Merger arbitrage

Once a deal is announced, a new game begins in the target's stock. It no longer trades on the target's fundamentals; it trades on the probability and timing of the deal closing. Merger arbitrage (risk arbitrage) is the discipline of harvesting the gap between the target's post-announcement price and the offer price, and it is a superb teaching lesson because it forces you to price a binary event, not a business.

The setup, for a cash deal. A buyer offers, say, $80.00 cash per share. The target, which might have traded at $60 before, jumps on the announcement toward $80 but not all the way there. It settles at, say, $77.50. Why the $2.50 gap? Because the deal is not certain and not instant: it must clear shareholder votes, antitrust and sector regulators, financing conditions, and the risk that the buyer walks. That gap is the arbitrageur's return for underwriting completion risk.

How is the merger arbitrage spread calculated?

The spread math (memorize these four numbers).

• Gross spread = offer price − current price (80.00 − 77.50 = $2.50).
• Gross spread % = gross spread ÷ current price (2.50 ÷ 77.50 = 3.23%): your return if the deal closes at the offer price.
• Annualized return = gross spread % × (12 ÷ months to close), or × (365 ÷ days), because a 3.23% return in 5 months is a very different thing from 3.23% in 2 years (3.23% × 12/5 = 7.74%; Worked example 5). Annualizing is what lets you compare a fast small spread against a slow large one.
• Market-implied completion probability. The market price is a probability-weighted average of the two outcomes. If the deal closes you get the offer price; if it breaks, the stock falls to a break price (the arb's estimate of the target's standalone value without the bid). Solve current = p × offer + (1 − p) × break for p: p = (current − break) ÷ (offer − break). In WE5, p = (77.50 − 62) ÷ (80 − 62) = 86.1%. The market is pricing an 86% chance of closing. Your edge, if you have one, is a better estimate of p than the market's.

What are the risks, and how do you hedge them?

The asymmetry that defines the trade. Merger arb is picking up small coins in front of a slow-moving truck: you make the modest spread if the deal closes, but you lose the (often much larger) drop to the break price if it fails. In Worked example 5 the upside is $2.50 and the downside is $15.50, a reward/risk of 0.16. This is why the discipline is completion handicapping, not valuation: your entire job is to judge whether the deal closes, and to size the position so that the occasional break does not ruin you. And breaks do happen: the Sony–Zee merger collapsed in January 2024; Elon Musk spent months trying to escape the Twitter deal before it closed at $54.20 in 2022.

Cash vs stock deals, and the hedge. In a cash deal you simply buy the target and wait. In a stock deal (target holders will receive acquirer shares at a fixed exchange ratio), the arb buys the target and shorts the acquirer in the exchange-ratio proportion, locking the spread and hedging out moves in the acquirer's price, because the value you will receive floats with the acquirer's stock. The risks that break deals are your real research agenda: antitrust/regulatory (the long fight over Microsoft–Activision, ultimately closed October 2023 at $95/share after FTC and CMA battles, kept that spread wide for over a year), financing failure, a material-adverse-change claim, shareholder rejection, or a required CCI (Competition Commission of India) or foreign-investment approval. The wider and more persistent the spread, the more completion risk the market sees. A wide spread is not free money, it is a warning you must price.