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Intro to Greeks Part 2: What is Theta?

by | Jan 4, 2022 | Strategy

Furthering the discussion on Options Greeks, after my last post about Delta the next most important Greek to options traders is Theta. Understanding how time passing affects an options price is crucial in determining how you select an expiration cycle and what strike prices and overall strategy you construct for a trade. A lot can impact an options price but one thing that is a certainty is that time will pass each day and that is where theta comes in. 

What is Theta?

Theta is the extrinsic value decay of an option, assuming all other factors stay equal. Since we know options are made up of both Intrinsic Value and Extrinsic Value and at expiration an option only has intrinsic value that means theta will be more of a factor the closer we get to expiration of an option. Theta is the option Greek that shows what amount the option will decrease with the passage of each day. 

This signifies a risk to the option trader because options are decaying assets. This simply means that prices will decline based on the passage of time. If you are an options seller then theta becomes your friend as you have increased potential to make money and buy back options at a lower price than you sold them for simply from time passing. If you are an options buyer then you are working to combat theta as your stock needs to move enough (delta) to offset the theta decay of the option you purchased. Both methods can work if used properly but theta will always be constant in an option since it has an expiration date. Think of an hourglass with sand draining away with each passing second. Or a bag of ice cubes tossed into a pool in the hot sun. Those ice cubes will melt away with each passing hour. That’s theta decay.

Another common example is using insurance since options are basically insurance contracts against stock positions. When you buy an insurance policy for your house you might consider buying 6 months of time for example. If nothing happens to your home in that 6 month timeframe then the time passed and the contract is now set to expire worthless. It served its purpose in insuring your asset for a specific set of time but since no damage was claimed, the insurance company collected that full premium which you paid. The theta of the contract was simply the daily decay you paid to be insured. Insurance companies in theory are just selling a bunch of options contracts and hedging around the risk of disaster.

The cool part about trading options is that you can be the insurance company or casino on a smaller scale and sell options to benefit from theta decay. As long as the stock does not move more than expected, an option value will decrease based on theta passing. Since extrinsic value decaying favors the seller, it’s a positive value for short option trades and theta is a negative number for long options. Theta also changes based on how close to expiration an option is. 

As the theta decay curve below shows, time value decay accelerates much more within 6-8 weeks prior to expiration. Roughly 45-60 days to expiration sees an increase in the magnitude of theta decaying with less than 30 days picking up speed even further. Options that have 4-6 months of time left will still have theta decay but the effects are much less pronounced that far out. The closer you get towards 2-3 weeks to expiration the steeper the curve but also the more gamma risk that enters the picture. Which just means theta won’t offset a potentially sharp delta move in the underlying stock.

The more time until expiration then the less theta will be. This is because theta is less of an impact the further out in time you go. If you have ever bought an option with 30 days of time left you know the theta played a much larger role on price movement and decay versus an option you might buy with 60 or 90 days of time remaining. If you haven’t done the comparison, it’s an interesting and educational exercise. 

To illustrate this let’s look at the example below with Apple (AAPL). The options chain shows the 180 calls at 4 separate expiration dates and the corresponding differences in theta values. From the weekly January 7th expiration with 3 days left to the longer dated March contract expiring in 73 days. You can see that the front week options expiring in 3 days have a theta of 38, which means the option contract will lose $38 per day as time passes, and all else is equal. This is a very large proportion of what the actual option is worth. Then going out to 17 days cuts that drastically down to a theta of 12. Going out to the February options with 45 days of life cuts this even further to just an 8 theta. Then the difference between Feb and March is not as pronounced since the theta in March for this at-the-money option is 6. The difference between 45 days and 73 days till expiration is not much different but if you compare the January to the March theta it’s wildly different. This is why it’s often best to buy time if looking for a directional stock move to play out over time. Buying an option with 17 days left will be impacted far greater by theta decay as shown here.

To further show the impacts of theta decay here is a visual with AAPL stock again using the price of the February 185 calls as of 1/4/22. These calls have never been in-the-money since AAPL has never yet traded above 185 as I write this. However, the price of the 185 calls have changed quite a bit over time. Theta is a large reason. On December 10th, AAPL stock closed roughly at 179.50 and the Feb 185 calls closed at about $7.00. As time has passed in the following 3 weeks, AAPL has traded around the same level and on January 4th closed about the same price just under 180. While the Feb 185 calls are now worth just $4.90. That’s a 30% decrease in option value in just 3 weeks all while the stock is unchanged! That’s the power theta and time passage. This is also why being a net options seller is so advantageous if you can stomach the swings and a key part to this is position sizing adequately. Overall if being an options net buyer, it often pays to use spreads because even buying a call spread instead of just a long call tends to offset most if not all the theta decay effects of a long option.

Takeaways:

  • Theta is the rate of decay of an option’s extrinsic value given a one day passage of time.
  • Theta is non-linear and is a number that accelerates the closer the option gets to expiration. 
  • The rate of theta decay tends to be more noticeable with 30 days or less until expiration.
  • Options sellers see theta as a positive number and option buyers will see theta as a negative number.
  • Using multi leg spread strategies is useful to combat the passing of time and thus theta affecting the option trade.