Question

The Optima Mutual Fund has an expected return of

20.9%

and a volatility of

21.5%.

Optima claims that no other portfolio offers a higher Sharpe ratio. Suppose this claim is​ true, and the​ risk-free interest rate is

4.5%.

a. What is​ Optima's Sharpe​ ratio?

b. If​ eBay's stock has a volatility of

43.8%

and an expected return of

11.4%​,

what must be its correlation with the Optima​ Fund?

c. If the SubOptima Fund has a correlation of

78%

with the Optima​ Fund, what is the Sharpe ratio of the SubOptima​ Fund?

Answer 1

a)

Sharpe ratio of Optima Mutual Fund = (Expected return of Optima Mutual Fund - Risk free rate) / Standard deviation of portfolio of Optima Mutual Fund

Sharpe ratio of Optima Mutual Fund = (20.9% - 4.5%) / 21.5%

Sharpe ratio of Optima Mutual Fund = 0.7628

b)

Sharpe ratio of eBay = (Expected return of eBay - Risk free rate) / Standard deviation of portfolio of eBay

Sharpe ratio of eBay = (11.4% - 4.5%) / 43.8%

Sharpe ratio of eBay = 0.1575

Correlation of Ebay with Optima Mutual fund = Sharpe ratio of Ebay / Sharpe ratio of Optima Mutual fund

Correlation of Ebay with Optima Mutual fund = 0.1575 / 0.7628

Correlation of Ebay with Optima Mutual fund = 0.2065

c)

Correlation of SubOptima fund with Optima Mutual fund = Sharpe ratio of SubOptima fund / Sharpe ratio of Optima Mutual fund

78% = Sharpe ratio of SubOptima fund / 0.7628

Sharpe ratio of SubOptima fund = 0.5950