Assume a market index represents the common factor and all stocks in the economy have a beta

Question:

Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 30%.

Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 3%, and one-half have an alpha of -3%. The analyst then buys $1 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1 million of an equally weighted portfolio of the negative alpha stocks.

a. What is the expected profit (in dollars), and what is the standard deviation of the analyst's profit?

b. How does your answer change if the analyst examines 50 stocks instead of 2010 stocks?

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