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2015 | OriginalPaper | Buchkapitel

35. Optimal Orthogonal Portfolios with Conditioning Information

verfasst von : Wayne E. Ferson, Andrew F. Siegel

Erschienen in: Handbook of Financial Econometrics and Statistics

Verlag: Springer New York

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Abstract

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.

The methodology in this paper includes 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. Our analytical results also provide economic interpretation for test statistics like the Wald test or multivariate F test used in asset pricing research.

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An alternative is to study conditional efficiency, where the weights minimize the conditional variance. This may be handled by simply reinterpreting the classical analysis.

Note the distinction between minimum variance efficient portfolios, which minimize the variance for the given mean return, and mean variance efficient, which maximize the mean return given its variance. The latter set of portfolios is a subset of the former, typically depicted as the positively sloped portion of the minimum variance efficient boundary when graphed with mean return on the y-axis and standard deviation or variance of return on the x-axis. The portfolio r _p is mean variance efficient when α = 0 and E(r _p) exceeds the expected excess return of the global minimum variance portfolio.

See Roll (1980), Gibbons et al. (1989), MacKinlay (1995), and Campbell et al. (1987) for analyses of optimal orthogonal portfolios in the classical case with no conditioning information.

Equation 35.11 cannot be used to determine μ _s when R _f(Z) is almost surely constant due to division by zero, and, in this case, every choice μ _s ≠ R _f uses the same (rescaled) portfolio of risky assets \( Q\left[\mu (Z)-{R}_f\underset{\bar{\mkern6mu}}{1}\right] \) in the formation of an efficient portfolio x _s(Z).

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Titel: Optimal Orthogonal Portfolios with Conditioning Information
verfasst von: Wayne E. Ferson
Andrew F. Siegel
Verlag: Springer New York
Buch: Handbook of Financial Econometrics and Statistics
Print ISBN: 978-1-4614-7749-5

Electronic ISBN: 978-1-4614-7750-1

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-1-4614-7750-1_35