Don’t Follow the Money (Follow the Greeks)

When trading options you will need to consider price, time, and volatility at the same time. That means understanding the interplay of a few options greeks and how they play off one another. reflection in mirror: options greeks
5 min read
Photo by Dan Saelinger

Key Takeaways

  • Understand how options greeks move together through the life of a trade
  • Analyze how options greeks move in a long call and long call spread
  • Learn how to visualize your trade using the risk profile on thinkorswim® from TD Ameritrade

Here’s what we know. Options aren’t stocks. And you can’t just track profit and loss (P&L) in a vacuum based on what the underlying stock is doing—making it tough to figure out your exit strategy. For that, you’ve got to consider stock price, time, and volatility (vol), which are measured individually by the options “greeks”—delta, theta, and vega. Knowing how each greek works alone is one thing. You should also know how they play off one another during the life of your trade. Master this, and you’re well on your way to mastering the art of the exit.

Comparing Two Trades

Let’s examine the greeks with a holistic approach. We’ll consider two different trades—a long call and a long call spread—from the time each trade is placed, to three days later, and then at the end of one week. We’ll also look at what can theoretically happen to those trades if the stock moves up or down $5, or if the price is unchanged.

On the day of the trade, suppose the underlying stock is at $125, and both trades expire in 30 days. Out of the gate, the trades have the following greeks:

Price  $4.50Price   $4.50
Delta   +50Delta   +30
Gamma   +3Gamma   0
Theta   -8Theta   -1
Vega   +14Vega   +1
Remember, these are theoretical numbers. Transaction fees and commissions may apply.

What Happens to the Long 125 Call?

Three Days Later

  • If the stock’s up $5: The long delta works in this trade’s favor, and it benefits from gamma. The long gamma measures how much the delta increases as the stock moves higher. With an incrementally higher delta, a larger profit can potentially be gained. Delta and gamma drive profits as the stock moves higher, but theta is working against this trade. We haven’t assumed any change to the implied volatility (IV), so vega isn’t going to factor into the P&L. What if IV dropped five points? For starters, profits wouldn’t be as high—something to consider at the start of the trade.
  • If the stock’s down $5: Based on delta, the downward move means the trade will lose. But the long call starts with a +50 delta, and by the time the stock is down to $120, the delta has dropped to +32. Even though the trade is losing, it’s losing at a slower rate (because the delta is declining, as measured by gamma). Long gamma can help the trade profit faster if the stock is going in the right direction, and it can slow down the rate of loss if it isn’t. Theta, which measures the effect of time decay, remains a drag and is responsible for more losses. If there’s one silver lining, it’s that theta is dropping because the option is now out of the money—nothing to brag about. Vega is still positive, which might help cushion the losses if IV increases (as it sometimes does when stocks drop).
  • If the stock price is unchanged: When there’s no stock movement, the delta and gamma don’t play a role in generating the P&L. It’s only theta and vega. And because we’re not looking at IV changes, the only culprit here is theta.

Visualize Your Trade

To view your trade profile and the impact of greeks, go to the Analyze tab on thinkorswim from TD Ameritrade, add a symbol, and select Risk Profile to get started.

Seven Days Later

  • If the stock’s up $5: Delta and gamma will contribute to the trade’s profitability based on the same dollar move in the underlying. What’s different now is that a full week has passed. And that means theta’s going to have a bigger say in the matter.
  • If the stock’s down $5: At this point, there’s not much working in this trade’s favor. Delta is a loser, and gamma does what it can to help slow the rate of loss. But a full week of theta sets in and drags the whole trade lower. Any increase in IV would help offset losses because vega gets smaller.
  • If the stock price is unchanged: Delta and gamma don’t play a role with the stock price unchanged, so it’s only theta in this example (and vega if there are any changes to IV).

Greeks Cheat Sheet/Long Call

$120 (stock down $5)$125 (unchanged)$130 (stock up $5)
Trade Date +3Delta and theta contribute to losses; gamma helps slow the losses from the delta. Net result is a loss of $234.No movement over three days, so theta results in a loss of $27.The trade profits from delta and gamma, while theta plays the role of spoiler. The net result is +$268.
Trade Date +7Delta and theta contribute to losses as the trade loses $265, another $31 since trade date +3.After seven days and no stock movement, the loss is $63, which is an additional loss of $36 since trade date +3.Delta and gamma drive profits but are tempered by the additional losses from theta. The net result is a profit of $237, $31 less since trade date +3.
For illustrative purposes only.

What Happens to the Long 120-129 Call Spread?

Three Days Later

  • If the stock’s up $5: Again, the delta generates a profit with the stock moving higher, but it’s a smaller delta to start with because the spread nets the delta from the long and short calls. In fact, this is why all the greeks for the call spread are smaller. With a smaller delta, and virtually nonexistent gamma, the profits from the stock moving won’t be as high as the individual call trade. Theta isn’t going to be a drag on the long call spread profits because the trade has a slightly positive theta. Why? In a vertical spread, the option that’s closest to the at-the-money (ATM) strike will be most sensitive to theta, gamma, and vega. Here, the short 129 strike influences the trade more than the long 120 strike. Therefore, time helps. Again, assume no changes to IV. But it’s worth noting the vertical spread has a negative vega, which gets increasingly negative with the stock up $5. This provides protection against a vol drop that the long call doesn’t have.
  • If the stock’s down $5: Again, delta is the main reason this trade loses with the stock down. Although it starts with a lower net delta, there’s little to no gamma to help lower the delta much further. Theta has flipped from slightly positive to slightly negative because the long 120 strike is now closer to the money than the 129 short strike. Overall, this is a slower-moving trade, so the losses will be less compared to the individual long call.
  • If the stock price is unchanged: As with the long call, delta and gamma play no part, so it’s only theta at this point.
Seven Days Later
  • If the stock’s up $5: The spread has the smaller delta and little to no gamma. But notice what happens to the theta as the stock moves closer to the short strike and more time passes. Theta gets more positive, which means time is helping this trade. You won’t get this from the long call.
  • If the stock’s down $5: The smaller delta means lower losses, and gamma is negligible. Theta is still negative, because the stock is closer to the long strike.
  • If the stock price is unchanged: Delta and gamma don’t affect the trade. But because the short strike is closer to being ATM, the trade maintains a slightly positive theta.

Bear in mind, there can be multiple forces to consider when calculating or predicting the P&L of an option. Visualizing the greeks working together helps.

Greeks Cheat Sheet/Long Call Spread

$120 (stock down $5)$125 (unchanged)$130 (stock up $5)
Trade Date +3A smaller delta leads to smaller losses; gamma is still not involved, and theta hurts trades minimally. There’s a net loss of $150. With a positive theta of around $1 per day, the trade profits $3.Profits from delta; gamma has no real impact; and theta can claim it helped out some. The net result is +$153.
Trade Date +7Smaller delta and negative theta lead to a loss of $161, $11 more since trade date +3.With a positive theta of around $1 per day, the trade profits $6, compared to $3 at trade date +3.Delta and theta drive profits; short gamma is negligible. Net profit of $168, which is $15 more since trade date +3.
For illustrative purposes only.

Key Takeaways

  • Understand how options greeks move together through the life of a trade
  • Analyze how options greeks move in a long call and long call spread
  • Learn how to visualize your trade using the risk profile on thinkorswim® from TD Ameritrade

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