Problem: 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
Investment Category Arithmetic Mean Geometric Mean Standard Deviation Of Return
Common stocks 10.28% 8.81% 16.9%
Treasury bills 6.54% 6.49% 3.2%
Long-term government bonds 6.10% 5.91% 6.4%
Long-term corporate bonds 5.75% 5.35% 9.6%
Real estate 9.49% 9.44% 3.5%
A) Explain why the geometric and arithmetic mean returns are not equal and whether one of the other may be more useful for investment decision making.
B) For the time period indicated, rank these investments on a risk-adjusted basis from most to least desirable. Explain your rationale.
C) Assume the returns in these series are normally distributed.
1) Calculate the range of returns that an investor would have expected to achieve 95 percent of the time from holding common stock.
2) Suppose an investor holds real estate for this time period. Determine the probability of at least breaking even on this investment.
D) Assume you are holding a portfolio composed entirely of real estate. Discuss the justifications, if any, for adopting a mixed asset portfolio by adding long-term government bonds.