The decay of time

Lesson in Course: Derivatives and options (advanced, 7min)

I understand that price movements introduce risk to options. Is there another big risk that I need to consider?


What it's about: The effects of theta or time decay on an option's price.

Why it's important: Accelerated theta decay loses value for the unprepared.

Key takeaway: Every option held loses value over time. This loss is accelerated in the last 30 days before maturity.

Many of us live in a country that celebrates Halloween where carved pumpkins have become an iconic doorstep decoration for many neighborhoods. The pumpkins, when lit, provide a charm that helps usher in nights of mischief with friends alongside the change of seasons. After a few weeks, Halloween passes and Christmas music starts to play on the radio. What's left of once cheerful or scary pumpkins are frumpy-looking orange messes that need to be cleaned up. The rapid decay over time catches many people off guard every year. 

997 Rotten Pumpkin Stock Photos, Pictures & Royalty-Free Images - iStock

Outside of pumpkins, time decay catches a lot of investors off-guard as well and it is a primary reason most inexperienced options traders lose money. Let's dive in and understand how time decay works.

Why does time cause decay?

An option's price includes both intrinsic and extrinsic values. The intrinsic value is the difference between the option's strike price and the stock price of the underlying depending on if the option is in-the-money or out-of-the-money. 

The intrinsic and extrinsic value of a call option

The extrinsic value is the remaining value that makes up the price and is highly dependent on the remaining time before the option reaches maturity. As the option gets closer to maturity, the extrinsic value of our options always diminishes to zero regardless if it's a put option or a call option.

In a simple way, we can also think about the extrinsic value as the opportunity left in our options contract. 

More time left means more chances for the unexpected

What are the chances for a radical outcome that changes the value of the contract? The chances diminish as the window of time shortens which impacts the extrinsic value. E.g., it's more likely for us to experience a hurricane sometime within our lifetime as opposed to encountering one a week from now. 

How much do we lose to time decay?

To understand how much time decay eats into the value of our options, we need to look at the Greek theta. Let's use the same working example covered in the price movement lesson to understand how theta applies to us.

Finding theta
$394 strike call option on Robinhood

The in-the-money $394 strike call option shown above is priced at $1.86. We can see that this option has a theta of approximately -0.17 which means that the contract loses $0.17 worth of value every day regardless of what happens to the underlying stock. For example, if the stock price holds steady at $395.86 per share, this call option's price would drop to $1.69 ($1.86-$0.17) tomorrow.

Theta's value changes every day depending on how much time is left before maturity. The rate at which theta changes depends on the type of option we hold.


Accelerated decay

Theta tends to accelerate and losses are magnified as the option gets closer to maturity. 

Theta accelerates over time

At-the-money options experience the most accelerated theta decay.

In the graph of the extrinsic value, we can see that the decay starts accelerating as we get closer to maturity—roughly 70% of the time premium is lost within the last 30 days.

The steep drop in value due to theta decay makes at-the-money options potentially dangerous to beginners. We could easily be tempted to buy at-the-money options with a short expiration date due to these options being low cost. Delta would tell us that we are looking at a 50/50 bet to mature in-the-money and we can justify to ourselves why we should take the risk. However, if the stock price stays steady (trades sideways), we would end up losing a lot of money to theta decay.


Not all options accelerate the same

Out-of-the-money and in-the-money options undergo slower theta decay and are more predictable.

In the graph above, we can see the effects of theta decay on options with different intrinsic values over a longer period of time. Our eyes may play tricks on us and it can look like theta affects out-of-the-money options less than at-the-money options since the blue line is the lowest. This isn't true. In reality, time decay affects at-the-money options more since more value is lost within the same time period.

If we decide to invest in options, these are some basic graphs we should memorize or revisit regularly.

Actionable ideas

Theta decay doesn't discriminate and affects both put and call options equally. Since time only moves forward, the only way we can hedge against theta risk is by selling options in a spread. A spread is an advanced strategy that simultaneously creates a short option position with a different strike price or maturity at the same time that an investor buys-to-open a position. We'll cover spreads more in advanced lessons, but for now, understanding the basics of theta decay will help us manage our risks better when it comes to buying options.

Helpful rules of thumb:

  • Short-term at-the-money options (30 days or less to maturity) have a higher risk of theta decay
  • Medium (30 -180 days to maturity) to long term (180 days +) options experience slower theta decay
  • Theta decay is more predictable for OTM and ITM options
  • When theta decay is high, the opportunity cost of holding onto an option is high