As financial markets have grown faster and more complex, it has become more difficult for managers to trade efficiently. The goal of maximizing returns while minimizing risk has grown more complicated.

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But researchers have devised a method that could help some traders, including those managing large portfolios or those working in statistical arbitrage groups who are seeking to capitalize on pricing inefficiencies between securities.

The work by Princeton University’s Jianqing Fan and Alex Furger and Chicago Booth’s Dacheng Xiu builds on the original framework of Modern Portfolio Theory, introduced by Harry Markowitz in 1952, where an investment manager aims to maximize a portfolio’s return while minimizing risk. With help from covariance matrix estimation, a measure of how assets move in tandem, the manager can build an optimal portfolio, or one that reaches a required rate of return with minimum volatility. The idea is to limit covariance between securities—covariance being the amount two random variables change together—so as to prevent them from all moving in the same direction at once.

Investing has grown more complex since Markowitz published the first optimization paper, and researchers have created new tools to help investors keep up. The Fama-French Three-Factor Model, designed by Chicago Booth’s Eugene F. Fama and Dartmouth’s Kenneth R. French, considers market correlation and a company’s size and valuation when building an optimal portfolio.

But the Fama-French model is not enough on its own when it comes to managing large portfolios, write Fan, Furger, and Xiu. They propose that considering a few additional factors, including industry classification, removes essentially all idiosyncratic covariances, keeping assets from moving in tandem.

The factors that the researchers consider include some associated with the nine rapidly traded SPDR S&P 500 sector exchange-traded funds. They further refine the model to capture the effects that these nine sectors—financials, energy, utilities, technology, materials, consumer staples, consumer discretionary, industrials, and health care—have on returns.

The covariances that remain “are sector specific,” says Xiu. “They are explained well by the classification code” used to define industries. He says they can be addressed on a sector-by-sector basis.

Fan, Furger, and Xiu suggest that managers of large funds, among other traders, may find their model potentially more accurate than Fama-French or other models being used to gauge risk.

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