Swimming Naked
#38: On Roulette, Volatility, and the Death of the Tails.
Imagine a roulette wheel.
This roulette wheel is split into 100 equal segments, of which 99 are Green and 1 is Red. It looks like this.
The game is simple - one player must bet on Red, the other player bets on Green, and the winner gets a payout of $100. Players dynamically wager on the game, and the sum of the wagers must equal the payout of $100. For example, if someone is willing to wager $2 on Red, the counterparty must pay $98 to pick Green.
For a game of chance, it is easy to calculate the fair wager. Red has a 1% chance of winning, and Green has a 99% chance of winning. A player should be willing to pay $1 for Red and $99 for Green. Both of these bets have an expected value of zero, assuming the game could be played an infinite number of times1.
But if you were to drop this wheel on a Las Vegas floor, this zero-sum game would suddenly become much more interesting.
Even if both players only wagered fairly, Green would win almost every time, taking a dollar from the Red player with each spin.
Over time, the Red players become exhausted with repeatedly losing and leave the table. Meanwhile the Green player becomes more comfortable with their downside risk because they haven’t lost yet. This imbalance in interest drives down the wager below $1, in favor of Red.
Eventually, Red hits. People go nuts as Red players make a killing and the Green players lose their shirts. The commotion draws in people from across the floor to come and play this cool game where you can make a ton of money betting on Red. The influx of new players drives up the wager above $1, in favor of Green.
Psychological factors - loss aversion and recency bias - would cause the actual wagers on this fixed-probability game to fluctuate from the $1 fair value. Practical limitations may be even more important - players may be forced to leave the table because they lost all their money.
The Volatility Wheel
Volatility - the financial product - is similar to this game of roulette. Volatility derivatives involve two counterparties with opposite cash flows - for every buyer there must be a seller. Selling volatility is like playing Green, and buying volatility is like playing Red. The price of volatility is determined by the relative willingness of buyers and sellers to transact - dynamic wagering.
Volatility also has a very skewed distribution of outcomes. Most of the time selling volatility earns a small premium from the buyer but, on occasion, the seller must payout a large sum to the buyer.
But volatility is far more complex and more important than a zero-sum game of chance. The volatility market is effectively an insurance market for the underlying asset class (most commonly equity markets, though increasingly important in other assets such as interest rates and FX).
And like most derivatives, cause and effect is a two-way street. Volatility is influenced by changes in equity prices, but changes in the price of volatility also influence the price of equities. Everyone invested in the stock market is indirectly tied to this high-stakes, high-variance game, whether they recognize it or not.
In late 2021, I became fixated on understanding the game of volatility, both because of its influence on the market and as a matter of speculative opportunism. I wrote extensively about the topic in The Volatility Squeeze Part I, Part II and Part III, The Volatility Curve, Volatility, Price and Pain, and The Fragile Market Hypothesis. These posts concluded that the structure of the volatility market was inherently unstable - inevitably leading to dramatic spikes in volatility and sharp market declines.
In hindsight, the posts simply explain the rules of the game - the distribution of returns and the consequences of landing on Red. Yet, they fail to address the cost to play - the wager.
Unlike this roulette wheel, no one knows the precise probability of a dramatic spike in volatility, and so it is much harder to price. The odds are constantly changing and are influenced by the wagers themselves. Spikes in volatility accelerate when sellers are caught offsides and are forced to cover. A higher “premium” paid by the buyer means a higher margin of safety for the seller, raising the bar necessary to trigger a short-covering feedback loop.
The thesis was too obvious and too popular. The table was crowded with players betting on Red.
Despite the year-long bear market, volatility as a hedge has failed and has added to losses instead. Volatility as a bet has been a donut2.
Pricing Tails
There are many ways to insure against market declines or buy volatility3 with a range of risk and payoff parameters. A simple short position against the market is the most simple with the lowest risk. Buying market puts provides additional leverage depending on the strike and expiry. You can also buy volatility exchange-traded-products (ETPs) which provide direct exposure to VIX futures contracts. The highest risk and most levered positions are options on the VIX or volatility ETPs.
Out-of-the-money (OTM) market puts or OTM volatility calls provide exposure to the extreme tails of the distribution - a dramatic spike in volatility or market crash. These instruments are like high-deductible insurance policies. They have the cheapest premiums, but with the highest threshold before they become profitable. The allure is an extraordinary payout - the risk is that they rarely ever pay.
But just as options can have a significant impact on a given stock, so too can options on volatility create dramatic moves in the price of volatility. Deep OTM options may not influence the price of volatility initially, but the inherent leverage in these products provide the fuel that accelerate spikes if they begin. They are tinder.
By late 2021, there was huge demand for these “crash protection” tail hedges, resulting in historically elevated prices. Over the past year, the market has declined and the absolute level of equity volatility has increased. Yet, without a crash, the most levered bets - OTM market puts and OTM volatility calls - have expired worthless.
Accordingly, buyers have walked (with empty pockets).
The defining characteristic of the volatility market over the past year has been the decline in the demand for, and cost of, tail hedges.
First, consider the CBOE volatility-of-volatility index, VVIX4, which measures the cost of options contracts on the VIX.
In prior episodes sudden market disruptions such as Volmageddon or the 2020 COVID crash, VVIX (and the VIX) spiked dramatically as the equities tanked. The cost of VIX options remained very elevated throughout the epic 2020-2021 bull run, as participants feared a repeat crash.
But this pattern reversed in the 2022 bear market. The further the market has fallen, the cheaper VIX options have become. Earlier this month VVIX closed at its lowest level since 2014.
Advanced measurements of tail hedge costs tell the same story. TailDex (TDEX) measures the cost of 30-day, 3 standard deviation OTM put options. This index is down ~65% from its average during the COVID boom, recently hitting lows not seen since 2014.
Finally, the SkewDex (SDEX), which compares the implied volatility of at-the-money options to out-of-the-money options, shows that demand for tail hedges peaked in late 2021 and has declined even more dramatically since. Current readings are the lowest on record since the index began in 2013.
What makes these movements astonishing is that they have not coincided with a period of market tranquility. Rather both realized and implied volatility of equity indices have increased significantly relative to the 2020-2021 COVID bull run and long-term historical averages. Realized volatility has remained above 15 for nearly a year - the longest period since 2008.
The macro backdrop isn’t exactly supportive either. The Fed is hiking at its fastest pace in decades, liquidity is drying up, leading economic indicators are plummeting, corporate earnings are rolling over, and the majority of economists expect a recession in the coming year.
Swimming Naked
Many have offered explanations to describe the strange behavior of volatility over the past year, ranging from plausible (0DTE options) to conspiratorial (the Fed is buying vol). To me, the simplest explanation is the human one.
Why are investors now convinced that a tail event is unlikely despite the obvious headwinds? Because so far, it hasn’t happened. Recency bias also explains why tail protection was so expensive in the midst of the QE-fueled bull market.
As Warren Buffet remarked, it's only when the tide goes out that you learn who has been swimming naked. As the size and importance of options and volatility grew over the past decade, we learned that the tide can go out in the blink of an eye.
The prior instances of volatility spikes have come suddenly, often as the market reached new all-time highs. It isn’t a surprise that investors feared a similar end to the great COVID bubble - many like me predicted it. Wary of exposing their shiny buns, investors bought protection at any cost.
But this tide has been different - slow and undulating. Attempts to hedge via volatility or OTM puts have merely added insult to injury. Collectively, the market has decided it’s better to skinny dip.
I can’t calculate the probability of landing on Red. Even if I could, I couldn’t tell you when it will happen. But I do know the buy-in has become quite cheap, as few Red bettors are left standing. This doesn’t necessarily mean it’s a smart bet today, only that it is smarter than it was a year ago.
The most likely outcome of betting Red is to lose. Almost always…
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As always, thank you for reading.
-TLBS
A smart player would play Green if the wager is greater than $1, and play Red if the wager is less than $1. But simple probabilities do not guarantee success, because there is a high degree of variance regardless of the wager. You could still make money with a “dumb” wager over $1 on Red, if Red hits before the hundredth spin. Conversely, you could lose money with a “smart” wager if it takes more than a hundred spins to hit.
Another wrinkle to consider. How many dollars is each player risking by playing the game? The intuition is to say that that each player is only risking his wager, and therefore Green is putting more capital at risk. This is technically true on any individual spin. But Red should expect to lose almost every time. On average, it will take Red one hundred spins to hit, which means that the Red player should expect to play the games a hundred times, wagering $100 in total.
This matters. If you are betting on a low probability outcome because you think it is mispriced, you still must be prepared to lose most the time and size your bets accordingly. Otherwise, you will not last long enough to see your thesis through.
Unless short-dated, and well timed.
For a more complete discussion of these interactions, refer to The Volatility Squeeze.
The VVIX calculates the implied volatility of the VIX based on options pricing in the same way that the VIX calculates the implied volatility of the S&P 500.
What’s nice read for Friday afternoon with a coffee. Thank you for all the work TLBS!
Great writeup Bear, been thinking about this subject a lot lately as well. thank you for all that you share!