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 = 9.58%; s = 14.19%
Vanguard Balanced Index: x = 9.06%; s = 12.53%

(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? Explain.

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

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

Explanation: The coefficient of variation for Pax World Balanced is,

The coefficient of variation for Vanguard Balanced Index is,

The coefficient of variation represents the relative measure of standard deviation which help us to compare the variability of data sets with another datasets. That is why the coefficient variation is better to use instead of standard deviation when comparing the variability of two data sets.

Since the coefficient of variation represents the risk per unit return, the CV of Venguard Balanced Index is less than the CV of Pax World Balanced. Hence the Venguard Balanced Index fund appears to be better.

b)

Correct Answer: Vanguard has a narrower range of returns, with less downside, but also less upside

Explanation:

According to Chebyshev's Theorem,

the number of standard deviation for 75% Chebyshev interval around the mean is computed as follow,

Now, the required Interval for X is obtained as follow,

For Pax World Balanced,

Mean, x = 9.58%; stnadard deviation, s = 14.19%

For Vanguard Balanced Index

Mean, x = 9.06%; stnadard deviation, s = 12.53%

	Pax	Vanguard
Lower Limit	-18.8	-16
Upper Limit	37.96	34.12

We can see that Vanguard Balanced Index has a narrower range of return compare to Pax World Balanced in both side.