benoitIf a drunk is walking randomly around a lamppost, then the fact that his first step of the day was away from the lamp post is supposed to tell us nothing about the direction of his next step, or his last step of the day. Of course, in saying so I’m rather stretching that old thought experiment, because I have to assume that the experimenters have kept him drunk all day – perhaps with an IV – and have kept him walking. Still, there shouldn’t be any ‘momentum’ to play on.

A recent study offers empirical evidence for the idea of momentum, especially intra-day momentum, and attributes the phenomenon at least in part to day traders who take a contrarian view in the morning and then try to get out of their morning positions before the closing bell. So the markets don’t work like our hypothetical drunk after all.

Lei Gao and colleagues make the case, working specifically form the S&P 500 ETF, that “the first half-hour return on the market predicts the last half-hour return….”

An Important Observed Inefficiency

In their 2004 book, Benoit Mandelbrot and Richard Hudson argued that momentum does exist, and prided themselves on taking the side of actual traders here, rather than theorists.

The dependence of future upon past events in the commercial world is naturally echoed in, and then feeds back into that world from, the financial world. Furthermore, in the “fractalist” view this momentum makes possible a cascade of bad fortune of the sort that doomed Long-Term Capital Management.

Mandelbrot, the discoverer of the set on the Argand plan that shares his name, saw this financial momentum as a point in favor of a broad fractal approach to the field of finance. After all, the “Mandelbrot set” is calculated in accord with a formula that incorporates momentum. The rule for its construction, phrased without mathematical symbolism, is this: “Pick a constant c and let the original z be at the origin of the plane; replace z by z times z; add the constant c; repeat.” This recurrence of c in the various iterations of z is of course definitionally non-random, and it sounds a bit like … momentum.

But let’s get back to Gao et al. For their paper, they classified all the trading days in their data set “into three equal groups according to the first half-hour volatility, low, medium, and high.” They found that the higher the volatility, the greater the correlation of opening and closing half-hour results. This, as they say, supports a theoretical model set out by X. Frank Zhang in 2006 that a trend serves as a proxy for information, so that the greater the uncertainty, the more persistent the trend.

Why This Isn’t Arbed Away

But what happens to the no-arb principle here? Shouldn’t any actual momentum effect, especially an intra-day momentum effect, be arbitraged into non-existence?

Well … no. As Gao et al explain it, on a day when the first half-hour return is up substantially, likely due to good overnight economic news, day traders often go short, providing liquidity to the market. But they will want to get flat by the end of the day, so the upward move at the start of the day will generate an echo at the end of the day.

A fact that tends to support this hypothesis: on the day following a day in which both opening and closing half-hours have been up, the opening price that following day is on average lower. This suggests “an adjustment of the price from the previous last half-hour buying pressure.”

Another finding of the study, dropped into the discussion almost casually about half-way through the paper, is that traders are very good at predicting what the Federal Open Market Committee is going to do. FOMC minutes are regularly released at 2:15 PM. On the days when this happens, the correlation of first half-hour returns (the consequence of trades made well before the minutes are released) are much more reliably predictive of the last half hour than on non-release days.

“[E]ven after the FOMC news release,” they write, “there is a strong reaction of the market to continue the trend of the same direction anticipated in the first half-hour.”

So either there is a lot of leakage, or the FOMC just isn’t as enigmatic as it is made out to be. Or perhaps the truth combines both of those possibilities.