Suppose the returns on an asset are normally distributed. Suppose the historical
ID: 2652962 • Letter: S
Question
Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 6.5 percent and the standard deviation was 8.5 percent. What is the probability that your return on this asset will be less than –6.9 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))
Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 6.5 percent and the standard deviation was 8.5 percent. What is the probability that your return on this asset will be less than –6.9 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))
Explanation / Answer
Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 6.5 percent and the standard deviation was 8.5 percent. What is the probability that your return on this asset will be less than –6.9 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))
Using Excel Formula
Probability = NORMDIST(-6.9%,6.5%,8.5%,1)
Probability = 5.75%
Answer
Probability 5.75%
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))
Upper Limit Probability = 95%/2 = 47.5%
Total Probability till upper limit= 50% + 47.5% = 97.5%
Z = normsinv(Total Probability till upper limit)
Z = normsinv(97.5%)
Z = 1.959964
Upper limit = Mean + Z*SD
Upper limit= 6.5% + 1.959964*8.5%
Upper limit= 23.16%
Lower limit = Mean - Z*SD
Lower limit = 6.5% - 1.959964*8.5%
Lower limit = -10.16%
Answer
95% level -10.16% to 23.16%
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))
Upper Limit Probability = 99%/2 = 49.5%
Total Probability till upper limit= 50% + 49.5% = 99.5%
Z = normsinv(Total Probability till upper limit)
Z = normsinv(99.5%)
Z = 2.575830
Upper limit = Mean + Z*SD
Upper limit= 6.5% + 2.575830*8.5%
Upper limit= 28.39%
Lower limit = Mean - Z*SD
Lower limit = 6.5% - 2.575830*8.5%
Lower limit = -15.39%
Answer
99% level -15.39% to 28.39%
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