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Assume returns on a porfolio are normally distributed. Suppose a portfolio have average return of 15%...

Assume returns on a porfolio are normally distributed. Suppose a portfolio have average return of 15% with a standard deviation of 40%. 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.

a) what percent of years does this portfolio lose money have a return less than 0%?

b) what is the cutoff of the highest 5% of annual returns with this portfolio?

c) You randomly sample a group of 20 of your friends who invested in a portfolio P and find out that on average, they got a return of 30% with a standard deviation of 5%. Construct a 95% confidence interval for your sample. WHat does it mean.

d) A wall street broker want to sell you some stock. He says the portfolio P has an average annual return of 80%. Do you believe the stock broker's sale pitch.

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