The Peculiarities of Volatility

ELI5/TLDR

Ernie Chan, ex-physicist turned hedge fund manager, makes three claims about volatility. First, predicting realized volatility — how much a stock actually wobbles tomorrow — is easy. A simple, decades-old model called GARCH gets the direction right about two-thirds of the time. Second, that prediction is almost useless on its own, because the thing you can actually trade (VIX-linked products) tracks implied volatility, and implied moves independently of realized about half the time. Third, the gap between predicted realized vol and current implied vol is itself tradeable — it is essentially the variance risk premium. And once a popular VIX strategy gets written up in a paper, it tends to die.

The Full Story

Predicting volatility is the easy part

Volatility is the size of the price wiggle, not its direction. The standard tool, GARCH, is a workhorse from the 1980s — Robert Engle won a Nobel for the family it sits in. The mechanics are unglamorous: take a weighted sum of past realized variances and past predicted variances, fit the coefficients by maximum likelihood, and you have a forecast for tomorrow’s variance. Think of it like a rolling thermostat that adapts when the room gets hotter.

Chan tests it out-of-sample from 2010 to 2016 on five instruments — SPY, USO, GLD, AAPL, EUR/USD — and asks only whether GARCH gets the sign of the next day’s vol change right. The hit rates: 66%, 67%, 59%, 60%, 62%. Statistically these are large.

If we have this kind of accuracy in predicting the sign of one-day price change, not volatility change, but price change, we would all be rich.

So why is direction easy for vol but impossible for price? Chan answers with an arbitrage argument. Anyone with a 65% edge on the sign of price moves would raise a trillion dollars and trade it into oblivion within months. Edges on volatility direction survive because there is no clean way to bet on them. You cannot buy a realized-volatility contract. You can only buy proxies — options, futures, ETFs — that are tethered to implied volatility, which is a different animal.

Realized and implied are barely on speaking terms

Here is the empirical bombshell. The day-to-day correlation between changes in realized vol and changes in implied vol is, statistically, zero. They move the same direction 51% of the time, which is what you would get from flipping a coin.

On days the market rises, the correlation actually flips negative. The intuition: when the S&P goes up, options sellers relax — fewer people want crash protection, so implied vol falls. But a big up-day still counts as a big absolute move, so realized vol mechanically rises. Insurance gets cheaper at the same moment the underlying is jumping around more. This anti-correlation on up-days is the leverage effect’s quieter cousin. (The classic leverage effect — vol spikes when markets fall — is well documented; Chan is pointing at the symmetric oddity on the upside.)

The practical sting: the naive idea of “GARCH predicts higher vol, so buy VXX” is a relentless loser. The strategy’s equity curve drops in a straight line. The only time it made money was the one-week chaos around the August 2011 US debt downgrade.

The lesson in this horrible equity curve is that just being able to predict realized volatility does not imply that you can predict implied volatility.

The arbitrage hides in the gap

Predicting realized vol still has a use — not as a directional bet on its own, but as a yardstick against implied vol. Chan’s trading signal is the spread: GARCH’s forecast of tomorrow’s realized vol minus today’s VIX. When the spread is positive, options look cheap, so buy VXX. When negative, options look expensive, so short.

This is the variance risk premium dressed in different clothes. Over long periods, implied vol systematically sits above realized vol — options buyers pay a premium for insurance. The premium is a real risk premium because when vol spikes, the people who sold the insurance get vaporized; expected returns from being short vol compensate for the occasional cratering.

Chan’s spread-based signal earned a 26% CAGR on VXX out-of-sample, Sharpe 0.7. Not statistically airtight, but the equity curve respects itself. The implied claim is that GARCH’s realized-vol forecast is a better predictor of future implied vol than today’s implied vol is — a quiet provocation to the options pit, which usually assumes it has already priced everything in.

A separate paper by Ahmad and Wilmott (2005) takes the same signal and bolts it onto a delta-hedging strategy: buy any option (put or call) whose implied vol sits below GARCH’s forecast, then delta-hedge it daily until expiry. Under Black-Scholes assumptions you can derive the profit analytically. Chan tried it on Apple, did not get the promised profit, and shrugged — the assumptions almost certainly broke.

Why VXX is not the VIX

The last third of the talk is about a structural quirk that surprises new vol traders. SPY tracks the S&P 500 cleanly because the index is a slow-moving basket of stocks. The VIX, by contrast, is a portfolio of S&P options between 23 and 37 days to expiry, with peculiar weightings. The CBOE itself admits the composition shifts minute to minute. You cannot hold a portfolio that replicates the VIX.

Worse, options decay. Even if implied vol stays perfectly flat, the portfolio underlying the VIX bleeds value through theta — the time decay of premium. VXX, which holds rolling VIX futures, inherits this bleed as a negative roll return. The VIX futures curve sits in contango about 90% of the time, meaning the future is priced above spot; as the future converges to spot at expiry, holders lose money mechanically. This is the structural cost of buying volatility.

Negative theta, or the time decay of options value, leads to… the VIX future has a negative roll return.

But this curse can be inverted. If contango bleeds you, sell it. The strategy: short VIX futures when the futures price sits above spot VIX (positive roll return for shorts), go long when the curve flips into backwardation. This is the carry trade in volatility — collecting an insurance premium while accepting tail risk.

From 2004 through 2013 this strategy looked like a money-printing machine — a 60% annualized return, Sharpe of 1, exponential equity curve. Then in 2012 a paper by Simon and Campasano described it. By 2013 it had stopped working. The arbitrageurs had crowded in.

Chan calls this the tail wagging the dog: enough capital trading VIX futures that the futures price now constrains where SPX option prices can go. If the VIX index is mostly a derivative of activity in the VIX futures pit, the index is no longer a clean forecast of realized vol. It is a price set by traders trading each other.

The questions afterward sharpened things

One audience member asked whether the roll-return strategy might still work on the long side — surely the VIX still spikes when people panic? Chan’s answer was careful: yes, the VIX still spikes, but the question is whether today’s VIX level predicts tomorrow’s spike. Often option traders overreact and push VIX too high; the right trade is then to short, not buy.

Another asked whether the GARCH-vs-implied trade is a risk premium or a mispricing. Chan thinks it leans toward arbitrage — there is no clear theoretical reason GARCH should win — while the roll-return short is unambiguously a factor return, compensation for taking volatility-tail risk.

Key Takeaways

GARCH gets the sign of next-day realized vol correct on roughly 60-67% of days across major instruments. The model is decades old and trivially available in any stats package.
Direction-of-vol forecasts survive because they are not directly tradeable. Direction-of-price forecasts at the same hit rate would be arbitraged away instantly.
Realized and implied vol changes are uncorrelated day-to-day (51% same direction). On up-days they are mildly anti-correlated.
Buying VXX because GARCH predicts higher vol is a “relentless loser.” The signal is right but the instrument is wrong.
The spread GARCH-predicted realized vol minus current VIX is a tradeable variance risk premium signal. Out-of-sample: 26% CAGR, Sharpe 0.7.
The VIX index is a portfolio of S&P 500 options whose composition shifts every minute. It cannot be physically replicated.
VIX futures sit in contango ~90% of the time. Holding VXX bleeds steadily through negative roll return — the structural cost of options theta passed up the chain.
Shorting VIX futures in contango (the vol carry trade) returned 60% annualized with Sharpe 1 from 2004 to 2013, then died after Simon and Campasano (2012) published the recipe.
Strategies arbitraged away can come back to life if enough participants give up on them. Worth re-checking dormant strategies periodically.
Trading VIX futures back-influences SPX option prices — the derivative now moves the underlying. This calls into question whether VIX still forecasts realized vol.

Claude’s Take

This is a careful, honest talk. Chan is not selling a strategy; he is explaining why the obvious volatility trades do not work and why the surviving ones rest on a real risk premium that occasionally eats your face. The Sharpe ratios he reports (0.7, 1.0) are also honest — these are not 3-Sharpe pitch-deck numbers.

The big idea is genuinely useful: volatility forecasts and volatility products live in different dimensions, and most of the alphabet soup of VIX ETFs is structurally designed to bleed. Anyone who has watched XIV implode in February 2018 — eleven months after this talk — knows the punchline that Chan was already gesturing at. People who short volatility “do not have a very long, happy life,” he says, almost in passing. That is the tail risk in a sentence.

A few caveats. The variance-risk-premium spread trade has a Sharpe of 0.7 on out-of-sample data and only one VIX-spike regime (August 2011) doing most of the heavy lifting in the equity curve. That is not enough to call it durable alpha; it is enough to call it directionally suggestive. The roll-return strategy got demolished by crowding by 2013 — Chan presents this almost as a parable about the half-life of published edges. The 2017 vintage is also pre-COVID, pre-2020 vol regime, pre-zero-DTE options, pre-most-of-what-makes-current-vol-markets-weird. The structural points (VIX construction, theta, contango) all still hold. The strategy results probably need a retest on post-2017 data.

There is no neat conclusion at the end of the talk — Chan asks an open question: if VIX is now driven by futures arbitrage rather than expectations of future realized vol, what is the VIX even measuring? That is the right place to leave it.

Score: 8. Genuinely educational talk from a practitioner who actually traded this stuff, gives empirical numbers rather than hand-waving, and tells you when his strategies stopped working. The half-point dock is for the dated empirical work — useful as scaffolding, but the markets have moved on. Pair with newer vol-surface literature for current calibration.