Question

1. Suppose that you are managing a portfolio with a standard deviation of 29% and an expected return of 22%. The Treasury bill rate is 9%. A client wants to invest 21% of his investment budget in a T-bill money market fund and 79% in your fund.

a. What is the expected rate of return on your client's complete portfolio?

b. What is the standard deviation for your client's complete portfolio?

c. What is the reward-to-volatility (Sharpe) ratio of your client's complete portfolio?

d. What is the Sharpe ratio of your portfolio?

2. Suppose that you manage a portfolio with a standard deviation of 24% and an expected return of 17%. Your portfolio consists of the following investments:

Type	Proportion
Stock A	33%
Stock B	29%
Stock C	19%
Stock D	19%

The Treasury bill rate is 8%. An investor wants to invest a proportion of his investment budget in a T-bill money market fund and the remaining proportion in your fund.

a. What proportion of the investor's money should be invested in your fund in order to achieve an expected return of 11%?

b. What proportion of the investor's complete portfolio will be invested in stock B?

Answer 1

a) Expected return on a portfolio = weighted average of the expected return of the different assets with weights being the allocated % of the portfolio

here, the expected return of the clients complete portfolio =T-Bill allocation * T Bill expected return + allocated in my fund* expected return of my fund

= 21% * 9% + 79% * 22%

= 1.89% + 17.38%

= 19.27%

b) Standard deviation on a portfolio: (Variance)^0.5

Variance = (Standard deviation of T- Bill)^2 * ( Allocation on T-Bill)^2 + (Standard deviation on fund)^2 * (Allocation on the fund)^ 2 + 2* Standard deviation of T -bill * Standard deviation of fund * Allocation on T-Bill * allocation on fund * correlation between the 2 assets     

Standard deviation of the T-BIll is also 0

Hence, variance = 0^2*21%^2 + 29%^2*79%^2 + 2*0*29%*21%*79%*correlation between the 2

variance = 0+ 0.5249+ 0

= 0.5249

Standard deviation = (0.5249)^0.5

= 0.2291

=22.91%

c) Sharpe ratio for client's complete portfolio

Sharpe Ratio = (Expected Portfolio return - Risk free rate of return)/ Standard deviation of the portfolio

T-bill return is risk free rate of return   

Sharpe ratio for client's complete portfolio = (19.27% - 9%)/22.91%

=0.4483  

d) Sharpe ratio for own portfolio = (22% - 9%)/29%

= 0.4483