Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds (see Viewpoint). Vanguard Balanced Index is another highly regarded fund that represents the entire U.S. stock and bond market (an index fund). The mean and standard deviation of annualized percent returns are shown below. The annualized mean and standard deviation are for a recent 10-years period.

Pax World Balanced: x̅ = 9.58%; s = 14.05%

Vanguard Balanced Index: x̅ = 9.02%; s = 12.50%

(a) Interpretation Compute the coeffi­cient of variation for each fund. If x̅ represents return and s represents risk, then explain why the coeffi­cient of variation can be taken to represent risk per unit of return. From this point of view, which fund appears to be better? Explain.

(b) Interpretation Compute a 75% Chebyshev interval around the mean for each fund. Use the intervals to compare the two funds. As usual, past performance does not guarantee future performance.