Question

Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 47%. The T-bill rate is 5%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. a. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.) Expected return % per year Standard deviation % per year b. Suppose your risky portfolio includes the following investments in the given proportions: Stock A 31% Stock B 31% Stock C 38% What are the investment proportions of your client’s overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.) Security Investment Proportions T-Bills % Stock A % Stock B % Stock C % c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Round your answers to 4 decimal places.) Reward-to-Volatility Ratio Risky portfolio Client’s overall portfolio

Answer 1

a. Given that:-

Expected return of risky portfolio = 15%

Return of risk free asset i.e. T-Bill = 5%

If the client is investing 70% in risky portfolio and 30% in risk-free then,

Total expected return of client's portfolio = 70%*15% + 30%*5%

= 12%

Now, is it given that standard deviation of risky portfolio = 47%

And since T-Bills do not carry any risk, the standard deviation of risk-free asset = 0%

The total standard deviation of client's portfolio =

√ (0.7)(0.7)(0.47)(0.47)

= 32.9%

b. Given that:-

Proportions of risky assets in the client's portfolio (70%) is the following classification:-

Stock A = 31%, Stock B = 31% and Stock C =38%

Proportion of risk free asset in the client's portfolio = 30%

Hence, the security investment proportion of assets in the client's overall portfolio is:-

T-Bills = 30%

Stock A = 70% * 31% = 21.7%

Stock B = 70% * 31% = 21.7%

Stock C = 70% * 38% = 26.6%

c. The reward-to-volatility ratio, also known as Sharpe Ratio has the following formula:-

S = (Expected Portfolio Return - Risk Free Rate) / Portfolio Standard Deviation

Hence, reward to volatility ratio of cient's overall portfolio = (12%-5%)/32.9%

= 7% / 32.9%

= 0.2128