Question

The Capital Asset Pricing Model (CAPM) is a nancial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual 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. (b) What is the cuto for the highest 15% of annual returns with this portfolio?

Answer 1

Answer:

49.02%

Explanation:

Given the following :

Population mean (m) = 14.7% = 0.147

Standard deviation (σ) = 33% = 0.33

The cut for the highest 15% of annual returns with this portfolio:

Highest 15% return = +ve (15/100) = +0.15 = 0.15 to the right of the normal distribution curve.

The Zscore which corresponds to 0.15 using the z-distribution = 1.04

Zscore = (x - m) / σ

1.04 = (x - 0.147) / 0.33

1.04 * 0.33 = x - 0.147

0.3432 = x - 0.147

x = 0.3432 + 0.147

x = 0.4902

Cut for highest 15% of annual return = (0.4902 * 100%) = 49.02%