Question

A security that your client has been following has a historical average annual return of 11% and a standard deviation of 6%. Knowing this, it would be expected that 95% of the time, your client could expect a return within the range of:

A)−66% and +66%.
B)+5% and +17%.
C)−7% and +30%.
D)−1% and +23%.

Answer 1

Using the empirical rule, we calculate that 95% of the time, the expected return range for the security with an average annual return of 11% and a standard deviation of 6% would be between -1% and +23%. Thus, the correct answer is Option D.

Step-by-step explanation:

The client is interested in knowing within which range they could expect a security's return to fall 95% of the time, given a historical average annual return of 11% and a standard deviation of 6%. To answer this, we apply the empirical rule (or 68-95-99.7 rule) which states that for a normally distributed data set:Approximately 68% of data falls within one standard deviation from the mean.Approximately 95% falls within two standard deviations from the mean.Approximately 99.7% falls within three standard deviations from the mean.So, to find the range for 95%, we calculate two standard deviations from the mean:Upper bound = Mean + 2(Standard Deviation) = 11% + 2(6%) = 11% + 12% = 23%Lower bound = Mean - 2(Standard Deviation) = 11% - 2(6%) = 11% - 12% = -1%.

Therefore, 95% of the time, your client could expect a return within the range of -1% and +23%, which corresponds to Option D.The expected range of returns for your client, based on the historical average annual return of 11% and standard deviation of 6%, can be calculated using a normal distribution. In a normal distribution, approximately 95% of the values fall within two standard deviations of the mean. For your client, the expected return would be:Mean - (2 x Standard Deviation) = 11% - (2 x 6%) = -1%Mean + (2 x Standard Deviation) = 11% + (2 x 6%) = 23%Therefore, your client can expect a return within the range of -1% and +23% with approximately 95% confidence.

Answer 2

The expected return range for the security in question, based on the empirical rule and given a historical average annual return of 11% and a standard deviation of 6%, is between -1% and +23% for 95% of the time.

Step-by-step explanation:

The question is focused on determining the expected range of returns for a security based on its historical average annual return and standard deviation, using the empirical rule (68-95-99.7 rule) for a normal distribution. Given a historical average annual return of 11% and a standard deviation of 6%, we would expect that 95% of the time the returns will fall within two standard deviations of the mean. Consequently, to calculate this range, we add and subtract two standard deviations (2 × 6% = 12%) from the average return. This gives a range from -1% (11% - 12%) to +23% (11% + 12%). Therefore, the expected return, 95% of the time, would be within the range of:

-1% and +23%.