Investment XYZ

Friday, May 19, 2006

The Myth of "Max Pain"

There is a now commonly known option phenomenon called "Max Pain": on option expiration Friday, stocks typically are attracted to the nearest strikes where there are large option open interests. For example, if QQQQ price is at 39.2, and there is big option open interest at strike 39 and strike 40, it is likely the stock will close at 39 or 40. For simplicity, I will refer to this phenomenon as "pin" or "Max Pain ™" (

Why is it called "Max Pain"? The theory is that option market makers like to push the stock price to a particular strike so that all the options on that strike would go poof -- all become worthless. The assumption is most likely the investors would be the option holders so such "pin" would cause maximal pain to the investors who see their investments in option disappear worthless -- thus the name "Max Pain". Sounds like a conspiracy theory (MM vs the poor investors, a very common source of conspiracy theory). The term "pin" is more neutral, it means the stocks tend to be attracted to the strike and then pinned down there.

Stickiness Around Strike on Expiration Dates

Before we try to understand "why" there is such phenomenon and how people interpret it, let's see whether there is such thing really exists. My cursory observation tells me that there is not a large percentage of stock showing such tendency, but the few that show does looks quite obvious. For investors, statistics probably doesn't matter, what matter is whether such "Max Pain" falls on the names he is holding.

Just look at the just past expiration (5/19/06). Among total 909 symbols which have market cap > $1 billion and have options, there 165 names showing "pin" - with stock settling with 0.1 of a strike. That's 18%. No prevailing, but very substantial. Statistically, if the stock prices are randomly distributed and the average strike spacing is $5, the chance of stock closing at within 0.1 of a strike is about 4%.

Among then pin names, here are a few examples that stocks are pinned down to within 5 pennies (stock closing prices in parenthesis, the second number is the price change on Friday): LFG (65.0, +0.5), RIMM (67.49, -1.74), DNA (80.03, +4.1), SNDK (62.49, +0.88), SLAB (40.04, +0.37), LEH (67.48, +1.27). Considering how volatile some of these names are (such as RIMM, SLAB, SNDK, LEH), it looks like volatile as they are, they still end up within pennies of the strike when the market close. Quite magical. The conspiracy theory seems quite well founded.

So the fact of “pin-to-strike” is established. Let's look at how much truth to "Max Pain" explanation of the "pin".

First of all, all expiring options, no matter what strikes, will go poof on expiration Friday after the market. What exactly I mean is the volatilities go poof, disappear, zip. For example, supposed on expiration Friday morning, a strike 40 call is priced at 1.5 with stock at 41.3, that means there is 0.2 volatility value in the option. When the market closes, if the stock is closed at 42, the option is worth $2, or the intrinsic value. The volatility value of 0.2 disappears. If the stock is closed at 40, the option is worthless, so is the 0.2 volatility. In other words, the volatility value disappears on expiration, no matter whether the option is in-the-money, at-the-money or out-of-money.

Disappearing of Volatility Value

So should the market makers try to push the stock prices to the strikes to make the options disappear, if they can push? Probably not necessary for them to do that. First of all, market makers would always hedge their options (which require calculating "Delta" of options using some model), and on expiration date, the hedging is relatively easy to understand without complicate math: option is either in-the-money or out-of-money, so the delta is either 1 (call), -1 (put) or 0 (mathematically, it means on expiration date, Delta becomes a discontinuous function, and Gamma becomes a Dirac-Delta function). As we see above, the volatility value of the options always evaporate away on expiration, so as long as an option is hedged, the market maker can capture (if he is short) or lose (if he is long) the volatility, no need for them to push the options to the strikes. Furthermore, market makers can be long or short options, so the disappearing volatility value may be good or bad for them, namely, the "max pain" may be exerted on themselves, which obviously doesn't make sense.

For investors who hold options and do not hedge, the disappearing volatility value works against them, no matter whatever the stock price is settling in. Unhedged options (purchased by investors) are to speculate on the intrinsic value (as the direction of stock), not on the volatility value. The volatility value is a premium that gives investors two benefits (thus the cost money to have it): 1) leverage: holding a $1.5 option in the morning (stock at 41.3), and stock closes at 42, the option increase to $2, that's 33% return, while if you hold stock, it gives you 1.7% return. So even though the investor loses the 0.2 volatility value, he should be happy since options give him a huge return rate that stock can't give him. 2) protection. If stock drops down to $39, the option expires worthless, so the option holder would loss $1.5, while the stock holder would lose 41.3 - 39 = $2.3.

Investors tend to feel the options (a contract) is less tangible than stock (equity), thus if an option disappears entirely when the stock settles on the strike, they feel they are lost something forever. Actually that is quite naive thinking. If they miss their stock, all they need to do is to buy the stock at the strike, and you have exactly the same results when the option expires in-the-money.

Can Hedging Cause It?

Nevertheless, I wouldn't whisker away the conspiracy theory altogether. The "pin" phenomenon may be actually related to trading behavior on expiration day. First of all, let's see who are trading options. In general there are 3 types: 1) investors who speculate on stock direction (option as a leverage tool); 2) market makers who take the opposite side of a trade and hedge (and make money on bid/ask spread); 3) Proprietary traders who trade on some dimensions other than delta (such as volatility traders, dividend traders). #1 (investors) typically won't hedge, 2) and 3) typically hedge.

Hedging activities on expiration tend to occur around the strike. Let's look at an example to see how it works: a trader longs a call (strike 40), stock is moving from 39.9 upward. When the stock crosses 40 line, now his position suddenly changes from no delta to 100 delta, so he has 100 shares per contract to sell (short). If the stock drops back below 40, he can buy the stock back, thus longing an option give he opportunity to scalp around a strike and make some extra profit. Conversely, if he shorts the call, the hedging is a risk management process to limit loss that can cause by stock movement. The moment the stock go above 40, he should immediately buy stock to hedge, if the stock drops below 40, he should immediately sell the stock. Such buy high/sell low would in general cause loss which should in theory (statistically), offset the volatility premium he should collect. In both cases (long and short), the hedging activities all center around strikes, which tends to pin down the stock there.

So who is more likely to cause the pin-to-strike, the long side or the short side? For the long (doesn't matter they long call or put -- "long" means long volatility, not long Delta), the scalping is some "extra" profit they can get if the stock does whipsaw around the strike. So when the stock price is above the strike, they would sell stock; below the strike, buy stock (sell high/buy low). If you have 500 contracts, that means you can sell 50,000 shares of stocks. Such selling action can certainly push the stock back down below the strike, where they can buy back the 50,000 shares. Of course if the stock moves above the strike and keep going, that can become a windfall for the long if he does not hedge. But typically the market makers or the hedgers won't take huge delta risk like this and would hedge instead. On the short side, any price move across a strike (up or down) is a big risk. A 5c option can suddenly become tens or hundreds times more expensive (remember GOOG on 1/20/06 expiration Friday, dropping almost $40 going through 3 or 4 strikes – that can be a big disaster for anyone shorting options and not hedge quickly and correctly). So moving the stock price toward a strike is not a good thing for the short side, and because he has to buy when the stock goes up, sell when the stock goes down, the hedging action on the short side can cause the stock to move further away (not toward) the strike.

So the "max pain" theory explains such pin-to-strike incorrectly in three areas: 1) You don't need to move the stocks to strike to make the option worthless. Volatility value will evaporate on expiration date, no matter what stock price is close on Friday. 2) The pin is likely due to hedging activities, rather than some MM conspiring to move the stock to strike; 3) The option traders (MM and proprietary) who might cause the pin is the long side, rather than the option writers (as the max pain theorists claim).

The Automatic Exercise Rule

So all these "Max Pains" are not the results of some conspiracy trying to cause pain on investor? Probably not as the "Max Pain" theorists commonly believe, but for a different reason. Option automatic exercise rule is the true reason behind such pain. After options expire, not all the in-the-money option are automatically exercised. The rule (which was recently updated, and may vary from broker to broker) states that only options more than 10c in-the-money will be automatically exercised. Those within the 10c limit, the option holders have to call their broker to give exercise instruction if they want to exercise. If you do not exercise them, they become worthless even theoretically they are in-the-money. Why there is such rule (which seems extremely unfair to the long side)? There are some understandable reasons behind it. Exercising an option involves two major risks: 1) after exercise, you hold stock thus no longer have the protection of an option. For a 5c option, if stock drops $10 on the Monday after expiration, you would just lose 5c/share, while if you exercise the 5c option into stock, you would lose $10/share. 2) You need to come up with capital to buy the stock. Imagine you own 10 contracts of GOOG 400 call, stock settles at 400.05, you decide to exercise to save the 0.05, you need to come up with $400,000 cash to buy 1000 shares of GOOG at $400.

Such 10c rule, though not unreasonable, can cause a windfall for the short side if the option holders decide not to (or more unfortunately, forget to) exercise. 10,000 contracts (a typical size of open interest of one option strike) of 10c options have a value of $100,000 that would be in the hand of the short side if not exercised. That is certainly a lot of risk-free money involved for one strike.

Is that a conspiracy again the investors who may not be so knowledgeable or vigilant? I doubt, considering the risk and capital requirement for exercising. But that certainly puts some responsibility in the investors' hand, and requires them to really know what they are doing and pay attention to their options when are near the strikes. Forgetting to exercise a 10c in-the-money option is unforgivable for a responsible investors.

What lesson can investors learn here?

1) Watch out for the automatic exercise rule of your broker. Check with your broker before the expiration date. Typically it is more than 0.1 in-the-money, but some may be 15c.

2) Watch out for your options holding that may end up out-of-money and fall into the non-automatic realm. If you do not intend to own the stock (which would cost you capital), make sure you sell the option BEFORE 4pm EST, even sell it at 0.05 is better that out-of-money. Before 4PM, you can usually sell it above the intrinsic value.

3) Even though option market close at 4PM EST, your right to the options actually still in your hand until 5PM or 5:30PM. So you can still exercise an out-of-money or non-automatic exercise option, if you want to. Why do you want to do that? Let's look at a fictitious example. You hold a DIA (1/100 of DJIA ETF) 115 put, and it closes at 115.01, so your option is out-of-money. At 4:30PM EST, President Bush eats a pretzel and chokes himself, unconscious (may be dead). So DJIA after-market drops 100 points ($1 in DIA). What can you do? You call your broker and exercise your put option, which effectively establish a short stock position at 115 (while at this point the market is trading at 114). If you don't want to wait until Monday morning to take profit (it is possible that Bush survives the incidence and end up like nothing happen for the market on Monday), you can buy the stock on the after-market at 114, thus lock in the profit immediately ($100/contract), without taking any uncertainty on Monday.

So "pin-the-strike" may still be a reasonable "technical indicator" to predict where the stock may end up on expiration Friday (I'm not for or against such analysis), but what cause it may be quite different from what is commonly believed.


In October 2006, the OCC (which governs the option trading regulations) change to the automatic exercise threshold for in-the-money options from 10c to 5c.

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