Theta Options

Time value. Theta. Theta burn. Time decay. How does time until expiration affect options pricing? How does theta burn change as expiration approaches? What does theta look like for an options portfolio? We explore how you can use time value to your advantage--or at least better understand its impact on a portfolio of options contracts.

Part one: Introduction to theta

Let’s start by defining theta and describing how it works. An option contract’s value is a combination of its intrinsic value and extrinsic value. Each of these two components of an option’s price, intrinsic and extrinsic value, have their own valuation calculations.

Intrinsic value refers to a contract’s moneyness. Yes, “moneyness” is actually a thing in options trading, and it’s important. Moneyness is the relationship between the contract’s strike price and the underlying security’s price.

The more a contract is in-the-money, or the closer a contract is to being in-the-money, the greater its value.

Extrinsic value refers to time value, volatility, interest rates, and dividends. Naturally, these are a bit more complex, though not impossible, to calculate compared to the simple moneyness calculation for intrinsic value.

Options traders tend to focus most on intrinsic value, time value, and volatility.

What is theta?

Theta represents the time value decline of an options contract. To help you remember: the “T” in theta stands for “Time.”

How does theta behave?

As expiration gets closer, the time value of an options contract decreases.

Before expiration, the time value of an option is at least 0. The longer the time until an options contract expires, the greater the opportunity for the underlying security’s price to move and increase its intrinsic value, so the contract has more time value. Basically, with more time on the clock, more price movement can happen.

Time decay, theta burn, and theta decay are synonymous and refer to the decline in the value of an options contract as expiration approaches. Time decay is non-linear, meaning the rate of change increases as the options contract approaches expiration. 

The time value of an options contract decreases at an accelerating rate as expiration approaches. For example, time decay increases more rapidly from 60 to 30 days than from 90 to 60 days.

Think about theta like a bike rolling down a hill. At the top of the hill, the bike begins rolling slowly. As the bike continues down the hill, it picks up speed, going faster and faster towards the bottom.

While an option’s time value decreases over time, other extrinsic factors, like implied volatility, may increase as expiration approaches, offsetting or exceeding theta decay. Still, it is important to know options are decaying assets and lose time value daily.

How do you calculate theta?

Theta is quoted in dollars and represents the amount the option’s price will decrease each day. For example, a theta value of -0.02 means the option will lose $0.02 ($2) per day. Theta is always represented in negative terms because the portion of an option’s premium related to time is always going down.

Theta value is smaller further away from expiration and is not constant--it accelerates the closer it gets to expiration. Theta is an advantage for the option seller and a disadvantage for the option buyer.

Circling back to the moneyness discussion from the introduction, theta varies depending on a contract’s strike price relative to the underlying asset’s price. This options Greek is known as delta. While theta decay occurs across all strike prices, the fastest decay occurs for contracts at-the-money. Contracts further out-of-the-money decay more linearly. 

Delta constantly changes as the underlying price changes. Changes in delta also impact an option contract’s theta. For example, an option with a delta of 0.30 will see increased theta decay if the underlying price changes and that option’s delta decreases to 0.15. “As an option moves from being logically in-the-money to an option that cannot end up in-the-money, this is when options give up the bulk of their value.”* Directly applying this concept to a strategy like an iron condor, as expiration approaches and the iron condor’s wings have a lower probability of becoming in-the-money, the bulk of the theta decay occurs.

How does moneyness impact theta decay?

For at-the-money options (~0.50 delta), as the time until expiration decreases, theta not only goes up but does so at an increasing rate.

For out-of-the-money options (~0.30 delta), theta increases as the time until expiration decreases, but the rate of change is less than the at-the-money options.

For further out-of-the-money (~0.15 delta), theta decay is more linear and the rate of change is largest at a point further out in the expiration cycle.

Why theta matters to options traders

If you’re an options buyer, it’s important to know how delta relates to theta. As an options buyer, the time and direction of the underlying security’s move matter. Buying options closer to expiration and near the money brings with it rapid theta burn.

If you’re selling options, theta is a tailwind.

Time value decay varies across strikes and maturities. What is your outlook, what is your timeframe, and what are you trying to accomplish? The call option or put option you sold’s strike price and time until expiration will greatly affect how quickly you may be able to close the position for a profit.

Remember, theta is just one piece of the puzzle, just one of the options Greeks. At-the-money options may have the most theta decay, but they also have the most gamma and vega. Options Greeks do not operate in a vacuum.

Part two: Theta by position type

Part One covered the basics of theta and examined theta decay across different expiration dates and deltas. Now, we'll examine theta by position type and compare theta burn for single-leg positions, credit and debit spreads, and multi-leg positions. 

Single leg options are the building blocks for more complex positions. Long calls, long puts, short calls, and short puts have one “leg” or component to the position. Multi-leg positions have two or more legs. Multi-leg positions are typically entered simultaneously but can also be “legged into” by entering multiple single-leg transactions. Single-leg positions have a directional bias, while multi-leg positions may be bullish, bearish, or neutral.

We’ll work through a series of examples, looking at theta for different position types, maturities, and deltas. The goal of this exploration is to understand the connection between strategy selection and theta’s impact on your portfolio value.

Single-leg position theta

Theta for single-leg positions is relatively straightforward. If you are long a single-leg position, a long call or long put, theta represents the amount the option’s price decreases each day. A theta value of -0.02 means the option will lose $0.02 ($2 in notional terms) per day. If you are short a single-leg position, you sold-to-open a short call or short put position, theta still represents the amount the option’s price will decrease each day, but the time decay works in your favor as an options seller. 

The following examples are snapshots of end-of-day data on SPY for monthly contracts with approximately 30, 60, and 90 days until expiration. If you look at similar contracts today, theta might be different for at-the-money, out-of-the-money, and far-out-of-the-money contracts. Why? Higher implied volatility levels result in higher theta values, and lower implied volatility leads to lower theta values. We’ll dive deeper into this in a later blog. 

A long at-the-money SPY call option with approximately 30 days until expiration has a theta of -0.16. That’s $16 of daily theta decay on a contract priced at $8.06. Remember from Part 1, if SPY remains at or near-the-money to this contract as expiration approaches, the theta decay will accelerate. As you move away from strike prices at-the-money, theta declines. A 0.30 delta call has a theta of -0.12, and a 0.15 delta call has a theta of -0.07.

A portfolio of long single-leg positions is subject to a lot of time value decay.

Remember, all else being equal, theta is the continuous erosion of a position's premium due to the passage of time.

Therefore, days of muted market movements can cause significant decreases in portfolio value as theta and vega decrease simultaneously.

Credit and debit spread theta

Consider a multi-leg, debit spread alternative. If you are bullish on SPY, a call debit spread with a long call purchased at-the-money and a short call sold $10 out-of-the-money has a theta of -0.06 because the at-the-money contract’s theta of -0.16 is partially offset by the short contract’s theta of -0.10. Recall that if you are long an options contract, theta works against you but if you are short an options contract, theta benefits you. A debit spread is still negatively impacted by theta, but the effects are less severe because of the short option.

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Now, consider a put credit spread where you are a net options seller. If you are bullish on the underlying security, you can sell a 0.30 delta put 30 days from expiration and buy a put $10 lower and out-of-the-money to create a risk-defined position. The credit spread has a slightly positive theta of 0.01 because the 0.30 delta short put’s theta is greater than the long put’s theta. Notice that as you go further out-of-the-money with the credit spread, the theta is essentially flat.

Out-of-the-money options lose more value to time decay earlier in the expiration cycle than at-the-money options that rapidly decay near expiration. Selling a 0.30 delta put credit spread with 60 days to expiration may initially have a flat theta as both contracts in the spread will likely have a similar theta value. But, as expiration approaches, the theta decay will diverge because the short option's theta will increase faster than the long option's theta.  

Alright. This all may seem a bit technical. So what? How does this affect you when trading options? Time decay accelerates at different points in a position’s life depending on many factors. Know your timeframe and choose your maturity prudently. Buying an at-the-money call option with limited time remaining until maturity will be significantly impacted by time decay. A put credit spread entered with 60 days to maturity may not seem to be impacted by time decay initially, but theta burn will increase over the life of the trade. 

Multi-leg position theta

As if there wasn’t enough to think about when trading options, there’s a world of strategies with more than two legs. These complex strategies with three or four legs may have a bullish, bearish, or neutral bias and are affected by volatility and time decay in different ways. Still, the overall concept we walked through in the previous section around net theta impact holds true, with some additional things to consider before placing your next trade.

Multi-leg positions, such as iron butterflies and iron condors, double up on theta decay because both sides of the trade benefit from theta burn. While there are many differences in outlook and risk/reward between iron butterflies, iron condors, and credit spreads, those differences relevant to this article relate to moneyness and outlook.

An iron condor has out-of-the-money wings, so the most time decay occurs when a wing's probability of ever becoming in-the-money decreases. This happens at different points in the trade depending on if you're trading daily, weekly, or monthly iron condors. On the other hand, iron butterflies are typically centered at-the-money, so their primary time value decay tends to happen closer to expiration.

How does theta impact other options strategies?

Credit spreads have a theta tailwind (positive theta) for the option seller, and debit spreads have negative theta.

Admittedly, it’s a bit more complicated than simply a positive or negative theta. Days until expiration, delta, and volatility’s impact vary for different strategies. As a result, theta’s impact on an option’s value varies depending on the type of strategy selected.

For example, strategies that start at-the-money, like iron butterflies or straddles, have greater theta burn at different points in the expiration cycle than an iron condor. This is because the short strikes of the inside wings on an iron condor are near or at-the-money and have higher rates of theta. Similarly, with two different contract expiration dates, calendar spreads will see the front-month contract decay faster than the back-month contract. Whether the calendar is a long (debit) or short (credit) spread significantly affects theta.

More specifically, a put credit spread with 45 days until expiration may have a positive theta burn of 0.01 ($1). An iron condor with 45 days until expiration may have a positive theta burn of 0.02 ($2) because two sides of the trade are decaying simultaneously. Yes, one position is neutral, and the other is bullish. But, when you are thinking about theta, remember that trade structure is something you can control and should be chosen intentionally.

Part three: Portfolio theta

Parts One covered the basics of theta and examined theta decay across different expiration dates and deltas. Part Two examined theta by position type and compared theta burn for various strategies. Finally, we'll consider portfolio theta and think about theta as a percentage of portfolio value to create a theta tailwind.

If you don’t already, you should pay serious attention to portfolio theta. The three data points I watch closest in my options selling portfolio are portfolio theta, portfolio delta, and available funds for trading. Everyone is different, and you may care about other metrics.

However, I try to maintain a balanced portfolio (portfolio delta close to 0), increase portfolio theta to create a theta tailwind, and keep an eye on cash reserves for volatility protection and future opportunities.

If you don’t have specific data points you watch for your portfolio, why not? The only way to know if your investment strategy or thesis is working is to measure its performance.

If you maintain a directional bias (bullish or bearish), does your portfolio reflect that bias? Naturally, you should look to measure what matters to you and your risk profile.

Theta tailwind

At the risk of dating myself and using an antiquated example no one has ever heard of, Captain Planet and the Planeteers was a 1990s American animated series with a group of heroes trying to save the planet. At the climax of each episode, the heroes would join together to summon Captain Planet (at least that is how I remember it). “With our powers combined,” they banded together to save the day. Every time I think about portfolio theta, I think, “with our powers combined.” Here’s why.

The combined theta of a collection of positions such as credit spreads, iron condors, iron butterflies, etc., results in portfolio theta.

As an options seller, portfolio theta is the tailwind that propels the portfolio forward with time on positions.

In Parts Two’s discussion of theta by position type, the slightly positive theta of a put credit spread or call credit spread may not have seemed super exciting. A 45-60 day, $5-wide put credit spread with the short put at 0.15 delta probably has a positive theta of 0.01 ($1 in notional terms) because the short put’s theta is slightly higher than the long put’s theta. This $1 doesn’t seem too exciting until you zoom out and think about a portfolio of similar positions. 

Consider a $10,000 portfolio comprised of risk-defined, $5-wide credit spreads with 45 days until expiration. If approximately 30% of the portfolio is held in cash reserves, that leaves $7,000 of buying power to enter positions.

Now, assume each $5-wide credit spread brings in $1.00 of credit. You could enter approximately 17 $5-wide credit spreads, each initially having a positive net theta of 0.01, while maintaining your desired cash reserves. 

With 17 positions, the portfolio theta is approximately 0.17 ($17). The $10,000 portfolio has a positive theta burn of $17 per day. $17 per day for 30 days is approximately $510 per month. That’s a really big number and represents about 5% of the initial portfolio value.

But that’s not really accurate either since theta is not fixed; it’s fluid and the rate of decay generally increases as expiration approaches.

Therefore, as expiration approaches and theta increases, it creates accelerating portfolio theta, likely rising above $20 per day. Seems a bit more exciting now, doesn’t it?

The full impact of seemingly small theta values from individual positions expanded to the whole portfolio over time is significant.

Theta, and your awareness of it, is much more important than you might have otherwise assumed and is most certainly a driving force for positive returns in an options selling portfolio.

Of course, there will be times when these credit spreads are challenged, need adjusting, and still result in a loss. This is a natural part of the trading process, and it’s going to happen (trust me, I know from experience).

Just like an insurance company that insures homes anticipates periodic losses but seeks consistent, adequate premiums to prepare for those losses, we traders should strive to mimic this preparedness ideology in our own portfolios.

Similar to the insurance company collecting premiums to prepare for losses, I think of the theta tailwind as my head start, preparing my portfolio for potential losses during times of increased volatility.

Building a portfolio of high-probability, net positive theta positions is the foundation of my options selling approach. There’s no free lunch, but theta burn feels like a headstart and a proactive way to use time decay to benefit your portfolio.

Next steps

We’ve broken down the theta discussion into three parts. We explored how you can use time value to your advantage--or at least attempt to better understand its impact on a portfolio of options contracts.

Different types of positions are impacted by theta in different ways. As you put all the pieces of your portfolio puzzle together, consider your goals. Is your goal directional bias or income generation?

You’re putting your hard-earned capital to work, so think conceptually about what you are trying to accomplish and then deploy the right tools to give you the highest chance of success at reaching that goal.

Education is foundational to a business-like approach to investing. It’s easier to focus on what you know than to dig into something new. Options Greeks may not be the most exciting thing to study. Ignoring them, though, is not a long-term recipe for success.

Where should you go from here? Consider learning new options selling strategies. Find a topic you don’t know much about, dig deep to develop a better understanding, and use your new knowledge to make progress towards your investment goals.

References:

*Chen, D., & Sebastian, M. (2012). The option trader’s hedge fund: A business framework for trading equity and index options. FT Press.