Explanation

Relationship between Stock's Sharpe Ratio and Market's Sharpe Ratio

According to the Capital Asset Pricing Model (CAPM), the Sharpe ratio of a stock is related to the market's Sharpe ratio by:

$\text{Sharpe Ratio}_{\text{stock}} = \rho \times \text{Sharpe Ratio}_{\text{market}}$

Where:

• $\rho$ = correlation between the stock and the market portfolio
• Sharpe Ratio is expressed as a decimal

Given Data

• Market portfolio's Sharpe ratio = 40% = 0.40
• Correlation ($\rho$) = 0.7

Calculation

$\text{Sharpe Ratio}_{\text{stock}} = 0.7 \times 0.40 = 0.28 = 28\%$

Result

The stock's Sharpe ratio is 28%.

Therefore, the correct answer is B. 28%.