How to Calculate a Merger Arbitrage Spread: Step-by-Step

What you need

• The merger agreement. It is usually filed as an exhibit to a Form 8-K shortly after the announcement. Find it through EDGAR search. You need the consideration per share, any collar or election terms, the dividend covenant, the conditions to closing and the outside date.
• Current prices for the target and, in a stock deal, the acquirer.
• Dividend history for both companies.
• The borrow rate on the acquirer's shares from your broker, if you hedge a stock deal.
• The undisturbed price: the target's price before the deal was announced or rumored.
• A spreadsheet. Every input below changes over the life of the deal, so set it up to recalculate.

Step 1: Value the consideration per share

Write down exactly what one target share receives at closing.

• Cash deal: the cash amount per share.
• Stock deal: the exchange ratio times the acquirer's current price.
• Mixed deal: the cash portion plus the exchange ratio times the acquirer's price.
• Election deal: holders choose cash or stock, subject to proration. If most holders are likely to elect the more valuable form, proration will push you toward the agreement's overall cash and stock mix, so value it at that mix.
• Collar: apply the pricing formula in the agreement. Inside a fixed-value band, the value is the stated dollar amount. Outside the band, the ratio locks and the value moves with the acquirer.

Treat a contingent value right as zero in the base calculation and count it separately as upside.

Step 2: Calculate the gross spread

Gross spread in dollars is deal value minus the target's current price. Gross spread as a percentage is that figure divided by the current price, because the current price is what you pay.

Company A trades at $47.50. The gross spread is $50.00 minus $47.50 = $2.50, or $2.50 / $47.50 = 5.26%.

In a stock or mixed deal, this number changes every time the acquirer's price moves. That is why stock deals are usually hedged: buying the target and shorting the acquirer in proportion to the exchange ratio locks in the dollar spread on the stock portion. In the example, each Company A share is paired with a short of 0.40 Company B shares.

Step 3: Adjust for dividends

Read the dividend covenant in the merger agreement. Many agreements allow the target to keep paying its regular dividend until closing; some forbid it.

• Target dividends you will receive before closing add to the spread.
• Acquirer dividends on shares you are short are paid by you to the lender, so they subtract.

Count only the dividends with ex-dividend dates before your expected closing date.

Step 4: Subtract hedge and financing costs

A short position carries a borrow fee, quoted as an annual rate on the value of the shares borrowed. For widely held acquirers the rate is often small; for hard-to-borrow names it can consume much of the spread. Multiply the rate by the value of the short and the fraction of a year you expect to hold it.

If you use margin to buy the target, subtract interest the same way. If you pay cash, the cost is the return the money could earn elsewhere, which is the yardstick in Step 6 rather than a deduction here.

Net spread: $2.50 + $0.26 minus $0.05 = $2.71 per share, or $2.71 / $47.50 = 5.71%.

Step 5: Date the closing

The closing date sets the annualized return, so build it from the actual approval steps instead of guessing a round number. Put each step on a catalyst calendar.

• HSR review. Under 16 CFR 803.10, the initial waiting period ends 30 days after filing, or 15 days for a cash tender offer. If either agency issues a Second Request, the period runs until 30 days after the parties substantially comply, or 10 days for a cash tender offer. See how the HSR waiting period works.
• Tender offer. Under SEC Rule 14e-1, a tender offer must stay open at least 20 business days, and at least 10 business days after any change in the price offered. See tender offer terms and timelines.
• Shareholder vote. Count the time to file a preliminary proxy, possible SEC review, mailing the definitive proxy, and the meeting date.
• Other approvals. Foreign antitrust reviews, CFIUS, and industry regulators often take longest. The merger agreement lists which are required.
• Outside date. The latest date the agreement allows before either side can walk away. Treat it as the long end of your range, not the base case.

Step 6: Annualize the net spread

Two common versions:

• Simple: net spread x 365 / days to close. 5.71% x 365 / 182 = 11.4%.
• Compounded: (1 + net spread) raised to (365 / days to close), minus 1. 1.0571 ^ (365 / 182) minus 1 = 11.8%.

Use one version consistently when comparing deals. Then compare the result with what the same money earns with no deal risk, such as a Treasury bill maturing near your closing date. The gap between the two is what you are paid for carrying break risk.

The table shows how much the closing date drives the answer, holding the 5.71% net spread fixed.

In practice a longer timeline also adds dividends and borrow costs, so rerun Steps 3 and 4 for each case.

Step 7: Estimate the downside

The upside is capped at the net spread. The downside is where the target trades if the deal breaks. Start from the undisturbed price, then adjust it for what has happened since: moves in the target's peer group, its own reported results, and any change in its balance sheet. A target that has spent heavily on deal costs or let its business drift during a long review may fall below its old price.

In a hedged stock deal, the acquirer often rises when a deal breaks, which adds a loss on the short. Estimate that leg separately rather than assuming it nets to zero.

Step 8: Calculate the implied probability and expected value

Setting the expected gain equal to the expected loss gives the probability of closing that the current price implies:

Implied probability = downside / (downside + upside) = $11.50 / ($11.50 + $2.71) = 81%.

Now use your own estimate. If your work on the conditions, regulators and financing says 90%, the expected value per share is 0.90 x $2.71 minus 0.10 x $11.50 = $1.29, or 2.7% on $47.50. If your estimate is 81% or lower, the spread pays nothing for the risk. This simple version ignores time value and assumes a single downside price, so treat it as a check on the spread, not a precise forecast.

Quick reference: the full calculation

Where this goes wrong

The arithmetic is simple. The errors come from the inputs.

• A stale deal value. In a stock deal, the spread printed this morning is wrong by the afternoon if the acquirer has moved and you are unhedged.
• Ignoring the dividend covenant. Assuming the target keeps paying when the agreement forbids it inflates the spread.
• A hopeful closing date. Management guidance is a target, not a commitment. Base the date on the approvals still outstanding.
• A flattering downside. The undisturbed price can be months old. Rebuild it from current peers and results.
• Election and proration surprises. In an election deal, the mix you receive depends on what other holders choose. See tender offer proration for how the mechanics work.
• Borrow recalls. A short can be recalled or the fee can jump, which forces you to close the hedge at a bad time.

Common mistakes

1. Dividing by the deal price instead of the current price. You invest the current price, so that is the denominator.
2. Annualizing a gross spread. Annualize the net figure, after dividends and costs.
3. Comparing deals on raw spread. A 3% spread closing in two months beats a 6% spread closing in eighteen months.
4. Counting a CVR at face value. Many expire worthless. Value it at zero in the base case.
5. Setting the calculation once. Recalculate after every price move, filing, regulatory step and delay.

For data sources that track live spreads and deal documents, see the 8 best merger arbitrage data sources. Dombey's published research works through deal timelines and downside in the same way before each catalyst; see the research archive.

The bottom line

A merger arbitrage spread starts as deal value minus price, divided by price, but the useful figure is the net spread after dividends and hedge costs, annualized over a dated closing estimate. Set that against a current downside price to see the probability the market implies. The calculation takes minutes; the work is in the inputs: the merger agreement, the approval timeline and an honest view of where the stock goes if the deal fails. Rerun it every time one of those inputs changes.