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

Question

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 7.2 percent and the standard deviation was 12.3 percent. What is the probability that your return on this asset will be less than –2.9 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.)

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.)

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 to 2 decimal places, e.g., 32.16.)

Suppose the returns on an asset are normally distributed. The historical average annual return for the asset was 7.2 percent and the standard deviation was 12.3 percent. What is the probability that your return on this asset will be less than –2.9 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.)

Explanation / Answer

AR = 7.20%
SD=12.30%
X= -2.9%

We first need to compute value of Z:

Z= (X-AR)/SD

   = (-2.9%-7.2%)/12.30%

   = 0.8211

Probability value using normsdist in excel, we got. Probability = 20.58%

b)

For 95% probability, range would be:

Range = AR -2SD to AR +2SD

            = 7.20% -(2x12.30%) to 7.20% + (2x12.30%)

            = -17.40% to 31.80%

c) For 95% probability, range would be:

Range = AR -3SD to AR +3SD

            = 7.20% -(3x12.30%) to 7.20% + (3x12.30%)

            = -29.70% to 44.10%

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