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. p-936