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 = 9.84%; s = 13.92%
Vanguard Balanced Index: x = 8.86%; s = 12.54%
(a) Compute the coefficient of variation for each fund. (Enter your answers to the nearest integer.)
I calculated that -
Pax - 142% Vanguard- 142%
b) Compute a 75% Chebyshev interval around the mean for each fund?
Pax Vanguard
Lower limit ? ?
Upper Limit ? ?
Pax World Balanced: x = 9.84%; s = 13.92%
Vanguard Balanced Index: x = 8.86%; s = 12.54%
(a) Compute the coefficient of variation for each fund. (Enter your answers to the nearest integer.)
I calculated that -
Pax - 142% Vanguard- 142%
b) Compute a 75% Chebyshev interval around the mean for each fund?
Pax Vanguard
Lower limit ? ?
Upper Limit ? ?
-
From Chebyshev's Theorem, a 75% interval would correspond to solving 1 - 1/k^2 = 3/4 => k = 2
So: Looking at the an interval 2 standard deviations away from the mean for each fund yields:
Pax: (-18%, 37.68%)
Vanguard: (-16.22%, 33.94%)
(i.e., notation is "Fund: (lower limit, upper limit)")
So: Looking at the an interval 2 standard deviations away from the mean for each fund yields:
Pax: (-18%, 37.68%)
Vanguard: (-16.22%, 33.94%)
(i.e., notation is "Fund: (lower limit, upper limit)")