Pax World Balanced is a highly respected, socially responsible mutual fund of st

Question

Pax World Balanced is a highly respected, socially responsible mutual fund of stocks and bonds. 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 = 9.51%; s = 14.04%
Vanguard Balanced Index: x = 9.37%; s = 12.63%

(a) Compute the coefficient of variation for each fund. (Enter your answers to the nearest integer.)

?%

(b) Compute a 75% Chebyshev interval around the mean for each fund. (Enter your answers to 2 decimal places.)

?%

Explanation / Answer

ANSWER:

1) Coefficient of variation of pax = s / x = 14.04% / 9.51% = 147.63%

coefficient of variation of vanguard = s / x = 12.63% / 9.37% = 134.79%

2) According to chebyshev theorem , a 75% interval equals = 1 - 1 / k ^ 2 = 3 / 4

k^2 - 1 = k^2 * ( 3 / 4)

(k^2 - 1) * 4 = 3k^2

4k^2 - 4 = 3k^2

4k^2 - 3k^2 = 4

k^2 = 4

k = (4) ^ 1/2

k = 2

it means 2 standard deviations away from the mean we get

pax upper limit = mean + 2 * std = 9.51% + 2 * 14.04% = 37.59%

pax lower limit = mean - 2 * std = 9.51% - 2 * 14.04% = -18.57%

vanguard upper limit = mean + 2 * std = 9.37% + 2 * 12.63% = 34.63%

vanguard lower limit = mean - 2 * std = 9.37% - 2 * 12.63% = -15.89%

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