"Risk and Asset Allocation" - Springer, by Attilio Meucci

Textbook: Bayesian Estimation

Risk and Asset Allocation, Springer 2005

The classical approach to estimation discussed in the second part of the book does not account for estimation risk. To tackle this issue, in this chapter we introduce the Bayesian approach in general, showing how to blend the investor’s prior and the market information to obtain the posterior distribution. Furthermore, we show how the Bayesian framework includes the classical approach to estimation in the form of “classical-equivalent” estimators. Finally, we discuss how to summarize the main features of a generic posterior distribution by means of its location-dispersion ellipsoid. We compute the posterior distribution of expected value and covariance matrix of the market invariants under the conjugate normal-inverse-Wishart hypothesis. Then we compute the classical-equivalent estimators of the above parameters, exploring their self-adjusting behavior. Finally we compute the joint and the marginal location-dispersion ellipsoids of expected values and covariance matrix provided by their posterior distribution.


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