Strategic Portfolio Theory, Black Swans, and [Avoiding] Being the Turkey7

Put another way, investors are more volatile than invest- ments. Economic reality governs the returns earned by our businesses, and Black Swans are unlikely. But emo- tions and perceptionsthe swings of hope, greed, and fear among the participants in our financial system govern the returns earned in our markets. Emotional fac- tors magnify or minimize this central core of economic reality, and Black Swans can appear at any time.

John C. Bogle, founder of The Vanguard Group8

Modern Portfolio Theory (MPT), like all theories, has been subject to much criticism. Most of that criticism is focused either on the failings of the theorys fundamental assump- tions, or in the way the theory and its assumptions have been applied. Ultimately, it has been accused of failing to predict the major financial crises of our time, like Black Monday in 1987, the credit crisis in the U.S. in 2008, or the current financial crisis over sovereign debt in Europe.

Criticisms of Modern Portfolio Theory

Modern portfolio theory was the creation of Harry Markowitz in which he applied principles of linear pro- gramming to the creation of asset portfolios.9 Markowitz demonstrated that an investor could reduce the standard deviation of portfolio returns by combining assets that were less than perfectly correlated in their returns. The theory assumes that all investors have access to the same information at the same point in time. It assumes all inves- tors are rational and risk averse, and will take on additional risk only if compensated by higher expected returns. It assumes all investors are similarly rational, although dif- ferent investors will have different trade-offs between risk and return based on their own risk aversion characteristics. The usual measure of risk used in portfolio theory is the standard deviation of returns, assuming a normal distribu- tion of returns over time.

As one would expect, the criticisms of portfolio theory are pointed at each and every assumption behind the

theory. For example, the field of behavioral economics argues that investors are not necessarily rationalthat in some cases, gamblers buy risk. All investors do not have access to the same information, that insider trading per- sists, that some investors are biased, that some investors regularly beat the market through market timing. Even the mathematics comes under attack, as to whether standard deviations are the appropriate measure of risk to minimize, or whether the standard normal distribution is appropriate.

Many of the major stock market collapses in recent his- tory, like that of Black Mondays crash on October 19, 1987, when the Dow fell 23%, were missed by the purveyors of portfolio strategy. Statistical studies of markets and their returns over time often show returns that are not normally distributed, but are subject to greater deviation from the mean than traditional normal distributionsevidence of so-called fat tails. Much of the work of Benoit Mandelbrot, the father of fractal geometry, revolved around the possi- bility that financial markets exhibited fat tail distributions. Mandelbrots analysis in fact showed that the Black Mon- day event was a 20-sigma event, one which, according to normal distributions (bell curve or Gaussian model), was so improbable as not likely to ever occur.10 And if something has not happened in the past, portfolio theory assumes it cannot happen in the future. Yet it did.

The argument and criticism that has been deployed with the greatest traction seems to be that portfolio theory is typically executed using historical datathe numbers from the pastassuming a distribution that the data does not fit.

Any attempts to refine the tools of modern portfolio theory by relaxing the bell curve assumptions, or by fudging and adding the occasional jumps will not be sufficient. We live in a world primarily driven by random jumps, and tools designed for random walks address the wrong problem. It would be like tinkering with models of gases in an attempt to characterise them as solids and call them a good approximation

Black Swan Theory

Nassim Nicholas Taleb published a book in 2001 entitled Fooled by Randomness in which he introduced the analogy of the black swan.12 The argument is quite simple: prior to the discovery of Australia and the existence of black swans, all swans were thought to be white. Black swans did not exist because no one had ever seen one. But that did not mean they did not exist. Taleb then applied this premise to financial markets, arguing that simply because a specific event had never occurred did not mean it couldnt.

Taleb argued that a black swan event is characterized by three fundamentals, in order, Rarity, Extremeness, and Retrospective Predictability:

1. Rarity: The event is a shock or surprise to the observer.

2. Extremeness: The event has a major impact.

3. Retrospective Predictability: After the event has occurred, the event is rationalized by hindsight, and found to have been predictable.

   Although the third argument is a characteristic of human

intellectual nature, it is the first element that is fundamental to the debate. If an event has not been recorded, does that mean it cannot occur? Portfolio theory is a mathematical analysis of provided inputs. Its outcomes are no better than itsinputs.Thetheoryitselfdoesnotpredictpricemovements. It simply allows the identification of portfolios in which the risk is at a minimum for an expected level of return.

Taleb does not argue that he has some secret ability to predict the future when historical data cannot. Rather, he argues that investors should structure their portfo- lios, their investments, to protect against the extremes, the improbable events rather than the probable ones. He argues for what many call investment humility, to acknowledge that the world we live in is not always the one we think we live in, and to understand how much we will never understand.

What Drives the Improbable?

So what causes the random jumps noted by Mandelbrot and Taleb? A number of investment theorists, including John Maynard Keynes and John Bogle, have argued over the past century that equity returns are driven by two fundamental forces, enterprise (economic or business returns over time) and speculation (the psychology or emotions of the individu- als in the market). First Keynes and then Bogle eventually concluded that speculation would win out over enterprise, very much akin to arguing that hope will win out over logic.

This is what Bogle means in the opening quotation when he states that investors are more volatile than investments.

All agree that the behavior of the speculators (in the words of Keynes) or the jumps of market returns (in the words of Mandelbrot) are largely unpredictable. And all that one can do is try and protect against the unpredictable by building more robust systems and portfolios than can hopefully with- stand the improbable. But most also agree that the jumps are exceedingly rare, and depending upon the holding period, the market may return to more fundamental values, if given the time. But the event does indeed have a lasting impact.

Portfolio theory remains a valuable tool. It allows inves- tors to gain approximate values over the risk and expected returns they are likely to see in their total positions. But it is fraught with failings, although it is not at all clear what would be better. Even some of historys greatest market timers have noted that they have followed modern port- folio theory, but have used subjective inputs on what is to be expected in the future. Even Harry Markowitzon the last page of the same article that started it all, Portfolio Selectionnoted that . . . in the selection of securities we must have procedures for finding reasonable ri and sij. These procedures, I believe, should combine statistical techniques and the judgment of practical men.

But the judgement of practical men iswelldifficult tovalidate.Weneedpredictionsofwhatmaycome,evenif it is generally based on the past. Kenneth Arrow, a famed economist and Nobel Prize winner relayed the following story of how during the World War II a group of statisti- cians were tasked with forecasting weather patterns.

The statisticians subjected these forecasts to verification and found they differed in no way from chance. The forecasters themselves were convinced and requested that the forecasts be discontinued.The reply read approximately like this:The Commanding General is well aware that the forecasts are no good. However, he needs them for planning purposes.13

Taleb, in a recent edition of Black Swan Theory, notes that the event is a surprise to the specific observer, and that what is a surprise to the turkey is not a surprise to the butcher. The challenge is to avoid being the turkey.

Mini-Case Questions

1. What are the primary assumptions behind modern portfolio theory?

2. What do many of MPTs critics believe are the funda- mental problems with the theory?

3. How would you suggest MPT be used in investing your own money?