Question 6 (15 marks) a. Suppose that you are evaluating two portfolio managers. The first manager has historically produced mutual fund returns with a historical average return of 15%, a beta () of 1.2, and volatility of 40%. The second manager has historically produced an average return of 12%, a beta of 1.0, and volatility of 20%. The market has had a historical return of 14% and volatility of 16%. The risk-free rate has been 6%.

i) According to the Sharpes Measure, which portfolio manager has produced superior returns? (3 marks)

ii) According to the Treynors Measure, which portfolio manager has produced superior returns? (3 marks)

iii) According to the Jensens Measure, which portfolio manager has produced superior returns? (3 marks)

b. A portfolio manager is currently invested 100% in the US stock market. His expected return on the US market is 12% with a volatility of 14%. The portfolio manager considers adding Hong Kong stocks into his portfolio mix, and he estimates its expected return to be 8% (in US dollar term) with a volatility of 20%. The risk-free rate (in US dollars) is 2% in the US and Hong Kong. The correlation between two markets is 0.50. Should the portfolio manager add some Hong Kong stocks into his portfolio mix, or short sell some Hong Kong stocks? Show your calculations. (6 marks)