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:

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: $\textdollar 1{,}000{,}000 / 0.0185 \approx \textdollar 54$ 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.