Question

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 7.3 percent and the standard deviation was 8.4 percent. What is the probability that your return on this asset will be less than –4.5 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Probability 8.0 % 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 % 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

Answer 1

To calculate the probability of getting return on asset less than-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 normal distribution). This gives us the result of 0.08004 in excel. That means there is 8.00 percent probability of getting return on asset less than-4.5%.

with 95% confidence, z -value for a normally populated data set is 1.96. But as here no sample size mention, we can take average trading 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 be in the 6.26% to 8.34%

with 99% confidence, z -value for a normally populated data set is 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 be in the 5.93% to 8.67%