Assume that historical returns
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Assume that historical returns
Assume that historical returns and future returns are independently and identically distributed and drawn from the same distribution.
a. Calculate the 95% confidence intervals for the expected annual return of four different investments included in Tables 10.3 and 10.4 (the dates are inclusive, so the time period spans 86 years).
b. Assume that the values in Tables 10.3 and 10.4 are the true expected return and volatility
(i.e., estimated without error) and that these returns are normally distributed. For each investment, calculate the probability that an investor will not lose more than 5% in the next year.
c. Do all the probabilities you calculated in part (b) make sense? If so, explain. If not, can you identify the reason?
T ables 10.3
Average Annual Returns for U.S. Small Stocks, Large Stocks (S&P 500), Corporate Bonds, and Treasury Bills, 1926–2011
|
Investment |
Average Annual Return |
|
Small stocks |
18.7% |
|
S&P 500 |
11.7% |
|
Corporate bonds |
6.6% |
|
Treasury bills |
3.6% |
T ables 10.4
Volatility of U.S. Small Stocks, Large Stocks (S&P 500), Corporate Bonds, and Treasury Bills, 1926–2011
|
Investment |
Return Volatility (Standard Deviation) |
|
Small stocks |
39.2% |
|
S&P 500 |
20.3% |
|
Corporate bonds |
7.0% |
|
Treasury bills |
3.1%
|
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