Question

CAPM. The Capital Asset Pricing Model (CAPM) is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio had an average annual rate of return of 14.7% (i.e an average gain of 14.7%) with a standard deviation of 33%. 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.

What percent of years does the portfolio lose money, i.e. have a return less than 0% What is the cutting for the highest 27% of annual returns with this portfolio?

Answer 1

Solution :

Given that ,

mean = = 14.7% = 0.147

standard deviation = = 33% = 0.33

(a)

P(x < 0) = P((x - ) / < (0 - 0.147) / 0.33)

= P(z < -0.4454)

= 0.328

Answer = 32.8%

(b)

P(Z > z) = 27%

1 - P(Z < z) = 0.27

P(Z < z) = 1 - 0.27 = 0.73

P(Z < 0.61) = 0.73

z = 0.61

Using z-score formula,

x = z * +

x = 0.61 * 0.33 + 0.147 = 0.35

The cutting for the highest 27% of annual returns with this portfolio = 35%