The following information is available concerning the historical risk and return relationships in the U.S. capital markets:
US CAPITAL MARKETS TOTAL ANNUAL RETURNS, 1990 – 2011
Investment Arithmetic Geometric Standard Deviation
Category Mean Mean of Returna
Common stocks 10.28% 8.81% 16.9%
Treasury bills 3.54 3.49 3.2
Long-term government bonds 5.10 4.91 6.4
Long-term corporate bonds 5.95 5.65 9.6
Real estate 9.49 9.44 4.5
aBased 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.