The Efficient Use of Conditioning Information in Portfolios

We study the properties of unconditional minimum-variance portfolios in the presence of conditioning information. Such portfolios attain the smallest variance for a given mean among all possible portfolios formed using the conditioning information. We provide explicit solutions for n risky assets, either with or without a riskless asset. Our solutions provide insights into portfolio management problems and issues in conditional asset pricing. SINCE THE PIVOTAL WORK of Markowitz (1959) and Sharpe (1964), mean variance analysis has been a central focus of financial economics. Mean variance theory is used in portfolio analysis, asset pricing, investment performance measurement, and topics in corporate finance. Mean variance analysis also has other important economic applications. Problems involving quadratic objective functions or loss functions generally incorporate a mean variance analysis. Examples include economic policy under uncertainty, labor markets, monetary policy, inventory problems, hedging, resource economics, and a host of other applications. This paper provides solutions to mean variance optimization problems in the presence of conditioning information. Conditioning information is present when the optimal solution may be a function of information to be received about the probability distribution of future outcomes. For example, empiri* Wayne E. Ferson is the Pigott-PACCAR Professor of Finance at the University of Washington and a Research Associate, NBER. Andrew F. Siegel is the Grant I. Butterbaugh Professor of Finance and Management Science and Adjunct Professor of Statistics at the University of Washington. We are grateful to Hank Bessembinder, Jonathan Berk, John Cochrane, Heber Farnsworth, the editor, Richard Green, Bruce Grundy, Lars Hansen, David Ikenberry, Patrice Poncet, Jeff Pontiff, Mark Ready, Ed Rice, Vance Roley, Richard W. Sias, Richard Startz, and an anonymous referee for helpful comments. The paper has also benefited from participants in workshops at the following universities: Arizona, Boston College, California at Berkeley, Duke, Illinois, Miami, New York University, Purdue, Rice, la Sorbonne, Southern California, South Carolina, Stanford, The Stockholm School of Economics, Utah, Wisconsin-Madison, the University of Washington (Finance, Management Science, and Statistics Departments), and Washington State University; also at the 1998 American Finance Association, the 1997 American Statistical Association (Anaheim), 1997 European Finance Association in Vienna, the 1997 Inquire Europe Autumn Seminar, the 1997 Euro Working Group on Financial Modelling Meeting in Venice, April 1997 meeting of the National Bureau of Economic Research Asset Pricing Group, VII International Conference on Stochastic Programming (1998) and the 1997 Western Finance Association meetings.