Question

Portfolio returns. The Capital Asset Pricing Model is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 15.3% (i.e. an average gain of 15.3%) with a standard deviation of 31%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. Round all answers to 4 decimal places.

a. What percent of years does this portfolio lose money, i.e. have a return less than 0%? %

b. What is the cutoff for the highest 17% of annual returns with this portfolio? %

Answer 1

Solution :

Given that ,

mean = = 15.3% = 0.153

standard deviation = = 31% = 0.31

(a)

P(x < 0) = P((x - ) / < (0 - 0.153) / 0.31)

= P(z < 0.494)

= 0.6893

Answer = 68.93%

(b)

Using standard normal table,

P(Z > z) = 17%

1 - P(Z < z) = 0.17

P(Z < z) = 1 - 0.17 = 0.83

P(Z < 0.9542) = 0.83

z = 0.9542

Using z-score formula,

x = z * +

x = 0.9542 * 0.31 + 0153 = 0.49

Cutoff = 49%