Question

You are given some information about two mutual funds: Fidelity Magellan (FMAGX) and T Rowe Price Health Sciences Fund (PRHSX).

Fund Average return Standard deviation Beta
FMAGX 1% 2% 0.5
PRHSX 1.5% 2.5% 0.8

The S&P500 made an average of 2% per month over the same period. The risk-free rate was zero throughout.

(a) Calculate the Sharpe ratio and alpha of each fund.

Answer 1

To calculate the Sharpe ratio and alpha of each fund, divide the excess return by the standard deviation and subtract the risk-free rate from the average return, respectively.

Step-by-step explanation:

To calculate the Sharpe ratio, divide the excess return of the fund by the standard deviation of the fund's returns. The excess return is the average return of the fund minus the risk-free rate.

For Fidelity Magellan (FMAGX), the excess return is 1% - 0% = 1%, and the standard deviation is 2%. So, the Sharpe ratio for FMAGX is 1% / 2% = 0.5. For T Rowe Price Health Sciences Fund (PRHSX), the excess return is 1.5% - 0% = 1.5%, and the standard deviation is 2.5%. So, the Sharpe ratio for PRHSX is 1.5% / 2.5% = 0.6.

To calculate the alpha, subtract the risk-free rate from the average return of the fund and divide by the standard deviation. The risk-free rate is 0% for both funds. For FMAGX, the alpha is (1% - 0%) / 2% = 0.5. For PRHSX, the alpha is (1.5% - 0%) / 2.5% = 0.6.