Suppose the returns on an asset are normally distributed. The historical average

Question

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.6 percent and the standard deviation was 10.3 percent.

What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

What range would you expect to see 99 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 5.6 percent and the standard deviation was 10.3 percent.

Explanation / Answer

mean return=mean=5.6% and the standard deviation =sd=10.3%

1)The 95% confidence range is (mean-1.96*sd,mean+1.96*sd)=(.056-1.96*.103,.056+1.96*.103)=(-0.14588,0.25788)

Thus i would expect to see range (-0.1459 to 0.2579) or (-14.59% to 25.79%) 95% of time.

2)

The 99% confidence range is (mean-2.58*sd,mean+2.58*sd)=(.056-2.58*.103,.056+2.58*.103)=(-0.20974,0.32174)

Thus i would expect to see range (-0.2097 to 0.3217) or (-20.97% to 32.17%) 99% of time.

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