Jun 23, 2023

# The Irrefutable Beauty of Options Delta

## Experienced options traders appreciate the predictive power of delta. Here's why ...

• Options delta gauges price movement, given the underlying stock movement.
• But options delta can also be used to approximate the probability of the options expiring in-the-money.
• Or it can measure directional bias at both the position level and the portfolio level.

In the world of trading, for every gimme there’s a gotcha, and Delta’s relationship with return provides a classic example.

### Option delta at the position level

The textbook definition of delta is that it measures how an options price changes when the underlying stock changes. But tastylive has two additional interpretations of this Greek. Traders can use delta as a quick approximation of probability and also to measure directional bias or exposure because it also represents the share equivalence of the options contract.

When looking at individual positions, we use delta as both a probability gauge and directional bias measure. When looking at the overall portfolio, we use delta exclusively as a measure of directional bias.

As an options trading veteran, if I’m considering a short put strategy at trade entry, I know a short put at the 35 delta will give me a probability of success of around 65% because delta gives me a quick approximation of the probability the option will expire in-the-money (ITM). As a premium seller, however, I ultimately want the option to expire out-of-the-money (OTM). So that my probability of success is 65%. If there is a 35% probability that what I don’t want to happen could happen, then there must be a 65% probability that what I do want to happen could happen, given there are only two possible outcomes: ITM or OTM.

Similarly, if I have a position on and the delta is 20, then I know this position will “feel” like holding 20 shares of stock, even though the full option contract is always for 100 shares of stock. This is because if there is still time left in the expiration cycle (which there always is), and some amount of extrinsic value in the option price (which there always is), the delta of the option will always be less than 100. In other words, the delta of an options contract can reach its full potential of 100 only if it is ITM and at expiration, when there is no time left and extrinsic value falls to zero.

### Option delta at the portfolio level

Lastly, delta as a directional bias can be used at the portfolio level by beta-weighting the delta to the SPY index. Doing this essentially converts your entire portfolio into an approximate SPY share equivalent. So, a portfolio delta of +150 feels like holding 150 long shares of SPY, and a portfolio delta of -200 feels like holding 200 short shares of SPY.

Jim Schultz, a quantitative expert and finance Ph.D., has been trading the markets for nearly two decades and hosts From Theory to Practice, Monday-Friday on tastylive. Dr. Schultz breaks down the mathematical relationships in the derivatives market and shows how to retail portfolios.

For live daily programming, market news and commentary, visit tastylive or the YouTube channels tastylive (for options traders), and tastyliveTrending for stocks, futures, forex & macro.

Trade with a better broker, open a tastytrade account today. tastylive, Inc. and tastytrade, Inc. are separate but affiliated companies.

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options before deciding to invest in options.

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