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 6.5 percent and the standard deviation was 8.5 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).) 95% level 1%to 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).) 99% level %to

Explanation / Answer

mean=6.5%

s.d.=8.5%

For any confidence interval

range=mean-Z*standard deviation to mean+Z*standard deviation

For 95% confidence interval, Z=1.96

So range=6.5%-1.96*8.5% to 6.5%+1.96*8.5%

Range=-10.16% to +23.16%

For 99% confidence interval, Z=2.576

So range=6.5%-2.576*8.5% to 6.5%+2.576*8.5%

Range=-15.396% to +28.396%

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