Consider the following table for different assets for 1926 through 2011. Series
ID: 2642010 • Letter: C
Question
Consider the following table for different assets for 1926 through 2011. Series Average return Standard Deviation Large-company stocks 11.8% 20.3% Small-company stocks 16.5 32.5 Long-term corporate bonds 6.4 8.4 Long-term government bonds 8.1 9.8 Intermediate-term government bonds 5.5 5.7 U.S. Treasury bills 3.6 3.1 Inflation 3.1 4.2 Requirement 1: What range of returns would you expect to see 68 percent of the time for large-company stocks? (Negative amount should be Indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.18).) Expected range of returns % to % Requirement 2: What about 95 percent of the time? (Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected range of returns % to %Explanation / Answer
Assume the return distribution to be normally distributed.
Based on the empirical rule of ’68 95 99.7’ of normal distribution, 68% of the observations lie within +/-1 standard deviation of the mean, 95% of observations lie within +/-2 standard deviation of the mean.
Requirement 1
So, for large company stocks, number of observations within 68% would be Mean return for these stocks +/- 1 standard deviation.
Hence, the upper limit would be: 11.8% + 20.3% = 32.10%
The lower limit would be: 11.8% - 20.3% = -8.50%
Hence range: -8.50% to 32.10%
Requirement 2
Number of observations within 95% would be Mean return for these stocks +/- 2 standard deviation.
Hence, the upper limit would be: 11.8% + (2 *20.3%) = 52.40%
The lower limit would be: 11.8% - (2 * 20.3%) = -28.80%
Hence range: -28.80% to 52.40%