Merger Arbitrage

When one company announces it will buy another for, say, $50 a share, you might expect the target's stock to jump straight to $50. It usually does not — it jumps to something like $48 and sits there. That $2 gap is the deal spread, and it exists for a reason: the deal is not certain. Regulators can block it, financing can fall through, shareholders can vote no. Merger arbitrage (also called risk arbitrage) is the business of buying the target at $48 to collect that spread, getting paid the $2 if the deal closes — and taking a large loss if it collapses.

The payoff has a very particular, lopsided shape: a small, near-certain gain most of the time, and a rare but severe loss when a deal breaks. In options language it looks like being short a put — you collect a steady premium for insuring the deal, and you pay out big in the uncommon event it fails. Understanding that asymmetry is the whole game.

The payoff

Sizing the bet with expected value

Whether the spread is worth taking is an Expected Value question. Let $p$ be the probability the deal closes, and compare the small gain if it does against the big drop if it does not:

$$\text{EV} = p\,(\text{deal price} - \text{price}) - (1-p)\,(\text{price} - \text{fallback}) .$$

Here "price" is what you pay for the target, "deal price" is the offer, and "fallback" is roughly where the stock trades if the deal dies (near its pre-announcement level). The first term is your spread if it closes; the second is the loss if it breaks. The trade only makes sense when this is comfortably positive — which, given the tiny spread versus the large break loss, demands a high close probability.

Worked example

You buy the target at $48. The offer is $50, and before the deal was announced the stock traded around $36. You judge the deal $90\%$ likely to close in three months.

$$\text{EV} = 0.90\,(50 - 48) - 0.10\,(48 - 36) = 0.90\times 2 - 0.10\times 12 = 1.80 - 1.20 = 0.60 .$$

That is, $0.60 — so you expect to make about that much per share. On a $48 stake over three months that is roughly $1.25\%$ per quarter, or about $5\%$ annualised — a modest, bond-like return for taking deal risk. Now find the break-even probability: set EV to zero and solve for $p$.

$$p\times 2 = (1-p)\times 12 \;\Rightarrow\; 14p = 12 \;\Rightarrow\; p = 0.857 .$$

You need at least an $85.7\%$ chance of closing just to break even. That is the sobering arithmetic of merger arb: because the loss on a break ($12) dwarfs the gain on a close ($2), a handful of failed deals can erase a long run of successes.

Cash deals versus stock deals

• Cash deal. The acquirer pays a fixed dollar amount. You simply buy the target and wait; the spread is the offer minus your price.
• Stock deal. The acquirer pays in its own shares at a fixed exchange ratio. Now the target's fair value floats with the acquirer's stock, so you short the acquirer in the exchange ratio to lock the spread and hedge out the acquirer's price moves. This turns a directional bet into a cleaner spread capture.

Where it stumbles

• Break risk is correlated with crashes. Deals are most likely to fall apart in market turmoil — financing dries up, buyers walk. So merger arb quietly carries hidden market beta: it looks market-neutral in calm times and loses badly in crashes, exactly when you can least afford it. Mitchell and Pulvino showed this is why the strategy earns a premium at all — it is compensation for that ugly timing.
• Fat left tail. The payoff's asymmetry means a smooth track record can mask enormous tail risk; one blocked mega-deal can undo a year of spreads.
• Regulatory and financing risk. Antitrust reviews, foreign-investment screening, and shareholder votes are hard to handicap, and a single hostile ruling can break a deal overnight.
• Crowding and thin spreads. When capital floods in, spreads compress to where they barely compensate for the break risk — the premium is a payment for a real hazard, not a free lunch.

In interviews

Define the deal spread and why it exists (the deal might not close), and draw the short-put payoff: capped small gain, large loss on a break. Frame position sizing as an Expected Value calculation and be ready to solve for the break-even probability — the punchline that the loss-on-break dwarfs the spread, so you need a very high close probability. The sophisticated closer is Mitchell-Pulvino's point: the premium is not free, it is compensation for deal breaks clustering in market crashes, so merger arb carries hidden beta and a fat tail. Contrast with Index Rebalance Arbitrage as another event-driven trade whose "arbitrage" label oversells how riskless it is.