Short gamma, why your hedges always chase the market

Question

You sold an at-the-money straddle (stock at $\$ 100 $) and you are keeping it delta-neutral. Over the day the stock grinds from$ $100 $to$ $103 $to$ $106$.

Trace your hedging trades. Why does being short gamma force you to "buy high and sell low," and how does that compare to being long gamma?

Accepted Answer

A short straddle is short gamma: your delta moves in the same direction as the stock, so hedging always means trading against yourself. Start delta-neutral at \100. As the stock rises to \103, the call you are short gains delta and the put loses delta, net, your position delta turns negative (you are now effectively short the stock into a rally). To get back to neutral you must buy stock, at the elevated price of \103. The stock rises again to \106: you are short even more delta, so you buy again, higher still. If the stock later falls, your delta swings positive and you sell into the decline…

Short gamma, why your hedges always chase the market

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