Managing Portfolio Greeks

Once you hold more than a few option positions, looking at each trade separately stops working. A long call here, a short put there and an iron condor somewhere else can add up to a book that is far more bullish, or far more exposed to a volatility spike, than you realised. Managing portfolio Greeks means measuring the combined exposures of all positions, comparing them with limits and adjusting the book so that its risks match what you intend.

Adding up the Greeks#

Greeks add across positions once each is expressed in the same units:

position delta = Σ (option delta × contracts × multiplier) + shares held

The same works for gamma, theta and vega.

Beta weighting delta#

Deltas on different stocks are not directly comparable: 100 deltas of a volatile tech stock carry more market risk than 100 deltas of a utility. Beta weighting converts each position's delta into equivalent units of an index such as the S&P 500:

beta weighted delta = delta × (stock price / index price) × beta

This gives a single number for the whole book's market exposure. See Alpha and Beta.

Setting limits#

Professional desks set limits for each Greek, and many individuals can do the same:

See Risk, Position, Loss and Drawdown Limits.

Scenario analysis#

Greeks describe small changes. For big moves, reprice the whole book under scenarios:

• Price moves of ±5%, ±10% and ±20% in the underlying or index.
• Volatility shocks of ±5 and ±15 points.
• Combined stress: a 10% fall with a 15 point volatility spike, which is what crashes often look like.
• Time: the book's value one week later with no price change.

Many broker platforms show these as risk graphs. See Stress Testing and Scenario Analysis.

Adjusting the book#

Greeks across expiries#

Vega and gamma behave differently by expiry. Short dated options carry high gamma; long dated options carry high vega. A book that looks vega neutral can still lose if short dated volatility jumps while long dated volatility barely moves. Many traders track vega by expiry bucket or weight it to reflect this. See Volatility Term Structure.

Correlation in stress#

Positions on different stocks look diversified in calm markets, but correlations rise in selloffs. Short puts on ten different stocks can behave like one big short put on the index in a crash. See Correlation Management.

A practical routine#

1. Check total beta weighted delta, gamma, theta and vega daily.
2. Compare with limits.
3. Run at least one combined stress scenario.
4. Adjust the largest exposures first.
5. Record the book's Greeks over time in your journal. See Trading Journal.

Frequently asked questions#

What are portfolio Greeks?#

The combined delta, gamma, theta, vega and rho of all option and stock positions in a portfolio.

What is beta weighted delta?#

A way to express the delta of positions in different stocks in terms of one index, so total market exposure can be measured with one number.

Why are Greeks not enough for risk management?#

They describe small changes. Large moves and volatility shocks require full scenario analysis and stress testing.

Next, see how option dealers' hedging can move markets in Dealer Gamma Exposure.