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Covariance

Terrorism and economic turmoil trump some basic assumptions about risk management.
David M. Katz, CFO.com | US
December 31, 2002

Put covariance on a "Where Are They Now?" list and you're sure to get some ugly, equation-laced memos in your in-box.

After all, the notion that corporations and investors should diversify their portfolios is hardly subject for dismissal. Combined with the theory of the rational market, covariance forms the underpinnings of modern portfolio theory (MPT), a notion so dominant that it's almost invisible these days.

Before Nobel Laureate Harry Markowitz, the originator of MPT, had his epiphany in the early 1950s, investors usually relied on brokers for guidance. The concept that an investor could actually lessen risk and still come out with a decent payoff was almost unheard of.

Decades later, technology -- and the ability to shift money quickly -- made it possible to put Markowitz's theory into practice. It also made covariance, a mathematical concept more often associated with time-of-flight mass spectrometry, seem like investment holy writ.

If you steer clear of the math supporting the theory, covariance is a relatively simple concept. According to Investopedia.com, covariance measures the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together; a negative covariance means returns vary inversely. The idea for money managers: Add assets with low covariance -- that is, assets that don't move in tandem with each other -- and you decrease portfolio risk.

Indeed, during the 1990s, many fund managers would cite covariance when explaining why the were pouring billions of dollars into stock markets in Europe and Asia. After all, they pointed out, if the U.S. market stayed flat for long enough, investors would eventually seek out better returns elsewhere. That, in turn, would boost share prices on those markets. When one market was down, another would be up.

And for a time, that argument held up pretty well. But for the past two years, it appears that the major stock markets appear to be moving more in lockstep than out-of-step. If the U.S. market is down, it's likely Hong Kong will also be down the next day. If the DJIA sheds 200 points in a day's trading, it's a solid bet the FTSE 100 will open lower the next day.

So what happened to the notion of covariance? It's still in use, still getting applied to all sorts of random events (risk management tables, the movement of subatomic particles, etc). The problem when applying covariance to investing, critics say, is that people interact less predictably than the theory implies. To be sure, the principle of covariance works swimmingly well in physics and insurance, says Nassim Nicholas Taleb, a well-known MPT gadfly and chairman of Empirica LLC, a hedge fund. In those fields, random variables can very well move as a unit in predictable ways.

Share price may be another matter, however. Portfolio theory "assumes that there exists a known structure to the variations in financial prices," says Taleb. "I believe that, unlike things in the physical world, [human] relationships are highly unstable--and tend to change over time."

Recent events have supplied a boost to those views. The 9/11 attacks, for example, made risks of all kinds suddenly seem a whole lot less predictable. What's more, the extreme contrast between the current economic downturn and the preceding decade-long bubble has shaken the assumptions of investors. The stock market no longer seems like such a rock-solid way to assure a poolside retirement, many feel.

Will the increased sense of uncertainty buckle the universal faith in rational markets, too? Judging from the brisk pace at which investment firms are introducing MPT-based risk models, it's a belief not likely to be shaken soon.

Still, investors might start using such measurement tools with a tad more caution. "The problems with risk model implementations really stem from misunderstanding what models can and can't do," explains one quant. "There is no risk model that can forecast large exogenous events."




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