A trader holds four open options positions across two underlying instruments. Net delta looks benign at +0.12. Then volatility spikes 6 points and the underlying drops 2.3%. The position loses $18,400 overnight — not because direction was wrong, but because gamma exposure was untracked at portfolio level. Delta told one story. The Greeks together told another.

Sensitivity analysis at portfolio level means aggregating each Greek across every leg simultaneously. A long call contributes positive delta and positive gamma. A short strangle contributes negative vega. A deep ITM put contributes significant rho sensitivity to rate changes. Each leg looks manageable alone. Stacked together, exposure concentrates in ways a single-position view never reveals.

CONCEPTPortfolio-level Greeks aggregate all legs into a single risk dashboard — delta, gamma, vega and rho summed and stress-tested together.
WARNINGA flat net delta with high net gamma means a 1% move in the underlying can flip your directional exposure entirely — size accordingly.
KEY IDEAVega is the silent killer in multi-leg books — a volatility crush of 4 IV points on a 10-contract short vega position equals roughly $2,000 gain or loss per 1-point IV move.

Position sizing in multi-leg structures typically uses a Greek-adjusted notional method. If maximum tolerable portfolio delta is ±50 deltas (each delta representing one share unit), and a proposed iron condor adds a net delta of +8, the remaining delta budget is ±42. Gamma limits might be set at ±15 per 1% underlying move. These are not arbitrary — they're derived from historical worst-case overnight moves in the specific underlying, multiplied by the gamma figure.

Portfolio Greek Exposure — Four-Leg PositionDelta+0.12GammaHighVega-ShortRhoLowBar height = relative magnitude of exposure per Greek at portfolio level

Stress-testing each Greek under defined scenarios — underlying ±5%, IV ±10 points, rates ±50bps — produces a P&L matrix traders use to set position limits before entry, not after. The options Greeks framework underpins this methodology, while formal sensitivity analysis provides the mathematical scaffolding for scenario construction. Rho often gets dismissed in short-dated books, but in positions with 90+ DTE, a 50bps rate move can shift position value materially — the rho calculation quantifies exactly that exposure.

A multi-leg position with unmonitored Greeks is not a strategy — it's a collection of unresolved risks waiting for the right catalyst.

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