‘Fat tails’ could be harmful to optimization, paper says

DENVER — Beware the fat tail when optimizing portfolios.

Andrew Clark, a Denver-based senior research analyst at Lipper, in an upcoming paper to be published in Quantitative Finance this month pushes for an optimizer called the Generalized Capital Asset Pricing Model, which goes beyond the traditional Capital Asset Pricing Model by underweighting or weeding out stocks with unusually large fat-tail distributions.

A fat tail refers to a return distribution bell curve in which one end of the curve is higher than the other — hence, the "fat tail" slang.

A security with a fat-tail return distribution generally is one that displays an unusual amount of upside or downside volatility, as a fat tail means the returns of a security tend to widely swing from its mean return over a given period of time.

In the paper, "The Use of Hurst in Effective Investing," Mr. Clark claims that in model portfolios, he used the optimizer to consistently beat a given index by 300 basis points net of fees, whereas the famed CAPM model created by William Sharpe beat an index by 70 to 80 basis points. Mr. Clark also found that traditional multifactor models, such as the well known four-factor model created by Mark Carhart, co-CIO of quantitative management at Goldman Sachs & Co., New York, consistently beat a given index by about 200 basis points.

"The main reason for the better returns is not by improving stock selection — which many managers do well — but rather, by assisting in portfolio assembly, i.e., how much of the chosen stocks or bonds will produce the best portfolio," said Mr. Clark in his paper.

"This is a fairly good approach," said Omar Aguilar, chief investment officer of quantitative management at ING Investment Management, New York. "What he's proposing here is, in the past people have looked at risk and return to measure risk. He's saying that we should talk about the fat tails in equity. CAPM models tend to underestimate risk because they use one factor. The lessons learned from CAPM is that you need to calculate a covariance matrix."

Covariance is the measure of the degree to which two securities act in tandem. A covariance matrix compares securities in a portfolio to each other.

"This seems like it is a new and nice variation of CAPM," said Charles Massare, director of quantitative research at Lord, Abbett & Co., Jersey City, N.J. "Given the concerns with hedge funds and portable alpha strategies by plan sponsors today, this model could be useful."

Mr. Aguilar said, however, the one flaw in the Clark model is that while it reduces volatility risk in a portfolio, it does not capture upside returns.

In response, Mr. Clark said, "That's an assumption he (Mr. Aguilar) is making. You can use the model to focus just on downside risk. In the paper, I did do both, but one can absolutely use the model to just minimize the losses and focus on the higher moments (of distribution)."