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## The Capital Asset Pricing Model (CAPM) is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfoli

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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?

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Mathematics
6 months
2021-08-18T07:23:52+00:00
2021-08-18T07:23:52+00:00 1 Answers
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## Answers ( )

Answer:a)the required percentage is32.64%b)the cutoff for the highest 15% of annual returns with this portfolio is49.02%Step-by-step 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%