Question

An investment adviser representative has been reviewing the likelihood that an equity investment will produce the desired return. He has determined that the mean return on the investment is 15%, with a 12% standard deviation, and a 95% probability of occurrence. This means that he would expect the range of returns to be approximately:

Answer 1

The investment adviser would expect the range of returns on the equity investment to be between 5% and 35%.

What is the range of the desired return?

The lower bound of the range is:

= Mean return - Standard deviation

= 20% - 15%

= 5%

The upper bound of the range is:

= Mean return + Standard deviation

= 20% + 15%

= 35%

The range is therefore 5% to 35%.

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Answer 2

The range of returns to be approximately 3.00% - 27.00%

What is investment?

An investment is a valuable item bought with the intention of increasing one's wealth. While stocks, bonds, and real estate are frequently included when discussing investments.

A 12% standard deviation means that the investment return can vary plus or minus 12% from the mean (average) return over the course of a year. With a 15% average (mean) return, it might fall as low as 3% (15% - 12% deviation); or it might rise as high as 27% (15% + 12% deviation).

The probability of the return falling in this range is 95%. This has nothing to do with the actual calculation of the range of returns.

As a result, 3.00% - 27.00% is correct.

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