For a security with an average return of 14.2% and a standard deviation of 8.4%, which statement describes where 68% of returns are expected to fall?

For a security with an average return of 14.2% and a standard deviation of 8.4%, which statement describes where 68% of returns are expected to fall?

• A. the security's annual volatility can be expected to be within a range approximately 8.4% above and 8.4% below the current fair market value.
• B. the security's returns can be expected to be between 5.8% and 22.6% approximately 68% of the time.
• C. the security's returns can be expected to never be negative.
• D. the security's returns can be expected to be between 8.4% and 14.2% approximately 95% of the time.

Answer: (B)

About 68% of a normally distributed set of returns lies within one standard deviation of the average return. With an average of 14.2% and a standard deviation of 8.4%, that range is 14.2% ± 8.4%, or 5.8% to 22.6%. So the statement that 68% of observed returns fall between 5.8% and 22.6% is the best description. The other options misapply how standard deviation defines the spread, refer to price levels instead of returns, or mix up 95% with an incorrect interval (two standard deviations would give roughly -2.6% to 31%).

About 68% of a normally distributed set of returns lies within one standard deviation of the average return. With an average of 14.2% and a standard deviation of 8.4%, that range is 14.2% ± 8.4%, or 5.8% to 22.6%. So the statement that 68% of observed returns fall between 5.8% and 22.6% is the best description. The other options misapply how standard deviation defines the spread, refer to price levels instead of returns, or mix up 95% with an incorrect interval (two standard deviations would give roughly -2.6% to 31%).