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

Question

Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 5.1 percent and the standard deviation was 14.5 percent. What is the probability that your return on this asset will be less than

Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 5.1 percent and the standard deviation was 14.5 percent. What is the probability that your return on this asset will be less than

Explanation / Answer

a).

Mean = 5.1%

SD = 14.5%

Z = (X-mean)/SD

for X = -8.1%

Z = (-8.1-5.1)/14.5 = -0.910344

P(X<-8.1) = P(Z<-.910344) = 18.132%

b).

for 95%

range is (5.1-1.96*14.5) to (5.1+1.96*14.5) = (-23.319 to 33.519)

c).

for 99%

range is (5.1-2.58*14.5) to (5.1+2.58*14.5) = (-32.250 to 42.450)

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