Normal probability distribution 1.55, answer the foilowing questions answer the

Question

Normal probability distribution 1.55, answer the foilowing questions answer the Assuming that the rates of return associated with a a. Find the standard deviation of returns,o b. Calculate given asset investment the range of expected return outcomes associated with the following are normally distributed, that the ex a. The standard deviation of retums, o, is (Round to three decimal places.) of occurrence: (1) 68%, (2) 95%, (3) 99%. The highest possbe expected return associated with the 68% probablity of occurrence is we, the 68% protablity of occurr-is%. (Round to two decimal places.) possble expected return associated with the 95% probablity of occurrence is (Round to two decimal places.) %. (Round to two deo mal places.) expected return associated wit, the 96% probability of occurrence (3) The lowest possible expected return associated with the 99% i % (Round to two dermal places ) probability of occurrence ability of our ence is The highest possible expected return associated with the 99% pro %. (Round to two decimal places.) Round to two decimal places %.

Explanation / Answer

a. Coefficient of Variation = Standard Deviation/Expected Return

The standard deviation of returns r = Coefficient of variation* Expected return

= 1.55 * 12.1% = 18.755%

b. Normal probability distribution rule
68% probability is average return +/- one standard deviation
95% probability is average return +/- two standard deviation   
99% probability is average return +/- three standard deviation

Therefore,

1) The lowest possible expected return associated with the 68% probability of occurrence is the average return - one standard deviation

= 12.1% - 18.755% = -6.655%

The highest possible expected return associated with the 68% probability of occurrence is the average return + one standard deviation

= 12.1% + 18.755% = 30.855%

2) The lowest possible expected return associated with the 95% probability of occurrence is the average return - two standard deviation

= 12.1% - 2* 18.755% = -25.41%

The highest possible expected return associated with the 95% probability of occurrence is the average return + two standard deviation

= 12.1% + 2*18.755% = 49.61%

3) The lowest possible expected return associated with the 99% probability of occurrence is the average return - three standard deviation

= 12.1% - 3* 18.755% = -44.165%

The highest possible expected return associated with the 99% probability of occurrence is the average return + three standard deviation

= 12.1% + 3*18.755% = 68.365%

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