Chapter 64. Bayesian Probability for Investors

JARROD W. WILCOX, PhD, CFA

President, Wilcox Investment Inc.

Abstract: Bayesian probability technique unifies and simplifies probabilistic reasoning. It is also conducive to the kinds of private science needed in many cases by active investors. It more efficiently uses weak predictors and accelerates learning. Bayesian hierarchical models are very powerful ways of combining group and individual evidence, and have assisted our understanding of how to improve Markowitz mean-variance optimization. This chapter illustrates Bayesian procedures in an investment context.

Keywords: Bayes' rule, Bayes' law, prior distribution, likelihood, posterior distribution, conjugate, sequential analysis, probability, probability distribution, Jaynes, Zellner, Ledoit-Wolf, Black-Litterman, Michaud, resampling, conditional probability, marginal probability, Gibbs sampling, Markov Chain Monte Carlo (MCMC), WinBUGS, hierarchical models

Numbers are not exactly foreign to investors. But their effective use through scientific thinking, both across the population of investors and across the types of decisions they confront, is the exception rather than the rule. Bayesian probability technique can help. This chapter introduces its fundamental ideas and procedures, providing simple illustrations in an investment context. Example algorithms are drawn from the statistical text by Gelman et al. (2004).

CONCEPT AND CONTEXT

Working with probability simply means using numbers ...

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