The Myth of Option Expiry

“70% of options expire worthless to the buyer! That means 70% expire profitable to the seller.”

Garbage! Unbelievable garbage! Absolutely unbelievable garbage! The logic in this statement is just plain incorrect and of course the website does not have statistics to back their claim.

To be fair this website was not the only place I have come across a statement like this. I have in fact seen a figure of up to 90% quoted. However even if it is a common belief does not make it correct.

Let’s first have a think about the logic, then let’s look at some stats and come to some real conclusions.

Profit Logic
Let’s assume 70% of options do expire worthless. How can anyone draw conclusions as to the profitability of a long trade or a short trade? You simply cannot.

If you sell an option at say 10pts, you could then watch it go to 100 or 200pts and wipe out all the money in your account. The market may then turn around and eventually see the option expire worthless, but that does not mean your trade has been profitable. This is not nit picking. This is real life trading - things move up and down and you cannot always afford to sit on a position and hope for a zero value at expiry.

It is simply not possible to draw a conclusion about profitability based on expiration statistics.

The statistics
In a book entitled Options on Futures by Summa and Lubow they quote the 80% figure and it is backed up by numbers from the Chicago Mercantile Exchange (CME).

In a section entitled “The Numbers Speak for Themselves”, they show a table of data sourced from the CME. The numbers represent the percentage of options that expire worthless. The data from the book is as follows:

YearCME optionsS&P optionsS&P putsS&P calls
199776.381.794.154.8
199875.882.293.143.9
199977.584.794.566.7
1997-9976.683.394.055.3

Assuming we have no reason the doubt these statistics, then this seems to back up the popular belief. On careful reading however, it appears the figures represent only those options that are held to expiration and not those that are closed out OR exercised before expiration (remember we are dealing with American style options here so some can be exercised before expiration).

Maybe we do not have the whole picture...

I also came across some more stats from the Chicago Board Options Exchange (CBOE) that I thought were interesting. Their figures are:

• Approximately 10% of options are exercised;
• 50-60% of options positions are closed prior to expiration;
• The remaining (about 30 – 40%) are held to expiry.

At first these figures might look rather contradictory, but they are not. The CME numbers are based on options that are held to expiry. That is they do not include options that are exercised or closed before expiry – and that’s 60-70% of all options according to the CBOE.

If we take both exchange’s statistics as fact, then drawing a conclusion from only the expiry numbers could be a bit biased.

Think about the CBOE numbers for a moment. The 10% that are exercised early would in all but very rare cases be in-the-money (why else would you exercise?) If we assume therefore that only in-the-money options are exercised, then this would leave more out-of-the-money options heading to expiry than in-the-money.

What about the options that are closed before expiry? One could hazard a guess that most options closed near expiry would be either in-the-money, at-the-money or just out-of-the-money.

Why? In-the-money options will behave more and more like the underlying the deeper they are in-the-money and the closer they get to expiration. Holding in-the-money options therefore will carry more risk. This could be a reason why some holders may want to close their in-the-money positions prior to expiration. Out-of-the-money options on the other hand may be worth very little and hold little risk (low delta/gamma/theta/vega). Therefore you might say there is larger chance of an out-of-the-money option being held until expiration.

Therefore, the 50%-60% of options that the CBOE claim are closed before expiration could also be weighted towards in-the-money options. For the numbers below, we will assume the split is 60-40% (60% in-the-money and 40% out-of-the-money).

So then, the majority of the 30-40% that go on to expiry would therefore be out-of-the-money and of course would expire worthless like out-of-the-money options do. Does that mean you should be a net seller? Does that mean 70% of options “expire profitable to the seller”?

Let’s play with some numbers. Let’s say we have an exchange with 1,000 open option contracts.

• First, 10% of the options (all in-the-money) are exercised early leaving 400 in-the-money and 500 out-of-the-money. There are 900 options remaining.
• Then 55%* or 550 of the initial pool are closed out leaving 350 open contracts. (* 55% is half way between the 50-60% CBOE number.)
• Of these 550, we need to estimate how many are in-the-money and how many are out-of-the-money. Since we have established a weighing towards in-the-money options, let’s assume 60% of these are in-the-money and 40% are out-of-the-money.
• In the end, we have 350 contracts run to expiration.

Based on our calculations, that would leave 70 in-the-money options and 280 out-of-the-money options that will run until expiration. (see table). Based on the one assumption above, 80% of the options that will go to expiry are out-of-the-money and therefore will expire worthless.

TOTALIn-the-moneyOut-of-the-money
1000500or 50%500or 50%
Early exercise (10%)1000
Remaining900400500
Closed positions (55% of 1000)550330220
Option to trade to expiry35070 or 20%280or 80%

So now the figures make sense. Perhaps 80% of options that run to expiry do expire worthless. (Perhaps the real figure is 70% or 90%.) However that is not the same as saying 80% of ALL options expire worthless. Can you see the difference? Furthermore, coming to the conclusion that is it better to be a seller than a buyer from a single biased statistic like this is plain nonsense.

In a topic like that of as options trading, it is easy to get caught up with statistics, but if we take the time to think and research before drawing conclusions, then surely we will become better traders.