Nonlinear Theory Explains May 6 Market Break

One week after stock markets dropped 10% in half an hour, regulators still confess bewilderment yet equally resolve never to let it happen again.  No one at the SEC or CFTC or any of the exchanges has been able to identify a particular cause of the flash crash.  They do say the precipitous decline was magnified by how some trading platforms, like the old-fashioned New York Stock Exchange, halted trading when the downward spiral began while electronic trading platforms did not.

A consensus appears to believe that this worsened the spiral because trades could still be made elsewhere but with fewer participants, in a thinner market. Adherents think the cure is obvious: such trading breaks should be adopted across all trading platforms so if there is ever any significant decline in price, all trading would halt.  I respectfully dissent.

This is a replay of the 1987 stock market crash: no one could figure out why it happened so everyone decided such circuit breakers were the thing to do about it.   The consensus is likely to be just as wrong today as it was wrong then, based on an alternative view, which I laid out in my 1994 GW Law Review article, From Random Walks to Chaotic Crashes: The Linear Genealogy of the Efficient Capital Market Hypothesis. Those seeking an explanation for the 1987 crash and last week’s flash crash presuppose things about stock markets and pricing that may simply be false.

They suppose prices accurately reflect collectively-rational behavior among informed traders whose spontaneously-coordinated actions invariably result in stock prices, and stock price changes, that linearly give up-to-the-minute best estimates of underlying business value. That is a delineated version of the popular efficient market hypothesis.  Things like the 1987 crash and last week’s flash crash are inconsistent with that, so stand out as anomalies needing an explanation outside the popular hypothesis.

But that isn’t how prices actually work and episodes like the 1987 crash and last week’s flash crash merely put the recurring reality in sharp relief. Stock price adjustments are not always elegantly fluid, linear, and endlessly up-to-date. They are nonlinear and often chaotic. Price changes do not move in increments of pennies and dollars but alter abruptly, non-linearly, skipping from $10 to $14 to $8, not moving between those figures from $10.01, $10.02, $10.03 . . . $14. . . .

The same is true of the aggregate Dow index: when it drops from 10,600 to 9,870 — whether in 20 minutes or 20 days — that doesn’t mean anyone could have traded at incremental levels in between during that time. Stock prices are driven by the volume of buy-sell orders and the relative imbalance.  Stock prices rise rapidly when buyers outbid sellers and vice versa.

Sometimes that means a massive rally in prices and sometimes it means a sharp plunge. Why is a combination of fundamental analysis and behavioral dispositions unrelated to that. So what, therefore, if stock prices rise 1000 points or fall 1000 points in a few minutes or a day or a month?  Let the market rise; let the market fall!

If you still believe, as regulators insist, that we simply cannot have 1000 point drops in half an hour, one prescription seems obvious to them: if markets start to fall like that, shut them down—don’t let them fall.  That is the logic behind the consensus that last week’s fall was magnified by trading halts (called circuit breakers) only applying at some, but not all, trading platforms.  But at least two issues arise from this digagnosis of circuit breakers that were too limited and cure that circuit breakers should be universal.

One: if you are going to interfere and shut down a market because price levels are rapidly falling, why are you not going to interfere and shut down a market because price levels are rapidly rising? Proponents of circuit breakers think they know it is a potentially bad thing when prices plummet, bad enough to shut down the market. But sometimes prices get so high that they should plummet.   (The reason circuit breaker proponents do not propose to shut markets down when prices are rising is not about policy logic but because that is party time and no one wants to take away the punch bowl!)

Two: if you think you are good at knowing that a market should shut down when prices have fallen by a certain amount within a certain time, how do you know ahead of time that your solution of automatically shutting them down will not exacerbate the problem you seek to correct? It is at least equally likely that, as a price change trigger is approached, the mere proximity to it induces panic selling by those fearful that the market soon will shut down and prevent them from getting out.

So far, officials officially are saying they don’t really know what happened last Thursday but they think whatever happened is a problem to which they need to find a solution.   But it is possible that it was simply normal market behavior, in its chaotic non-linear beauty, merely magnified in its visibility, yet still quotidian.   There is good news in this mix of professed regulatory ignorance about cause coupled with regulatory confidence about the cure: the SEC-CFTC are setting up a special committee to have a closer look.  I hope they consider nonlinear market realities.

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1 Response

  1. Ken says:

    An observation: I think you may have used “non-linear” to mean “discontinuous.”

    More importantly, though, is that the cause of sudden plummeting prices is not non-linearity, nor is it discontinuity of prices; rather, it is a very simple concept known well in physics and mechanical engineering–unstable equilibrium. When an object is at rest in stable equilibrium, any displacement from its equilibrium point will result in a restorative force tending to push it back towards its equilibrium point. To the extent that market price is driven by “best estimates of underlying business value,” any price movement away from that estimated value point will result in corresponding buy or sell orders tending back towards the “value” point.

    Unfortunately, what you’ve characterized as the “efficient market hypothesis” has little to do with the speculative market most trading takes place in. Warren Buffet buys stock because of its underlying business value. Most speculators/traders buy stock because of their short-term expectations of price movement. And to the extent that their expectations are bayesian, strongly influenced in the time domain by most recent evidence, the market is always teetering on the edge of unstable equilibrium.

    And BTW, the answer to your question about the suggestion of an assymetric market is simple: Unstable equilibrium never causes an object to suddenly fall up. Or in the terms of your terminology, we’ve yet to see a market crash up because of panic buying.