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Summary

Raw greeks cannot be added across products: a 1-point move in a $10 stock is not a 1-point move in SPX. Portfolio risk management therefore requires converting greeks to a common denominator — dollar terms or a reference product — so that delta, gamma, and vega can be summed into a true risk dashboard1. Theta and vega are exceptions: they attach to premium, not to the underlying, and need no cross-product weighting1.

Why Weighting Is Needed

A 1-point move means different things: $1 in IBM is ~0.5%, but $1 in Ford is ~6%. Unweighted position delta therefore overstates exposure in cheap, high-percentage-vol names and understates it in expensive ones1.

Delta and Gamma Weighting

Delta represents correlation to a 1-point move; when combining products, weight by contract size via conversion ratios1:

Pair Ratio (small : SPX)
SPY : SPX ≈ 10 (SPY delta 30 = SPX delta 3)
OEX : SPX 2.23
DIA : SPX ≈ 11
  • Delta weighting: multiply each product's deltas by its conversion ratio before summing.
  • Gamma weighting: gamma is computed for a 1-point move regardless of contract size, so scale by the underlying's move. Example: SPY drops $3 (2.5%) ⇔ SPX drops $30 (2.5%) — SPY gamma 5 → 3 × 5 = 15 SPX-deltas; SPX gamma 0.5 → 30 × 0.5 = 15. They match1.

Dollar greeks are the general form: dollar delta = position delta × price per point (× multiplier); dollar gamma similarly. This makes exposure comparable across SPY, SPX, IWM, or single names without picking a reference index.

What Does Not Need Weighting

Theta and vega are tied to the premium amount, not the underlying product: $3,000 of premium sold in SPY or SPX has the same theta and vega. This is why cross-hedging (e.g., SPY options against SPX options) works for vega/theta even though delta and gamma must be converted1.

Beta Weighting and the Portfolio Dashboard

For a multi-underlying book, each position's delta can be further translated into a benchmark-equivalent (e.g., SPX) using the underlying's beta — the standard "beta-weighted delta" check that answers "what is my book if the market gaps 2%?" Passarelli's position-delta arithmetic (Σ delta × contracts × 100, plus stock) is the per-underlying building block that this aggregation extends2.

The dashboard discipline12:

  1. Convert delta/gamma to dollar or benchmark terms per product.
  2. Sum portfolio delta (directional risk), gamma (hedge drift risk), vega (vol risk), theta (daily carry).
  3. Re-check after every fill — greeks are local estimates and go stale as price, time, and IV move.

Links

Footnotes

  1. Chen & Sebastian, The Option Trader's Hedge Fund — Greeks topic: delta weighting, gamma weighting, conversion ratios, unweighted theta/vega. ↩↩↩↩↩↩↩

  2. Passarelli, Trading Option Greeks — delta topic: position delta arithmetic and hedge ratios. ↩↩