Q1. A stock portfolio has had a historical average annual return of 12% and a standard deviation of 20%. The returns are normally distributed. The range –27.2 to 51.2% describes a:

A)   68% confidence interval.

B)   99% confidence interval.

C)   95% confidence interval.

Q2. A stock portfolio's returns are normally distributed. It has had a mean annual return of 25% with a standard deviation of 40%. The probability of a return between -41% and 91% is closest to:

A)   65%.

B)   95%.

C)   90%.

Q3. For a normal distribution, what approximate percentage of the observations fall within ±3 standard deviation of the mean?

A)   66%.

B)   99%.

C)   95%.

答案和详解如下：

Q1. A stock portfolio has had a historical average annual return of 12% and a standard deviation of 20%. The returns are normally distributed. The range –27.2 to 51.2% describes a:

A)   68% confidence interval.

B)   99% confidence interval.

C)   95% confidence interval.

Correct answer is C)

The upper limit of the range, 51.2%, is (51.2 − 12) = 39.2 / 20 = 1.96 standard deviations above the mean of 12. The lower limit of the range is (12 − (-27.2)) = 39.2 / 20 = 1.96 standard deviations below the mean of 12. A 95% confidence level is defined by a range 1.96 standard deviations above and below the mean.

Q2. A stock portfolio's returns are normally distributed. It has had a mean annual return of 25% with a standard deviation of 40%. The probability of a return between -41% and 91% is closest to:

A)   65%.

B)   95%.

C)   90%.

Correct answer is C)

A 90% confidence level includes the range between plus and minus 1.65 standard deviations from the mean. (91 − 25) / 40 = 1.65 and (-41 − 25) / 40 = -1.65.

Q3. For a normal distribution, what approximate percentage of the observations fall within ±3 standard deviation of the mean?

A)   66%.

B)   99%.

C)   95%.

Correct answer is B)

For normal distributions, approximately 99% of the observations fall within ±3 standard deviations of the mean.