The models that won’t die

As a trained physicist, I constantly wonder why economists and finance professionals are so adamant to draw investment recommendations from models and theories that are obviously useless. My favourite example of this behaviour is the use of the Capital Asset Pricing Model (CAPM) in finance. As most readers of this blog will know, the CAPM was developed in the 1960s by Sharpe and Lintner. The model predicts that financial assets should follow a simple linear model and returns should merely be a reflection of the systematic risk of the asset relative to the market.

When I studied towards my economics degree at university, I already had a postgraduate degree in mathematics and physics so I was confronted with the CAPM and thought to myself: “This is a nice toy model, but surely nobody thinks that you can describe a complex dynamic system like the financial market with a linear model like the CAPM.”

But when I entered the world of professional finance and asset management I learned to my astonishment that the largest asset managers in the world would take the CAPM not only seriously, but literally.

As a physicist, you are trained to assess a theory or a model in two ways. First, you assess the predictions the model makes in the real world. If it is empirically useful, it probably has some element of truth in it. Milton Friedman famously claimed in his essay “The Methodology of Positive Economics” that one should not judge a model by the realism of its assumptions. That is, of course, total nonsense and unworthy of a genius like Friedman. It is nonsense because there are a large number of random models can make predictions that are remarkably accurate. All the examples of the butter price in Thailand being highly correlated with the price of oil in the United States or the like are such cases of false causalities. But let’s stay with the argument of empirical accuracy for the moment.

The CAPM has been violated not just once, but hundreds of times. Factor investing started with the seminal research of Eugene Fama and Ken French in the 1990s who described the value and size factors. By now, researchers have discovered more than 300 different investment factors. And remember what an investment factor such as value or momentum is. It is a statistically significant violation of the CAPM observed in the market.

Karl Popper tells us that a theory should be abandoned – or at least modified – once it has been empirically violated and so, I cannot understand how professional investors or academics still use the CAPM as a viable benchmark or model to describe the world. In the natural sciences, you would be laughed out of the room if you tried to defend a model that has empirically been violated hundreds of times, yet in finance, companies make money with recommendations derived from the CAPM and academics win prizes for research based on it.

Indeed, for academics, a safe career path has been to start with the CAPM and work on an extension of the model that relaxes some of its famously unrealistic assumptions:

  • Investors aim to maximise their utility function (Never mind that nobody can measure a utility function or even knows how such a function looks like in principle).

  • Investors are rational and risk-averse (Never mind that we by now have forty years of evidence how investors deviate from this assumption, it is still used as a fundamental building block).

  • All investors trade without transaction costs and are not taxable (Remind me to ask the HMRC for tax exemption so I can optimise my investments).

  • Investors can borrow and lend unlimited amounts under the risk-free rate of interest (Great, I’ll buy myself a villa in the Caribbean and send the mortgage application to my bank telling them to go to Bill Sharpe and let him explain why they should give me the money at the risk-free rate of interest).

  • Investors are price takers and cannot influence prices (Ok, this seems like a reasonable assumption).

  • All investments are highly divisible into small parcels (This used to be doubtful, but in the 21st century it is true for all practical purposes).

  • All information is available to all investors at the same time (Calling Michael Milken, Ivan Boesky, Raj Rajaratnam, Steve Cohen…).

That academics still use the CAPM a lot can be seen by searching for the CAPM in Google Scholar, the search engine that restricts hits to academic papers. Over the last 20 years, CAPM-related papers have grown roughly at the same rate as papers mentioning the research of Fama and French (which I used as a proxy for work on factor investing). Of course, I cannot say, how many of these papers are critical of the CAPM and how many are supportive, but my impression from scanning the results is that the vast majority of papers mentioning the CAPM try to use the CAPM either as a benchmark model against which to test empirical predictions or try to expand the CAPM by modifying some of the above-mentioned assumptions.

Academic research papers referencing CAPM and factor models

Source: Google Scholar.

At least, the larger investment community seems to slowly abandon the CAPM. The chart below shows the 12-month moving average of Google searches for the CAPM, Fama and French as well as factor investing. While searches of CAPM and Fama and French are declining, factor investing as a topic has become more popular, indicating that investors are increasingly using more realistic approaches to investing.

Google searches for CAPM and factor investing

Source: Google Trends.

Which brings me to the second way in which physicists tend to assess the validity of a model, by assessing the realism of the assumptions underlying the model. As you might have guessed, the assumptions of the CAPM shown above are so fundamentally flawed and violated in practice that the entire model is beyond repair. The academic efforts to expand the CAPM into a multi-factor model or relax some of its assumptions are in my case just efforts to ride a dead horse.

And my belief that the CAPM is a dead horse comes from more than a refutation of any of the assumptions underlying the model. It comes from a belief that the entire process of modelling financial markets is based on a flawed assumption: the wisdom of crowds.

Almost all models in finance and economics are built on the core assumptions that individual investors may not be rational, may be taxable or face other frictions like transactions costs, but if you average them out, the market overall acts as if the assumptions were true.

It is the assumption made so often about the wisdom of crowds described so elegantly by James Surowiecki. Yet, many people tend to forget that there are some fundamental requirements that have to be met for a wise crowd to emerge. As Surowiecki points out in his book:

  1. There has to be a diversity of opinions.

  2. People’s opinions cannot be influenced or determined by other people but have to be fully independent.

  3. People can draw on localised or specialised knowledge that informs their opinion.

  4. A mechanism to aggregate different opinions fairly and quickly must exist.

  5. Each person trusts the collective opinion to be fair and unbiased.

In financial markets only conditions one and four are met. Financial markets are a fantastic mechanism to aggregate millions of individual opinions quickly and efficiently. That is what markets are all about. But in practice, people’s opinions are not independent. Instead, we are influenced by the media, expert opinions and influencers, our friends and family and even our past experiences. This gives rise to herd behaviour and collective misjudgement in various forms. Indeed, whenever a company executive goes on TV to spin his business as a success story he or she tries to influence a large part of the public to NOT make independent judgements. And similarly, it is by far not obvious why each person trusts in the fairness of the collective opinion. In the age of fake news and the rise of conspiracy theories, the belief in the fairness of the system (be it the political or financial system) is eroding fast and leads to a breakdown of the wisdom of crowds.

In the end, I believe that every theory that assumes representative agents (i.e. an average decisions maker who represents the entire population) is doomed to fail. There simply does not exist such a representative agent, rational or irrational. The world is full of people with different beliefs and motivations that cannot be averaged out and it is high time we devote more efforts to develop theories that reflect this diversity.