Put another way, investors are more volatile than investments.
Economic reality governs the returns earned by our businesses, and Black Swans are unlikely. But emotions and perceptions—the swings of hope, greed, and fear among the participants in our financial system—
govern the returns earned in our markets. Emotional factors 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 theory’s fundamental assumptions, 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 programming 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 investors 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 different 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 distribution 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 rational—that in some cases, gamblers buy risk. All investors do not have access to the same information, that insider trading persists, 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 history, like that of Black Monday’s 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 distributions—evidence of so-called fat tails. Much of the work of Benoit Mandelbrot, the father of fractal geometry, revolved around the possibility that financial markets exhibited fat tail distributions.
Mandelbrot’s analysis in fact showed that the Black Monday 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 data—the numbers from the past—assuming a distribution that the data does not fit.
Any attempts to refine the tools of modern portfolio theory by relaxing the bell curve..........

Mini-Case Questions 1. What are the primary assumptions behind modern portfolio theory?
2. What do many of MPT’s critics believe are the fundamental problems with the theory?
3. How would you suggest MPT be used in investing your own money?