Consider the following table for the total annual returns for a given period of time. |
Series |
Average return |
Standard Deviation | ||
Large-company stocks | 10.8 | % | 21.1 | % |
Small-company stocks | 16.4 | 33.0 | ||
Long-term corporate bonds | 6.2 | 8.4 | ||
Long-term government bonds | 6.1 | 9.4 | ||
Intermediate-term government bonds | 5.6 | 5.7 | ||
U.S. Treasury bills | 3.8 | 3.1 | ||
Inflation | 3.1 | 4.2 | ||
Requirement 1: | |
What range of returns would you expect to see 95 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 answers as a percentage rounded to 2 decimal places (e.g., 32.16).) |
Expected range of returns | % to % |
Requirement 2: | |
What about 99 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 % |
Part 1
For 95% probability, range would fall within +-2 SD.
Range = Average return – 2 SD to average return + 2 SD
= 10.80% - 2 x 21.10% to 10.80% + 2 x 21.10%
= -31.40% to 53%
Part 2
For 99% probability, range would fall within +-3 SD.
Range = Average return – 3 SD to average return + 3 SD
= 10.80% - 3 x 21.10% to 10.80% + 3x 21.10%
= -52.50% to 74.10%
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