The ergodic axiom and the shortcomings of risk management

11 Feb, 2013 at 15:47 | Posted in Economics, Statistics & Econometrics | 2 Comments

uncertaintyroadUnfortunately as we have all learned in the world of experience, little is known with certainty about future payoffs of investment decisions made today. If the return on economic decisions made today is never known with certainty, then how can financial managers make optimal decisions on where to put their firm’s money and householder’s where to put their saving today?

If theorists invent a world remote from reality and then lived in it consistently, then Keynes [1936, p.16] argued these economic thinkers were “like Euclidean geometers in a non-Euclidean world who discover that apparent parallel lines collide, rebuke these lines for not keeping straight. Yet, in truth there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required to-day in economics” …

As any statistician will tell you, in order to draw any statistical (probabilistic risk) inferences regarding the values of any population universe, one should draw and statistically analyze a sample from that universe. Drawing a sample from the future economic universe of financial markets, however, is impossible. Simply stated the ergodic axiom presumes that the future is already predetermined by an unchanging probability distribution and therefore a sample from the past is equivalent to drawing a sample from the future … Assuming ergodicity permits one to believe one can calculate an actuarial certainty about future events from past data.

Efficient market theorists must implicitly presume decision makers can reliably calculate the future. The economy, therefore, must be governed by an ergodic stochastic process, so that calculating a probability distribution from past statistical data samples is the same as calculating the risks from a sample drawn from the future. If financial markets are governed by the ergodic axiom, then we might ask why do mutual funds that advertise their wonderful past earnings record always note in the advertisement that past performance does not guarantee future results …

This ergodic axiom is an essential foundation for all the complex risk management computer models developed by the “quants” on Wall Street. It is also the foundation for econometricians who believe that their econometric models will correctly predict the future GDP, employment, inflation rate, etc. If, however, the economy is governed by a non-ergodic stochastic process, then econometric estimates generated from past market data are not reliable estimates that would be obtained if one could draw a sample from the future …

In sum, the ergodic axiom underlying the typical risk management and efficient market models represents, in a Keynes view, a model remote from an economic reality that is truly governed by non-ergodic conditions. Keynes, his Post Keynesian followers, and George Soros all reject the assumption that people can know the economic future since it is not predetermined. Instead they assert that people “know” they cannot know the future outcome of crucial economic decisions made today. The future is truly uncertain and not just probabilistic risky.

Paul Davidson


  1. How can efficient markets drive results towards an equilibrium? I have difficulties understanding how the supposedly efficient market can be aggregated into a huge lump and used to draw meaningful conclusions especially if one looks at the time constants to reach equilibrium, or the possibilities of ever reaching equilibrium given intervening ‘informational’ events. The difference between speed of ‘flash trading’ and say, manufacturing an airliner (sorry Boeing) are several orders of magnitude. Flash trading provides an efficient market for specific purposes that clears in milliseconds, yet it will be literally decades before the wisdom of Boeing’s multi-billion dollar Dreamliner gamble in research, hardware and manufacturing technologies can be judged to have been a success or failure.

    It’s an old book, but if one wishes to understand long range technological developments, I recommend ‘The Sporty Game’, about the development of passenger aircraft in the age of deregulation. It was originally published in the ‘New Yorker’ and is available on line at:

    Essentially, aircraft manufacturers are forced to literally bet the company on the development of a new aircraft, and production costs are dependent on rate of manufacture planned against a very uncertain future.

    The point is, that in ‘flash trading’, markets can clear almost instantly (unless the software goes wrong) whereas the longer the time it takes to ‘clear’ the market, the more time there is for interceding changes to influence the outcome, especially the fate of the airline industry customers.

    Thus, for example, on aircraft manufacturing stocks, we’re back to Keynes uncertain future and the animal spirits of those who like to build aircraft, stretched over years and decades, and the stock price, on a short term basis, that has very little to do with the initial success, or lack thereof, of the aircraft, and everything to do with Wall Street speculation rather than an overall efficient market.

    (Edited and cross posted from Noahpinion)

  2. In practice, all decision makers extrapolate. What has happened in the past will continue in the future, only more so. If there is a stront tendency, this tendency will be even stronger, probably all-embracing. And when this doesn’t turn out, the decision makers have us believe that they had predicted so all along.

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