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 68 percent of the time for long-term corporate bonds?

Requirement 2: What about 95 percent of the time?

  Series

Average return

Standard Deviation   Large-company stocks 11.7 % 20.6 %   Small-company stocks 16.4 33.0   Long-term corporate bonds 6.4 9.7   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 68 percent of the time for long-term corporate bonds?

Requirement 2: What about 95 percent of the time?

Explanation / Answer

Part A

68% returns falls within +- 1 Standard Deviation. Therefore, the range would be

Range = Average return – 1 SD   to Average Return + 1 SD

             = 6.40% -1 x9.70%   to 6.40% + 1 x9.70%

             = -3.30% to 16.10%

Part B

95% returns falls within +- 2 Standard Deviation. Therefore, the range would be

Range = Average return – 2 SD   to Average Return + 2 SD

             = 6.40% -2 x9.70%   to 6.40% + 2 x9.70%

             = -13% to 25.80%

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