Question

The risk-free rate over the last ve 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 find the fund that performed better.

Answer 1

The excess return of an investment relative to the return of a benchmark index is the investment’s alpha.
In the given example, copper fund has an alpha of 2.5 % per year as compared to the gold fund having an alpha of 3.6 %
However, based on this data we cannot conclude that gold funds performed better than the copper funds.
an alpha of 2.5 means the copper fund outperformed its benchmark index by 2.5 percent, and gold fund outperfomed its benchmark index by 3.6 % .
but it's far less impressive when the market return is 13 %
As per Beta ( measure of volatality of the fund as compared to the market ), gold fund is more volatile than the copper fund.
Invest in funds with a higher beta is with the aim of achieving higher returns due to the higher volatility.
Expected return as per CAPM model
Return =	Rf + ( Rm - Rf ) * B
Rm = 13 % , Rf= 1%
	Expected
	Return
Copper fund	9.40
: = 1 + ( 13- 1) * 0.7
Gold fund	17.80
: = 1 + ( 13- 1) * 1.4