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Nonlinear portfolio views: an efficient extension to the Black-Litterman approach

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Abstract

Two efficient approximate methods for optimal (Bayesian) blending of views on portfolios of assets with nonlinear payoff profiles are introduced. The idea is based on the observation that the application of the Black-Litterman model, with respect to market views, is equivalent to the measurement update in the linear filtering problem in engineering and statistics. The approaches suggested here are motivated by results from nonlinear filtering theory. In particular it is shown that the simple Gaussian framework can be approximately maintained, despite of nonlinear relations with the respective risk factors, by using the extended Kalman filter update or the unscented transform. Both methods are well suited for high dimensional problems from a computational point of view, and can thus be applied to large portfolios of derivatives.

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Notes

  1. To be more precise, the initial state vector, containing the returns of the DJI members, has to be extended by the returns of the respective option positions, as already exercised before.

  2. The DJI members were ordered lexicographically with respect to their ticker-symbols. Thus, the sequence of the first four members is Alcoa (AA), American Express (AXP), Boeing (BA), and Bank of America (BAC).

  3. The analysis was also conducted with 5000 and 10,000 replications. The runtimes for Monte Carlo simulation did not differ much between prior and posterior selection. They were recorded approximately as 1.94 s (5000 replications), 3.85 s (10,000 replications), and 38.47 s (100,000 replications). The EKF and UKF solutions were available in order \(10^{-3}\) s. There was a noticeable difference in the results due to the increasing number of replications.

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Authors and Affiliations

  1. Department of Economics and Finance, University of Greifswald, Greifswald, Germany

    Thomas Mazzoni

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  1. Thomas Mazzoni
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Correspondence to Thomas Mazzoni.

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Mazzoni, T. Nonlinear portfolio views: an efficient extension to the Black-Litterman approach. J Bus Econ 85, 693–717 (2015). https://doi.org/10.1007/s11573-015-0767-3

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