Suppose there is a single market factor and all stocks have a beta of 1 with respect to it, and a firm-specific volatility of 30%. You research 20 stocks and find 10 that have an alpha of +2% each that you invest $1MM into, which you finance by shorting the other 10 stocks that you find have an alpha of -2% each.

a. What is the expected dollar profit and standard deviation of this trade?

b. How would your trade profit and risk change if you researched 50 stocks and found 25 with alpha of +2% and 25 with alpha of -2%?

c. How would it change if you researched 100 stocks and found 50 with alpha of +2% and 50 with alpha of -2%?

d. Would you consider forming a portfolio with fewer than the maximum number of stocks possible in each scenario? Why or why not?