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