When trading options, one of the most important "Greeks" that we should concern ourselves with is "delta."

Collectively, the "Greeks" provide a way to link the sensitivity of an option's price with quantifiable factors.

Delta is an extremely dynamic member of the Greek family because there are so many different ways that this value can be applied.

Tom Sosnoff and Tony Battista take on the "delta" challenge in a recent episode of *Market Measures* and present the four most common ways that option traders use delta:

- Theoretical change in an option's price relative to movement in the underlying
- Underlying share equivalency
- Hedge ratio
- Probability of the stock expiring $0.01 beyond the strike of the option (in-the-money)

Aside from the four topics listed above, it's important to note that delta can also be used to denote directional bias. Positive delta indicates a bullish directional strategy, whereas negative delta indicates a bearish directional strategy.

Delta is also indicative of the degree of risk at stake - higher deltas equating to more risk and lower deltas equating less risk.

Beyond those directional and risk considerations, delta also has some more complex applications - the four bullet points above.

First, delta represents the amount that an option's price will change for every $1 move in the underlying stock. For example, a delta of 0.6 means that for every $1 the underlying stock increases/decreases, the option will increase/decrease by $0.60.

The second more practical application of delta is related to the concept described immediately prior. The delta of an option also tells us our approximate directional exposure in terms of stock. For example, a long call spread with a delta of .28 means that the position equates to 28 shares of long stock.

For option trades that utilize delta neutral trading, the delta additionally indicates the hedge ratio - the number of shares that need to be traded to hedge the option position with stock.

For example, if a delta neutral trader buys 100 calls with a delta of 0.50, that would mean the trader would need to sell 5000 shares of stock (100 contracts x 0.50 delta x 100 shares/contract = 5,000 deltas).

This makes sense because 100 contracts represents 10,000 shares (100 contracts x 100 shares/contract = 10,000 deltas). So if a trader is executing .50 delta calls, he/she would hedge the position half as many shares of the underlying.

In the *Market Measures* episode, Tom and Tony introduce another example involving selling 50 shares of SPY. In order to hedge that position, a trader could execute two different option trades to compensate for those short deltas - sell a put (gets long deltas) or buy calls (gets long deltas).

Under the "sell a put" scenario, a trader could sell two contracts with a .25 delta (2 contracts x .25 delta x 100 shares/contract = 50 deltas) or sell five puts with a .10 delta (5 contracts x .10 delta x 100 shares/contract = 50 deltas). In either case, the net delta will be 0 when combining the short SPY position with one of those two short put positions.

It's important to note that in this example, using 5 of the .10 delta puts to hedge the position carries more notional risk than selling 2 of the .25 delta puts.

Another common use of delta, which is more of a "rule of thumb," is to use the delta of an option to estimate the likelihood that the option expires in the money.

The example that Tom and Tony use in the episode is a .50 delta option that has a 50% chance of expiring at least $0.01 in-the-money, as illustrated below:

Although the multi-faceted application of delta may seem daunting for new traders, most find that with additional experience these four common uses of delta become almost instinctive.

Effectively, delta helps a trader understand how an option's price will change for a given change in the underlying stock price. Keying in on that relationship will similarly increase a trader's awareness of how to hedge those risks (hedge ratio) and the probability of an option expiring in-the-money.

We encourage you to watch the entire episode of *Market Measures* focusing on delta when your schedule allows. Additional information on delta, or any of the "Greeks," can be accessed through the "Learn" tab on the tastytrade website as well as the site's search engine.

Please don't hesitate to contact us with any questions or comments at support@tastytrade.com.

Happy Trading!

*Sage Anderson has an extensive background trading equity derivatives and managing volatility-based portfolios. He has traded hundreds of thousands of contracts across the spectrum of industries in the single-stock universe.*

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