If a stock has an average return of 9.0% and a standard deviation of 7.0%, what is the range of expected returns that covers about 68% of outcomes?

If a stock has an average return of 9.0% and a standard deviation of 7.0%, what is the range of expected returns that covers about 68% of outcomes?

• A. +2.0% to +23.0%
• B. -5.0% to +16.0%
• C. +2.0% to +16.0%
• D. -12.0% to +23.0%

Answer: (C)

In a normal distribution, about 68% of outcomes fall within one standard deviation of the mean. With a mean of 9.0% and a standard deviation of 7.0%, the 68% range is 9.0% ± 7.0%, which gives 2.0% to 16.0%. This interval is symmetric around the mean and uses exactly one standard deviation on each side. Other ranges either widen the span to about two standard deviations (roughly corresponding to a 95% band, e.g., -5% to 23%) or are not centered at the mean, so they don’t represent the 68% interval.

In a normal distribution, about 68% of outcomes fall within one standard deviation of the mean. With a mean of 9.0% and a standard deviation of 7.0%, the 68% range is 9.0% ± 7.0%, which gives 2.0% to 16.0%.

This interval is symmetric around the mean and uses exactly one standard deviation on each side. Other ranges either widen the span to about two standard deviations (roughly corresponding to a 95% band, e.g., -5% to 23%) or are not centered at the mean, so they don’t represent the 68% interval.