Question

The Capital Asset Pricing Model (CAPM) is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 15.1% (i.e., an average gain of 15.1%) with a standard deviation of 35%. 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 your answers to two 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 15% of annual returns with this portfolio?

Answer 1

a) the required percentage is 32.64%

b) the cutoff for the highest 15% of annual returns with this portfolio is 49.02%

Explanation:

Given that;

mean μ = 14.7 %

standard deviation σ =33%

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

P( portfolio lose money )

= P( x< 0) P( 0-14.7 / 33 )

P( Z < -0.45 ) = 0.3264 ≈ 32.64%

Therefore, the required percentage is 32.64%

b)

the cutoff for the highest 15% of annual returns with this portfolio will be:

P( X ≥ x) = 15%

1 - P(X ≤ x) = 0.15

P(X ≤ x) = 0.85

P(Z ≤ x-14.7 / 33 ) = 0.85 ----------let this be equation 1

form tables, P(Z ≤ 1.04) = 0.85 -----LET THIS BE EQU 2

from the equations;

(x-14.7 / 13 ) = 1.04

33 × 1.04 = x-14.7

34.32 = x-14.7

x = 34.32 + 14.7

x = 49.02%

Therefore, the cutoff for the highest 15% of annual returns with this portfolio is 49.02%