Fear Predicts Returns: Bollerslev, Tauchen and Zhou

Predicting stock market returns is a graveyard. Generations of researchers have proposed variables that should tell you whether the coming years will be good or bad: the price-earnings ratio, the dividend yield, the default spread, the ratio of consumption to wealth. Most of them work weakly, work only over very long horizons, work only in-sample, or stop working the moment someone publishes them.

In 2009, Tim Bollerslev, George Tauchen and Hao Zhou proposed a new one, and it is unusual in three ways. It works at a short horizon, a matter of months rather than a decade. It beats the established predictors on their own turf. And it comes not from accounting data or macroeconomics, but from the options market's fear.

The problem: the traditional predictors are slow and unreliable

The classic return predictors, like the price-earnings ratio, all share a shape. They are slow-moving valuation measures. When stocks are cheap relative to fundamentals, subsequent long-run returns tend to be higher. Fine. But these variables move at a glacial pace, they only say anything meaningful at horizons of many years, and the statistical evidence behind them is notoriously fragile because you have so few genuinely independent observations.

What nobody had was a predictor that says something useful about the next quarter. That is the gap this paper fills.

The key idea via analogy: how scared is the market, relative to how dangerous the world actually is?

Start with the variance risk premium: the gap between what the options market charges for future variance and what variance actually turns out to be. Roughly, and with some care about the details, it is the difference between the VIX squared and a forecast of realized variance.

Think of it as a fear gauge, adjusted for reality. The VIX alone is not enough, because a high VIX might simply mean the world genuinely is dangerous right now. What you want to know is: how much are people paying for protection over and above what the danger warrants?

• When that gap is narrow, investors are relaxed. They are not paying much of a premium to be insured. They are comfortable holding risk.
• When that gap is wide, investors are frightened. They are paying handsomely for protection, far more than the objective risk seems to justify. They are desperate to offload risk.

Now apply basic economics. When everybody is desperate to offload risk, whoever is willing to take the other side must be compensated generously. Which means expected returns to holding risky assets should be high at exactly those moments.

That is the hypothesis: a wide variance risk premium today should predict high stock returns going forward.

What they found

It does. And the effect is strongest at an intermediate horizon of about one quarter, which is a striking result in itself, because it sits in a horizon range where nothing else works well.

More pointedly, at that horizon, the variance risk premium outperforms the traditional predictors, including the price-earnings ratio, the default spread and the consumption-wealth ratio. A variable read off the options market, capturing how much investors are paying for fear insurance, forecasts the market better over a quarter than the accounting-based measures the profession had been arguing about for decades.

The economic story hangs together well. The variance risk premium is a real-time, market-based measure of how much risk aversion is in the system right now. Valuation ratios are indirect and slow. The options market repraices continuously, and it is where nervousness is most directly expressed in money.

Why it mattered

• It found a short-horizon predictor that works. That is rare, and it is why the paper has been so heavily cited and so heavily built upon.
• It gave macro-finance a job to do. The finding is naturally explained by models where investors fear not just volatility but uncertainty about volatility, so-called volatility-of-volatility. The paper is closely tied to that theoretical literature, and it gave those models a sharp empirical target.
• It turned the VIX into an asset allocation signal. Practitioners took the obvious lesson: a wide variance risk premium is a signal to take more equity risk. Whether that works after costs and out of sample is another matter, but the idea entered the toolkit.
• It complements Carr and Wu. Carr and Wu measured the premium and showed it exists. Bollerslev, Tauchen and Zhou showed it contains information about the future. Together they are the foundation of the variance risk premium literature.

The honest limitations

• Return predictability findings are fragile, and everyone knows it. This is the big one. The history of return prediction is a history of variables that worked beautifully in-sample and then quietly stopped. Small samples, overlapping return horizons that inflate significance, and the fact that hundreds of researchers were hunting for predictors at once, all mean that a healthy scepticism is warranted here as everywhere.
• The premium must be estimated, not observed. You can read the VIX off a screen, but the "expected realized variance" that you subtract from it is a forecast, and the answer you get depends on how you construct that forecast. Different reasonable choices give measurably different variance risk premium series, and therefore different predictive results.
• The sample is short. The data starts in the 1990s because that is when the necessary options data begins. That is not many independent quarters.
• The mechanism could run the other way. A wide variance risk premium and high subsequent returns could both be driven by something else entirely. Establishing the causal story is much harder than establishing the correlation.
• Trading it is not trivial. A signal that says "hold more equity when fear is high" tells you to lean in during panics, which is psychologically brutal and, if the panic keeps deepening, expensive.

The one-line takeaway

Bollerslev, Tauchen and Zhou showed that the gap between what options charge for volatility and what volatility actually delivers is a real-time measure of how frightened investors are, and that when that fear premium is wide, the stock market tends to reward you over the next quarter, beating the price-earnings ratio and the other traditional predictors at their own game.