The risk-free rate over the last five years was 1% per year. The market return a

Question

The risk-free rate over the last five years was 1% per year. The market return averaged 13% per year with a standard deviation of 20%. The Copper Fund had an alpha of 2.5% per year with a beta of 0.7 while the Gold Fund had an alpha of 3.6% with a beta of 1.4. The Sharpe ratios of the two funds were 0.48 and 0.39 respectively. Investors hold these mutual funds in conjunction with others to create a well-diversified portfolio of risky securities.

Is it valid to conclude that Gold Fund performed better because it had a higher alpha? Why or why not? Calculate appropriate performance metric to nd the fund that performed better.

Explanation / Answer

No it is not a valid statement. We need to determine the return generated per unit of market risk (?).

Alpha is the return of the portfolio over the required return (CAPM)

?= Rp – (Rf + ?(Rm-Rf))

Therefore, we can calculate the return of portfolios of Copper Fund and Gold Fund as:

Copper Fund:          2.5 = Rp – (1 +0.70(13-1))

                                  2.50 = Rp – (9.40)

                                    Rp = 11.90%

Gold Fund:             3.60 = Rp – (1 +1.40(13-1))

                                  3.60 = Rp – (17.80)

                                    Rp = 21.40

To judge the performance of a diversified portfolio   Treynor measure is used. It is the excess return generated per unit of market risk:

Rp – Rf/?

Copper Fund:   11.90-1/0.70= 15.57

Gold Fund : 21.40 – 1/1.40 = 14.57

Thus, we can say Copper fund has performed better.

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