Question

CAPM: 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 12% (i.e. an average gain of 12%) with a standard deviation of 23%. 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. (please round answers to within one-hundredth of a percent)

1) 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 20% of annual returns with this portfolio?

Answer 1

a)

µ =    12          
σ =    23          
              
P( X ≤    0   ) = P( (X-µ)/σ ≤ (0-12) /23)      
=P(Z ≤   -0.52   ) =   0.30093 or 30.09% (answer)

b)

µ=   12  
σ =    23  
P(X≤x) =   0.80000  
      
z value at 0.8=   0.8416   (excel formula =NORMSINV(0.8))
z=(x-µ)/σ      
so, X=zσ+µ=   0.842   *23+12
X =   31.357   (answer)