Wednesday, March 3, 2010

Price discovery as a chaotic process

Jeff Augen’s book The Volatility Edge in Options Trading: New Technical Strategies for Investing in Unstable Markets (FT Press, 2008) is a treasure trove of thought-provoking ideas, and not just for the option trader. Today I want to share his thesis that “price discovery cannot operate properly unless the market is chaotic” (p. 7) and, its corollary, that the lack of market chaos can cause a small drawdown to become a crash.

Augen uses the word “chaos” in “the true mathematical sense—a system that appears random but behaves according to a well-defined set of rules.” (p. 8) Or, as others have described a chaotic system, it exhibits three main characteristics. (Here I’m relying on good old Wikipedia although I’ve written more than once about chaotic systems on this blog.) First, it is “highly sensitive to initial conditions,” what is known as the butterfly effect. Second, it is deterministic. And third, despite its deterministic nature, it is not predictable.

According to Augen the market is chaotic because it is “characterized by large numbers of investors pursuing divergent strategies based on different goals and views of the market.” He gives a “microscopic” example which is worth quoting in full, mainly because there’s no efficient way to summarize it. “Investor #1, on hearing a piece of bad news, decides to sell a stock. The stock falls slightly and triggers another investor’s (#2) stop-sell limit order. This new sell order causes the price to fall further. However, investor #3, who has a longer-term view of the company and believes that the stock is undervalued, has been waiting for a dip in the price. He aggressively buys a large number of shares, momentarily stabilizing the price. However, a large institutional investor with a computer program that tracks this particular stock, looking for such behavior, suddenly receives notice that a sell-short trigger has been activated. The large institutional sell order causes the stock to fall rapidly. It also triggers stop-sell limit orders from other investors who are protecting their profits. The sell-off accelerates as investors aggressively run from their positions in the stock. However, a small group of speculators who previously anticipated the bad news and sold short now begin buying the stock to cover their short sales and lock in a profit. They are using automated systems with triggers that generate a buying decision as soon as a certain profit level has been reached. The stock begins to climb again as aggressive buy-to-cover orders accumulate. As the stock climbs, short sellers begin to see their profits evaporate. They become increasingly aggressive about buying back the stock. The trend begins to slow as short sellers take themselves out of the market by unwinding positions. The price does not stabilize, however, because other investors witnessing the sudden rise and looking at particular chart patterns interpret the emerging rally as a buying opportunity and flock to purchase the stock before it runs up too much. The process continues indefinitely because price discovery is a dynamic and never-ending process.” (pp. 7-8)

By contrast, consider what would have happened if, as the scenario began to unfold, every investor had made the same sell decision as investor #1. In this case the stock would have plummeted. “A new fair-market value would not have been discovered until a very low point had been reached. In this scenario the lack of market chaos would have caused a small drawdown to become a crash.” (p. 8)

Augen claims that “the size of the resulting decline is closely related to the lack of chaos exhibited just prior to the sell-off. . . . The initial days of the ’29, ’87, and ’00 crashes all had a distinctly nonchaotic character.” (p. 8)

On one level, I suppose, these points are obvious to anyone who has followed markets, especially intraday. We know that market participants have a range of time horizons that affect their views of the market. At one extreme are the high frequency traders who provide liquidity and some very short-term directionality. (And here, parenthetically, let me quote Augen once again: “If liquidity is the fuel that powers the price discovery engine, chaos is certainly the principal ingredient in that fuel.”) At the other extreme are the buy and hold--until it becomes excruciatingly painful--investors. We also know that traders have different market biases, some long and others short. And we know that some are discretionary traders and others follow systems, in many cases triggered by algorithms.

But what appeals to me is the notion that chaos is such a positive force. Remove it and things get sucked into a black hole. As regulators rightfully try to rein in Wall Street excesses they would do well to keep this principle in mind. It’s important to keep a wide range of players at the table; we just don’t want them to be playing with marked cards.

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