On the non-Gaussianness of finanical markets

In 2002, Malcolm Gladwell published an essay in the New Yorker called Blowing Up: How Nassim Taleb turned the inevitability of disaster into an investment strategy.

It is sort of a soft profile of 1) Victor Niederhoffer and 2) Nassim Taleb and his hedge fund (Empirica). Taleb's investment strategy begins by noting that people tend to be risk-averse in an asymmetric way (favoring smaller but steady gains and erratic but larger losses (which, I am inferring, shows up in the behavior of the stock market)) [as shown by Kahneman and Tversky]. Also stock market fluctuations do not really follow a normal distribution/Gaussian distribution/bell curve (which describes the statistics of a bunch of identical but independent things...This was one of the assumptions of the Markowitz model.). If you look at the tails (where the largest fluctuations occur), you find that these large fluctuations are much more likely than a Gaussian distribution would predict (as in, they happen perhaps once every few years rather than once very few millennia). This is referred to casually as "fat tails". Eugene Fama first discovered this, and the mathematician Benoit "Fractal Guy" Mandelbrot wrote a book analyzing this discrepancy and proposing an alternative model of financial markets.

Mandelbrot's calculations show that a Cauchy distribution (a.k.a, Lorentzian distribution) is a better model for such market fluctuations. But is there something better? Probably there are more sophisticated models that require more computation. Fama's collaborator French talks about performing calculations without assuming a distribution. I am looking at academic papers to try to learn more.

Today, Fama argues though that the average passive investor really needs only to know that the Cauchy fat tails mean that market crashes and surges are more likely than many expect. Unfortunately, many non-passive investors operating in the fat tails without understanding them are believed to be responsible for the collapses of Long Term Capital Management, and more recently, AIG.

According to posts on the Bogleheads forum, Taleb's hedge fund had to close because (back in 2004) the excess market volatility that they were betting on was simply not there to earn sufficient profit from.

The statistics of bombshells and the efficient-market hypothesis

Justin Fox has been promoting his book The Myth of the Rational Market. In this piece for Time Magazine, he summarizes the historical development of the efficient-market hypothesis.

This tantalizing excerpt from the piece, talks about the connection between solving an optimization problem and the mathematics of the market:

A key figure in the revival was the University of Chicago's Milton Friedman... [who] convinced himself and other economists (without much evidence) that speculators tended to stabilize markets rather than unbalance them.

But Friedman was a scientist too. During World War II, he used his mathematical and statistical skills to help determine the optimal degree of fragmentation of artillery shells. Officers flew back to the U.S. in the middle of the Battle of the Bulge to get his advice on the trade-off between the likelihood of hitting the target (the more fragments, the better) and the likelihood of doing serious damage (the fewer and bigger the fragments, the better).

Emboldened by this work, economists began to apply their number-crunching skills to the postwar market. Chicago graduate student Harry Markowitz devised a model for picking stocks that was, in Friedman's estimation, "identical" to his artillery-shell-fragmentation trade-off. And in the late 1950s, scholars at Chicago and the Massachusetts Institute of Technology became enamored of the idea that stock-market movements were, like many physical phenomena, random.

The two strands of statistics and pro-market ideology came together in the mid-1960s. It was the great MIT economist Paul Samuelson who made the case mathematically that a rational market would be a random one.

From browsing the Wikipedia entry on Markowitz, it sounds like his work was the first to incorporate risk (or second moments) in his estimates of the value of a portfolio. Markowitz is also responsible for the concept of the "Efficient Frontier" (the set of all investment portfolios which maximize expected return for a given level of risk) which eventually led to the efficient-market hypothesis. I would still like to know the exact mathematical details of Friedman's modelling...

My interest in investing

My current interest in investing started in 2007 when I read an article from San Francisco Magazine called, "The Best Investment Advice You'll Never Get". It starts with a story:

As Google’s historic August 2004 IPO approached, the company’s senior vice president, Jonathan Rosenberg, realized he was about to spawn hundreds of impetuous young multimillionaires. They would, he feared, become the prey of Wall Street brokers, financial advisers, and wealth managers, all offering their own get-even-richer investment schemes. ... [T]o protect Google’s staff, he proposed a series of in-house investment teach-ins... One by one, some of the most revered names in investment theory were brought in to school a class of brilliant engineers, programmers, and cybergeeks on the fine art of personal investing, something few of them had thought much about.

John Bogle and Burton Malkiel gave talks on the statistical superiority of indexed mutual funds and their low fees. Like income taxes, the friction provided by the transaction costs of frequent stock trades or the commission fees of actively managed mutual funds can easily reduce the total value of your investment portfolio by half. You may wind up with more money than you started out with (as investing is not a zero-sum game) but far less than you could have had with a balanced portfolio of index funds.

The simplicity and nonconformity of such thinking appeals to me.

But given that investors using such strategies lost a lot of money in 2008 (knocking out gains from the past five to ten years in some cases), is this still a valid approach? And if so, is it the best approach?

John Bogle was recently quoted as saying:

I read all the time that investors need to move beyond a buy-and-hold strategy, but this strikes me as being a dumb idea. What is the advantage of swapping stock with other people? The stock market system is based on the idea of pitting the interests of one investor against another, knowing that only one will win. People say it's a stock-picker's market but, if your stock picker is good, then mine is bad. It's all a gimmick.

There are other approaches beyond picking stocks and investing in index funds with fixed allocation percentages. At this stage, I still have more questions than answers. In this blog, I will document my attempts to understand economics and learn how to invest.