Drawing the Curve of Fear: Engle and Ng on the Impact of News

By the early 1990s the volatility modelling field had a happy problem. There was ARCH. There was GARCH. There was EGARCH. There was GJR. There were half a dozen other variants with names like alphabet soup. Every one of them claimed to describe how market volatility evolves, and every one of them made a slightly different claim.

How do you compare them? You could look at fit statistics, but those are abstract. Robert Engle and Victor Ng found something better: a way to make each model draw a picture of itself, so you can literally look at what it is claiming and compare that to what the data says.

They called the picture the news impact curve.

The problem: comparing models by squinting at parameters

Every volatility model in the ARCH family is a rule that says: given what happened today, here is my forecast for tomorrow's volatility. The rules differ, but they all boil down to a single relationship: how does today's surprise map into tomorrow's volatility?

The trouble is that the rules are written in different mathematical dialects. GARCH squares things. EGARCH takes logarithms and absolute values. GJR has an on-off switch. Comparing their parameter tables tells you almost nothing about whether they agree or disagree about the world.

The key idea via analogy: make every model draw the same chart

Engle and Ng's move is disarmingly simple. Take any volatility model. Freeze everything about the past at its average level. Then feed in one single surprise, today's unexpected return, and ask: what does the model say tomorrow's volatility will be?

Sweep that surprise across a range, from a big negative shock, through zero, up to a big positive shock, and plot the answer. You get a curve. The horizontal axis is today's news. The vertical axis is tomorrow's volatility. That is the news impact curve, and every model in the family has one.

Now the comparison becomes visual and obvious:

• Standard GARCH draws a perfect U, symmetric around zero, with the bottom sitting exactly at "no news." Good news and bad news of the same size raise volatility identically. The model is, by construction, politically neutral about direction.
• EGARCH and GJR draw a lopsided U, steeper on the left. Bad news raises volatility more than good news. The lowest point of the curve is shifted to the right of zero, meaning a small positive surprise, not zero news, is the calmest possible outcome.

Once you can see the curves, you can test them. Engle and Ng also built diagnostic tests, which they framed in terms of "sign bias" and "size bias," that ask a blunt question of any fitted model: are its errors systematically different after down days than after up days? If yes, the model's news impact curve is the wrong shape, and it is mis-forecasting volatility in a predictable, exploitable way.

What they found

Running these tests on Japanese stock return data, they confirmed what the asymmetric models had suspected. The news impact curve is genuinely lopsided. Standard symmetric GARCH fails the diagnostic tests: it systematically under-forecasts volatility after bad news and over-forecasts it after good news.

They also compared the asymmetric models against each other, and their evidence pointed toward a curve of roughly the GJR shape, where negative surprises get an extra kick, over EGARCH's more aggressive exponential response, which tends to overreact to very large shocks. It is worth being careful here: that is a finding about a particular market and sample, not a universal ranking.

Why it mattered

• It gave the field a common language. "What does your model's news impact curve look like?" became a standard question. Textbooks reproduce these curves. It is one of those visualisations that reorganises how people think.
• It turned model comparison into hypothesis testing. The sign bias and size bias tests are still routinely run as diagnostics after fitting a volatility model. They tell you not just that your model is wrong but how it is wrong.
• It settled the asymmetry question empirically. Nelson and GJR had proposed asymmetric models. Engle and Ng provided the formal statistical evidence that the asymmetry is really there and that ignoring it is a specification error, not a stylistic choice.
• It connects to what options traders see. The lopsided news impact curve is the statistical cousin of the volatility skew in the options market. Both say the same thing: the downside is treated differently from the upside.

The honest limitations

• The curve is a snapshot, not the whole model. By construction it holds the past fixed at average conditions. In reality, how a model responds to today's news depends on the state it is currently in, and the curve does not show that.
• The tests tell you something is wrong, not what to do. A rejection tells you the news impact curve is misshapen. It does not hand you the correct shape.
• A better in-sample shape is not a better forecast. Passing the diagnostics is necessary but not sufficient. A model can have the right-shaped curve and still forecast poorly out of sample, a point later horse races drove home hard.
• Findings are market-specific. The evidence here comes from one equity market over one period. Asymmetry is strong in stock indices, weaker in individual names, and largely absent in currencies. Do not import the conclusion blindly.

The one-line takeaway

Engle and Ng invented a simple chart, surprise today on one axis, volatility tomorrow on the other, that makes every volatility model state its beliefs in plain sight, then built the tests that check those beliefs against the data, and confirmed that the true curve is lopsided: markets are more scared of falling than they are excited by rising.