Question

Capital Asset Pricing Model
The Capital Asset Pricing Model is a financial model that assumes returns on a portfolio are normally distributed. 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. 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%.

Select the most apropriate answer from the drop down lists.
What percent of years does this portfolio lose money, i.e. have a return less than 0%?   32.64, 67.36, or 98.75 %

What is the Z score corresponding to the top 15%?   1.04, 1.64, or 1.96

What is the cutoff for the highest 15% of annual returns with this portfolio?   49.02, 69.15, or 79.05 %

Answer 1

Solution: Population Mean u 14.7% = 0.147 Standard deviation a 33% 0.33 Part-A: P(x < 0): Percentage of years this portfolio lose money Z-score for (x 0): Z = 0 0.147 Z= 0.33 z -0.45 Hence, P(x < 0) = P(z<-0.45) From normal distribution table; P(z <-0.45) 0.3264 Hence, percentage of years this portfolio lose money 32.64% Part-B: Value of z-score, such that area under the normal curve to the right of it equal to 0.15, is given by: z 1.04 Hence, Z-score corresponding to the top 15% 1.04 Part-C: Value of z-score, such that area under the normal curve to the right of it equal to 0.15, is given by: z = 1.04 Z = x 0.147 1.04 0.33 x0.4902 Hence, cut-off for the highest 15% of annual returns 49.02%