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:
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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.
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:
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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.
For a normal distribution, what approximate percentage of the observations fall within ±3 standard deviation of the mean?
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For normal distributions, approximately 99% of the observations fall within ±3 standard deviations of the mean.
The mean return of a portfolio is 20% and its standard deviation is 4%. The returns are normally distributed. Which of the following statements about this distribution are least accurate? The probability of receiving a return:
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The probability of receiving a return greater than 16% is calculated by adding the probability of a return between 16% and 20% (given a mean of 20% and a standard deviation of 4%, this interval is the left tail of one standard deviation from the mean, which includes 34% of the observations.) to the area from 20% and higher (which starts at the mean and increases to infinity and includes 50% of the observations.) The probability of a return greater than 16% is 34 + 50 = 84%.
Note: 0.16 is the probability of receiving a return less than 16%.
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