Shifting away from mean-variance investment paradigm

Investors need a model to guide their investment decisions. Previously dominant Mean-Variance Paradigm has been proven inaccurate and needs to be replaced.

Mean-variance Paradigm (MVP) is a theoretical model and a set of quantitative methods for making investment decisions such as portfolio construction and risk management. It originates from 1952 paper by Harry Markowitz¹ on portfolio selection. The paper assumes that investors are concerned with maximizing their expected returns on investment while minimizing the portfolio risk. This thesis was later expanded by William Sharpe and others, and led to such constructs as ‘Modern portfolio theory’ (MPT) and ‘Capital Asset pricing model’ (CAPM)². ‘Efficient market hypothesis’ developed by Eugene Fama³ and other distinguished economists became an important theoretical foundation supporting core assumptions of the MVP.

Familiar linear statistical tools

The authors of Mean-variance paradigm assumed that market returns were best described as random independent variables (i.e. market prices followed ‘random-walk’). This allowed them to bring about a set of well-developed tools from the field of Gaussian linear statistics. For example, actuaries who dealt with population lifespan probabilities using Gaussian normal distribution assumed they could directly apply their knowledge to pension fund asset allocation decisions.

Distribution of truly random variables (like dice throws where each outcome is not dependent on the previous one) over time tend to form a bell-shaped curve. Properties of this distribution can be described by relatively few variables, such as its ‘mean’ (average outcome) and ‘variance’ (volatility of outcomes).

The Mean-variance Paradigm⁴ assumes that average (mean) past returns on a portfolio asset provide the best forecast of the future. Correspondingly, observed past variance of these returns is the best available estimate of the asset’s risk.

This linear statistics framework promises additional benefits due to a concept of diversification. If individual asset returns were indeed an independent random variables, then in the large collection of securities individual asset risk would be less and less important.

The ‘modern portfolio theory’ looks at past correlation of financial assets and offers sophisticated mathematical methods to construct an ‘optimal’ portfolio, assuming that the past correlation will continue to hold in the future.

During the past fifty years investment industry and academia have been producing mathematical methods of ever increasing complexity, while never departing from their core assumption about the market as a stochastic (random) process.

Random-walk hypothesis proved wrong

In 1963 mathematician Benoit Mandelbrot published results of his study of commodity prices⁵, followed a few years later by the analysis of stock prices, interest rates and exchange rates. His work demonstrates that:

• The distribution of data has much fatter tails than a Gaussian bell-shaped curve implied by market random walk hypothesis;


• The extreme price swings happen much more often than random walk hypothesis predicts. In fact, a few violent price swings explain most of asset return variance.


• The statistics describing market prices is not stationary as random walk hypothesis implies.


• There is some temporal structure embedded in prices, some price movements are clustered in time.

Benoit Mandelbrot suggested that market returns distribution can be described by power laws, which we now know is a signature of a complex dynamical system. Unfortunately, at that time non-linear dynamics theory did not exist, so Mandelbrot’s work has been largely ignored by economic and investment establishment.

In 1986 Andy Lo and Craig MacKinlay performed a rigorous statistical test of market random-walk hypothesis and decisively rejected it, simultaneously supporting previous Mandelbrot’s findings. Unlike Mandelbrot’s their work has been broadly discussed and accepted by the scientific community⁶. By then study of complex dynamical systems had become a very active scientific field, supported by advances in computer power that allowed experimentation never possible before.

Why Mean-variance investment framework is still in use?

Mean-variance paradigm has been extremely useful and influential in the past fifty years. But today it can be described as an obsolete scientific theory, a crude approximation of the reality that may work some of the time but fails to address the most important market risk factors that dominate investment results of the portfolio.

It may appear surprising that MVP and its constituent ‘Modern portfolio theory’, ‘Capital asset pricing model’ and ‘Efficient markets hypothesis’ are still widely referred to in the academia and the official investment industry.

Proponents of random market theory usually put forward two reasons as an explanation:

Reason 1. Investors do not have anything as ‘scientific’, objective and removed from human speculative opinion as linear statistics methods based on Gaussian normal distribution.

This is simply not true. Several branches of science have been attacking the problem of understanding behavior of complex systems in the field of weather and earthquake prediction, cardiology, prevention of epileptic seizures and now in the financial markets risk analysis. There is a number of effective numerical methods that forecast sharp changes in the system state (leading to ‘fat tail’ events). The problem is that these methods are very different from the linear statistics methods that mainstream investment industry is familiar with.

Reason 2. The industry knows about the Gaussian model’s limitation with regards to high-impact market moves (‘fat tails’), but these events are caused by exogenous factors, they are impossible to predict anyway. Most of the time, the model works well.

This is partly true, because certain events affecting the market are indeed unpredictable (like 9/11 attack). However, large proportion of high-impact market events are caused not by external factors, but by the build-up of non-linear endogenous risk factors in the system. By monitoring non-linear properties of the market it is possible to account for periods of heightened endogenous risk, and in some cases to directly predict critical events.

There is a third rarely mentioned reason why mean-variance framework is still widely referred to in the investment management circles.

Reason 3. Mean-variance Paradigm is blessed by academia and included in government regulation as part of institutional investment manager’s fiduciary duty framework ⁷. Compliance with investment theory consensus is crucial for professional survival of institutional fund managers who complete for public money mandates.

This is a serious problem in the path of adoption of modern investment methods. The issue is not that old entrenched ideas are yielding only slowly, as is common with any paradigm shift. Government policy makers should take note of apparent ‘agency problem’ between institutional investment managers' personal incentives to ‘herd’ around industry consensus, and their duty to identify and manage their portfolio risk using newly available science.

On the other hand, some investors would prefer for to see Mean-variance Paradigm to stay around for a bit longer. Since markets are proven not to be efficient, the uneven distribution of modern knowledge and technology in the investment industry creates business opportunities for sophisticated institutional managers and private investors who can afford to deviate from the consensus.

Reference

¹ Markowitz, H.M. (March 1952). “Portfolio Selection”. The Journal of Finance 7 (1)

² Sharpe, William F. (1964). “Capital asset prices: A theory of market equilibrium under conditions of risk”. Journal of Finance 19 (3)

³ Fama, Eugene. (May 1970). “Efficient Capital Markets: A Review of Theory and Empirical Work”. Journal of Finance 25 (2)

⁴ Sharpe, William F. The Arithmetic of Active Management

⁵ Mandelbrot, Benoit. (1963). “The variation of certain speculative prices”. The Journal of Business of the University of Chicago 36

⁶ Andrew W. Lo, A. Craig MacKinlay. A Non-Random Walk Down Wall Street

⁷ US FDIC Trust Manual says: “The Prudent Investor Act, which was adopted in 1990 by the American Law Institute’s Third Restatement of the Law of Trusts (”Restatement of Trust 3d"), reflects a “modern portfolio theory” and “total return” approach to the exercise of fiduciary investment discretion."

Igor Drozdov is an investment strategist and decision process researcher. He runs ChaosMonitor.com, a pioneering investment strategy service that focuses on nonlinear dynamical properties of the financial markets. Previously Igor managed Global tactical asset allocation portfolio at one of the largest European pension funds. He started his investment industry career in the early 1990s and worked as a bond trader at investment banks in London, New York and Amsterdam.