Question

4. The historical returns on a balanced portfolio have had an average return of 8 % and a standard deviation of 12 %. Assume that returns on this portfolio follow a normal distribution a. What percentage of returns were greater than 20 %? b. What percentage of returns were below -16 %?

Answer 1

Solution :

Given that ,

mean = $\mu$ = 0.08

standard deviation = $\sigma$ = 0.12

a.

P(x > 0.2) = 1 - P(x < 0.2)

= 1 - P[(x - $\mu$ ) / $\sigma$ < (0.2 - 0.08) / 0.12)

= 1 - P(z < 1)

= 1 - 0.8413

= 0.1587

Percentage = 15.87%

b.

  P(x < 0.16) = P[(x - $\mu$ ) / $\sigma$ < (0.16 - 0.08) /0.12 ]

= P(z < 0.67)

= 0.7486

Percentage = 74.86%