Tempus Fugit - Time flies. An understatement if I have ever heard one. Time moves in a smooth and continuous flow out of the past through the present and into the future. Options, by their nature, have a limited existence. The contracts have a beginning and a very definitive end at their expiration date. This move towards expiration can affect an option's price adversely, as it will have little time left before the contract disappears.
Option theta is how we measure the affect time has on an option's price. As we will explore theta does not have a linear effect on an option's price nor is it always accurate. With a clear understanding of option theta, we will know how our options will move through time and also when we should take certain option strategies at certain expiration dates.
Where To Find An Option’s Theta
Before we can even begin to define or talk about all the cool attributes of theta, you need to know where to find an option’s theta. An option’s theta, along with the other Greeks, come out of the option pricing model.
Due to the fact that Greeks are a byproduct of a calculation means they have a model risk. A model risk means; the outputs are only as good as the inputs. If you plug in the incorrect implied volatility, you can’t expect to receive proper Greeks.
Now, model risk in terms of option pricing and Greeks, is not a serious risk. Out of the 7 factors that affect an option’s price only one of them is unknown, implied volatility. It would be difficult to mess up the model so much that it throws off your Greeks.
It is more important to understand how Greeks are derived and that you can’t always trust the numbers for how they are.
The best place to find the theta of your option is through an option chain. An option chain displays all the calls and puts for a given expiration and underlying. You can usually customize your option chain to display the various Greeks that you are interested in. Most traders will use their option brokerage, but you can also use free tools such as Nasdaq.com to view an option chain.
What Is Option Theta
Theta is expressed as a negative number in terms of dollars. As each day ticks by the option's price will drop by the theta.
For example, you have a The Option Prophet (sym: TOP) long call at a price of $5.50 and a theta of -0.35. The next day our long call would be worth $5.15 and the day after $4.80. Theta will continue to drop the option price until it reaches expiration.
5.50(current price) – 1(days passed) x 0.35(theta) = $5.15
5.15(current price) – 1(days passed) x 0.35(theta) = $4.80
Depending on your position, the theta can be either positive or negative. If you are net long in a position your theta will be negative. As time passes your option will lose value which is not what you are looking for. However, if you are net short in a position your position theta will be positive. Being short you want your position to lose value, that is how you make money, hence a positive position theta.
The Theta Curve
As mentioned above, theta is not linear. That is to say, the affect theta has on an option's price is not straightforward and does not reduce an option's price by the same amount with every passing day.
The effect theta has on an option's price is not straightforward. It does not reduce the price by the same amount throughout the life of the contract. As the days pass, an option has less time to make a move and thus it will be worth less.
Let's take a second to think about this. If an option has 100 days till expiration, that is an eternity for it to make a move, so that option would be more expensive. Contrarily, if an option expires tomorrow then the time to make a move is very limited and the value of that option will be low.
When an option's time to expiration is under 20 days, the amount of theta begins to increase exponentially. This is worth noting, if you are long options near expiration you will be fighting an uphill battle against time. On the other hand, if you are short options near expiration, time will be your new best friend.
How Theta Changes Based On Time To Expiration
Now that we understand the theta curve, let's talk about when it lies to you. It turns out not all options have the same pattern for rate of decay. In fact, the ones that follow the path and chart mentioned above are just at-the-money options. Out-of-the-money options actually decay a lot slower and without the rapid acceleration as an at-the-money option.
Deep out-of-the-money options will actually decay more in 40-50 days till expiration than near expiration. Why is this? Out-of-the-money options, especially puts, carry an insurance attribute with them.
That means, investors and traders will purchase these options to protect or hedge a portfolio or position and cause these options to hold value. You will notice, especially if you ever been short out-of-the-money options, that the value seems to stop decreasing when we get closer to expiration.
If you are running a strategy to short deep out-of-the-money options, when do you want to enter your trades? At 30 days until expiration or 60 days until expiration? If you want to take advantage of the rapid decay of theta, you would enter the trade 60 days out and take it off when it is 30 days out. This is the same thought process we use when entering and exiting an iron condor. Put the probability in your favor when you take on new trades to increase your success.
Is Option Theta Accurate?
Nobody said the Greeks are an exact science, and it couldn't be more apparent in theta. Theta gives a rough generalization on the drop of option value as each day passes. As you get closer to expiration, the number begins to get wonky (that's the technical term), especially for out-of-the-money options.
If we look at these out-of-the-money puts, delta of -0.23, with 19 days left till expiration. We could sell them now for 0.99 and collect a theta of 0.06 a day. Even if theta does not increase and remains at 0.06 it would run the option premium out in 17 days, not the 19 till expiration. Here is the math:
0.06 (theta) x 17 (days) = 1.02 (value lost in our option)
0.06 (theta) x 19 (expiration) = 1.14 (value lost in our option)
The math above shows that at expiration the value of our option would be worth -0.15, and we cannot have a negative option value. You still want to use theta to get a rough idea of how your option is going to react through time, but don't put a lot of faith in it the closer you are to expiration. Don't hold your short options open longer than needed because you want to collect a few more bucks of theta.
How Time Decays Over The Weekend
What if we open a new short position Friday afternoon and then close it Monday morning? That way we get to collect two free days of theta and the risk of the position moving is very minimal. In theory, that is a great idea but in reality it is not possible to get free money from the market.
The market makers who are on the other side of these options are not going to take losses every weekend because they have a bunch of option sellers come in on Friday. Instead, what they will do is either adjust their volatility or time to expiration in their system. On Thursday or Friday, depends on the market maker, they will go in and raise the volatility to account for two days of decay (the weekend). On Monday they would go back in and drop down this volatility so it would appear that options only had one day of decay. They could also go in and move their days to expiration forward to keep the same effect.
Mark Sebastian, an ex-market maker, has said how he would handle weekend theta decay, “I would notice around [Thursday to Friday] that other traders would begin trying to sell me premium. I obviously do not want to be buying a bunch of premium that will decay for two days that the market is closed. So I had two choices. I could lower my theoretical volatility. This would lower my options prices based on the all of the premium sellers I was seeing, or I could move my theoretical date forward.”
If you are short options, showing a good profit and wondering if you should take it off on Friday, know that it is probably a good idea to close the position. You are not going to get any big payoff holding it over the weekend. If you close your position and change your mind there is a good possibility of reentering the position on Monday around the same price for which you exited.
How Volatility Minimizes The Effect of Theta
As we alluded to earlier, when discussing time decay over the weekend, volatility can negate the effects of theta. One place this is apparent is over the weekend. Look at the volatility of the S&P 500, how it increases on Friday and decreases on Monday.
Another way we can observe volatility's effect on time decay is during earnings. An option's price won't typically increase or decrease leading up to earnings as time passes. The reason for this is, volatility is also moving higher and offsetting time.
In practical terms, let's look at this from a market makers point of view. TOP is trading at $50.00 and their earnings announcement is coming up in a week and we want to price the move. We believe, as a market maker, TOP has the potential to move $10 in either direction. We should see the at-the-money straddle trading for $10.
As the days pass, theta would naturally take the price of our straddle down. The day before earnings it could only be worth $6.00. As a market maker, if we expected a $10 move but it is only selling at $6, well that leaves us open to a lot of risk. Now our straddle is underpriced, traders are purchasing them left and right, TOP releases earnings and moves $10 and we are stuck holding the bill.
A market maker will offset this by moving their theoretical volatility higher. Now, right before the earnings announcement, our TOP straddle will still be worth $10.
How To Cover Your Theta With Option Movement
By combining our option theta with our delta, we can calculate how much movement we need in the underlying to cover our daily loss.
Your TOP long call has a delta of 0.24 and a theta of 0.06. We know as each day passes our option price will lose 6 cents a day. That means we need TOP to move $1 in 4 days for our option to breakeven.
By knowing how much you need your option to move you can better plan your trades.
Time may be flying but now you can put it on your side. By understanding theta, you know it will have a negative effect on your long positions and a positive effect on your short positions. You now know when options have accelerated time decay, which allows you to take the right strategy at the right time. Remember, there is no edge in trading options over the weekend, and volatility can negate time decay, especially around an earnings announcement.