Implied Deal Completion Probability

When Company A agrees to buy Company B for $50 a share, B's stock jumps toward $50 — but rarely all the way there, even instantly. It typically settles a bit below, at say $48. That gap isn't market inefficiency; it's the market pricing in two real possibilities: the deal closes at $50, or it breaks and the stock falls back toward where it traded before the announcement. The size of the gap tells you, roughly, how confident the market is in each outcome.

Backing out the probability

If $P$ is the offer price, $M$ the current market price, $B$ the price the stock would fall to if the deal breaks, and $p$ the probability of completion, the market price should sit at the probability-weighted blend of the two outcomes:

$$M = p \times P + (1-p) \times B$$

In words: today's price is a mix of the deal-completes price and the deal-breaks price, weighted by how likely each is. Solving for $p$:

$$p = \frac{M - B}{P - B}$$

In words: the implied probability is how far the current price has moved from the break scenario, as a fraction of the total distance between the break scenario and full completion.

Worked example

Company B is trading at $48 after an all-cash $50 offer is announced. Based on where the stock traded before the deal and how similar names in the sector trade, the merger-arb desk estimates a break price of $40. The implied completion probability is $p = \frac{48 - 40}{50 - 40} = \frac{8}{10} = 0.80$, or 80%. If the desk's own view — based on regulatory risk, financing conditions, and shareholder approval odds — is that completion is more likely than 80%, say 90%, the stock looks cheap relative to that view, and a long position captures the gap between the market's implied probability and the desk's estimate if the deal closes as expected.

What this means in practice

This framework is the backbone of merger arbitrage: desks don't need to predict the exact deal outcome, only whether the market's implied probability is mispriced relative to their own research into the deal's regulatory, financing, and shareholder-vote risk. The expected return on a merger-arb position is asymmetric — a modest gain if the deal closes on schedule, a much larger loss if it breaks — so position sizing has to reflect that skew, not just the expected value.