Even your best trading plans can change because options greeks such as delta, theta, and vega are constantly changing. if you have a portfolio with many positions, managing trades can be difficult. These guidelines can help keep you on track.

By thinkMoney Authors
March 30, 2020

Photo by Dan Saelinger

- Understand how options greeks such as delta, theta, and vega can change and why you have to keep an eye on them when trading options
- Be aware of the benefits of beta-weighting your portfolio
- Know how to evaluate overall risk to determine how much an option can impact your portfolio’s risks

Hey, option trader! This article is for you. It doesn’t matter what type of options strategy you use—long calls, covered calls, short puts, protective puts, two-legged, three-legged, or four-legged spreads.

Generally speaking, three things govern the success (profit) or failure (loss) of options trades—directional bias, time, and changes in volatility (vol). In options trading lingo, that’s delta, theta, and vega. But you know that already, right? Well, you might know the textbook definitions of options greeks. But do you know how they change, and why you have to stay closely engaged with your options trades?

Stock prices move up, down, or don’t change at all. Time moves forward relentlessly. Vol, like stock, moves up or down (or not). These three things come together in options trades in different proportions and at different times in the options expiration cycle. Delta, theta, and vega, like all options greeks, are dynamic. In effect, they change when the stock price or vol changes and as time passes. For example, a short put is a bullish strategy. But short puts don’t all have the same exposure to these three elements. Let’s explore why.

Say stock XYZ is trading for $200. Compare two short puts—a 195 put with 60 days to expiration and a 195 put with 10 days to expiration. Same stock, same strike, different expirations. But their deltas, thetas, and vegas are significantly different. Assuming the two options have the same vol, the 195 put with 60 days has a theoretical delta of-0.39, theta of 0.06, and vega of 0.62. Meanwhile, the 195 put with 10 days to expiration has a theoretical delta of -0.26, theta of 0.13, and vega of 0.21. The delta of the 195 put with 10 days is a bit lower, but its theta is double, and vega is one-third of the 195 put with 60 days.

The option with 10 days to expiration has less directional bias, greater sensitivity to time passing, and less sensitivity to a change in vol than the option with 60 days to expiration. More important, these differences in the greeks are nonlinear with respect to time. That means, for example, that if one day passes and the stock price and vol stay the same, the delta of the 195 put with 60 days to expiration will change a small amount. But the delta of the 195 put with 10 days to expiration will change more. Theoretically, the 195 put’s delta with 59 days to expiration is still -0.39 (almost no change after one day passes), while the 195 put’s delta with nine days to expiration is -0.24 (changes by 0.02 after one day passes).

Looking at it another way, suppose you sold that 195 put when it had 60 days to expiration because the stock moved up and vol was dropping. Then 50 days later, assuming no change in the stock price or vol, when the option has 10 days to expiration, it’s a profitable trade because of theta. But holding that short put in expectation of a vol drop may not seem like such a smart strategy now that the put’s vega is one-third of what it was when it had 60 days to expiration. If vol does drop, the short put with 10 days to expiration may be showing a profit, but not as much as from short theta. The vol drop might have been more helpful when the put had 60 days to expiration. In other words, the nonlinearity of delta, theta, and vega means that things change.

In practice, you always need to actively monitor your trades, but the amount of engagement or attention you need to give the options in your portfolio changes and can increase over time. The way you treat those trades changes, too. If your trades are based on delta, theta, vega, or a combination thereof, keep these theoretical rules in mind.

**Rule 1.** Delta moves toward 1 or 0 as time passes. The delta of an at-the-money (ATM) option is relatively stable at 50, no matter how many days to expiration the option has. If an option is even slightly in the money (ITM), its delta will move toward 1 as expiration approaches. The delta of an out-of-the-money (OTM) option will move toward 0. This assumes that only time is passing and stock price and vol don’t change.

**Rule 2.** Theta increases as time passes and the option gets closer to expiration. But that increase is greatest for ATM or closer OTM options. Theta likewise decreases for further OTM options. If an option is further OTM and its value is small, its theta could drop as time passes.

**Rule 3.** Vega decreases as time passes and the option gets closer to expiration. Vega for OTM options is less than vega for ATM or near-the-money options all else equal.

To see these concepts in action, consider a simple portfolio of two stocks—long 100 shares of FAHN and long 100 shares of PHYL—with covered calls sold against them. (This portfolio is for illustrative purposes only and is not diversified.) Even with only two stocks, it can be helpful to beta weight the deltas for a theoretical estimate of how much risk each one adds to the portfolio in apples-to-apples terms.

For instance, if you beta weight your portfolio to the S&P 500 Index (SPX), maybe the PHYL position has a delta of 6.01, a theta of +0.45, and vega of -0.55. The FAHN position has a delta of 1.37, a theta of +2.78,and vega of -20.91 (see figure 1).

In terms of the beta-weighted delta, PHYL has more theoretical risk in the portfolio than FAHN, while the FAHN position is contributing more positive theta and negative vega. Perhaps you want the two stocks to contribute equal amounts of beta-weighted delta, theta, and vega. To do that, you could reduce PHYL’s delta and increase its theta and vega, and/or increase FAHN’s delta and decrease its theta and vega.

Where are those deltas are coming from? In PHYL, it’s the long stock and a short 155 call (covered call). But that covered call is far OTM and close to expiration with only eight days left. We know that a call’s delta is lower the further OTM it is, and the OTM call’s delta decreases as expiration approaches. Compared to the delta of PHYL’s long shares, the short call’s negative delta isn’t very big. Also, its theta and vega are relatively small.

One way to reduce PHYL’s delta might be to look to roll the short call (i.e., buy to close the existing short covered call and sell to open a new covered call) to a further expiration at a lower strike price. Rolling the short 155 call to the short 140 call with three more weeks to expiration takes the beta-weighted delta of the PHYL position to 5.08, its theta to 1.73, and its vega to -10.67 (see figure 2).

Now let’s look at FAHN. It’s long 100 shares of stock, short a 135 call that’s ITM, and expires on January 17, 2020. That ITM call has a large short delta, which is reducing the FAHN position’s beta-weighted delta. And it’s still close enough to the stock price to generate relatively high theta and vega. To increase FAHN’s delta and reduce its theta and vega, you might consider rolling the short call to a higher strike price in the same expiration. Rolling the short 135 call to the 155 call with the same expiration takes its beta-weighted delta to 4.63, its theta to 1.91, and its vega to -17.63.

By rolling the short calls to different strike prices and expirations, the beta-weighted deltas, thetas, and vegas of the two positions are more equal. As time passes, the stock prices will likely change, and vol may move up or down. The two stocks may become unequal again—so the short calls might need to be rolled to different strikes and expirations to get them back in line. In practice, this doesn’t mean you roll the options in your portfolio every time the greeks change. All that might do is run up commissions and transaction costs, and liquidity is never guaranteed to allow for it.

When you step back, you can better determine how much risk exposure you want your portfolio to have overall. Analyzing how much each position contributes can help you create a comprehensive portfolio management strategy. With time, you’ll be able to look at an option, see its impact on your portfolio’s risk, and adjust accordingly. To get started, consider logging in to your account and monitoring your positions every day to stay more in control.

- Understand how options greeks such as delta, theta, and vega can change and why you have to keep an eye on them when trading options
- Be aware of the benefits of beta-weighting your portfolio
- Know how to evaluate overall risk to determine how much an option can impact your portfolio’s risks

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