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.
To learn more options Greeks and how they can help you choose the right options strategy, check out our lesson on The Greeks and podcast, Which Options Greeks are the Most Important?
Part 2: 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.
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? As we’ve established, 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.
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.
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.
Part Three will consider portfolio theta and think about theta as a percentage of portfolio value to create a theta tailwind.
*Chen, D., & Sebastian, M. (2012). The option trader’s hedge fund: A business framework for trading equity and index options. FT Press.