The merger arbitrage spread
After a deal is announced, the target trades just below the offer. That gap pays for the wait and for the chance the deal fails.
- Calculate the gross and annualized spread on a cash deal
- Find the highest price that still clears a return hurdle
- Hedge a stock-for-stock deal by shorting the acquirer
- Say what the hedge does and does not protect against
The intuition
Someone agrees to buy your car for $10,000, paying in four months once the paperwork clears. A dealer offers you $9,700 today for the right to that payment. The $300 pays the dealer for waiting four months and for the risk the buyer walks away. If that risk is small, $300 over four months is a good return.
When a company agrees to be bought, its shares behave the same way: they jump toward the offer but stay a little below it. That gap is the spread. A merger arbitrageur (an arb) buys the shares and collects the spread when the deal closes. To compare deals with different timelines, arbs annualize the spread.
Gross spread = offer ÷ price today − 1. Annualized spread = gross spread × 365 ÷ days to close. In a stock deal, short the exchange ratio × the target shares held, in acquirer stock, to lock in the spread.
Why it works
- The conventions here: a fixed offer per share; the spread is annualized simply (× 365 ÷ days), not compounded; no dividends or financing costs. In a stock deal the target holder receives a fixed number of acquirer shares.
- The spread is an insurance premium. Holding the target means selling certainty to shareholders who would rather have cash today; the risk is the deal failing.
- The same spread is worth more over a shorter wait. 3% over 90 days is about 12% a year; over a year it is 3%.
- A return hurdle sets a highest price: offer ÷ (1 + hurdle × days ÷ 365).
- Stock deals need a hedge. The offer is worth the exchange ratio × the acquirer's price, so short that many acquirer shares per target share. Whatever the acquirer's shares do, the locked profit is the original spread.
- The hedge does nothing about a break. If the deal fails, the target falls and the acquirer often rallies, so both legs lose.
| Gross spread: 50 ÷ 48.50 − 1 | 3.09% |
| Annualized: 3.09% × 365 ÷ 120 | 9.4% |
| Spread the hurdle needs: 10% × 120 ÷ 365 | 3.29% |
| Highest price: 50 ÷ 1.0329 | $48.41 |
| Stock deal at 0.5 acquirer shares, acquirer at $100, 10,000 target shares | short 5,000 acquirer shares |
| Locked profit: (50 − 48.50) × 10,000 | $15,000 |
If the acquirer falls 10% before closing, the target converges to $45: the long loses $35,000, the short gains $50,000, and the $15,000 is still there.
The formulas
What closing pays.
Simple, so deals with different timelines compare.
Run it backwards.
The target is worth acquirer shares.
Locks in the spread whatever the acquirer does.
Worked example
Offer over price, less one; then scale by 365 over the days to close.
See it move
Same deal and the same offer. Change the spread, the days to close and your hurdle; for the stock-deal version, change the exchange ratio and what the acquirer's shares do before closing.
- Widen the spread. Today's price falls and the annualized spread rises; the highest price for your hurdle does not move.
- Lengthen the days to close. The annualized spread falls, and so does the highest price you can pay.
- Raise your hurdle. The highest price you can pay falls.
- Move the acquirer's shares. The target long and the acquirer short swing opposite ways, and the hedged bar stays put.
- Change the exchange ratio. The hedged bar still does not move.
Run it backwards
Same deal, reversed: your fund will not put on an arb below a set annualized return. What is the most you can pay for the target?
Turn the yearly hurdle into a spread for the holding period, hurdle × days ÷ 365, then divide the offer by one plus that spread.
If the stock trades above that price, wait: spreads widen on every worrying headline. If it trades below, size the position to the risk of a break, not to the size of the spread.
Traps
Say it in the interview
“What is merger arbitrage, and how do you tell whether a spread is attractive?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Gross spread = offer ÷ price − 1.
- Annualized = gross × 365 ÷ days.
- Highest price = offer ÷ (1 + hurdle × days ÷ 365).
- Stock deals: short the exchange ratio in the acquirer to lock the spread.