Merger arbitrage as a short put

(a) Prove (6A.13). Then generalise: if the deal completes when $S \ge L$ for some $L < D$ and fails otherwise, write the payoff as a riskless amount minus an option, and say what kind of option it is. (b) A deal offers a 3% gain with probability 0.9 and a 25% loss otherwise. Compute the expected return, the break-even probability and the Kelly fraction. Repeat the expected return at $p = 0.88$. (c) An arbitrageur holds 20 such deals. Explain why treating them as independent understates the risk, using the evidence of Mitchell and Pulvino (2001). (d) What does (6A.13) imply about the correct benchmark for a merger-arbitrage fund's returns?