Answered: Pax World Balanced is a highly…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 = 9.70%; s = 13.95%
Vanguard Balanced Index: x = 8.88%; s = 12.35%

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

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.

A. 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.

B. 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.

C. 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.

D. 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. E. 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.

F. 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.) (find lower and upper limit for pax and vanguard).

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

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

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

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

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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