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Why Spot Moves Hurt a Delta-Hedged Short-Gamma Position

Article Quant Q&A · Author: Marcus
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Summary

This note explains why a delta-hedged position that is short options can lose when the underlying price moves. A zero net delta at the hedge point describes the position’s immediate sensitivity; it does not mean the option price falls when spot rises. For a short call paired with a long futures hedge, a rising market increases the call’s value, creating a loss on the short option.

Because the call has positive gamma, its delta grows as spot rises. The fixed futures position’s gain therefore does not keep pace with the option loss over the move, and the combined position loses value. The example is qualitative: it clarifies the role of curvature in changing hedge sensitivity, without quantifying losses or covering effects such as rebalancing frequency, volatility changes, or transaction costs.

Key ideas

  • Delta neutrality describes local exposure at the hedge point, not how option value responds over a larger spot move.
  • A short call loses value for its holder when spot rises because the call itself becomes more valuable.
  • Positive option gamma makes the call’s delta increase as the underlying rises.
  • A fixed futures hedge may not offset the growing loss on a short call during a market rise.

Tags

OptionsDerivatives pricingRisk management
Full text
# If you have a delta-hedged position and you're short gamma, why are spot price movements bad?


# If you have a delta-hedged position and you're short gamma, why are spot price movements bad?












I simply can't wrap my head around the concept of Gamma. I've read multiple sites and explanations and for some reason can't wrap my head around the logic, so I feel that it'll really help for me to explain my understanding and have someone point out where I'm incorrect/flawed. Apologies for the elementary question.

If I have a delta-hedged position (so delta = 0) and I'm short options, this means I'm short (negative) gamma, from what I've read. Now, my thoughts are that if the spot price increases, this implies that my delta is now negative, which means that as the spot price increases, the option price is decreasing. If I've sold this option, why isn't this fall in price good for me?

I know that I'm incorrect, I just don't understand $why$ or where I'm going wrong. Any help or pointing out my errors would be much appreciated. Thank you

## Answer by Enrico Schumann (score 1, accepted)

https://quant.stackexchange.com/a/39286

Just because your position's delta is negative does not imply that the option price is decreasing when spot increases.

Suppose you are short calls and long futures. The market moves up, so the call price increases. But since you have a short position in the call, you lose money. Since the call has a positive gamma, it will lose money (increasingly) faster than the constant long-futures position makes money.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.