Merger Arbitrage: A Takeover Spread Is Not a Completion Probability

A company agrees to pay 100 for a stock that still trades at 95. The tempting interpretation is that five points are waiting to be collected. The more useful question is what must happen before the investor receives 100—and what the shares could be worth if it does not happen.

A takeover spread prices a conditional payment, a waiting period and a downside scenario together. It is neither a deposit yield nor a direct reading of the chance of completion. Even a correct view that the deal will probably close can produce an unattractive investment at the current price.

Start with what the shareholder is actually entitled to receive

Separate a rumour, an announced proposal and a signed agreement. Then identify the consideration: a fixed cash amount, a fixed number of acquirer shares, a mixed payment or a formula with adjustment bands. A headline transaction value is not necessarily the amount payable for each share bought on the market. Dividends, elections, different share classes and amended terms can change the cash-flow calculation.

The signed document and subsequent company filings are the starting point, not a broker screen showing an attractive percentage. Read the remaining conditions, approval timetable, financing commitments and termination provisions. A termination fee may be payable to a company under specified circumstances; do not treat it as an automatic payment protecting every shareholder. A deadline may create a termination right rather than guarantee settlement on that date.

Five points of upside are not a ten-percent locked-in yield

Use a wholly hypothetical cash offer of 100 and an executable purchase price of 95. Assume no dividends, currency changes, tax or dealing costs initially. Successful completion gives a holding-period return of 100/95−1 = 5.2632%. If cash arrives in exactly six months, the compound annualised equivalent is (100/95)²−1 = 10.8033%. If it takes twelve months, it is only 5.2632%.

Annualisation changes the unit of measurement; it does not create a second successful deal into which the proceeds can be reinvested. Nor does it account for failure. Suppose the failure value is 70: the loss is 25 per share, or 26.3158% of the purchase price. One such loss offsets five successful five-point gains before costs, assuming equal share counts. A high win rate can coexist with a poor result.

Reverse the price equation without mistaking it for a forecast

In the simplest two-outcome model, both outcomes occur at the same time. Let P be the price paid, C the completion payment, B the share value on failure, T the years to that common outcome date, and r an effective annual cash comparison rate. The probability threshold q that makes the expected terminal value equal to cash is:

q = [P × (1+r)^T − B] / (C−B).

With P=95, C=100 and B=70, ignoring time gives 83.33%. At a 4% cash rate and a six-month horizon, the threshold rises to 89.60%. Cash turns 95 into 96.8814 during the wait, so an expected outcome merely equal to 95 is not enough. The table changes only the assumed failure value and horizon; the offer and purchase price stay fixed.

This is a model hurdle, not an observed physical probability. Reverse-engineering a market price cannot identify completion probability independently of risk premiums, liquidity, funding constraints and investors’ different failure-price estimates. Using a cash rate does not remove the risk of the equity position. If a calculation gives more than 100%, the assumed deal cannot match that cash hurdle even with certain completion under those inputs; do not clip the result and call it “100% likely”.

Suppose an analyst independently assigns a 90% completion probability to the six-month, 70-failure scenario. Expected proceeds are 0.90×100+0.10×70 = 97. Discounting at 4% gives 95.1163: an apparent advantage of only 0.1163 over the purchase price, before any extra compensation for risk. An all-in cost equivalent to 0.40 paid today eliminates it. Replacing P with 95.40 raises the cash-matching threshold to 90.96%.

The failure price deserves at least as much work as the offer

The pre-announcement share price is a reference, not a floor. Since the announcement, sector valuations, earnings, debt and the value of assets may have changed. A failed process may also leave new costs or strategic damage. Build a stand-alone valuation range using updated fundamentals and comparable market moves; do not simply freeze the last unaffected quote.

The sensitivity table contains a useful warning: a lower failure value raises the completion threshold even though the quoted five-point spread has not changed. A wider spread after bad news can mean a better entry price, worse deal prospects, a longer wait, a lower failure value—or several at once. The chart alone cannot choose among these explanations.

If success occurs in six months but failure could emerge in one month or two years, the common-date shortcut no longer applies. Value each outcome’s cash flows at its own time, and state what happens to proceeds after an early failure if comparing terminal wealth. A third outcome such as a higher bid needs its own probability and payoff. Probabilities must sum to one, and mutually inconsistent events must not be double counted.

A share-for-share hedge solves a different problem

In a fixed-exchange-ratio stock deal, a long target position may be paired with a short position in the acquirer based on the contractual shares to be received. This can offset part of the acquirer-price exposure on successful delivery. It does not hedge away rejection, changed terms, stock-borrow costs, recalls or the unwind after failure. Cash offers do not automatically call for the same short leg.

A contractual exchange ratio is also not the regression coefficient used in statistical pairs trading and cointegration analysis. One rests on enforceable transaction terms if conditions are met; the other estimates a historical relationship. Confusing them can leave the wrong number of shares to deliver. Mixed consideration, collars and elections require their actual payoff rules, not a fixed-ratio shortcut.

Turn the spread into a document-led decision process

1. Record the latest signed terms, amendments, share class and exact payment formula. Distinguish a proposal from a binding agreement and identify the jurisdiction and transaction structure.
2. List each unresolved approval or condition with its documentary evidence and next dated milestone. A completed vote is evidence about that condition, not proof that all conditions are satisfied.
3. Build independent stand-alone failure values and realistic completion dates. Recompute both net conditional returns and the cash-matching probability threshold across those ranges.
4. Include spreads, fees, funding and any stock-borrow or currency exposure. Compare executable quotes at the intended size, not stale last trades or optimistic midpoint marks.
5. Set explicit review triggers: revised consideration, missed milestones, financing changes, regulatory remedies and termination notices. Reopen the model when an input changes rather than defending the original percentage.

The relevant confirmation is progress toward actual payment on the stated terms. The thesis fails when new evidence makes those terms, timing or downside assumptions untenable—not only when the share price crosses an arbitrary chart line. A spread becomes analytically useful only after the investor can explain which uncertainty it compensates for and how that conclusion would be disproved.