Steady with the Skew
Vol #131: June 1st, 2023
The last step before you were put on a badge was Phase III. As much of a final test as a victory lap, this three city tour was intended to be the capstone training class and office visit for the next class of risk takers.
New York’s sessions focused on corporate actions and stock loan. The risk desk there explained the murky underworld of equity borrows, and we were well rested and eager to learn. Chicago was mock central. The biggest size pit traders haunted the CBOE’s halls. Our very own VIX godfather gave classes on special situations. By the time Philadelphia came around we were pretty beat.
The schedule was light, the main reason for being there was a class with the firm’s head of quant research. At the end of our tour now, we’d become experts in gaming the firms per diem. Saving up some scraps we headed to Smith & Wollensky for lunch because class didn’t start until after the bell.
The famous steak house sat in a decadent old building on Rittenhouse Square, amongst money older than the Liberty Bell. We couldn’t have been more out of place, but for six floor creatures the only option was a nice big round table set against the window. Someone said the steak sandwich was good, and at $22 it had to be true, so a half dozen of those adorned our white table cloth.
I remember more about that steak sandwich than I do about the class afterwards. We didn’t even touch martinis but the food coma was enough to turn a long mathematical proof into a lullaby.
It’s too bad, because it took me a bit to really grapple with the concepts I initially snoozed over. We had all seen skew graphs on the traders machines, and I roughly understood why it exists. But probably not the way someone who was risking his career and other people's capital on it should.
The first layer explanation is simple supply and demand. More buyers than sellers is not just the cheeky response to why the market ticked green today, but a sensible gesture at why downside puts typically have a higher implied volatility than upside calls.
Most people are long equities. The simplest and most common use of options is to buy protective puts and sell covered calls. Supply and demand, voila. There’s a romantic notion of the pre-computer floor trader feeling in his gut that more custys come for these, I better raise price.
After a couple cycles (like living through the 1987 crash) he might even have the intuition that when things move down, they move down fast. You’re worried about stock going through your short put by dollars, not nickels. There’s something to that too - returns exhibit skewness to the downside. Though ultimately it is only the short upside call that has truly unbounded risk, all puts stop at 0.
That might pass a CNBC sniff test, but things like put call parity and the potential for arbitrage leave that a bit unsettling if you stare at these curves long enough. Spot:volatility correlation is likely to start to take hold.
This rule of thumb suggests that as equity prices go down, volatility goes up and vice versa. This also makes intuitive sense and is well demonstrated by price charts. AAPL stock in orange goes up and to the right almost 20% in the last three months while 30 and 90 day implied volatilities drift from over 30% to under 20%.
Implied volatility is the options market's combination of thermometer and barometer, predicting what comes next. When stock prices are going down, the heat and the pressure go up. Skew is just showing that, right?
Drilling all the way down, stocks are CUSIP ledger items in your broker’s broker’s DTCC account that represent a slice of ownership in a company, with all those rights and rewards. If the value of a company is going down, that is by definition stormy weather. If the general business climate is worse, stocks fall and vols rise for macro reasons. If thinner margins or flattening growth forecasts rain on the quarterly earnings call, your downside is yours alone to own.
When business is rosey, there's calm and cool in the air. Rising stock prices make everyone but short sellers happy. Except of course what can contemporaneously be referred to as the NVDA objection.
The stock is up 180% this year. Hundreds of billions of dollars of wealth created in months. They are selling the picks and shovels to whatever web3 or AI revolution you’re marching towards. Isn’t a crash inevitable? The mighty CSCO who sold routers to the web1 heads is still only 60% of its bubbalicious Y2K peak.
Shouldn’t the implied volatility rise, or at least not fall as much when a stock like this floats weightlessly to trillion dollar dreams? That’s the difference between movement along the curve, and movement of the curve. Skew is not static.
A vol surface is a snapshot in time. It reverse engineers market prices, and then performs some basic scrubbing of wonky or bad datapoints. Then to create a curve, skew can most simply be plotted explicitly - each strike with its implied volatility. In highly liquid markets like SPY shown below, that curve looks pretty close to the type of polynomial that today’s multi factor spline models would produce.
Models point out potential mispricings. You won’t last long though if you’re whacking every funny looking kink in the curve. There are frictions like transaction costs and capital, but also constraints that the pricing model can’t know about like takeover deals or debt triggers.
This snapshot is predicting that with all the information known and priced today, if SPY heads up towards $430 and $435 by June expiration, we’d expect implied vol of the ATM options to be around 12-13%. We’ve just slid along the curve.
Movement of the curve is when new things are priced in, and the market starts to get queasy from their fear of soaring new heights. How this fear gets priced in varies widely, and it’s not always a fear of falling prices. Implied vol can rise to the upside.
The below chart shows how NVDA’s 30 day options skew has changed since their blow-out earnings. The light green line is the 60 day average of the implied skew for these options, and the dark green in todays. The market is implying higher volatility to the upside. “If this thing goes, it could really go.”
That also feels right. We’ve seen fan favorites like TSLA, AMC or GME exhibit this type of skew and price behavior. From a supply and demand perspective this can get explained away by more buyers than sellers for upside. Speculators are buying calls, because even as the price rises, everyone from basement retail to buttondown asset managers who is under-allocated is going to start chasing this darling’s performance.
Moving beyond just equities, other assets have their own unique prediction of how volatility will behave. Currency implied volatility charts look much more smiley with both upside and downside wings rising with equal slope from the at-the-money. The Yen/Dollar pair moving sharply or significantly in one direction almost certainly indicates some heightened temperature in either the US or Japan.
Commodity assets have the opposite skew to equities. Prices will rise for soybeans and corn if there’s a drought or weevil infestation. All of this leads to higher implied volatility.
Bitcoin and Ethereum also had a “reverse” skew for long periods of 2020 and 2021. They were a commodity currency with a meme stonk fan base and regulatory moats that created double digit interest rates. If you thought crypto assets are going up, this can be a gift. Puts are cheaper and calls are more expensive, meaning the traditional long put/short call collar paid you for protection.
Without a single drop of math, all different shapes of volatility smiles make intuitive sense for their asset class or underlying situation. The skew curve says that when stock moves to X price, implied volatility is expected to be Y. But today it hasn’t, and that downside put option is trading 25% and this upside call option is trading 15%, why can’t I pocket the spread?
One of the tools we used to track electronic trading activity was a summary of trades by implied vol levels bought and sold. You could easily have a nice big difference between the two that masks a dangerous skew position. It’s not dangerous just because of the short stock risk you have likely accumulated, or even because your net long or short the wrong vol level.
It’s because of the path you take to expiration.
This last nugget of intuition about how multiple implied volatility levels can coexist in the same expiration at the same time and not represent arbitrage is inspired by the options pricing explanations in Financial Hacking by Philip Maymin.
Volatility means a bumpy ride, but the bumpiness of those pressure pockets is non-uniform. We’ve talked a bit before about heteroskedasticity of volatility. The distribution of variance is not normal. A lot of nickels and then a few dollars.
On the course of realizing a volatility of 20%, an asset will have moments of 25%. It will have moments of 15%. Those moments of 25% will tend to occur when stock is down, and the 15% will occur when stock is higher. 20% can be the fair and realized historical volatility for that underlying, all while 25% was the fair implied volatility for the short put and 15% was fair for the long call.
In the stylized price chart, I set the volatility to be a function of the stock price, so when stock was below 99 it was a 40 vol stock, and above 101 it was a 10 vol stock. Around 100 vol was 25. Stock doesn’t move much when it’s high, but it jumps around a lot when price dips.
When stock is near your short downside it will be realizing a much higher vol. To hedge yourself delta neutral, you are in a short gamma nightmare, buying high and selling low. Even if the implied vol on your now far out of the money upside option increases, this is all about the short gamma where you’re sitting.
Conversely on the upside, when you’ve got long gamma, stock isn’t actually going to move and provide you with the opportunity to scalp your theta bill. There’s no such thing as a free lunch in the markets. Skew locks or arbitrage are mostly fantasy.
If you want a straight bet on what the realized volatility will be, you’re in the market for a variance swap. Those are big boy contracts, so sign up for an ISDA here. In vanilla equity options the skew exists because the path is crooked and varied.