Question

# Normal probability distribution   Assuming that the rates of return associated with a given asset investment are...

Normal probability distribution   Assuming that the rates of return associated with a given asset investment are normally​ distributed; that the expected​ return,

r​,

is

12.3​%;

and that the coefficient of​ variation,

CV​,

is

1.11​,

answer the following​ questions:a.  Find the standard deviation of​ returns,

σr.

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,

σr​,

is

13.65313.653​%.

​(Round to three decimal​ places.)b. ​(1) The lowest possible expected return associated with the​ 68% probability of occurrence is

nothing​%.

​(Round to two decimal​ places.)The highest possible expected return associated with the​ 68% probability of occurrence is

nothing​%.

​(Round to two decimal​ places.)​(2) The lowest possible expected return associated with the​ 95% probability of occurrence is

nothing​%.

​(Round to two decimal​ places.)The highest possible expected return associated with the​ 95% probability of occurrence is

nothing​%.

​(Round to two decimal​ places.)​(3) The lowest possible expected return associated with the​ 99% probability of occurrence is

nothing​%.

​(Round to two decimal​ places.)The highest possible expected return associated with the​ 99% probability of occurrence is

nothing​%.

​(Round to two decimal​ places.)

a). Standard deviation (SD) = CV*expected return = 1.11*12.30% = 13.65%

b).

Lowest probability of occurrence = average - (z*SD) and

Highest probability of occurrence = average + (z*SD)

z = 1 for probability of 68%; z = 2 for probability of 95%; z = 3 for probability of 99%

b-1). Lowest possible return (P = 68%) = -1.35%

Highest possible return (P = 68%) = 25.95%

b-2). Lowest possible return (P = 95%) = -15.01%

Highest possible return (P = 68%) = 39.61%

b-3). Lowest possible return (P = 99%) = -28.66%

Highest possible return (P = 99%) = 53.26%

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