Tag Archives: crooked timber

Efficient markets and the digits of pi

John Quiggin had a good post yesterday on Crooked Timber about the various flavors of the Efficient Market Hypothesis, which according to Quiggin is a piece of shuffling zombie social science that won’t die no matter how many flaming sticks you jam through its skull.

The weakest form of the EMH is the so-called “random walk hypothesis” that the future behavior of a stock price is independent from its prior behavior.  If that’s the case, no amount of staring at charts is going to help you beat the market.  The random walk hypothesis is pretty well-supported by the data we have; a really nice popular account is Burton Malkiel’s A Random Walk Down Wall Street, one of the mathiest bestsellers I know of.  It makes a great present for anyone in need of a good rationale for not paying attention to their investments.

Quiggin writes

The success of the random walk hypothesis showed that the existence of predictable price patterns in markets with rational and well-informed traders was logically self-contradictory.

But this doesn’t seem quite right.  The EMF, even in its weakest form, holds that the current price of a stock is a best estimate arrived at by an aggregate of profit-maximizing investors with knowledge of the stock’s previous price:  if there were a reliable way to use previous prices to determine that tomorrow’s price would be Y, then the investors would figure that out, and today’s going price would be Y as well.

But the random walk hypothesis is much weaker.  It makes no claim about the etiology of stock prices.  It’s compatible with EMF, but it’s compatible with plenty of other models too — for instance, the one in which stock prices really are a random walk, where the price at time t+1 is the price at time t plus, let’s say, a normally distributed random variable X.  Such a market would be as impossible to beat as a roulette wheel — but evidently not because stock prices are best estimates of the future price of the stock, or of the underlying value of the company, or of anything at all.  (Fellow mathematician David Speyer makes a similar point in the comments at CT.)

You can dress this up a bit:  suppose price(t+1) – price(t) is the random variable X + [(.001) x t’th digit of pi] – (.045).   Unless something very weird is going on with the digits of pi, this version of the stock market would also satisfy the random walk hypothesis.  But unlike the pure random walk it’s a market where you can make some money; if I’m lucky enough to have access to the “digits of pi” rule, I can make a small average profit.  So the random walk hypothesis can hold for markets that are neither efficient nor unbeatable.

Stronger versions of the EMH hold that the market price already takes into account, not only the previous prices of the stock, but also publicly available information about the stock.  So what would happen if I let my secret investing strategy slip out?  This isn’t a rhetorical question; I’m authentically curious about what the rational-investor model would say about a market in which prices are publically revealed to have been governed, up until now, by some completely deterministic but “random-looking” sequence like the digits of pi.

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Letter from Belgium

One complains about the American political situation a lot, of course, and why not? But it’s good to keep in mind that other countries face structural dilemmas which are totally alien to us. In a long and brilliant post on Crooked Timber, Ingrid Robeyns explains the deadlock between the Flemings and the Walloons, and why Belgium has no government. Just to give a taste:

Governments in Belgium, both the federal and the regional ones, are always made up from coalitions. But these coalitions are not the same in all governments. In part this is due to the non-coinciding elections [Federal elections are held every 4 years, but elections for the regions and communities every 5 years, together with the European elections. Local elections are every 6 years.], in part this is also due to the fact that the parties do not have the same size at both sides of the language border. For example, the Flemish Christian democrats are the biggest party in Flanders, but are a rather small party within Francophone Belgium. Flanders also has a considerable extreme-right seperatist party, Vlaams Belang (which, ironically, is receiving some votes from Francophones in Brussels thanks to their security and anti-muslim agenda), whereas there is no such political factor in Wallonia. So these asymmetries create difficult situations. For examples, at the last regional elections the Christian Democratic Parties became part of the regional governments in Flanders and Wallonia, but they were part of the opposition in the Federal Government (which was made up from the (Flemish and French) Social Democratic Parties, and the (Flemish and French) Liberal Parties). This can lead to strange party-dynamics, which in the present crisis of the negotiations the federal level are also an explanatory factor why there is still no Belgian government. For example, the French Christian Democratic Party (CDH) is currently part of the government of the Walloon region, together with the French Social-Democratic Party (PS). But at the last federal elections, the PS (and its Flemish sisterparty SP) lost many seats, such that the current negotiations at the federal level are between the Christian Democratic parties and the liberal parties. This leads to the difficult situations for parties that are in different positions at the different levels. CDH is part of the center-left coalition at the Walloon regional level, but is negotiating to become part of a center-right government at the federal level. Since the voters are likely not to make a distinction between whether the acts of parties are made in their capacities as rulers at the federal versus the regional levels, it may be very difficult for any particular party to be in a center-right coalition at one level, and a center-left at another level.

There are some advantages to the calcified two-party system that Americans, to some extent, enjoy.

If you want to listen to the Mountain Goats song “Letter from Belgium” (and I really think you might!) you can listen to a live performance (19 Oct 2004, Mt. Pleasant, SC) here, via the remarkable Live Music Archive:

“That’s good, we can always use some more electrical equipment!”

Update:  If you listen to more of the linked concert, you hear John Darnielle getting the news of the Red Sox winning game 6 of the 2004 ALCS, right after “Going to Georgia.”

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