# Suppose the returns on an asse

Suppose the returns on an asset are normally distributed. Thehistorical average annual return for the asset was 7.3 percent andthe standard deviation was 8.4 percent. What is the probabilitythat your return on this asset will be less than –4.5 percent in agiven year? Use the NORMDIST function in Excel® to answer thisquestion. (Do not round intermediate calculations. Enter youranswer as a percent rounded to 2 decimal places, e.g., 32.16.)Probability 8.0 % What range of returns would you expect to see 95percent of the time? (Enter your answers for the range from lowestto highest. Negative amounts should be indicated by a minus sign.Do not round intermediate calculations. Enter your answers as apercent rounded to 2 decimal places, e.g., 32.16.) 95% level % to %What range would you expect to see 99 percent of the time? (Enteryour answers for the range from lowest to highest. Negative amountsshould be indicated by a minus sign. Do not round intermediatecalculations. Enter your answers as a percent rounded

Answer:

To calculate the probability of getting return on asset lessthan-4.5%, we are using NORM.DIST function in excel as follows:

NORM.DIST(-0.045,0.073,0.084,1), where, -0.045=number(x),0.073=mean, 0.084=std. deviation, 1 for cumulative normaldistribution). This gives us the result of 0.08004 in excel. Thatmeans there is 8.00 percent probability of getting return on assetless than-4.5%.

with 95% confidence, z -value for a normally populated data setis 1.96. But as here no sample size mention, we can take averagetrading days of 252 days in NASDAQ as sample size here.

So, with 95% confidence, for this population mean CI will be(0.073-1.96*(0.084/(252^0.5))), (0.073+1.96*(0.084/(252^0.5))).that is (0.0626, 0.0834) . So, for 95% of the time, return will bein the 6.26% to 8.34%

with 99% confidence, z -value for a normally populated data setis 2.58

So, with 99% confidence, for this population mean CI will be(0.073-2.58*(0.084/(252^0.5))), (0.073+2.58*(0.084/(252^0.5))).that is (0.0593,0.0867) . So, for 99% of the time, return will bein the 5.93% to 8.67%