Please answer question $3$ with parts a and b answer with work shown, please. Assume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of $1\mathrm{.}2$ on

the market index. Firm$-$specific returns all have a standard deviation of $38\%.$

Suppose that an analyst studies $20$ stocks and finds that one$-$half of them have an alpha of $+1\mathrm{.}8\%,$ and the other half have an alpha of

$-1\mathrm{.}8\%.$ Suppose the analyst invests $$1\mathrm{.}0$ million in an equally weighted portfolio of the positive alpha stocks, and shorts $$1$ million of an

equally weighted portfolio of the negative alpha stocks.

a$.$ What is the expected profit $($in dollars$)$ and standard deviation of the analyst's profit? $($Do not round intermediate calculations.

Round your answers to the nearest whole dollar amount.$)$

b$.$ How does your answer change if the analyst examines $40$ stocks instead of $20$ stocks? $80$ stocks? $($Do not round intermediate

calculations. Round your answers to the nearest whole dollar amount.$)$