Question

A financial advisor informs a client that the expected return on a portfolio is 8% with a standard deviation of 12%. There is a 25% chance the return will be negative and a 15% chance that the return would be above 16%. Does her assessment follow a normal distribution? Calculate the probabilities for a normal distribution and compare.

Answer 1

Answer:

A) The assessment does not follow a normal distribution

B ) P(r<0) = 0.2546 ( from standard normal table ),     P( r > 0.16 ) ≠ 0.15

Explanation:

Expected return on portfolio  E (r) = 8%

Standard deviation (STD) = 12%

chances of Negative return  P(r < 0 )  = 25%

calculate the probabilities for a normal distribution

E (r) = 0.08 , STD = 0.12,  P(r < 0 ) = 0.25

P( r > 0.16 ) = 0.15

calculating the value of the probability  P(r < 0 )

P(r < 0 ) = P $(Z < \frac{0-E(r)}{STD} )$

              = P ( Z <  $\frac{0-0.08}{0.12}$ )

              = P ( Z < - 0.667 )

P(r<0) = 0.2546 ( from standard normal table )

calculating the value of the  probability P( r > 0.16 )

P( r > 0.16 ) = $P ( Z > \frac{0.16- E(r)}{STD})$

                  = P ( Z > $\frac{0.16-0.08}{0.12}$ )

                  = P ( Z > 0.667 )

to compare if p(r>0.16 ) is = 0.15

 P(R > 0.16 ) = 1 - P ( Z < 0.667 )

                    = 1 - 0.7454 ( value from standard normal table )

                    = 0.2546

hence P( r > 0.16 ) ≠ 0.15

The assessment does not follow a normal distribution