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How Is the Gamma of a Portfolio Calculated?

The Gamma of a portfolio is calculated by summing the individual Gamma values of all the options held in the portfolio, weighted by the number of contracts. Since Gamma is a linear measure of the rate of change of Delta, the portfolio's total Gamma is simply the algebraic sum of the Gammas of its components.

This net Gamma indicates the overall convexity risk of the portfolio.

How Is a Portfolio’s Overall Delta Calculated?
Why Is Gamma Considered a Key Measure of an Option’s Directional Convexity?
Explain the Concept of “Convexity” in Relation to Gamma
How Does the Concept of Convexity in Bond Derivatives Compare to Gamma in Options?