Lesson 3 of 7
Merger arbitrage
Read the gap between a target's price and the deal price as the odds the market gives the deal, and weigh the small gain against the large loss.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- Once a merger is announced, a target's share price usually sits below the deal price. That gap is called the spread.
- The spread is not free money. It is the market pricing in some chance the deal breaks, plus the time value of waiting to close.
- Solve the spread for the probability it implies, then weigh the small gain if the deal closes against the large loss if it does not.
After a merger is announced, a target's shares almost always trade below the price the acquirer agreed to pay. That gap exists because the deal is not certain and because closing takes months. Reading the spread as an implied probability turns it from a puzzle into a number you can check.
Three prices for one deal
- Deal price · What the acquirer agreed to pay$50
- Trading price · Where the target trades today$47
- Price if the deal breaks · An estimate, not a certainty$35
The spread is a probability, priced
The gap between the trading price and the deal price, here $3 on a $50 deal, is not a mispricing waiting to be collected. It reflects the market's own weighting of two outcomes: the deal closes at $50, or it breaks and the stock falls back toward what it would be worth on its own, here estimated at $35. The $47 trading price is a blend of those two outcomes, not a discount off a sure thing.
Solve for the market's implied probability
Because the trading price is a blend, you can run the formula backward and solve for the probability the market is pricing in.
This ignores the months of waiting. Part of the $3 pays for time, so the odds the market implies are somewhat above 80 percent.
Weigh the small gain against the large loss
An 80 percent implied probability does not mean an 80 percent return. If the deal closes, a buyer at $47 earns $3, about 6.4 percent, usually over some months. If it breaks, the same buyer loses $12, about 25.5 percent, often in a single trading day. Mitchell and Pulvino describe this payoff as similar to writing a put option on the market: little link to the market in flat or rising years, and an occasional sharp loss concentrated in steep market declines, when more deals fail together. The implied probability tells you what the market thinks the odds are. It does not tell you whether that price is fair compensation for taking them.
What moves the spread
A wider spread usually means the market sees more that could go wrong. That can be an antitrust review, unfinished financing, an unheld shareholder vote, or a material adverse change clause the acquirer could invoke. The merger proxy and any Form S-4 filed for a stock deal state the closing conditions in full. This includes which side can walk away, under what terms, and any termination fee written into the agreement.
Check yourself
A stock trades at $47 while the announced deal price is $50. What does the $3 gap most likely represent?
- A pricing error the market has not yet corrected
- The market's weighting of the deal closing against it breaking, plus the cost of waiting
- A dividend the target is expected to pay before closing
Show the answer
Answer: B.
The spread blends two outcomes, the deal closing at $50 and it breaking at some lower estimated price, and pays for the months until closing. It is not simply uncollected value.Using a deal price of $50, a trading price of $47 and a break price of $35, what probability of closing does the market imply?
- 47 percent
- 94 percent
- 80 percent
Show the answer
Answer: C.
Solving p × 50 + (1 − p) × 35 = 47 gives 15p = 12, so p = 0.8, an 80 percent implied probability.Mitchell and Pulvino compare merger arbitrage returns to which kind of payoff?
- A bond held to maturity
- Writing a put option on the market
- A lottery ticket: a small steady loss, and a rare large gain
Show the answer
Answer: B.
Their paper likens the returns to writing put options on the market: little link to the market in flat or rising years, and sharp losses in severe market declines, when more deals fail.Sources
- Mitchell and Pulvino, 'Characteristics of Risk and Return in Risk Arbitrage', Journal of Finance, 2001, on merger arbitrage's asymmetric payoff and its resemblance to a written put option.
- Merger proxy (Schedule 14A, DEFM14A) and Form S-4, which state a deal's closing conditions, termination rights and termination fee.
What this leaves out
- The $50, $47 and $35 prices are round invented numbers, chosen so the implied probability can be checked by hand.
- The example is a cash deal. In a stock deal the deal price moves with the acquirer's shares, and a target can trade above the offer when a higher bid is expected.
- A break price is always an estimate. The actual price after a real deal fails depends on why it failed and what else has changed by then.
- Nothing here is advice about any security, and nothing here says a given deal will close.