Optimal Orthogonal Portfolios with Conditioning Information

Optimal orthogonal portfolios are a central feature of tests of asset pricing models and are important in active portfolio management problems. The portfolios combine with a benchmark portfolio to form ex ante mean variance efficient portfolios. This paper derives and characterizes optimal orthogonal portfolios in the presence of conditioning information in the form of a set of lagged instruments. In this setting, studied by Hansen and Richard (1987), the conditioning information is used to optimize with respect to the unconditional moments. We present an empirical illustration of the properties of the optimal orthogonal portfolios. From an asset pricing perspective, a standard stock market index is far from efficient when portfolios trade based on lagged interest rates and dividend yields. From an active portfolio management perspective, the example shows that a strong tilt toward bonds improves the efficiency of equity portfolios. Our analytical results provide economic interpretation for test statistics like the Wald test or multivariate F test used in asset pricing research. The empirical applications in this paper make use of regression and maximum likelihood parameter estimation, as well as method of moments estimation. We form maximum likelihood estimates of nonlinear functions as the functions evaluated at the maximum likelihood parameter estimates.

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