6. The time value of options: Theta
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Next up in Option Greeks is Theta. But before we jump into the technicalities, let’s go back to the basics!
Time is Money
Remember the golden adage Time is money? When it comes to options trading, you might want to keep this proverb at your fingertips. But for now, let’s keep the Greek talk aside and go back to my trip to Goa. If you remember, I went to Goa for 14 days. Now that’s a fairly long time for a domestic vacation! I wanted to explore the best off-beat experiences in Goa. Do you think I simply boarded a plane and left? Or do you think I planned before I left for my long vacation?
That’s right, before I took my trip, or even decided that I would be spending fourteen days in Goa, I invested time in careful planning. In fact, one of the reasons why my trip was such a success was precisely because I spent time thoroughly researching, looking for the best places to stay, hidden beaches to visit and the top places to eat at. Without this, I would have probably had a haphazard trip and I wouldn't have made the optimum use of my days in Goa. So let’s leeLet’s keep this in perspective and figure out the likelihood of passing the exam against the time spent preparing for the exam.
Number of days of research |
Likelihood of a successful trip |
3 days |
Very high |
1 day |
Moderate |
1 hour |
Very Low |
Quite obviously, the longer one spends on researching, the higher are the chances of a successful trip.
Keeping the same logic in mind, think about the following situation – Nifty Spot is 8500, you buy a Nifty 8700 Call option – what is the likelihood of this call option to expire In the Money (ITM)? Let’s explore this in more detail:
- Given Nifty is at 8500 today, what is the likelihood of Nifty moving 200 points over the next 30 days and therefore 8700 CE expiring ITM?
- The chance for Nifty to move 200 points over next 30 days is quite high, hence the likelihood of option expiring ITM upon expiry is very high
- What if there are only 15 days to expiry?
An expectation that Nifty will move 200 points over the next 15 days is reasonable, hence the likelihood of option expiring ITM upon expiry is high (notice it is not very high, but just high). - What if there are only 5 days to expiry?
5 days is a very short period of time to allow for an increase of 200 points, hence the likelihood of 8700 CE expiring in the money is low. - What if there was only 1 day to expiry?
The probability of the Nifty to move 200 points in 1 day is quite low, hence I would be reasonably certain that the option will not expire in the money.
So what can we infer from the above information? Clearly, the more time for expiry, the higher is the likelihood for the option to expire In the Money (ITM). Now keep this point in the back of your mind as we now shift our focus on the ‘Option Seller’.
Option Seller
We know an option seller sells/writes an option and receives the premium for it. When he sells an option, he aims to carry unlimited risk and limited reward potential. The reward is limited to the extent of the premium he receives. He gets to keep his reward (premium) fully only if the option expires worthless. Now, think about this, if he is selling an option early in the month he very clearly knows that:
- He carries unlimited risk and limited reward potential.
- By virtue of time, there is a chance for the option he is selling to transition into ITM option. This means that he will not get to retain his reward which is the premium received.
Due to time, there is always a chance for the option to expire in-the-money. However, this chance gets lower as the expiry date approaches. You might wonder, given this, an option seller would not want to sell options at all right? After all, why would one sell options when there is scope for the option you are selling to expire in-the-money? There’s no doubt that time in the context of an option seller acts as a huge risk.
Now, let’s take another case. What if in order to entice the option seller to sell options, the option buyer offers to compensate for the time risk that the option seller assumes? In such a case, evaluating time risk versus compensation is the right thing to do. This is precisely what happens in real world options trading.
Whenever you pay a premium for options, you are indeed paying towards:
- Time Risk
- Intrinsic value of options.
Therefore, Premium = Time value + Intrinsic Value.
(Recall earlier in this module we defined ‘Intrinsic Value’ as the money you are to receive, if you were to exercise your option today.)
What is Theta?
Theta measures the rate of time decay in the value of an option or its premium. Time decay represents the erosion of an option's value or price due to the passage of time. With passing time, the chance of an option being profitable or in-the-money reduces. In fact, time decay accelerates as the expiration date of an option draws closer because there is less time left to earn a profit from the trade.
Theta is always negative for a single option since time moves in the same direction. Think of it like this, as soon as an option is purchased by a trader, the clock starts ticking, and the value of the option quickly begins to deteriorate until it expires at the predefined expiration date. This means that Theta values are always negative for long options and will always have a zero time value at expiration since time only moves in one direction, and time runs out when an option expires.
Theta is good for sellers and bad for buyers. A good way to understand this is to imagine an hourglass. In this hourglass, value is flowing from the buyer’s side to the seller’s side. Therefore, there is a continuous, rapid loss for the buyer. Therefore, the buyer must decide what to do before time runs out.
Wrapping up
How To Use Theta To Trade Options?
Theta value or time decay is a “silent killer” for an option buyer as it indicates the lessening in value of the option held by the buyer. On the other hand, Theta is a favorable position for the seller who benefits from delay in buyer’s exercise of the option.
For this reason, the general strategy should be to buy options with a longer lead period to expiration to reduce the effect of time decay and minimize the Theta loss on options.
A Quick Recap
- Option sellers are always compensated for the time risk
- Premium = Time Value + Intrinsic Value
- Theta measures the rate of time decay in the value of an option or its premium.
- All else equal, options lose money on a daily basis owing to Theta.
- Time moves in a single direction hence Theta is always negative.
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