The Optima Mutual Fund has an expected return of 20%, and a volatility of 20%. Optima claims that no other portfolio offers a higher Sharpe ratio. Suppose this claim is true, and the risk-free interest rate is 5%.

a. What is Optima's Sharpe Ratio?

b. If eBay's stock has a volatility of 40% and an expected return of 11%, what must be its correlation with the Optima Fund?

c. If the SubOptima Fund has a correlation of 80% with the Optima Fund, what is the Sharpe ratio of the SubOptima Fund?

(a) 0.75

(b) 0.2

(c) 0.6

Explanation:

(a) Calculating Sharpe ratio-

Given-

Expected return = 20%,

Risk free rate of return = 5%,

Volatility = 20%

Sharpe ratio = (Mean portfolio return - Risk free return) : Standard deviation of portfolio

Sharpe Ratio = (20% - 5%) : 20%

= 0.75

(b) Given-

Standard deviation = 40%,

Portfolio return = 11%,

Risk free return will remain same as 5%

Sharpe Ratio of Ebay = (11% - 5%) : 40%

Sharpe Ratio of Ebay = 0.15

Correlation of Ebay with Optima fund:

= Sharpe ratio of Ebay : Sharpe ratio of Optima fund

= 0.15 : 0.75

= 0.2

(c) Correlation of Sub-Optima fund with Optima fund = 80%,

Sharpe ratio of Optima = 0.75

Correlation of Sub-Optima fund with Optima fund:

= Sharpe ratio of Sub-Optima fund : Sharpe ratio of Optima fund

0.80 = Sharpe ratio of Sub-Optima fund : 0.75

Sharpe ratio of Sub-Optima fund = 0.80 * 0.75

= 0.6