Portfolio Greeks and hidden correlation

A share portfolio's risk is read through its correlations; an options book's is read through its aggregate Greeks, which is where its hidden correlations live. This lesson aggregates the dashboard of lesson 6 across the whole book.

The aggregate view

• Total delta: the book's net directional exposure - several positions that each look modest can sum to a large directional bet, or cancel to less than they appear; only the aggregate says which.
• Total vega: the book's net volatility exposure - and the one most often hidden, because a book diversified across underlyings can still be uniformly long or short volatility, one big vega bet wearing many names.
• Total theta and gamma: the book's daily decay bleed or income, and how fast its delta shifts - the aggregate carry and the aggregate instability, read across every position at once.

The hidden correlations

Options positions correlate in ways shares do not. A vega correlation: options on different underlyings are all exposed to volatility, and in a market-wide volatility event they move together - so a book long options across many names is long volatility once, and a volatility collapse hits all of it. A delta correlation: options expressing the same directional or volatility view across correlated underlyings sum to a concentrated bet. And an event correlation: options positioned around the same event (an earnings season, a macro decision) share its outcome. The aggregate Greeks reveal these; the position-by-position view hides them, exactly as reading shares individually hid their sector correlation.

Sizing the aggregate

The options risk plan caps the aggregate Greeks, not just each position: a total vega limit (so the book is not one large volatility bet), a total delta limit (so it is not one large directional bet), and an eye on the shared-event exposure that clusters the risk. The correlation-to-one lesson, in the Greek dimension: a book that looks diversified across names can be concentrated in volatility or direction, and only the aggregate Greeks show it. Reading the book through its total Greeks - and capping them - is how an options portfolio's real, correlated risk is managed, where reading positions separately would miss the concentration entirely.