Question

Portfolio returns. The Capital Asset Pricing Model is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 15.3% (i.e. an average gain of 15.3%) with a standard deviation of 31%. 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 all answers to 4 decimal places. a. What percent of years does this portfolio lose money, i.e. have a return less than 0%?

Answer 1

From given data,

Suppose a portfolio has an average annual return of 15.3% (i.e. an average gain of 15.3%) with a standard deviation of 31%.

mean = = 15.3% = 0.153

Standard deviation = = 31% = 0.31

a. What percent of years does this portfolio lose money, i.e. have a return less than 0%?

P(x < 0) = P((x - ) / < (0 - 0.153) / (0.31))

P(x < 0) = P(Z < 0.494)

P(x < 0) = 0.6893

Answer = 68.93%

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