Butterflies of Chaos
Vol #147: September 21st, 2023
Last night my college roommate texted our dad group a picture of himself in a chef’s hat. Never mind I also have a picture of him wearing a pita on his head 20 years ago, he was the only one of us four to go on to get a PhD, and is now an esteemed professor of early childhood education.
He has just started taking night classes at the local culinary school to scratch a long time itch. I’m extremely jealous. The skills will be as durable as the confections are ephemeral. What is most tantalizing about this is that he’s stepping into a new arena, trying things. For real.
A preschool classroom, exchange floor, or short order kitchen look like chaos to the casual observer. The beauty of these organic systems is that there is a deeply embedded process obeyed by the participants which keeps them functioning like a tightly oiled machine.
When two burgers get fired and a two hundred lot goes bid, a half dozen highly attuned ears perk up and immediately respond. “Yes chef” takes one more syllable than “sold”, but in either case the grunts, sweat, and enthusiasm mirror the precise execution that follows.
Chaos theory is the study of dynamic systems, and the sensitivity of their patterns to initial and changing conditions. The weather is a perfect example, and it was creating a meteorological model that clued Edward Lorenz into the fact that something was going on under the hood.
In the early 1960s he was working at MIT, and in an effort to minimize compute in the originally scarce blockspace, rounded the decimal places on his calculations from 6 digits to 3 digits. This wasn’t just cheapskatedness; amongst the top mathematicians at the time this type of variable sensitivity was considered unimportant to the ultimate outcome.
As the forecast outputs changed dramatically, Lorenz realized that the inputs mattered - a lot. And most importantly, they mattered in an unpredictable way. Rounding didn’t lower the precision to just the broad side, it missed the barn completely.
Traders (like chemistry teachers) know decimal places can be significant. If you’ve ever stumbled into the back alley of retail FX trading, you’ll find soon to be bankrupt brokers that offer 100x margin and make the difference between 1.0915 and 1.0916 Euro to the dollar worth quite a few croissants.
Leverage magnifies the amplitude. The wave length is the same, the peaks are just further from the troughs. Chaos theory takes that sine pattern and shakes it like a battle rope. It’s not that inputs matter in that Superman III / Office Space kind of way where you skim interest calculations, in a dynamic system the slightest change can create a completely different outcome.
Lorenz’s speech debuting the concept was titled “Predictability: does the flap of a butterfly's wing in Brazil set off a tornado in Texas?” Options traders remember the day the VIX doubled, and how a previously thought to be benign rebalance triggered a fury with its programmatic demands.
The butterfly is a delicate creature. Derivative strategies are more commonly named for condors or seagulls; gritty birds with sturdy wings. Whether a painted lady or red admiral, the butterfly is much more likely to ride the air pockets than create them.
Perhaps that’s why the butterfly options structure is so elegant. These surface defining structures are a paradox in that long butterflies get you short volatility. They can also be a profitability mirage, where maximum value is practically impossible to attain.
Options are components. They’re tools to overlay on your portfolio that snip and tailor risk appropriately. Combined together in spreads they are even more powerful, where they are teased, pulled, and stacked on top of each other to define outcomes.
Black and Scholes taught us that calls are puts and puts are calls -direction is just a matter of the hedge. A long call spread is the same bet as a short put spread. Now if you sell a call spread and sell a put spread, you’ve got an iron condor.
Push those together so they have the same short strike and you have a butterfly. With all calls or all puts it looks like a long call spread (green) and a short call spread (red) above that. Finding the max profitability is intuitive because you want the long call spread to be worth its maximum and the short to be worth nothing. The one place that happens is exactly in the middle.
To put on this long butterfly trade you will pay slightly more for the long call spread than you collect from the short call spread, so it’s a debit trade. The most you can lose is the price you pay, with the ATM butterfly worth the most and flys getting cheaper as you move further away.
The profitability mirage comes because of the butterfly’s innate sensitivity. As expiration approaches, even if the underlying is sitting right at your short strike, the spread will still remain far below its maximum value. This is because the short leg refuses to completely decay until the buzzer rings.
So long as there’s a little bit of time left, that ATM option has increasingly more gamma. Whether the 100 call is in the money or out of the money when stock is trading $99.99 or $101.01 is a huge difference. For most intents and purposes the minimum price variation in equities is a penny. But a single penny difference in input will change billions of dollars in exercise value in products with significant open interest.
Butterflies need to close at EXACTLY the center strike to hit that peak of profitability. Because options automatically expire/assign on $0.01 values, if the butterfly isn’t closed down in advance of the bell, you risk some funky assignment potential. At $100.01, you’re short 2 calls but long only one to offset.
While you might not hit that max value where you buy for $0.15 and sell for $2.00, there are still some very interesting trades to do here. Wider butterflies are more expensive, but you are also benefiting from a larger target zone. The wings can be adjusted so that you have some directional bias in the trade.
The hockey stick payoff of options convexity comes because they are so sensitive to initial inputs. How they are traded is also chaos. A vintage clip of Robert Downey Jr. visiting Wall Street in 1992 confirms this at face value. But an important part of true “chaos” is the determinism of a highly ordered system.
The way a butterfly swings in value or a pit gobbles up a big order with carps and elbows is cacophony to the untrained eye. But the pricing model, allocation rules, and clearing margin provided are all highly structured systems, efficiently functioning.
Below are a few samples of some other writing I’ve done the past week. While The Till is more of an essay, these pieces are targeted trading research and theory about investing strategies. Both of the paywalls are open.
Thanks to everyone for subscribing, and happy trading.
A Ring of Champions: Spinning the Wheel With Dividend Aristocrats:
This piece from “Portfolio Design” looks at how to construct a basket of stocks for executing options strategy known as the Wheel.
It focuses on dividend payers as both an identifier of quality and examines the benefits of cash flow compounding.
We finish with execution considerations when rolling or closing your position.
The One Day Fed Straddle: 0DTEs are pricing little activity for today's FOMC
With the benefit of hindsight, we know that the market moved more than expected yesterday, but what signals did we have early on?
Examining reports from TheTape, we compare how 0DTE options were priced going into a big event compared to normal. (Hardly any difference.) We also look at the relative performance of short vol strategies over the past month.
My $0.02 - these products have interesting use cases for professional traders to micro-tweak their exposures, and for retail traders to learn and have fun. Any fears about them creating Volmaggedon 2.0 or predictive power they have on SPX direction is massively overblown.