Don’t Follow the Money (Follow the Greeks)

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:

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.

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

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.

• 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