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

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?

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RobertKer 6 months 2021-08-18T07:23:52+00:00 1 Answers 9 views 0

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    2021-08-18T07:25:11+00:00

    Answer:

    a) the required percentage is 32.64%

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

    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%

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