March 25, 2007
Weekend Weakenings of The Weak Form Efficient Capital Market Hypothesis
Posted by Seth Chandler

It's somewhat risky to blog in an area in which one does not specialize and that has been written about imensely by very smart people. But, on the assumptions that no one will bring all of this up at my confirmation hearings and that risk is what blogs are for, could I venture some grave doubts this weekend about the weak form of the Efficient Capital Market hypothesis. That's the still-prominent, still-taught concept that says that investors can not expect (except by luck whose success goes to zero asymptotically) to profit by technical trading strategies, i.e. those that look solely at the time series of returns on a security. (Good discussions here and here). My doubts are strong enough that I am willing to cast aside any empirical studies purporting to find successful technical strading strategies and to assume for the sake of argument that all legitimate studies heretofore conducted have not found a successful strategy.

The basic problems are that the search space is infinite and what we see in the market are the coarse features of what is likely a much more finely grained and difficult-to-observe process. Suppose, for example, it were true that the market could be predicted extremely well as a function of the past 10 market returns. Could one find the right model or would one end up saying that no successful investing strategy could be found? One might try some sort of linear or polynomial multiple regression. But even if one confined oneself to models in which each variable appeared only once and the only interactions among the variables took the form of multiplication and addition (simple, arithmetic models), there would still be 115,975 models to examine. (The number of models is equal to the Bell Number of 10). To be sure, a modern computer could chomp through all that without ill effects, but once we relax the unreasonable assumption that all interactions amongst the variables are multiplicative or additive, the search space expands geometrically. Moreover, if there were 20 pieces of data rather than 10 that one wished to examine, there would be 51724158235372 simple arithmetic models that one would need to examine. Even Deep Blue might not enjoy that work flow. To be sure, there are sophisticated ways such as genetic programming of cutting through that large a search space to find pretty good models, but even these sophisticated methodologies may end up foundering as the variety of arithmetic operations permitted increases or one relaxes the one-use-per-variable constraint. (Has anyone actually tried this methodology on stock data?)

So even assuming researchers did not find an algorithm that correctly predicted investment return movements, that does not prove that no such algorithm exists but simply that it is difficult to find. And while, at the limit, the distinction between non-existence and unfindability may evaporate, it does not strike me as impossible that someone dedicated to finding a good algorithm for a particular investment or collection of investments might succeed through diligence and industry where academic researchers had failed. And, if they did, if they were not particularly altruistic, they might keep that information private and trade at a low enough level to prevent piggybacking on their strategies.

And now, to really cause trouble, the whole debate on the subject reminds me of efforts to prove or disprove the existence of alien life on the presence or absence of intelligible signals from space. To begin with, negative results from searches of portions of space over a short period of time provies little either way. Moreover, the space of signals that might be "intelligently" generated is likely infinite and I doubt we could eliminate bias in our efforts to focus on the sort of signals that would "most likely" be generated.

The question I end up with is what legal rules or practices change if we become less confident in the truth of the weak form of the Efficient Capital Market Hypothesis?

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