Bayesian Analysis and Portfolio Choice

Bernd Scherer

9.1 AN INTRODUCTION TO BAYESIAN ANALYSIS

9.1.1 Theoretical foundations

We have seen in the previous chapter that confining ourselves solely to the information available within a sample will not allow us to tackle the effect of parameter uncertainty on optimal portfolio choice. Not only do we need non-sample information (eg, additional data) to overcome this problem, but it would also be irrational of us to ignore other information based on the experience or insights – also called priors or preknowledge – of investors, statisticians and financial economists. The optimal combination of sample and non-sample information is found in Bayesian statistics. As Nobel laureate Harry Markowitz put it, “the rational investor is a Bayesian” (Markowitz 1987, p. 57).

To appreciate the implications of Bayesian statistics for portfolio choice we first need to understand the main differences between the Bayesian approach to statistics and the traditional, or “frequentist”, approach. The traditional approach creates point estimates for distributional parameters. Estimates are either significant and believed to be 100% true, or insignificant and not believed at all, depending on the researcher’s re

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