Question

Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 39%. The T-bill rate is 6%. 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	23%
Stock B	32%
Stock C	45%

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) Expected return and standard deviation

Expected standard deviation is given by mathematical relation:

E[R] = 0.105 + 0.018 = 12.3%

Standard deviation of a T-bill is zero. So standard deviation of portfolio is, using the formula above is:

SD = 70% * 39% = 27.3%

b) Proportion of investment

30% of portfolio in T-Bills and 70% in risky portfolio.

So, proportion of T-bills = 30%

Proportion of stock A = 70% * 23% = 16.1%

Proportion of stock B = 70% * 32% = 22.4%

Proportion of stock C = 70% * 45% = 31.5%

c. Reward to Volatility Ratio

Reward to volatility ratio, also know as Sharpe's ratio, is excess over risk free rate return earned by an investment per unit of standard deviation.

For risky portfolio,

reward to volatility ratio = (15% - 6%)/39% = 0.2308

For client's overall portfolio,

reward to volatility ratio = (12.3% - 6%)/27.3% = 0.2308