330 Models Walk Into a Horse Race: Does Anything Beat GARCH(1,1)?

Twenty years of volatility research had produced a bewildering menagerie. GARCH, EGARCH, GJR, APARCH, IGARCH, FIGARCH, threshold GARCH, quadratic GARCH, component GARCH, and dozens more, each announced in a paper explaining why it captured some feature the others missed.

Every one of these papers, naturally, showed its own model doing well. What nobody had done was line them all up and race them against each other, fairly, out of sample, using a statistically honest procedure.

Peter Hansen and Asger Lunde did exactly that. They assembled 330 different volatility models and asked a deliberately provocative question, which they put right in the title: does anything actually beat the simplest, oldest, most boring member of the family, plain GARCH(1,1)?

The problem: everyone grades their own homework

Comparing forecasting models sounds easy and is full of traps.

Trap one: in-sample fit is not out-of-sample skill. A model with more parameters will always describe the past better. That tells you nothing about the future.

Trap two: with 330 models, someone wins by luck. If you run enough horses, one of them finishes first regardless of whether any of them is actually fast. Declaring the winner "significantly better" without accounting for the fact that you tried 330 candidates is exactly the data snooping problem that plagues quantitative finance. Hansen had already built the tool for this, a procedure for testing whether the best model in a large set is genuinely better than a benchmark, or merely lucky.

Trap three: what are you grading against? Volatility is unobservable. If you grade forecasts against noisy squared daily returns, the noise can swamp the differences between models and even reverse the ranking. Hansen and Lunde used realized variance built from intraday data as their benchmark, a far better answer key.

They ran the whole thing on two datasets: a currency pair, and IBM stock.

The key idea via analogy: the reigning champion nobody can knock out

Picture GARCH(1,1) as an ageing, unglamorous boxing champion. It has two punches. It has no footwork. Everybody's new challenger has a special technique designed to exploit a specific weakness.

Hansen and Lunde put 330 challengers in the ring, one after another, and scored the fights honestly.

On exchange rate data: nobody knocked the champion out. Across the whole zoo of alternatives, they found no evidence that any model was significantly better than plain GARCH(1,1) at forecasting currency volatility. Twenty years of innovation, and the original still stood.

On IBM stock data: the champion lost, and lost to a specific punch. Models that allow for asymmetry, the leverage effect, where bad news raises volatility more than good news, beat GARCH(1,1) clearly and significantly.

The contrast is the whole story of the paper, and it makes complete economic sense. Why is there a leverage effect in stocks? Because a company's equity falling in value makes the company more leveraged and more fragile, and because falling stock markets frighten people. Why would there be a leverage effect in an exchange rate? There is no "down" for a currency pair. A dollar falling against the euro is a euro rising against the dollar. The asymmetry has nowhere to come from.

So the answer to the title question is: it depends on the asset, and the thing that matters is the one economic feature that is actually present.

Why it mattered

• It punctured the model proliferation. The paper is, politely, a warning that most of the volatility zoo adds nothing. Complexity for its own sake does not forecast better. A great deal of the literature had been building models in search of a problem.
• It vindicated asymmetry specifically. The finding is not "all fancy models are useless." It is "the fancy feature that reflects a real economic mechanism is the one that helps." Asymmetry earns its keep. Most other bells and whistles do not.
• It set the methodological standard. Testing 330 models and honestly correcting for the fact that you tested 330 models is exactly how model comparison should be done. Many horse races before this paper, and some since, quietly skipped that step and reported a "winner" that was pure luck.
• It reinforced the case for good volatility proxies. Using realized variance rather than squared returns was central to getting reliable rankings.
• GARCH(1,1) remains the default for a reason. Practitioners who reach for the simplest model are not being lazy. They have a serious paper backing them up.

The honest limitations

• Two assets is not a universe. One currency pair and one stock. The conclusions may not extend to bonds, commodities, crypto, or equity indices, and equity indices in particular have a stronger leverage effect than single names.
• It is a comparison within the ARCH family. The 330 models are all variants of the same basic idea. Models from outside the family, most notably HAR and other realized-volatility models, are not in the race, and they do routinely beat GARCH(1,1) when high-frequency data is available. The question "does anything beat GARCH(1,1)" has a clear affirmative answer if you are allowed to use intraday data as an input and not merely as a scorecard.
• Statistical significance is not economic significance. A model can fail to be significantly better and still be a bit better, and in a large risk book, a bit better may be worth money. The tests are conservative by design.
• The horizon is short. The comparison focuses on one-day-ahead forecasting. Rankings can change at longer horizons, where persistence and mean reversion assumptions bite harder.
• The loss function matters. How you score a forecast error affects the ranking, a point Andrew Patton made rigorous a few years later.

The one-line takeaway

Hansen and Lunde raced 330 volatility models against the plainest one in the family and found that for currencies nothing beat it, while for stocks the only models that did were the ones capturing a real economic fact: that a falling market frightens people more than a rising one reassures them.