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 for a recent 10-years period.

†. Pax World Balanced: x = 9.55%; s = 13.83% Vanguard Balanced Index: x = 8.79%; s = 12.32%

(a) Compute the coefficient of variation for each fund. (Round your answers to one decimal place.)

Pax Vanguard

CV ( ) % ( ) %

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. From this point of view, which fund appears to be better?

( )Since the CV is s/s2 we can say that the CV represents the risk per unit of return; the Pax fund appears to be better because the CV is smaller.

( )Since the CV is s/s2 we can say that the CV represents the risk per unit of return; the Vanguard fund appears to be better because the CV is smaller.

( )Since the CV is s/x we can say that the CV represents the risk per unit of return; the Pax fund appears to be better because the CV is smaller.

( )Since the CV is s/x we can say that the CV represents the risk per unit of return; the Vanguard fund appears to be better because the CV is smaller.

( )Since the CV is s/x we can say that the CV represents the risk per unit of return; neither fund is better because the CV's are equal.

( )Since the CV is s/s2 we can say that the CV represents the risk per unit of return; neither fund is better because the CV's are equal.

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

Pax Vanguard

Lower Limit   ( )   ( )

Upper Limit ( ).   ( )

Use the intervals to compare the two funds. As usual, past performance does not guarantee future performance.

( )Vanguard has a wider range of returns, with less downside, but also less upside.

( )Vanguard has a narrower range of returns, with more downside, but also more upside.

( )Vanguard has a narrower range of returns, with less downside, but also less upside.

( )Vanguard has a wider range of returns, with more downside, but also more upside.

Answer 1

a)

since  coefficient of variation =(s/x)*100;

	Pax world	Vanguard
CV	144.8%	140.2%

Since the CV is s/x we can say that the CV represents the risk per unit of return; the Vanguard fund appears to be better because the CV is smaller.

b)

from Chebychev's theorem: 2 standard deviation form mean value contains 75% of values

	Pax world	Vanguard
lower limit	-18.11	-15.85
upper limit	37.21	33.43

Vanguard has a narrower range of returns, with less downside, but also less upside.