13. Chapter 3, Section 3.2, Problem 20 Aa Aa E Pax World Balanced is a highly re

Question

13. Chapter 3, Section 3.2, Problem 20 Aa Aa E 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 based on the years 1993 through 2002 (Source: Morningstar). Pax World Balanced: X 9.58%; s 4.05% Vanguard Balanced Index: X 9.02%; s 2.50% Compute the coefficient of variation for each fund. If X represents return and s represents risk, then explain why the coefficient of variation can be taken to represent risk per unit of return. CV for Pax CV for Vanguard The CV gives the ratio of the to the hence it can be taken to represent risk per unit of return From this point of view, which fund appears to be better? Explain. O Pax fund has slightly less risk per unit of return O Vanguard fund has slightly less risk per unit of return. Compute a 75% Chebyshev interval around the mean for each fund. O Pax, 32.57% to 51.73%; Vanguard, 28.48% to 46.52% O Pax, 8.52% to 37.68%; Vanguard 5.98% to 34.02%. O Pax, 46.62% to 65.78%; Vanguard, 40.98% to 59.02%

Explanation / Answer

1)CV for PAX = sigma/mu =14.05/9.58 = 1.46659707724

2)CV for Vanguard = sigma/mu =12.50/9.02 = 1.38580931264

3)CV is ratio of standard deviation to the mean

4)Vanguard has slightly less risk than PAX from CV value

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