Hedge the Book

Question

You just sold 100 call contracts (each on 100 shares) with delta 0.40. What trade flattens your delta right now, and what risk remains after you do it?

Accepted Answer

The hedge. Short 100 contracts × 100 shares × Delta = 0.40: textposition delta = -100 times 100 times 0.40 = -4000 text share-equivalents. Buy 4,000 shares. Now a small move in the stock leaves your P&L unchanged: delta-neutral. What remains, everything beyond first order: - Gamma (the big one): you are short gamma. As the stock rallies, the calls' delta rises above 0.40, so you're effectively short more than 4,000 shares → you must buy MORE as it rises and sell as it falls, buying high, selling low, bleeding money on every round trip. Delta hedges decay as the price moves; short-gamma books re-hedge at a loss. - Vega: implied volatility rises → the calls you're short gain value → you lose, regardless of stock direction. - Theta (your compensation): time passing decays the options you're short, you collect theta as payment for the gamma bleed. - Plus pin/strike risk near expiry, dividend and rate risk, and the practical costs of discrete re-hedging. The phrase that signals you understand: "delta-neutral is not risk-neutral, I've hedged the first derivative only, and I'm short the second." The follow-up game is usually walking the gamma rebalancing through a price path.

Hedge the Book

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