Archimedes Finance

Become a better investor

The decay of time

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

I understand that price movements introduce risk to options. What is another big risk?

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, provides a charm that helps usher in nights of mischievous with friends and the change of seasons. In a few weeks, Halloween would have passed and Christmas music would have started 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.


The three takeaways for this lesson are:

  • Learn about the risk of time decay
  • Understand why short-term options are the riskiest
  • Gain basic knowledge of how to manage theta

Avoiding losing our hard-earned money to accelerating theta decay can be the difference between a good option bet or big losses even when we were right.

Why time decay?

Options have both intrinsic and extrinsic values. Intrinsic value is based on if the option is in-the-money or out-of-the-money. The extrinsic value is the value that's found in volatility over time. In a simple way, we can think about the extrinsic value as the optionality left in our options contract. As in, is there a chance for a radical outcome? This chance diminishes as the window of time shortens, e.g. it's a lot more likely for us to experience a hurricane sometime within our lifespan as compared to a week from now. As the chance diminishes, the diminishing extrinsic value of our options results in a drop in premiums for our outcome. To understand how much, we need to revisit the Greek theta.

Let's use the same working example covered in the price movement lesson to understand how theta applies to us.

untitled image
Call option on Robinhood

Percent decay

As a refresher, theta is a measurement of time decay for an option on a daily basis. 

In the in-the-money call option above, our premium is $1.86 and we have a theta of approximately -0.17. This means that if we keep the effects of delta out, the contract loses $0.17 worth of value every day. So again, even if the stock price does not drop and holds steady at $395.86 per share, this call option would drop to $1.69 ($1.86-$0.17) tomorrow. It's also important to know that tomorrow, the theta will most likely be different.

To complicate matters further, time decay is felt differently depending on the intrinsic value of the option.

Accelerated decay

At-the-money options experience accelerated theta decay.

At-the-money options

In the graph of the extrinsic value, we can see that the decay greatly accelerates when there are 30 days left before maturity. As a beginner, we could be lured into a false sense of security when we are tempted to buy at-the-money options with a short expiration date. After all, at-the-money options are usually more affordable than in-the-money options and are generally safer than out-of-the-money options. Unless stock price movements created big delta profits, we would have ended up losing a lot of money to theta decay.


linear decay

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

Options time decay: it does not affect options the same way

In the graph above, we can see the effects theta decay has over the time value of options with different intrinsic values. Deceivingly, our eyes might play a trick on us—the decay may look like it affects out-of-the-money options less than at-the-money options. While this is true for the tail end, the decay for out-the-money actually starts at a much faster rate (steeper line) and is distributed evenly. Put simply, we lose much more every day at a predictable rate. If we decide to invest in options, this is a graph we should memorize or revisit regularly.

Theta decay does not discriminate and affects both put and call options equally. It's also not a risk that we can hedge against since time only occurs in one direction. Understanding the basics of theta decay will help us manage our risks better when it comes to options trading. 

A few takeaways:

  • Short-term options (30 days or less to maturity) are risky and should be considered as lottery tickets.
  • Medium (30 -180 days to maturity) to long term (180 days +)at-the-money options is the most effective management of theta decay
  • Theta decay is predictable for OTM and ITM options, and we can calculate the delta needed to offset theta
  • It's often better to sell an option at a loss early than to hold it and hope for a turnaround.

 In advanced lessons, we will cover how we can sell options to capture theta decay on premiums.

At Archimedes, our goal is to make investment literacy accessible and free for everyone.

Join our investment learning hub for more free lessons like this, connect with our trusted community, and get hands-on experience by playing a game!