Mambo 5: Problems with Modern Portfolio Theory and other famous investment theories

December 1st, 2009
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Contributed by: Claude Bovet, SFCS Capital
Everyone knows the mambo, but I am guessing few know that mambo means “a conversation with the Gods”. I thought this would be a fitting title for a discussion on modern portfolio management, a practice entirely based on the work of many of our perceived financial Gods. Let’s start with Modern Portfolio Theory (MPT), a theory developed in 1952 by the Nobel laureate Harry Markowitz.

Without a doubt, MPT is the cornerstone of portfolio management. It is not only taught in all the business schools and to CFA’s but is used throughout the portfolio management industry. Its shortcomings, and there are some fundamental ones, are therefore important to understand. In a nutshell, MPT advocates the optimization of the risk/return profile of a portfolio through proper diversification (investing in assets/securities that are not perfectly correlated). It relies heavily on standard deviation (volatility) as the measure of risk, and correlations. MPT is best showcased on the efficient frontier: the “optimal” portfolio is the one that lies on the Capital Allocation Line (CAL) drawn from the risk free asset to the efficient frontier (the tangency portfolio in the chart below). Risk in MPT terms is defined as the standard deviation. But is this really the best measure of risk…?

Here’s the catch; in order for MPT to work, the theory relies on some (over-) simplifying assumptions namely***

Asset returns are normally distributed random variables
- Correlations between assets are fixed and constant forever
- All investors aim to maximize economic utility (in other words, to make as much money as possible, regardless of any other considerations)
- All investors are rational and risk-averse
- All investors have access to the same information at the same time
- Investors have an accurate conception of possible returns
- There are no taxes or transaction costs
- All investors are price takers, i.e., their actions do not influence prices
- Any investor can lend and borrow an unlimited amount at the risk free rate of interest

I think we would all agree these are some pretty big assumptions. The first assumption, that assets are jointly normally distributed, is a biggy, to say the least. The normal distribution is bell-shaped, clearly discernable from the picture below. It was described by Carl Friedrich Gauss (hence the name Gaussian distribution that is used interchangeably) to analyze astronomical data (a “hard” science – more on this later).

I think we would all agree these are some pretty big assumptions. The first assumption, that assets are jointly normally distributed, is a biggy, to say the least. The normal distribution is bell-shaped, clearly discernable. It was described by Carl Friedrich Gauss (hence the name Gaussian distribution that is used interchangeably) to analyze astronomical data (a “hard” science – more on this later).

Now here’s the problem: Asset and security prices, even when combined together in a portfolio, are not normally distributed; they suffer from “tail risk” and other more fundamental problems relating to uncertainty. To better understand these problems, let’s turn to another God-like being (the real McCoy this time), Nassim Taleb and an excerpt from his essay The Fourth Quadrant:

“The technical appendix shows why these metrics fail: they are based on “variance”/”standard deviation” and terms invented years ago when we had no computers. One way I can prove that anything linked to standard deviation is a facade of knowledge: There is a measure called Kurtosis that indicates departure from “Normality”. It is very, very unstable and marred with huge sampling error: 70-90% of the Kurtosis in Oil, SP500, Silver, UK interest rates, Nikkei, US deposit rates, sugar, and the dollar/yen currency rate come from 1 day in the past 40 years, reminiscent of figure 3 (see chart below). This means that no sample will ever deliver the true variance. It also tells us anyone using “variance” or “standard deviation” (or worse making models that make us take decisions based on it) in the fourth quadrant is incompetent.” [The Fourth Quadrant is where a complex world and Black Swans collide, Extremistan to those that have read his seminal book – CB].

Where would modern finance be without Value at Risk (VAR) and the Black-Sholes option pricing formula? Taleb fervently believes that the source of today’s financial problems can be identified as the inappropriate use of statistical models (e.g. VAR) and “false” theories (e.g. Black-Sholes). These models and theories do not properly take into account the fat tails (i.e. the Black Swans), a far more common event than the statistics underlying these models and theories suggest. It is the uncertainty of the fat tail (in a modern world that is and becoming more replete with Black Swans) that makes these theories and models dangerous. They not only do not properly describe reality but they create a false security that has lulled us into believing that our world is safer than it actually is. To quote Nassim Taleb in the Financial Times:

“Let us start with the bystander. Almost everyone in risk management knew that quantitative methods – like those used to measure and forecast exposures, value complex derivatives and assign credit ratings – did not work and could provide undue comfort by hiding risks. Few people would agree that the illusion of knowledge is a good thing. Almost everyone would accept that the failure in 1998 of Long Term Capital Management discredited the quantitative methods of the Nobel economists involved with it (Robert Merton and Myron Scholes) and their school of thought called “modern finance”. LTCM was just one in hundreds of such episodes.

Yet a method heavily grounded on those same quantitative and theoretical principles, called Value at Risk, continued to be widely used. It was this that was to blame for the crisis. Listening to us, risk management practitioners would often agree on every point. But they elected to take part in the system and to play bystanders. They tried to explain away their decision to partake in the vast diffusion of responsibility: “Lehman Brothers and Morgan Stanley use the model” or “it is on the CFA exam” or, the most potent argument, “modern finance and portfolio theory got Nobels”. Indeed, the same Nobel economists who helped blow up the system at least once, Professors Scholes and Merton, could be seen lecturing us on risk management, to the ire of one of the authors of this article. Most poignantly, the police itself may have participated in the murder. The regulators were using the same arguments. They, too, were responsible.”

And to quote the gents at Monty Python: And now for something completely different…

For better insights into the workings of the financial markets and the thought processes of investors, one must turn to Behavioural Finance (BF) and specifically Prospect Theory as defined by the last on our list of “Gods”, Nobel Laureate Daniel Kahneman and his collaborator Amos Tversky. Kahneman and Tversky are world-renowned psychologists that focus on heuristics and biases to describe human errors. Unfortunately, BF had a tough time competing with Markowitz’s MPT partly because of the difficulty in quantifying it. Psychology does not easily lend itself to a mechanical process; MPT, which utilizes statistical methods that are highly adaptable to computers, certainly does. Variance (a measure of volatility) was, after all, far easier to calculate, even on the less-powerful computers of a half century ago, than the far subtler nuances of psychology, hence the domination of MPT and its associated theories and models with the “quants” on Wall Street and portfolio managers worldwide.

There is a serious problem (danger even) with utilizing statistical methods that have been successfully implemented in the hard sciences (e.g. physics) in econometric and financial models. The financial markets are where human beings (and not atomic particles) interact and transact. Human beings are emotional and irrational (see Prospect Theory). We are also adaptive because we are substantially influenced by past events. Taleb believes it is ludicrous to think that we can predict our future behavior by using financial models that rely on 95% confidence levels. What about the outliers, the other 5% that is conveniently excluded from the model? Does past measured data represent ALL of the potential outcomes? We have been lulled to sleep by these flawed models that supposedly describe the intricate and highly emotional thought processes of investors. It may be past time for us to wake up.

***Source: Wikipedia
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For Detailed Investor Profiles on these Investors, click below:
Universa Investments (Black Swan)
Related People: Mark Spitznagel; Nassim Taleb
Related Entities: Black Swan Fund; Black Swan Hedge Fund; Black Swan Protection Protocol Inflation Fund; Universa Asymmetry Fund LP; Universa Asymmetry Master Fund
Related Article Tags: Multi-Strategy, Long Short, Equity, Debt and Global Macro Hedge Fund News; Hedge Fund Resources and Featured Partner News

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