Saturday, July 11, 2009

The statistics of bombshells and the efficient-market hypothesis

Justin Fox has been promoting his book The Myth of the Rational Market. In this piece for Time Magazine, he summarizes the historical development of the efficient-market hypothesis.

This tantalizing excerpt from the piece, talks about the connection between solving an optimization problem and the mathematics of the market:
A key figure in the revival was the University of Chicago's Milton Friedman... [who] convinced himself and other economists (without much evidence) that speculators tended to stabilize markets rather than unbalance them.

But Friedman was a scientist too. During World War II, he used his mathematical and statistical skills to help determine the optimal degree of fragmentation of artillery shells. Officers flew back to the U.S. in the middle of the Battle of the Bulge to get his advice on the trade-off between the likelihood of hitting the target (the more fragments, the better) and the likelihood of doing serious damage (the fewer and bigger the fragments, the better).

Emboldened by this work, economists began to apply their number-crunching skills to the postwar market. Chicago graduate student Harry Markowitz devised a model for picking stocks that was, in Friedman's estimation, "identical" to his artillery-shell-fragmentation trade-off. And in the late 1950s, scholars at Chicago and the Massachusetts Institute of Technology became enamored of the idea that stock-market movements were, like many physical phenomena, random.

The two strands of statistics and pro-market ideology came together in the mid-1960s. It was the great MIT economist Paul Samuelson who made the case mathematically that a rational market would be a random one.
From browsing the Wikipedia entry on Markowitz, it sounds like his work was the first to incorporate risk (or second moments) in his estimates of the value of a portfolio. Markowitz is also responsible for the concept of the "Efficient Frontier" (the set of all investment portfolios which maximize expected return for a given level of risk) which eventually led to the efficient-market hypothesis. I would still like to know the exact mathematical details of Friedman's modelling...

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