Suppose the current price ratio of a pair of stocks in the energy sector (P_A1/P_B1) is 3 which is below its normal level of 5.

Can you make profit in the event of price convergence at time 2 by shorting an arbitrary number of X of shares of stock B for each sahre of stock A longed? Is so, Please prove it. If not, what would be the required range of X that would result in the event of price convergence at time 2?

A HF has a capital of $10 million but need to retain cash of $1 million for unforeseen situations. Shares can be borrowed from the prime broker at an margin ratio of 18%. The HF has identified a list of underpriced shares A and a list of overpriced shares B, B BB 1.5 E(RB) 22% ERA 30% Assume CAPM: R 5%, E(RM) 20% ECR) under CAPM 5 1.5 (20 5) J 27.5% A's ex-ante alpha 2,5% B's ex-ante alpha 5.5% A HF has a capital of $10 million but need to retain cash of $1 million for unforeseen situations. Shares can be borrowed from the prime broker at an margin ratio of 18%. The HF has identified a list of underpriced shares A and a list of overpriced shares B, B BB 1.5 E(RB) 22% ERA 30% Assume CAPM: R 5%, E(RM) 20% ECR) under CAPM 5 1.5 (20 5) J 27.5% A's ex-ante alpha 2,5% B's ex-ante alpha 5.5%