Which of the following statements are true? Explain.a. A lower allocation to the risky portfolio reduces the Sharpe (reward-to-volatility) ratio.b. The higher the borrowing rate, the lower the Sharpe ratios of levered portfolios.c. With a fixed risk-free rate, doubling the expected return and standard deviation of the risky portfolio will double the Sharpe ratio.d. Holding constant the risk premium of the risky portfolio, a higher risk-free rate will increase the Sharpe ratio of investments with a positive allocation to the risky asset.

The formula for the Sharpe ratio = [tex]\frac{Required return on portfolio - Risk free return}{Standard deviation for the portfolio's excess return}[/tex]

With a levered portfolio, money has been borrowed.

Assuming the rate of the money borrowed is r then this rate will need to be subtracted from the required return such that the formula becomes;

= [tex]\frac{Required return on portfolio - borrowing rate - Risk free return}{Standard deviation for the portfolio's excess return}[/tex]

Notice now that as the borrowing rate rises, the numerator for the ratio will be smaller which would lead to a lower ratio when divided by the standard deviation.