What Is Beta-Weighted Delta? Comparing Delta Across Different Stocks

Reviewed by Leon Moyer - Published October 9, 2026 - Last reviewed October 9, 2026

Beta-weighted delta converts the delta of positions on different stocks into one number measured in shares of a single index, so you can see how the whole portfolio is likely to move when the market moves. The formula, in one sentence: beta-weighted delta = position delta x the stock's beta x (stock price / index price).

What Is Portfolio Delta? added up deltas on one stock, the XYZ book, to get a net delta of +113.14. That works because every position responds to the same stock. Once a second stock enters the account, raw deltas stop adding up. This lesson shows why, and how beta-weighting fixes it.

What is beta?

Beta measures how much a stock tends to move relative to a benchmark index, which has a beta of 1. FINRA describes it as a measure of "how a stock moves relative to the market movement, not the total volatility of a stock" (FINRA on volatility and beta). A stock with a beta of 1.2 has historically moved about 1.2% for each 1% move in the index; a stock with a beta of 0.8 has moved about 0.8%.

Beta is estimated from past prices. Different data providers use different lookback periods and benchmarks, so the same stock can show different betas on different platforms.

Why can't you add deltas across stocks?

Add a second position to the account: one long ABC 200 put, bought for $6.48 ($648) with ABC at $200 and 30 days left, at the same 30% implied volatility. The model gives it a delta of -46.57 ABC shares.

Now try three ways of totalling the two:

• Raw delta sum: +113.14 + (-46.57) = +66.57 "shares". That suggests the account is long. But 113 shares of a $50 stock and 47 shares of a $200 stock are not the same unit, so the sum means nothing.
• Dollar delta: XYZ is +113.14 x $50 = +$5,657; ABC is -46.57 x $200 = -$9,314. Net: -$3,657. In dollars, the account leans short.
• Beta-weighted delta: next section. It gives a third answer: almost flat.

Three methods, three different signs or sizes. Only the last one tries to answer the question most traders are actually asking: what happens to my account when the market moves?

How do you calculate beta-weighted delta?

Pick one index to measure everything against. This example uses a hypothetical S&P 500 index fund priced at $500, with hypothetical betas of 1.2 for XYZ and 0.8 for ABC.

The price ratio converts each stock's shares into index-fund shares of the same dollar value. The beta then scales for how far each stock tends to move when the index does.

How can you check a beta-weighted delta?

Run a market move through each position by hand. If the index rises 1% ($5) and the betas hold, XYZ rises 1.2% ($0.60) and ABC rises 0.8% ($1.60).

• XYZ book: +113.14 x $0.60 = about +$67.89.
• ABC put: -46.57 x $1.60 = about -$74.52.
• Net: about -$6.63.

The beta-weighted figure predicts the same thing: -1.32 index shares x a $5 move = about -$6.60, with the small gap down to rounding. That match is the whole point of beta-weighting. One number now stands in for the account's response to the market, which you can compare from day to day.

A guest article on Cboe's site about sizing XSP index-option hedges uses the same idea, weighting each stock by its beta to estimate how a portfolio moves with the S&P 500 (Cboe guest article on beta weighting).

What does beta-weighted delta not tell you?

Beta-weighted delta is a useful summary with real blind spots:

• Stock-specific moves. A near-zero beta-weighted delta does not protect the XYZ book from a bad XYZ earnings report. If XYZ alone falls $5, the book loses hundreds of dollars and the ABC put does nothing.
• Beta is historical. It describes how a stock has moved, not how it will. Betas can change, and in sharp selloffs many stocks move together more than their betas suggest.
• It is still delta. It is a small-move estimate. Gamma changes every delta behind it as prices move, so a large market move can leave the account far from neutral.
• It depends on your inputs. A different index, a different beta source or a different lookback gives a different number. Pick one setup and keep it.

Does OptionsPro show beta-weighted delta?

Not today. The Portfolio Greeks card on the Risk & Insights page (Pro) adds up raw option deltas across your open positions; it does not beta-weight them or include shares. To get a beta-weighted figure, take each stock's net delta, apply the formula above, and add the results in a spreadsheet or by hand. Many brokerage platforms also offer a beta-weighting view, and they differ in the index and beta source they use, so check yours.