Table below gives summary statistics on annual returns of two portfolios. A portfolio of small

stocks, and a portfolio of big stocks. The last column shows data for a portfolio that buys the

small portfolio and shorts the big portfolio. The sample has N = 100 observations.

Measure Small Big Dfference

Mean 15.50% 11.00% 4.50%

Standard Deviation 35.00% 20.00% 15.00%

(a) Construct a 95% condence interval for the next year's annual return on Small and Big portfolios. What is the probability of next year return on Small stocks to be less than zero? What is the probability of the average of the next four-years of return on Small stocks to be less than zero?

(b) Formulate the null and alternative hypothesis consistent with testing whether the average return on Small and Big portfolios are dierent from zero. Use a signicance level of 5%.

(H0 : = 0 versus Ha : 6= 0, two-sided hypothesis test)

(c) Test the null hypothesis of equality of mean returns between Small and Big portfolios. The data for a portfolio that buys small and shorts the big portfolio is provided in the column titled "Difference". Use a signicance level of 5%.