Question

Suppose you are a mutual fund manager. Your fund owns a risky portfolio with an expected rate of return of 20% and a standard deviation of 30%. The T-bill rate is 5%. Assume a client decides to invest in your risky portfolio a proportion (y) of his total investment budge and invest in a proportion (1-y) of risk-free T-bills.

(i) If his overall portfolio will have an expected return 15%, then how much is the proportion y?    

(ii) How much is the standard deviation of this client’s overall portfolio?  

Answer 1

Part 1:

Portfolio Ret is weighted AVg Ret of securities in portfolio.

Let y be weight in Risky portfolio and 1-y is weight in Risk free Asset.

Stock	Weight	Ret	WTd Ret
Risky portfolio	y	0.2000	0.20Y
Risk Free Asset	1-y	0.0500	0.05 - 0.05Y
Portfolio Ret Return			0.05+0.15Y

Thus 0.05 + 0.15Y = 0.15

0.15Y = 0.15 - 0.05

= 0.1

Y = 0.1 / 0.15

= 0.6667

Weight in Risk Portfolio is 66.67%

weight in Risk free Asset is 33.33%

Part 2:

Portfolio SD = Weight in Risky Asset * SD of Risky Asset

= 0.6667 * 30%

= 20%

Risk of new portfolio is 20%