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Proving Causation in Finance



I said in an entry last week that a downgrade from Morgan Stanley was a reasonable candidate for the cause of a downward stock price move, as we intuitively understand the idea of cause.

But proving this would be a trickier matter. It would require showing that there was nothing else happening that evening or morning that may also have had consequences for that demand. Or, if there were other things happening, if would require some measure by which we could distinguish this causation candidate as more potent that the others.

Even if it is a very general rule that similar announcement proceeds stock price fall, other explanations are possible. After all, since we’re assuming that Morgan Stanley’s analyst was working from publicly available information, we could hypothesize that a lot of traders and in-house buy-side analysts reached the same conclusion at the same time Joe Smith did and would have reached it even if Joe Smith had had nothing to say, or had through some analytical failure of his own reached the contrary conclusion.

If we had easily repeatable conditions, as in a chemistry laboratory, we could address this. Let’s re-set everything so that it is exactly as it was last Tuesday, and let the world run forward again from that moment with only one difference: Morgan Stanley’s report doesn’t go out (or, in a variant, perhaps it does go out to a favored paying clientele but is not widely reported in free media.) Does the price go down then? 

Sorry: that kind of experimentation isn’t feasible.

So what can we do to get some sense of how cause and effect applies to market movements? We have to work with some background assumptions, and of late the dominant background assumptions are those of probability theory.

Mathematicians studying probability talk a good deal about the normal or Bell curve. Suppose you are measuring the errors of 17th century cartographers. Sometime, you find, those old mapmakers got distances just right. Sometimes they overstated the distance. Sometimes they understated it. You might collect a lot of old maps of England and measure how far off they were (and in which direction) in displaying the distance between London and Plymouth.

You’ll likely find this: the largest group of mapmakers got it right – showing the two places at 191 miles apart by the flight path of a crow. Among those who made mistakes, the mistakes were likely symmetrical: there are as many mapmakers showing it as a 171 mile distance as there are those who show it at 211 miles. The larger the mistake, the less likely: so that it would be truly extraordinary to find a map showing this distance as 151 miles, or as 231. Thus, you could chart the errors by drawing a curve that would indeed look a bit like a bell.

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