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The Capital Asset Pricing Model (CAPM) is a financial
Chapter , Problem 3.8(choose chapter or problem)
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 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 doesnt change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. (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?
Questions & Answers
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 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 doesnt change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. (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?
ANSWER:Step 1 of 2
The financial model assumes that, the returns on a portfolio follows a normal distribution with mean 14.7% and standard deviation 33%
a) Compute the percentage of years the portfolio loses money. That is, P(X<0%)
\(\begin{aligned} P(X<0 \%) & =P\left(\frac{X-\mu}{\sigma}<\frac{0 \%-14.7 \%}{33 \%}\right) \\ & =P(Z<-0.4455) \\ & =0.3264 \quad \text { (From Normal area table values) } \\ & =32.64 \% \end{aligned}\)
Therefore, 32.80% years, the portfolio loses money.