第一道：Assume that all stock returns have the market index as a common factor, and that all stocks in the economy have a beta of 1 on the market index. The firm-specific components of stock returns have a standard deviation of 30%. Suppose that an analyst studies 50 stocks, and finds that one half have an alpha of 2.6%, and the other half have an alpha of -4%. Suppose the analyst buys $1million of an equally weighted portfolio of the positive alpha stocks, and sells $1 million of an equally weighted portfolio of the negative alpha stocks.
1. What are the expected profit (in dollars) and the standard deviation of the analyst’s profit (in dollars)?
2. What would your answer be if the number of stocks was 100 instead of 50? Explain your results.

第二道： You have gathered following information about stock X and Y.
Stocks         Forecast Return           Std Dev            Beta
X                14%                          36%                0.8
Y                17%                          25%                1.5
Market Index 14%                         15%                 1.0
Risk Free rate 5%
1. Calculate expected return and alpha for each stock.
2. Identify and justify which stock would be more appropriate for an investor who wants to
a. add this stock to a well-diversified equity portfolio.
b. hold this stock as a single-stock portfolio.