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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
| 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 |
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 |
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