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Karo-lina-s
2 months ago
6

The Optima Mutual Fund has an expected return of 20%, and a volatility of 20%. Optima claims that no other portfolio offers a hi

gher 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?
Business
1 answer:
Mariulka [3.8K]2 months ago
6 0

Answer:

(a) 0.75

(b) 0.2

(c) 0.6

Explanation:

(a) For the Sharpe ratio calculation -

Given:

Expected return = 20%,

Risk-free rate = 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%,

The risk-free return remains at 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) The correlation of the Sub-Optima fund with the Optima fund is 80%,

Sharpe ratio for the Optima = 0.75

Correlation of the Sub-Optima fund with the 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 the Sub-Optima fund = 0.80 × 0.75

= 0.6

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