Question

Assume that you manage a risky portfolio with an expected rate of return of 16% and a standard deviation of 22%. The T-bill rate is 5%. Your client chooses to invest 80% of a portfolio in your fund and 20% in a T-bill money market fund. What is the reward-to-volatility ratio of the client's portfolio?

Answer 1

Expected return of the risky portfolio = RR = 16%, Standard deviation of the risky portfolio = σR = 22%

Expected return of the T-bill = Risk-free rate = RF = 5%, Standard deviation of the T-bill = 0 [T-bills are risk-free asset]

Weight of the risky portfolio = WR = 80%

Weight of the T-bill = WF = 20%

Expected return of the clients portfolio = E[RP] = WR*RR + WF*RF = 80%*16% + 20%*5% = 13.80%

Standard deviation of the client's portfolio when one of the asset is risk-free is calculated using the formula:

Standard deviation of the client's portfolio = σP = WR*σR = 80%*22% = 17.6%

reward-to-volitility ratio = (E[RP] - RF)/σP = (13.8% - 5%)/17.6% = 0.5

Reward-to-volitility ratio of the client's portfolio = 0.5

Answer -> 0.5