Final answer:
The Sharpe ratio measures the risk-adjusted return of an investment or portfolio. It is found by subtracting the risk-free rate from the expected return and dividing by the standard deviation. If the risk-free rate declines, the Sharpe ratio increases. However, if the risk-free rate becomes higher than the expected return, the Sharpe ratio becomes negative.
Step-by-step explanation:
The Sharpe ratio measures the risk-adjusted return of an investment or portfolio. It is calculated by subtracting the risk-free rate (in this case, the T-bill rate) from the expected return of the portfolio, and then dividing that result by the standard deviation of the portfolio. In this case, we have:
Sharpe ratio = (expected return - risk-free rate) / standard deviation
Using the given information, for portfolio A with an expected return of 7.65% and standard deviation of 9.25%, and a risk-free rate of 3.75%, we can calculate the Sharpe ratio:
Sharpe ratio = (7.65% - 3.75%) / 9.25% = 0.43
If the T-bill rate declines to 2.95%, the new Sharpe ratio would be:
Sharpe ratio = (7.65% - 2.95%) / 9.25% = 0.51
If the T-bill rate rose to 8% and became greater than the expected return of 7.65%, the new Sharpe ratio would be negative. Since the risk-free rate is higher than the expected return of the portfolio, the Sharpe ratio would be negative, indicating that the risk-free rate is a better investment option than the portfolio.