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.†. (a) Compute the coefficient of variation for each fund. (Round your answers to one decimal place.) (the answers to both are not 1.4%). (b). 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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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.†.
(a) Compute the coefficient of variation for each fund. (Round your answers to one decimal place.) (the answers to both are not 1.4%).
(b). 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/s2 we can say that the CV represents the risk per unit of return; neither fund is better because the CV's are equal.
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