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In part two of my series on options pinning and maximum pain theory, with a focus on Apple (AAPL), I interview University of Illinois Professor of Finance and Harry A. Brandt Distinguished Professor of Financial Markets and Options Neil Pearson.
As Pearson's faculty profile indicates, he has authored several papers on the options market, with considerable focus on the notion of pinning (or "clustering," as he and his research team calls it). Pearson co-authored a landmark 2005 study on the subject that both academic and mainstream authors continue to cite today.
Rocco Pendola: Please define pinning and the theory of maximum pain. Please provide basic explanations of these two terms.
Neil Pearson: “Pinning” and “maximum pain” are closely related. Pinning refers to the phenomenon that on option expiration Fridays the prices of optionable stocks tend to close on or very near to option strike prices. This is not to say that this Friday AAPL will necessarily close on or near to an option strike price, but rather that AAPL is more likely to close on or near to an option strike price on Friday than on any other day of the week.
The theory of maximum pain goes further, saying that the stock price will tend to move toward the price where the total value of options contracts, both puts and calls together, is the lowest. This theory thus identifies the specific option strike price that will tend to attract the stock price. If the stock price closes at the strike that minimizes the total value of options contracts, this minimizes the value received by buyers and paid by option sellers when the options expire. Because this benefits option writers, some market participants claim that the stock price movement is caused by option writers manipulating the stock price to create profits for themselves and losses to option buyers.
RP: These concepts can be confusing for readers (and authors) to get their heads around. Take us through what actually happens when a stock pins or "clusters" to a particular strike price. Why does it happen? And, while we will get deeper into the "how" of it all in a minute, what does it look like in the simplest terms?
NP: Let’s use AAPL as an example. Friday, AAPL’s closing price was near $340. Further, let’s suppose that there is a large trader or group of traders who follow a hedging strategy that requires them to sell aggressively if AAPL rises above $340, and buy aggressively if AAPL falls below $340. If this is the case, their trading will have a tendency to “pin” AAPL at or near $340. It is only a tendency, because during the week there might be some event, either a news announcement or trading by some other investors, that dwarfs the effect of the hedging strategy and moves AAPL away from $340.
In the explanation above, AAPL pinning at $340 is an incidental byproduct of the hedging strategy. An alternative, more cynical, view is that sometimes some traders will deliberately trade in a way (sell if AAPL rises above $340, fall it AAPL falls below $340) with the intent of pinning AAPL at $340.
RP: What do you think causes pinning?
NP: I think most pinning is caused by hedge rebalancing, i.e. it is an incidental byproduct of perfectly legal hedging activities. You might wonder, whose hedging? What large trader or traders could possibly be following hedging strategies that cause stock prices to pin? The answer is that delta-hedging trades executed by options market makers can have this effect.
RP: Could you explain delta hedging a bit more?
NP: Option market makers often have a lot of natural hedging in their portfolios, e.g. satisfying customer demand might lead them to buy some $55 strike calls, and write some $60 strike calls that partially hedge the $55 strike calls. But this natural hedging is not perfect, and to the extent that it is not, options market makers trade in the underlying stocks to hedge their options positions. When the stock price moves, or as time passes, or when they execute new option trades, they need to rebalance their hedges, that is buy or sell the underlying stock.
Option market makers (and many other options traders) use the concept of option “delta” in establishing and adjusting their hedges. The option delta is the change in the value of the option or option portfolio resulting from a one dollar change in the price of the underlying stock. For example, on a “per share” basis an at-the-money AAPL call will have a delta of about 0.5. This means that if AAPL moves by $1, say from $339.50 to $340.50, the price of the 340 strike call will change by about $0.50 per share. The value of the option contract on 100 shares will change by about 100 × $0.50 = $50, and the value of say 40 contracts will change by 40 × 100 × $0.50 = $2,000. An option market maker who owns 40 contracts (and no other options) will hedge the position by short-selling 2,000 shares of AAPL. If AAPL falls by $1 the gain of $2,000 on the short position will offset the loss of $2,000 on the options position, while if AAPL rises by $1 the loss of $2,000 on the short position will offset the gain of $2,000 on the options position.
RP: How can delta-hedging by option market makers lead to pinning?
NP: Consider our options market maker who owns 40 calls (on 40 ×100 = 4,000 shares) with a strike of $340, and suppose that AAPL is trading just a bit above $340. The delta of the option position is 2,000, and the market marker will hedge by short-selling 2,000 shares. If AAPL stays above $340 all week until expiration, the call will be exercised, resulting in the purchase of 4,000 shares. Because a stock position of 4,000 shares has a delta of 4,000, the delta of the options position (which, on exercise, becomes a stock position) will increase throughout the week, ending up at 4,000. The delta increases from 2,000 to 4,000 because the calls eventually get exercised, and the call owner receives 4,000 shares. As the option position delta increases from 2,000 to 4,000, the market maker must sell AAPL to increase the short stock position from short 2,000 shares to short 4,000 shares. This has the effect of pushing AAPL down toward $340.
This assumed that AAPL was above $340. If for some reason AAPL drops below $340 and stays below $340, the calls will expire worthless. This means that the options delta will drop to zero at expiration. As expiration approaches, the market maker must maintain a stock position opposite to the option delta. Because the option delta is dropping from 2,000 to zero, the stock position must change from 2,000 short to zero, i.e. the options market maker must buy AAPL to cover the short. This has the effect of pushing AAPL up toward $340.
The effect is that when AAPL is above $340 the hedge rebalancing trades involve selling AAPL, and when AAPL is below $340 the hedge rebalancing trades involve buying AAPL. These trades tend to “pin” AAPL at $340.
In this example, I focused on the change in delta due to the passage of time. Option deltas also change as the stock price moves, leading to an additional source of hedge rebalancing trade. (The change in delta as the stock price changes in known as “gamma.”) Close to expiration, hedge rebalancing trades due to changes in delta caused by changes in the underlying stock price work in the same direction as hedge rebalancing trades caused by changes in delta as time passes.
RP: But doesn’t this depend on the market maker’s position? You assumed that the market maker has purchased options.
NP: Yes, that is a crucial point. If the options market maker had written the calls his hedge rebalancing trades would be in the opposite direction, and would tend to move AAPL away from the strike of $340. Whether hedge rebalancing trades tend to cause pinning or “anti-pinning” (or “clustering” or “declustering”) depends crucially on whether market makers in aggregate have a net purchased or net written options position. If the aggregate market maker position is purchased, hedge rebalancing trades will tend to push stock prices toward option strike prices, while if the aggregate market maker position is written hedge rebalancing trades will tend to push stock prices away from option strike prices.
Because the effect of hedge rebalancing trades is to push stock prices toward the strike when option market makers in aggregate have a purchased option position and away from the strike when option market makers in aggregate have a written option position, pinning caused by hedge rebalancing does not benefit option market makers but rather hurts them.
RP: In terms of manipulation, again, as plainly as possible, how does this look?
NP: The hypothesis that pinning is caused by manipulation says that some option traders who have written options trade in order to cause the options to expire unexercised. If we use AAPL as an example, the manipulation hypothesis says that traders who have written 340 strike AAPL calls would sell AAPL to push the price below $340.
RP: What makes you say that most pinning is caused by hedge rebalancing rather than manipulation?
NP: Pinning is much more frequent when, in aggregate, options market makers have a net purchased option position than when the aggregate market maker position is written. In fact, the aggregate market maker position is a strong predictor of whether a stock will pin. This is exactly what the hedge rebalancing explanation predicts. And on average options market makers are hurt by pinning - they don’t benefit from it.
However, stocks also pin when the aggregate market maker position is written, though the frequency of pinning is lower than when the aggregate market maker position is purchased. The hedge rebalancing story cannot explain why stocks pin when the aggregate market maker position is written. Also, the probability of pinning is higher when firm proprietary traders (e.g., traders at large banks) sell options to open new option positions during the expiration week. These two things suggest that sometimes, some option traders manipulate stock prices to cause options they have written to expire out-of-the-money.
RP: Thinking of heavily-traded stocks like Apple, how could they possibly be manipulated? I mean I picture all of the sellers of $340 May calls sitting in a room next Friday cooperating like Wall Street hedgies have never cooperated before.
NP: You shouldn’t think about cooperation or a conspiracy. You should think that traders often have similar trade ideas, and as a result sometimes end up with similar positions. Then each independently tries to “protect” his or her written options position by trading in the underlying stock so as to prevent the written options position from expiring in the money.
In thinking about whether it is plausible that stock trades executed by options traders have material impacts on the prices of the underlying stocks, you should keep in mind that the only other explanation for pinning is that (hedging) stock trades executed by option traders cause pinning. That is, the only two plausible explanations for pinning involve stock trades executed by options traders. The two explanations differ only in the motivations for the stock trades.
Also, keep in mind that if AAPL is currently at $341 and I think that there is a chance that it will pin at $340 on Friday, I have an incentive to wait until Friday afternoon or Monday morning before I buy AAPL. Of course I might be in a hurry and not wait, but I have some incentive to wait. On the other hand, I will be sure to sell now at $341 rather than at $340 on Friday. Thus, expectations of pinning can themselves contribute to pinning.
RP: Clearly there are stocks where this does not come into play at all. I am thinking of thinly-traded underlying stocks with low options volume and low open interest.
NP: Of course, if there is no option open interest there is no pinning. But both smaller and larger stocks pin. Smaller stocks tend to have lower option open interest, but it also takes less stock trading to move the stock price.
RP: How much of a role does chance play here? Are there any purely statistical/mathematical bases to support clustering?
NP: It is important to keep in mind that when I say that stocks “pin,” this is a statistical statement. I don’t know that AAPL will close at or near $340 on Friday. But, I do know that APPL is more likely to close at $340 on Friday than on Thursday or Monday.
On the other hand, there is no doubt that the probability that APPL closes at or near an option strike price on Friday is elevated, relative to the probability on other days. Options have been traded for a long time, on a large number of underlying stocks. Thus, a large sample of option expirations has been studied, and we can be highly confident that the phenomenon of pinning exists. And there is no doubt that the phenomenon is somehow caused by option trading. Stocks with traded options pin, and stocks without traded options don’t pin. And crucially, stocks without traded options start to pin once option trading begins, and stocks for which options trading ends stop pinning. Finally, the probability that a stock pins is related to the aggregate position of option market makers.
Disclosure: I have no positions in any stocks mentioned, I may initiate a long or short position in AAPL at any time.
Source: Digging Deeper: Options Expert Discusses Pinning, Max Pain and Apple (Part Two)