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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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The following information is available concerning the historical risk and return relationships in the U.S. capital markets:

U.S. CAPITAL MARKETS TOTAL ANNUAL RETURNS, 1990-2015
Investment Category	Arithmetic Mean	Geometric Mean	Standard Deviation of Return^a
Common Stocks	10.28%	8.81%	16.90%
Treasury Bills	3.54%	3.49%	3.20%
Long-Term Government Bonds	5.10%	4.91%	6.40%
Long-Term Corporate Bonds	5.95%	5.65%	9.60%
Real Estate	9.49%	9.44%	4.50%

a = Based on arithmetic mean.

a. Explain why the geometric and arithmetic mean returns are not equal and whether one or the other may be more useful for investment decision making.

b. For the time period indicated, rank these investments on a relative basis using the coefficient of variation from most to least desirable. Explain your rationale.

c. Assume the arithmetic mean returns in these series are normally distributed. Calculate the range of returns that an investor would have expected to achieve 95 percent of the time from holding common stocks.

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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