Monday, February 10, 2014

why stocks get pinned to a strike price at expiration

some stocks will pin an option strike price at expiration. by "pin" i mean they kind of get glued to a particular strike price on the afternoon of expiration friday, cycling between trading a little above the strike then a little below it. there's this mythology floating around the web that this occurs in order to inflict the most pain on option traders - the so-called max-pain theory. nothing could be further from the truth. the market has no emotions and does not care if you win or lose. pinning is a real phenomenon. it happens because a large population of retail traders wait til friday expiration to close their short options, counting on the accelerated time-decay to work in their favor.

firstly it is important to understand the actions of option market-makers. there are three roles that mm's play:
  1. counterparty locater. when you place an option order the mm will attempt to locate a counterparty willing to take the other side. if successful then the mm collects two commissions and the bid-ask spread and has no risk.
  2. default counterparty on open. if the mm cannot find a counterparty then he becomes the counterparty but he will hedge his position so as to take no risk.
  3. default counterparty on close. a party to an option contract can unilaterally close out his position without affecting the counterparty. if a new party cannot be located the mm will step in to take the place of the party but will hedge his position so as to take no risk.
the thread that is common to all these roles is that the mm takes no risk. the mm's cannot take risk and be put in a position where they might be biased or hurt by the moves in the market. thus the option mm's are always liquid, available and impartial facilitators of trading. this is possible due to the principle of put-call parity. in its simplest form put-call parity says that a covered-call is the synthetic equivalent of a shorted-put, given same strikes and expiration. this is typically expressed algebraically as:
+stock -call = -put     (1)
where the pluses and minuses indicate long and short, resp. this can be manipulated algebraically in many ways to obtain useful relationships such as:

-call = -put -stock    (2)
by subtracting stock from both sides of equation (1).

the mm uses put-call parity to neutralize risk on their side of a transaction. for example, if the mm is counterparty to your short-put then they acquire a long-put on their books. in order to neutralize the risk of being long a put they create a synthetic short-put by buying stock and shorting a call. thus their position looks like this:
+stock -call +put
this is a position called a locked trade, or a collar, in which the mm can neither make nor lose money because synthetically it adds up to zero.

if the mm is also making a market for shorted calls then they are locking the trade the other way 'round:
-stock +call -put
notice that this is just the negation of the collar hedge above.

so what happens if client A shorts a put then client B shorts a call? at the time client B shorts a call, the market maker simply flattens the hedge acquired for client A. in this situation the mm carries on his books that client A is short a put and client B is short a call and no hedge. likewise, a retail call buyer will flatten the hedge a market maker took to neutralize risk of a prior retail put buyer. thus, whenever there are balances between short puts and short calls or between long puts and long calls the market maker is unhedged.

now suppose in the above example that client A decides to close his position unilaterally by buying back his shorted put. this leaves the mm with an unhedged long call position because he is the counterparty of client B's shorted call. so the mm has to go out and hedge that position by creating a synthetic short-call, by shorting stock and shorting a put per equation (2). this is very much the idea of what happens on expiration friday when retail clients are liquidating their positions ahead of expiration. the mm's have to hedge their positions as retail traders liquidate positions.

there are various other mixtures possible. after client A shorts a put, client B might buy a put. in that case the market maker assigns B to be the counterparty of A and closes his hedge. similarly if client A shorts a call and client B buys a call then the market maker is left with no hedge. short-call then long-put and short-put then long-call both leave the mm with full hedges. however, i argue that there is a big tendency for long option traders to liquidate early while there is time-value left on their options. so most of the open-interest going into expiration friday is short-option traders waiting for the accelerated time-decay to work. thus, it is premium-sellers and underhedged market-makers running the show.

here's how this plays out: on expiration friday afternoon the price of a stock hovers a little above the big-strike and the price of puts drop to the level where a short-put holder decides to close his position. if the mm was the counterparty to that closed short-put then he now is net long one call as the counterparty to someone else's short-call position. to hedge that risk he creates a synthetic short-call to neutralize the risk the excess long-call position puts on his book. if another retail client was the counterparty to that closed short-put then the mm becomes the counterparty to the long-put holder's contract. in order to neutralize this new risk the mm creates a synthetic long-put position by shorting stock and buying a call (the negation of equation (1)). both of these transactions, synthetic long-put or synthetic short-call, are bearish for the stock, so if enough retail short-puts are liquidated the mm's will drive the price of the stock down as they hedge risk. the drop in price of the underlying reduces the price of calls and the short-call holders start buying back their positions. this, in turn, engenders new risk for the mm's so they start hedging the liquidated short calls and these hedges are bullish for the underlying. in this way the stock price circles around the big strike while retail option holders close out their positions. when this population of retail option positions is depleted then the stock can break the pin and the price moves unhindered by the option market.

so here's what i look for to suss-out pinning opportunities. first of all, the equity has to be high- priced (think aapl) because this is going to keep a big population of premium seller's around until friday afternoon. secondly, there needs to be a lot of open interest concentrated in select strikes, like tens of thousands of contracts. third, there needs to be relatively equal numbers of puts and calls in that concentration as any imbalance will be hedged already. lastly, the price needs to wander close enough to the big strike to get pulled toward the strike. this is like magnets - hold them far apart and nothing happens; close together and you can't pull them apart.

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