Revisionists correct the questionable premises of modern portfolio theory through small fixes that lack any guiding principle and do not improve matters sufficiently. The bearish answer is that large market swings are anomalies, individual “acts of God” that present no conceivable regularity. This contention leads to the question of whether a rigorous quantitative description of at least some features of major financial upheavals can be developed. Though sometimes acknowledging faults in the present body of thinking, its adherents suggest that no other premises can be handled through mathematical modeling. Modern portfolio theory poses a danger to those who believe in it too strongly and is a powerful challenge for the theoretician. But should financial markets then be described as abnormal? Of course not-they are what they are, and it is portfolio theory that is flawed. Granted, the bell curve is often described as normal-or, more precisely, as the normal distribution. (The fluctuations are greater than 10 standard deviations.) But in fact, one observes spikes on a regular basis-as often as every month-and their probability amounts to a few hundredths. Big price jumps become more common as the turbulence of the market grows-clusters of them appear on the chart.Īccording to portfolio theory, the probability of these large fluctuations would be a few millionths of a millionth of a millionth of a millionth. Moreover, the magnitude of price movements (both large and small) may remain roughly constant for a year, and then suddenly the variability may increase for an extended period. A substantial number of sudden large changes-spikes on the chart that shoot up and down as with the Alcatel stock-stand out from the background of more moderate perturbations. These patterns, however, constitute only one aspect of the graph. Charts of stock or currency changes over time do reveal a constant background of small up and down price movements-but not as uniform as one would expect if price changes fit the bell curve. Typhoons are, in effect, defined out of existence.ĭo financial data neatly conform to such assumptions? Of course, they never do. The width of the bell shape (as measured by its sigma, or standard deviation) depicts how far price changes diverge from the mean events at the extremes are considered extremely rare. The second presumption is that all price changes are distributed in a pattern that conforms to the standard bell curve. As a result, predictions of future market movements become impossible. First, they suggest that price changes are statistically independent of one another: for example, that today’s price has no influence on the changes between the current price and tomorrow’s. The risk-reducing formulas behind portfolio theory rely on a number of demanding and ultimately unfounded premises. If the weather is moderate 95 percent of the time, can the mariner afford to ignore the possibility of a typhoon? An inescapable analogy is that of a sailor at sea. But the picture it presents does not reflect reality, if one agrees that major events are part of the remaining 5 percent. It is true that portfolio theory may account for what occurs 95 percent of the time in the market. The mathematics underlying portfolio theory handles extreme situations with benign neglect: it regards large market shifts as too unlikely to matter or as impossible to take into account. A cornerstone of finance is modern portfolio theory, which tries to maximize returns for a given level of risk. The classical financial models used for most of this century predict that such precipitous events should never happen. In a reversal, the stock shot up 10 percent on the fourth day. Last September, for instance, the stock for Alcatel, a French telecommunications equipment manufacturer, dropped about 40 percent one day and fell another 6 percent over the next few days. Fortunes are made and lost in sudden bursts of activity when the market seems to speed up and the volatility soars.
#A MULTIFRACTAL WALK DOWN WALL STREET PROFESSIONAL#
Individual investors and professional stock and currency traders know better than ever that prices quoted in any financial market often change with heart-stopping swiftness. We are posting it in light of recent news involving Lehman Brothers and Merrill Lynch. Editor's Note: This story was originally published in the February 1999 edition of Scientific American.