5 (1.5 points) a. Explain the relationship among arithmetic mean return, geometr

Question

5 (1.5 points) a. Explain the relationship among arithmetic mean return, geometric variability of returns. mean return, and b. Contrast the use of the arithmetic mean return to the geometric perspective of an investor concerned with the investment's terminal value. mean return of an investment from the c. Contrast the use of the arithmetic mean return to the geometric mean return of an investment from the perspective of an investor concerned with the investment's average one-year return 6. (1.5 points) Below are percentage returns for two portfolios run by subsets of the Executive MS in Finance instructors Year Ladies Guys 2010 1 2011 0 2012 2 2013 1 a. Create a combined portfolio consisting of 75% of the Guys portfolio and 25% of the Ladies portfolio. What is the arithmetic mean of this combined portfolio? Is the historic distribution of returns of the combined portfolio skewed or symmetric? b. If the risk-free rte was 3% in years 2010 and 2011 and was 4% in years 2012 and 2013, calculate the excess return. What is the variance of the excess return? c. Calculate the Sharpe ratio for the four-year period

Explanation / Answer

a) For two numbers x and y, let x, a, y be a sequence of three numbers. If x, a, y is an arithmetic progression then 'a' is called arithmetic mean. If x, a, y is a geometric progression then 'a' is called geometric mean. If x, a, y form a harmonic progression then 'a' is called harmonic mean.

   Let AM = arithmetic mean, GM = geometric mean, and HM = harmonic mean. The relationship between the three is given by the formula : AM * HM = GM2 .

b) the geomtric mean return is more meaningful than the arithmatic mean return for an investor concerned with the terminal value of an investment. the geometric mean return is the compound rate of growth, so it directly relates to the terminal value of an investment. by contrast, a higher arithmetic mean return does not necessarily imply higher terminal value for an investment.

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