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

16.7​%;

and that the coefficient of​ variation,

CV​,

is

1.06​,

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%.

Answer 1

a)

Coefficient of variation (CV) = Standard deviation / expected return

1.06 = SD / 16.7%

standard deviation = 1.06 x 16.7%

= 17.702%

b)

1) 68%

Expected range = expected return +/- 1 standard deviation

= 16.7% +/- (1x17.702%)

= 16.7% +/- 2.96%

upper range = 19.66%

lower range = 13.74%

2) 95%

Expected range = expected return +/- (2 x standard deviation)

= 16.7% +/- (2x17.702%)

= 16.7% +/- 5.91%

upper range = 22.61%

lower range = 10.79%

3) 99%

Expected range = expected return +/- 3 standard deviation

= 16.7% +/- (3x17.702%)

= 16.7% +/- 8.87%

upper range = 25.57%

lower range = 7.83%