Focus: The Market Isn’t All Random

Published August 18, 1999  |  Phys. Rev. Focus 4, 10 (1999)  |  DOI: 10.1103/PhysRevFocus.4.10

Noise Dressing of Financial Correlation Matrices

Laurent Laloux, Pierre Cizeau, Jean-Philippe Bouchaud, and Marc Potters

Published August 16, 1999

Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series

Vasiliki Plerou, Parameswaran Gopikrishnan, Bernd Rosenow, Luís A. Nunes Amaral, and H. Eugene Stanley

Published August 16, 1999
Figure 1
Copyright 1999 PhotoDisk, Inc.

Risky business. Traders at La Bourse Stock Market in Paris should be careful about how they spread risk among seemingly uncorrelated stocks, according to two new analyses of stock prices.

Any investor can tell you that stock prices seem to vary randomly at times, but a pair of reports in the 16 August PRL suggests that they aren’t entirely random. The France- and US-based teams used analyses borrowed from the physics world to look at correlations among stock prices and found that most of the correlations are random. But they found a few exceptions: some collections of stocks have price correlations that are stable over time. Although this concept is not new to investors, the analyses are the first statistically precise descriptions of this phenomenon, and they suggest that some commonly used financial methods find correlations that are not real. The results cannot be used to predict market trends, but may be useful for the proper balancing of risk within a stock portfolio.

To minimize overall risk, investors are often urged to “diversify” their financial portfolio: “Don’t put all your eggs in one basket,” is the common warning. “But what happens if all the baskets are being carried by the same person?” asks Luis Amaral of Boston University. If you don’t know there is a single basket carrier–a correlation among seemingly uncorrelated stock prices–all your holdings could suffer when he stumbles. So financial analysts try to identify which stock prices tend to react in similar ways to external influences and which ones react differently. The two teams, based at Boston University and at the company Science & Finance in Paris, approached the problem in a new way that includes a precise definition of “random” behavior.

The researchers analyzed the correlations in several years of price data for a large number of US stocks using a technique that isolates a series of “modes” or “trends” from the background. With another technique called random matrix theory they could clearly see which of these modes could be accounted for entirely by randomness–at least 95% according to both teams. But the remaining modes were not random, the largest being the “full market” mode. It implies that the most important and stable influence on a stock price is the movement of the whole market, rather than any other stock price. The other nonrandom modes require more detailed analysis to unravel which collections of stocks they may represent. Laurent Laloux of Science & Finance speculates that they might be specific market sectors, such as technology companies or utilities.

Laloux explains that many analysts use correlation information as part of their risk analyses, but they don’t have solid methods for differentiating real trends from randomness. Amaral summarizes the conclusions this way: “Knowing that your baskets were carried by different people during the last year does not assure you that they will not be carried by the same person this year.”

Anirvan Sengupta of Lucent Technologies in Murray Hill, NJ, says the results illustrate that conventional theories for optimizing portfolios work only under more idealized conditions–few stocks and a market with unchanging external influences. He hopes more research will lead to a better understanding of the few nonrandom modes the researchers discovered, perhaps even a basic dynamical theory a physicist could be proud of. “Now that would be really interesting,” he says.

–Anonymous


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