Blinded by the Numbers

How the Efficient Market Hypothesis (EMH) leads to sub-optimal decision-making.

Whether it’s called the Efficient Market Hypothesis (EMH), Modern Portfolio Theory (MPT) or the Chicago School, this widely used mathematical framework makes explicit assumptions about investors and market behavior. For years now, research from different disciplines has challenged many of these assumptions including: complete/symmetric market information, rational risk averse investors, maximum utility, Gaussian distributions, dividend/debt indifference, and fixed correlations between assets. Moreover, the 2008 credit crisis made it clear that none of the EMH assumptions worked in the ways the theory predicted. Yet EMH and its associated methodologies including Value at Risk (VaR) are still being used extensively. This may in part be due to the lack of a robust alternative and the deep sunk costs in the current IT and compliance systems. It is the considered opinion of a number of quants that there is much room for improvement.

My claim is whatever the degree of revision or refinement, the fundamental assumptions – with all their strengths and all their weaknesses – will continue to decisively blind their users to large “unanticipated effects.” What needs to be recognized is that every form of analysis, every plan of action, every description of the world, or some portion of it, is a simple or complex model of that world. One of many possible alternatives – each of which will be more or less useful, more or less accurate, more or less entrancing to us. Knowing the assumptions of the models we use confers the advantage of knowing when, and how, to apply them. The decision maker can then become strategically decisive.

First, a model is not a copy, just like a map is not what it describes. A model is a description, a diagram, even an object that highlights particular, and hopefully important, features of some phenomena including: key elements, relations, properties and dynamics. A model also hides, or omits, other details as well as other models. A road map won’t show zoning. A stock price chart won’t show employment. Whether it’s a price chart, a money flows diagram, or the description of a risk management process, it’s a model.

With this in mind, let’s restate a couple of the key assumptions of EMH/MPT.

  1. Markets are information efficient and complete.
  2. Market participants are identical rational decision makers.

When you look out the windows of a skyscraper at the people below, they appear small. Get high enough and they become moving specks. Forget about age, gender, race, wealth, education or anything else individual. These can’t be seen. At this altitude, it’s all atoms. That is, markets are information on the transactions of “social atoms” – also known as Brownian motion. That’s the basis of the Efficient Market Hypothesis (EMH) model. It is the beginning of modern finance with Louis Bachelier (1900) – the first person to model stochastic processes or random walks. And that is what it is: a model.

As mathematical finance giant Robert Merton stated, “At times we can lose sight of the ultimate purpose of the models… The mathematics of models can be applied precisely, but the models are not at all precise in their application to the complex real world. Their accuracy as useful approximations to that world varies significantly across time and place. The models should be applied in practice only tentatively, with careful assessment of their limitations in each approximation.” ­

Of course, this isn’t what we social atoms do. We apply our models wherever they incur an advantage. Which is to say, as widely as possible. And then we forget they are models, and take them to be the world. This happens in every endeavor, every discipline, every domain of knowledge – from the ‘unsinkable’ Titanic to sub-atomic physics (Are there really quarks with color and infinitesimal strings?) to the fixtures of modern finance.

The Efficient Market Hypothesis / EMH is (only) a Model

Some of the slippages between the EMH / mathematical finance models and the world have been pointed out by others. These include philosophical and behavioral (finance) critiques – for example, the use of Gaussian functions, and failure to account for an S-shaped utility curve respectively. Recent research suggests a neurobiological basis for these and other more basic assumptions. These will follow the more obvious ones.

  • EMH ‘smoothes out’ data outliers with its Gaussian assumptions.

(Ex. Market crashes and fat tails, which are real phenomena, are omitted)

See Benoit Mandelbrot and Nassim Taleb on extreme events (Black Swans).

  • EMH database selection biases results.

Ex. Data sources, data periods, data comparisons, start and end dates, smoothing)

See James Montier and Behavioral Finance, Michael Covel and Trend Following.

  • EMH assumption of identical individual rational decision-makers ‘hides’ herd behavior.

(Ex. Financial bubbles as well as normative behavior like managers seeking Beta)

See Irving L Janis and Philip Tetlock (on Group Think), Behavioral Finance (on herds)

  • EMH assumption of individual rational decision-makers hides traditional ‘bonds’ between debtors and creditors.

(Ex. Debtor/Creditor known to each other, community, reputation and shaming)

See Charles Morris “The Two Trillion Dollar Meltdown” among sub-prime titles.

  • EMH Volatility is a proxy for Risk. Markowitz Optimization: Volatility = Poor returns

(Ex. Trending markets are considered risky, low volatility markets considered safe.             Also, there is no distinction is made between gain volatility and loss volatility.)

See James Montier “Behavioral Investing.”

In the statistical world of mathematical finance, there are only be a few ways to gain an advantage: Knowing what’s going to happen next (insider trading), being faster at taking advantage of arbitrage opportunities (high frequency trading/HFT), trying to build the perfect portfolio (Modern Portfolio Theory), and predicting what will happen next. (More on this later.) These are, in fact, among the principle activities of the investment industry.

Why anyone would use these rational financial models of human behavior is the story of the advantages conferred on its early adopters. Remember, data aggregation and computerization is just a couple of generations old. The lack of prefect/symmetrical market wide knowledge at that time conferred an advantage on those who could recognize arbitrage opportunities and execute them more rapidly. And optimizing a portfolio that reduces loss and stabilizes gains does confer a long-term advantage. Moreover, the “social atoms” modeling was, and is, highly computable, so it fit with the automation trend of the times. And there are other, albeit social, advantages of making finance mathematical. Academics, equations and the resulting spreadsheets and charts and published projections ‘professionalized’ the activities of bankers, brokers, traders, financial planners and others – infusing them with a credibility and seriousness that had previously been lacking.

Which makes it all the more ironic that it was these very human ego gratifying advantages for invoking EMH that the EMH model could not see as they were outside of the model. And there were more of these human characteristics that were not accounted for.

  • EMH assumption of independent individual rational decision-makers could not account for local optimization of a system – in this case, company caretakers/managers colluding.

(Ex. Fraternities of CEOs and Boards of Directors, Regulatory Capture)

See Barry Ritholtz “Bailout Nation” and Andrew Ross Sorkin “Too Big to Fail.”

  • EMH assumption of risk averse decision-makers and necessity of Risk Premium

(Ex. Higher returns do not necessarily require higher risks; carry trades, etc.

Some higher returns do have higher risks. This is confused by investment firms:             “Higher risks = Higher returns” as in “What is your risk tolerance?)

See most any investor risk questionnaire offered by any investment firm.

Finally, the deepest and most obvious assumption of the EMH/mathematical finance model is everything is about numbers. This would seem like a perfect fit given money is counted. The thing is, all the assumptions that people have about numbers and counting come along with them including: Numbers are definite. There are right and wrong answers. Projections and performance models have some basis in exact numerical facts and are calculated accurately by equations. These ideas affect the framing of risk with unanticipated effects.

  • EMH CAPM of Alpha and Beta makes normal trading variance into tracking error.

(Ex. EMH-based risk managers think that losses (below Beta) are errors in the                 trading system rather than normal variance in trading (probabilistic outcomes).

A predictable conflict breaks out between the traders and the risk managers.

  • EMH assumptions of advantages result in examining & acting on shorter time frames.

Because EMH equations can be computed on shorter periods of time, they are.

(Ex. Quarterly earnings and even shorter term arbitrage (HFT) becomes the norm.)

  • EMH assumptions of limited arbitrage advantages result in many attempts at prediction.

(Ex. While EMH & IT were being developed, actual edges/advantages were identified.

Now new edges/advantages are sought with better, faster data and/or execution.)

As well as the opposite:

  • EMH assumptions of limited arbitrage advantages result in new products/revenues.

(Ex. Since markets are efficient, financial institutions make money from ‘advice,’ structured products and fees.)

Thinking of this in terms of mental processes, numbers are models of distinctiveness, and with that, taken as equivalents for certainty. In our minds, the number 1 is distinct from the number 2, and 10 very much from 10,000. We reveal this when we say things like, “The numbers don’t lie.” This clarity carries over to their representation on a page or spread sheet. We say things like, “It’s all there in black & white.” Black and white is what numbers typically look like on a page of paper or a screen, but it means much more to our minds. The neuro-biology of our brains makes contrast binary. This is different from that. “It’s clear cut.” Thus we are seduced by the fact of there being numbers that claim to tell us what the risk of something is whether it’s VaR or some other measure whether they do or not. We are calmed by this misplaced certainty that we are doing the right thing. We relax. This is known as the ‘Illusion of Control’ – which predates Behavioral Finance. We not only don’t control the risks, we don’t even know what they are, while we continue think and feel we do.

  • EMH MVO emphasizes information measurement and production over decision-making.

(Ex. VaR & other risk management protocols address our needs for certainty more than devising effective risk management processes.

  • EMH cannot account for how an individual’s sense of safety can actually increase risk.

(Ex. VaR – risk managers see the number everyday and nothing happens = safe.

A 1% chance looks so small even though it means 2.2 times per business year.

Better built cars/financial models increase speed/leverage while felt risk remains constant.)

These (mostly) unintentional misuses of mathematics mislead investors, investment firms, risk managers, traders and other financial industry players at every level. They do not know what they think they know. They are not measuring what they think they are measuring. So, they are not making decisions on what they think they are making decisions on. While, almost all around them, it looks and feels like they do.