Question

You manage an equity fund with an expected risk premium of 10.4% and a standard deviation of 18%. The rate on Treasury bills is 5%. Your client chooses to invest $45,000 of her portfolio in your equity fund and $55,000 in a T-bill money market fund. What is the reward-to-volatility (Sharpe) ratio for the equity fund? (Round your answer to 4 decimal places.)

Answer 1

Solution :

As per the information given in the question we have

Expected risk premium of Equity Fund = 10.4%

Risk free rate = Rate on Treasury bills = 5%

Standard Deviation of the equity fund = 18 %

We know that Expected return on equity fund = Expected risk premium + Risk free rate

Thus the Expected return on equity fund = 10.4 % + 5 % = 15.4 %

The formula for calculating the reward to volatility ratio ( Sharpe Ratio ) is

= ( R_E – R_F ) / σ_E

Where R_E = Expected Return on Equity Fund ;   R_F = Risk free rate    ;  

σ_E   : Standard Deviation of the Equity Fund

As per the Information given in the question we have :

R_E = 15.4 %    ;     R_F =   6 %    ;      σ_E = 18 %

Applying the above values in the above formula we have

= ( 15.4 % - 6 % ) / 18 %

= 9.4 % / 18 %

= 0.522222

= 0.5222 ( When rounded off to four decimal places )

Thus the reward to volatility Ratio of the Equity Fund = 0.5222