Delta Hedging While Retaining Positive Gamma Exposure

Summary

The document addresses whether a position with positive gamma should remain delta neutral. Its answer distinguishes delta from gamma: adjusting delta exposure does not, by itself, eliminate gamma exposure. A position can therefore be delta hedged while retaining sensitivity to changes in the underlying’s price movement.

The response invokes the Black–Scholes relationship to describe the tradeoff under its assumptions: gains associated with gamma are offset by theta decay. It argues that if frequent delta hedging removed the gamma benefit, the position would be left with theta losses and negative expected return. This is a brief conceptual explanation, not a full hedge policy or empirical result. It does not specify transaction costs, discrete rebalancing effects, or conditions under which gamma exposure is profitable, so it should not be read as a guarantee that a positive-gamma position earns a return.

Key ideas

• Delta neutrality and gamma neutrality are distinct conditions.
• A delta hedge can leave a position with positive gamma exposure.
• Under the Black–Scholes assumptions described, gamma gains are offset by theta losses.
• The response does not account for transaction costs or establish that positive gamma guarantees profits.

Tags

# Hedging delta when gamma is positive


# Hedging delta when gamma is positive












If I have an aggregate position with a positive gamma, should I still be delta neutral? I feel like I'm giving up the positive benefits of being gamma positive because I'm killing my delta constantly.

## Answer by Mild_Thornberry (score 1)

https://quant.stackexchange.com/a/50064

Delta neutral does not imply gamma neutral, so you still get gamma benefits. Looking at the Black Scholes equation, if you remove delta and hit your assumptions, your gamma gains will be offset by theta losses. If a delta hedge removes those gamma gains, then you’d just be losing on Theta, and your expected return would be negative!

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.