What a difference a week makes. Last week, markets plodded higher for 5 consecutive days. That type of movement is fine for buy and hold investors but excruciating for traders. Even decidedly negative data on PPI and consumer sentiment were unable to deter the S&P 500 Index’ (SPX) trend. The seeming lack of interest in potentially detrimental news caused me to label this a Nihilist market earlier this week.
This week we had much more back and forth trading. Yet I would argue that until the release of the FOMC minutes we had vastly different reactions to similar types of news. A shortfall in retail sales led to a sharply negative reaction on Tuesday before markets recouped about half their losses. I believe that it was less about a change in psychology than a change in expiration week dynamics.
As we approach expiration, the effects of volatility get magnified. When a trader holds expiring options, even small moves in underlying stocks can cause big moves in his overall exposure. Depending on the size of the move and who is on the long side vs. the short side (for options for every long there is a short), the moves can get exaggerated or dampened. This is because of the way that changes in delta and gamma in near-the-money options accelerate as we approach expiry. In the ensuing paragraphs I hope to explain that effect, hopefully in layman’s terms.
Let’s get an important mathematical concept out of the way first. The quick wonky explanation of delta and gamma is that delta is the first derivative of an option price with respect to stock price, while gamma is its second derivative. The longer answer is much more useful.
An option’s delta is the amount that an option will move for each dollar change in the underlying share price. For example, a trader who is long a .50 delta option would need to sell 50 shares of stock for each contract they own. (Remember that standard North American options contracts represent 100 shares of stock.) Although it is not strictly a measure of probability, one can think of it as a measure of the likelihood that a trader will find their option in the money at expiration. An in-the-money option has a higher delta than an out-of-the-money option because it is more likely to be in the money at expiration.
The problem for traders is that deltas are always subject to change over time. As stocks move toward or away from strikes, the delta changes. That is gamma, which is the change in an option’s delta for each $ change in the underlying share price. Because many traders like to stay hedged, they must constantly trade stock against changing delta exposures.
What makes expiration so treacherous is that gamma is magnified as we approach expiration. Let’s say we are long $20 calls on a stock that goes from $19.95 to $20.05. If we have several days to go until expiration, the delta may go from 0.48 to 0.52, because the stock has plenty of time to move around before the options expire. Even active hedgers may not find that move sufficient to concern them.
Now let’s say we are right around the close on expiration Friday. If a stock is at $19.95, the calls are out of the money with a delta approaching zero. If we are just before expiration, they are unlikely to be exercised. If the stock suddenly jumps to $20.05, the delta flips to nearly 1.00 because holders would now be quite likely to exercise the calls to get long stock. That forces a lot of hedging. The long call holders went from unlikely to own stock after expiration exposure to highly likely. They may be incentivized to sell shares to lock in a profit. On the flip side, those who are short the calls found themselves much more likely to be short stock. They may want to cut their losses by buying stock.
We just offered two highly different cases involving the same stock. In the former case, the delta changed only marginally. We can say that the gamma was low because a move caused only a small change. In the latter case, the gamma was almost infinite, because the same move caused a complete flip in delta from 0 to 1.0 almost immediately. As with most calculations involving derivatives, the changes in delta and gamma are not linear. The rise in gamma accelerates as we approach expiration, meaning that hedging activity is likely to increase.
As noted earlier, much depends upon who owns the expiring options. Bear in mind that whoever is long gamma is incentivized to buy low and sell high, while those who are short gamma find themselves needing to do the opposite. Trust me, it is much more uncomfortable to be short gamma in a volatile market as we approach expiry. The market becomes a contest of wills. If the hedgers are long and in control, they tend to dampen wild moves. If not, the moves become exacerbated.
Remember that each of the last few expirations saw major moves on major news. We had a June swoon in response to an FOMC meeting and Powell press conference that occurred just ahead of a quarterly expiration. In July, we had an adverse reaction to negative economic numbers like PPI and Michigan sentiment. (Yes, the same numbers that were ignored last week). Now we are in trying to digest a potential change to Fed stimulus. The minutes of the June FOMC meeting that were released earlier this week have morphed the discussion from whether the Fed will taper to when they will begin doing so. We would be remiss to think that volatility couldn’t result from that.
And bear in mind that a rally like we are seeing this morning is still a form of volatility. It’s simply socially acceptable volatility. Volatility measurements consider up and down movements more or less equally, but people react quite differently. A ½% rise is taken largely in stride, while a down move of that magnitude has people wondering why. Investors have become somewhat inured to quiescent markets over the past year. Expiration weeks provide an important reminder that complacency is not always a winning strategy.
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