Consider the following table for the total annual returns for a given period of

Question

Consider the following table for the total annual returns for a given period of time.

  Series

Average return

What range of returns would you expect to see 95 percent of the time for large-company stocks?

Requirement 2:

What about 99 percent of the 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

Explanation / Answer

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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