Normal probability distribution Assuming that the rates of return associated wit

Question

Normal probability distribution Assuming that the rates of return associated with a given asset investment are normally distributed, that the expected return, r, is 18.9%; and that the coefficient of variation, CV, is 0.75, answer the following questions a. Find the standard deviation of returns, o, b. Calculate the range of expected return outcomes associated with the following probabilities of occurrence: (1) 68%, (2) 95%, (3) 99%. a. The standard deviation of returns.,, is (Round to three decimal places.)

Explanation / Answer

1. Coefficient of variance = (standard deviation/ expected return)
Standard Deviation = Coefficient * expected return = 0.75 * 18.9% = 14.175%

Range of Returns = Mean +/- z * standard deviation
for 68% probabiliy z = 1 ,range of Returns = 18.9% +/- 1 * 14.175% = 18.9% +/- 14.175%
Range is from 33.075% to 4.725%  
for 95% probabiliy z = 1.96 ,range of Returns = 18.9% +/- 1.96 * 14.175% = 18.9% +/- 27.783%
Range is from -8.883% to 46.683%  
for 99% probabiliy z = 1 ,range of Returns = 18.9% +/- 2.58 * 14.175% = 18.9% +/- 36.5715%
Range is from -17.6715% to 55.4715%  

Best of Luck. God Bless

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