The implied probability of a deal closing: the formula, and what it misses

When a target trades below the offer price, the discount is the market's estimate of the risk that the deal breaks. You can turn that discount into a probability with one formula.

The formula

With an offer (upside) price U, an estimated downside price D if the deal breaks, and the current market price P:

Implied probability = (P - D) / (U - D)

A worked example

Offer at 42.50, downside estimated at 36.00, stock trading at 41.20:

(41.20 - 36.00) / (42.50 - 36.00) = 5.20 / 6.50 = 80%

The market is pricing roughly an 80 percent chance of completion. If your own estimate is higher, the spread is attractive; if lower, the market is being generous to the deal.

Getting the inputs right

The formula is only as honest as its inputs. The upside is not always the headline offer: dividends paid before settlement add to it, and withholding tax on those dividends subtracts from what a foreign holder actually receives. The downside is a judgement call: the unaffected price is a starting point, but sector moves since announcement, the stake the bidder retains, and the chance of a competing bid all shift it.

What the formula cannot see

Implied probability compresses every risk into one number, and most of that risk is regulatory. A deal needing only one domestic merger control clearance and a deal needing three FDI screenings in three jurisdictions can show the same implied probability while carrying very different timelines and tail risks. The formula also says nothing about time: an 80 percent probability over four months is a different trade from the same probability over fourteen.

Compare it to your own estimate, systematically

The useful discipline is to hold the implied number next to your own probability estimate, deal by deal, and to know why they differ. FPM computes the implied probability on every assessment from the recorded offer terms, next to the analyst's own estimate and the regulatory path that justifies it. See how that works in the merger arbitrage software tour, or read how event-driven funds run the whole workflow.