Corporate actions: adjustments, dividends and merger arbitrage

Corporate actions are where mechanical detail becomes profit and loss. A split changes the quoted price but nothing real; a dividend transfers value out of the stock on a known date; a merger turns a share into a claim on a deal completing. Each has a precise adjustment, and getting it wrong is a real and recurring source of losses.

Action	Effect on the stock	Effect on a listed option
2-for-1 split	Price halves, shares double	Strike halves, contract size doubles
3-for-2 split	Price $\times 2/3$ , shares $\times 3/2$	Strike $\times 2/3$ , size $\times 3/2$
Ordinary dividend	Price drops by the dividend on the ex-date	No adjustment — it is priced into the forward
Special dividend	Price drops by the amount	Strike typically reduced by the dividend
Spin-off	Price falls by the value distributed	Deliverable becomes a basket
Cash merger	Converges to the offer price	Deliverable becomes cash; volatility collapses

Table 3.1 · What each action does. The two dividend rows are the ones that catch people. Ordinary dividends are expected and already sit in the option price through the forward; only unexpected special dividends trigger a contract adjustment.

Proposition 3.2

The ex-dividend drop is not a loss

On the ex-date the stock opens lower by roughly the dividend, because a buyer from that morning no longer receives it. Nothing has been destroyed — value has moved from the share price into a cash payment. For an option holder, though, it is entirely real: a call holder receives no dividend and watches the underlying fall, which is why a large dividend can make early exercise of an American call rational.

Holds when

Early exercise of an American call is worth considering only when the dividend exceeds the remaining time value.
Borrow costs work the same way inside put–call parity, and a hard-to-borrow name behaves like one paying a large dividend.

Equation 3.3

The merger spread

The current price is a probability-weighted blend of the deal completing and the deal failing. Invert it and the market is quoting a completion probability.

P_{\text{now}} \approx p\,P_{\text{deal}} + (1-p)\,P_{\text{break}}

$P_{\text{deal}}$: The offer price, discounted for the time to close.
$P_{\text{break}}$: Where the stock would trade if the deal collapsed — the hardest input to estimate.

Example 3.4

A target is bid for $\$50$ cash and trades at $\$47$ . You judge it would fall to $\$35$ if the deal broke. What completion probability is the market implying?

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Worked solution

Formula $p = \frac{P_{\text{now}} - P_{\text{break}}}{P_{\text{deal}} - P_{\text{break}}}$
Substitute $= \frac{47 - 35}{50 - 35}$
Solve $= \frac{12}{15}$
Answer $p = 80\%$

Sanity check. The payoff is skewed: $\$3$ to gain against $\$12$ to lose. At $80\%$ the expected value is $0.8 \times 3 - 0.2 \times 12 = 0$ , which is the definition of the implied probability — and it shows why merger arbitrage is picking up a small premium in front of an occasional large loss.

Corporate actions: adjustments, dividends and merger arbitrage

After this lesson you should be able to

The ex-dividend drop is not a loss

The merger spread

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