The Memory of Markets: Why Volatility Is Predictable When Returns Are Not

In the long, smoky hallways of financial theory, few ideas are as paradoxical as volatility. It is the heart of uncertainty—an elusive ghost in the machine of modern capitalism. Yet, among all the variables that markets hinge upon, volatility may also be the most statistically predictable. This tension—between the chaos of price swings and the predictability of their patterns—is what Stephen Marra of Lazard elegantly dissects in his treatise, Predicting Volatility.

This article takes you into the mind of volatility itself, drawing upon decades of market behavior, statistical models, and the logic of fear.

The Curious Predictability of Risk

It begins with a simple question:

“If the market is unpredictable, why is volatility easier to forecast than returns?”

Returns are fickle. They dance to news, rumors, macro shifts, and mass psychology. Volatility, however, carries memory. It clusters. It reverts to the mean. And it does so not just in stocks, but across bonds, currencies, and commodities.

This is where we meet the first foundational concept.

Volatility Clustering: The Echo of Panic

In the aftermath of shocks, markets don’t calm immediately. Big swings beget big swings, and calm periods lull investors into complacency. This temporal inertia of volatility is measurable—returns may not be serially correlated, but the absolute values of returns are. That’s the essence of volatility clustering.

This insight, found in Mandelbrot’s early chaos theories and confirmed through decades of empirical data, gives rise to the first generation of statistical models that attempt to forecast volatility.

Beige Box: ARCH Foundations

Autoregressive Conditional Heteroskedasticity (ARCH), introduced by Robert Engle in 1982, embodies this insight:

σ²ₜ = α₀ + α₁ · ε²ₜ₋₁

Where today’s variance is conditional on yesterday’s squared return error. But ARCH had limits—it only looked one period back.

That led to its smarter cousin: GARCH:

σ²ₜ = α₀ + α₁ · ε²ₜ₋₁ + β₁ · σ²ₜ₋₁

Which adds persistence: today’s variance also depends on yesterday’s variance.

The Leverage Effect: When Fear Moves Faster than Greed

Markets fall faster than they rise. Negative returns, especially large ones, spike volatility more than equally large gains. This asymmetry is not just psychological—it’s structural. As prices fall, firms become more leveraged (their debt remains constant while equity shrinks), making them riskier.

This is the leverage effect, which GARCH extensions like EGARCH and GJR-GARCH attempt to model. They capture this asymmetry by letting negative shocks weigh more heavily than positive ones.

Mean Reversion: Volatility Always Comes Home

Volatility never stays extreme forever. High-volatility regimes calm down; low-volatility regimes eventually break. This mean-reverting behavior forms the basis for long-term forecasting and options pricing models.

σ̂ₜ = μ + φ · (σₜ₋₁ - μ)

Where volatility reverts toward a long-term mean μ. The speed of that reversion is captured by φ.

Empirically, the half-life of volatility—how long it takes to move halfway back to average—is about 15–16 weeks for realized volatility, and even faster (11 weeks) for implied volatility like the VIX.

Cross-Correlation: Volatility’s Contagion

During crises, asset classes become more correlated—not in returns, but in volatility. Bonds, equities, currencies—all catch the fever. GARCH models can be expanded to multivariate versions (MGARCH) to capture this web of interdependencies.

This matters deeply for risk parity and volatility-targeting portfolios, which rely on knowing not just how much risk exists, but where it's coming from.

The Models: Simplicity vs. Specificity

Marra walks through the evolution of models with the clarity of a market physicist:

1. Random Walk: Tomorrow’s volatility is today’s.

2. Historical Mean: Reverts to long-run average. Poor for fast shifts.

3. Moving Average / EWMA: Better for short-term, but may overreact.

4. ARMA: Adds structure by regressing on past vol.

5. GARCH: The king—blends memory, mean reversion, and persistence.

6. Implied Volatility (ISD): Extracted from option prices. Market’s guess—but distorted by supply/demand and tail risk.

7. Exogenous Factor Models: Add macro data like interest rates and GDP. Helpful—but often unstable.

Beige Box: Forecasting Performance

Marra’s empirical findings across 1988–2015 (S&P 500 monthly returns) show:

• Best Forecasting Models:

  • Discrete Historical

  • ARMA

  • GARCH(1,1)

  • EWMA

• Worst Performer: Historical Mean

• Most Likely to Overestimate: Implied Volatility (84.7% of time)

Choosing a Model: The Art of Humility

Ultimately, the volatility model you choose depends on your mission.

• Running a volatility-targeted fund? Use EWMA or ARMA.

• Hedging options? Watch the VIX but temper your trust.

• Allocating across asset classes? Consider MGARCH or discrete historical models across horizons.

But beware overfitting. Each model is a story about the past, not a prophecy. The more precisely it fits yesterday, the more brittle it may be tomorrow.

A Final Word: Uncertainty’s Silent Shape

Volatility is not the chaos. It’s the shape of chaos. It’s the way fear lingers after a crash, and the hush that precedes it. Predicting it is not magic—it’s statistics. But it takes a careful hand to wield the models without succumbing to illusion.

In a world that demands certainty, volatility reminds us that the most valuable knowledge is not a prediction—but the confidence to prepare.

References for Further Reading

• Campbell, Lo, and MacKinlay, The Econometrics of Financial Markets

• Engle (1982) on ARCH models

• Poon & Granger (2003) Forecasting Volatility in Financial Markets

• Blair, Poon, Taylor (2001) on Implied vs Realized Volatility

• Fleming, Whaley (1995) on VIX as a forecast tool

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