How do you aggregate Greeks across a multi-instrument portfolio?

Question

AcadiFi · Accepted Answer

Portfolio Greeks aggregate linearly when instruments share the same underlying. For n positions with quantities q_i and per-contract Greek G_i, the book Greek is Σ q_i · G_i · multiplier. Delta and vega are most commonly netted; gamma is netted cautiously because positive and negative gamma across strikes can mask convexity concentration near specific spots.

Example: Halcott Macro Desk holding on EuroStoxx 50:
- +500 Dec calls K=4800 (Δ=0.55, Γ=0.004, ν=18)
- -300 Dec calls K=5000 (Δ=0.35, Γ=0.005, ν=22)
- +200 Dec puts K=4600 (Δ=-0.28, Γ=0.004, ν=16)
- -100 futures (Δ=1.00)

Net delta (per unit, multiplier 50): 500·0.55 + (-300)·0.35 + 200·(-0.28) + (-100)·1 = 275 - 105 - 56 - 100 = 14. Multiplied by 50 = 700 index-equivalent delta.

```mermaid
flowchart LR
    A[Option positions] --> D[Sum q·G·multiplier]
    B[Futures positions] --> D
    C[Exotics via PDE/MC] --> D
    D --> E[Net portfolio Greek]
    E --> F[Compare to limits]
```

Pitfalls: (1) Different multipliers — index options vs single-stock options require consistent conversion. (2) Cross-Greeks — vanna and volga don't add cleanly across strikes. (3) Basis risk — Greeks on SPX can't net with SPY without scaling. (4) Exotic Greeks from Monte Carlo have sampling noise; firms like Pemberton Risk Analytics use common random numbers to reduce variance. FRM candidates must also understand cross-gamma matrices for multi-underlying books.

How do you aggregate Greeks across a multi-instrument portfolio?

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