Sizing a Merger Arb Book

A single merger arb position looks almost boring: buy the target below the offer price, collect a few percent when the deal closes in six months. Put fifty of those together and the book looks like a bond fund — until one deal breaks. Then the position doesn't lose a few percent, it can lose twenty or thirty, because the stock falls back to where it traded before the deal was announced. Sizing a merger arb book means building a portfolio where dozens of small, likely wins can absorb that one large, unlikely loss.

Why average spread is the wrong number to size on

If a deal offers a 4% annualized spread with a 95% chance of closing, the "expected return" looks attractive on its own. But expected return blends two very different outcomes: a small, near-certain gain, and a rare, large loss. Sizing purely to maximize expected return — putting the most money into whichever spread looks widest — ends up concentrated in the riskiest deals, since wider spreads usually mean more perceived break risk, not free money. The fix is to size by the loss a deal can inflict, not the yield it offers.

A simple sizing rule

A common approach caps the loss-given-break per position as a fixed fraction of the book, rather than capping the dollar size directly:

$$\text{position size} = \frac{\text{max acceptable loss}}{p_{break} \times \text{drop if broken}}$$

In words: decide how much of the book you're willing to lose if this one deal fails, then divide by how likely a break is and how far the stock would fall — the riskier the deal looks on either count, the smaller the position has to be to keep the loss constant.

Worked example

A fund runs a $100 million book and wants no single broken deal to cost more than 1% of the book, i.e. $1 million. Deal A: offer $60, trading at $58.50 (spread $1.50), and if it breaks the stock is expected to fall to $45 — a $13.50 drop. The market-implied break probability is about 8%.

1. Loss-given-break per share. $13.50.
2. Expected loss per dollar invested at $58.50/share: $13.50 / 58.50 \times 0.08 \approx 1.85\%$ of position value.
3. Max position size: \1{,}000{,}000 / 0.0185 \approx $54$million face — but that alone would be nearly the whole book, so the fund also caps single-name exposure at 5$5 million) regardless of what the spread math allows.

Both constraints bind at once: the break-risk formula sets an upper bound, and the flat cap catches deals whose true break probability is mismeasured — common, since "8%" is only the market's guess.

What this means in practice

Real books add a third layer beyond per-deal caps: correlation. Antitrust reviews and market-wide risk appetite can cause several deals to break together, so a book diversified across forty names can still behave like one large position when the common driver is regulatory or macro, not company-specific.