We are going to learn to speak some Greek...or at least a letter. 

If you’ve poked around our the tastyworks trading platform, you may have seen the word “Delta” on the table trade page with some corresponding number like “34.85 Δ”.

The numbers listed are the deltas of each selected option, and the Δ symbol next to the numbers is the Greek letter that you will be learning about - delta. 

Seeing another language might initially be confusing, so if it relaxes your mind you can think of it as a triangle and we can brush up on our Greek later. 

You don’t necessarily need to know what delta is to trade options. However, once you start putting on positions, knowing about delta will make your trading life a lot easier.

What Does Delta Tell Me?

Instead of going through different positions and strategies to figure out which way you need the market to go to make money, delta will give you a snapshot of this information for each position, strategy, and ultimately your overall portfolio.

On the simplest level, delta (positive or negative) tells us which way we want the underlying to go to make money. 

A positive delta is listed in tastyworks as a number and a triangle “34.85 Δ” and a negative delta is listed with a minus sign before it “-22.39 Δ.”

To answer our question on a very basic level, delta simply tells you this:

  • Positions with positive delta increase in value if the underlying goes up
  • Positions with negative delta increase in value if the underlying goes down

Portfolio delta and market direction

Looking at the beta weighted delta of your portfolio makes it easy to see if your assumption of the market (bullish, bearish or neutral) is in line with the positions you currently have in your portfolio.

You can see in the snapshot to the right, my beta weighted delta is 7.80 (it is beta weighted to SPY). Translated, that means that means that for every $1.00 that SPY goes up, it is estimated that my portfolio will go up by $7.80 (we'll look at this calculation more in the next section).

If you're bullish on the market, you want to put on positions with a positive delta and if you are bearish on the market, you will want to put on positions with a negative delta. 

I like to think of it as wanting the underlying to do what my delta shows me. If my delta is positive, then I want the market to go up (positive market move). If my delta is negative then I want the market to go down (negative market move).

Now that you know positive and negative delta correlate with which direction you need an underlying to move, let's look at what the number next to the delta symbol represents.

What does the delta number represent?

The delta number is how much the option price will change if the stock moves $1. If a stock goes up $1 and an option has a delta of “0.50 Δ” then the option price will increase by $0.50. Every additional dollar the stock goes up the option will increase by its delta value. If the stock goes up $10 the option will go up in price by $5.00, assuming the delta value remains the same.

We know that the option will increase in price because it has a positive delta and the stock has gone up. We calculate how much the option price will go up by multiplying the delta, “0.50 Δ”, by the amount the price has changed, “$10”, (0.50 * $10 = $5.00).

If the stock had instead gone down by -$2, we know that we're losing money because our position has a positive delta and the stock has gone down. We calculate the amount of loss by multiplying the option delta by the stock price decrease, (0.50 * -$2 = -$1) to get a -$1 loss.

DOES STOCK HAVE A DELTA VALUE?

We have briefly discussed the delta of options, but does stock have delta?

Yes!

If I own one share of stock and the stock increases $1, my one share of stock will also increase $1. Each share of stock has a direct one to one relationship with how the underlying moves, giving it a delta of “1.00 Δ”. One difference in stock delta is that we have to multiply the delta value with the amount of shares we have. One share of stock is 1.00 Δ, but one hundred shares of stock is 100.00 Δ. This is where it can get tricky, since option deltas are displayed on a per-share basis, meaning the range of delta will never exceed 1.00Δ or -1.00Δ for options. Since stock deltas will always be 1.00Δ or -1.00Δ, we can simplify the calculation:

Shares * Stock Price Change = Change In Price of Position

If a stock goes up $2.35, we can use the above equation to calculate our gain by multiplying the price change by the delta, (1 * $2.35 = $2.35). Two hundred shares of stock have a total delta of 200.00Δ and the same underlying move would lead to a real total price change of $470, (200 * $2.35 = $470). A stock’s delta is not much use when calculating a pure stock position. However, for multiple positions that combine stock and options it’s important to incorporate the stock delta to get an overall underlying position delta.

The farther a delta position is from 0, either positive or negative, the greater the position will fluctuate with moves in the underlying. As we know now, the delta value is multiplied by the change in the underlying to determine price change. A bigger delta, or a bigger change in the underlying, will increase the total price change. 

The larger the delta position, the more risk you have if the underlying moves against you. If the delta position is “0.99 Δ” and the stock goes down -$1.00 the position will lose -$0.99. Higher levels of risk come when multiple positions have deltas that combine together to compound moves in the underlying. 

If someone had 10 option positions each with “0.80 Δ” they would have a total delta position of “8.00 Δ”. This is the theoretical equivalent to 800.00Δ of stock, or 800 shares. They would lose -$8.00 or $800 for every $1 the stock went down. Delta positions combine as long as they are in the same underlying. It is crucial to always remember that one option contract controls 100 shares of stock.

0 shares of stock is “0.00 Δ”

100 shares of stock and an option with “0.50 Δ” is “1.50 Δ” total deltas

100 shares of stock and an option with “(0.50) Δ” is “0.50 Δ” total deltas 

Talking about deltas might feel like speaking Greek now, but with a little practice it will feel natural. Once you get comfortable understanding how price movements affect your positions, you can look at more advanced strategies like trading delta neutral positions and beta weighting your portfolio.

Now if I can just learn the Greek for "Where is the hotel?" …

Recap

  • Positions with positive delta increase in value if the underlying goes up
  • Positions with negative delta increase in value if the underlying goes down
  • An option contract with a delta of 0.50 is theoretically equivalent to holding 50 shares of stock
  • 100 shares of stock is theoretically equivalent to an option contract with a 1.00 delta

Learn more trading strategies by watching Step Up to Options