Where the stock goes if the deal breaks
The spread is what you earn if the deal closes. The break price is what you are left holding if it does not.
- Estimate a break price from the unaffected price, the sector move and a damage haircut
- Measure the upside, the downside and the ratio between them
- Find the lowest break price a desk's risk limit accepts
- Show what ignoring the sector does to the downside
The intuition
A house was on the market at $400,000 before a buyer agreed to pay $500,000. Months later the sale falls through. It will not simply go back to $400,000: local prices may have risen or fallen in the meantime, and a house whose sale collapsed makes the next buyer wonder what the first one found.
An arb estimates the break price the same way. Start from the unaffected price (before the deal leaked), move it with the sector since then at the stock's beta, and take off a damage haircut. The gap from today's price down to it is the downside; the gap up to the offer is the upside.
Break price = unaffected price × (1 + beta × sector move) × (1 − damage). Upside = offer − price today. Downside = price today − break price. Downside ÷ upside = dollars risked for each dollar you can make.
Why it works
- The conventions here: the unaffected price is moved with the sector since the deal was announced, at the stock's beta, then cut by a stated damage haircut. No time value.
- The world moves on during a deal. The unaffected price is where the stock was, not where it would be now.
- Damage is a judgment: the company was shopped and not bought, management was distracted, customers and staff may have left. It is where two arbs with the same data disagree.
- Arb is lopsided by design. The downside is usually several times the upside; it works because most deals close.
- A desk limit on downside ÷ upside sets the lowest acceptable break price: price today − limit × upside.
- Ignoring the sector errs both ways. After the sector falls, it makes the downside look smaller than it is; after a rise, bigger.
| Sector adjustment: 40 × (1 − 1.2 × 10%) | $35.20 |
| Break price: 35.20 × (1 − 5%) | $33.44 |
| Upside: 52 − 50 | $2.00 |
| Downside: 50 − 33.44 | $16.56 |
| Downside ÷ upside: 16.56 ÷ 2.00 | 8.3x |
| Lowest break price for a 5x limit: 50 − 5 × 2 | $40.00 |
Ignoring the sector: 40 × 95% = $38.00, a downside of $12.00 and a ratio of 6.0x. The lazy number makes the trade look safer than it is.
The formulas
Where the stock lands without the deal.
What closing pays.
What a break costs.
Dollars risked per dollar of upside.
Run it backwards.
Worked example
Move the unaffected price with the sector at the stock's beta, then take off the damage.
See it move
Same deal and the same prices. Change the damage you assume and your desk's limit on downside ÷ upside. The chart shows what the sector move does; New company and numbers draws a different sector move and beta.
- Raise the damage. The break price falls, so the downside and the ratio both grow.
- Raise the desk limit. The lowest acceptable break price falls; your own break price does not move.
- Set the damage to zero. The break price is simply the unaffected price moved with the sector.
- On the chart, a stronger sector lifts the break price and so shrinks the downside.
Run it backwards
Same deal, reversed: your desk only takes arbs where the downside is at most a set multiple of the upside. What is the lowest break price that passes?
The downside allowed is the limit × the upside. Take that off today's price.
Then compare with your own estimate. The sector move can be observed; the damage is a judgment, so check how much more damage your estimate could take before the trade fails.
Traps
Say it in the interview
“How do you think about the downside in a merger arbitrage trade?”
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.
- Break price = unaffected × (1 + beta × sector) × (1 − damage).
- Upside = offer − price; downside = price − break price.
- Lowest acceptable break price = price − limit × upside.
- Ignoring the sector misjudges the downside.