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 6.4 percent and the standard deviation was 12.4 percent. What is the probability that your return on this asset will be less than -5.3 percent in a given year? Use the NORMDIST function in Excel(R) to answer this question. (Do not round intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) 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 and round your final answers 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 and round your final answers to 2 decimal places, (e.g., 32.16))

Explanation / Answer

a) Mean = 6.4%

SD = 12.4%

Z = (X-mean)/Sigma

P(X<-5.3 )= P(Z<-.9435) .17269 = 17.27%

b).

we have to calculate the range between

Probability of 2.5% to 97.5%

value of X at P<2.5% = -17.90%

value of X at P<97.5% = 30.70%

range for 95% interval is (-17.90%) to (30.70%)

C).

Now the required range of Probability is between .5% to 99.5%

value of X at P<.5% = -25.54%

value of X at P<99.5% = 38.34%

range is (-25.54%) to (38.34%)

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