Consider a single factor model of returns where the residuals (epsilons) are uncorrelated across assets.

Suppose you form a large equal-weight portfolio.

Suppose half of the stocks in your portfolio have a beta of 0.8 and the other half have a beta of 1.4. Suppose your portfolio return has an alpha of 0.04.
Now you arbitrage this by either investing +$200 (you long) or -$200 (you short) into the portfolio (you have to decide if long or short).
What is the dollar value you invest in the market?
(If you buy $50 of the market, write 50; If you sell $50 of the market, write -50)
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