free Asset 88.89%

Part B:

Portfolio SD = Weight in RIsky portfolio * SD

= 0.1111 * 17%

= 1.89%