Confidence in prior knowledge: Calibration and impact on portfolio performance

The specification of prior parameters is a common practical problem when implementing Bayesian approaches to portfolio optimization. The precision parameter of the prior on the expected asset returns reflects the confidence of the investor in the prior knowledge. Within the framework of the normal-inverse-Wishart model, this paper investigates which factors drive this confidence in order to deduce reasonable values of the precision parameter. We recommend that the investor concentrates on the specification of the precision parameter. By contrast, experts should assess the values of the prior location and dispersion parameter. In the second part of the paper, the impact of the investor's confidence on the performance of investment strategies is examined by a simulation study. The study focusses less on detecting superior portfolio strategies, and more on providing a sensitivity analysis for different levels of confidence. In addition, we show how the posterior distribution of the normal-inverse-Wishart model can be used as a starting point of a simulation process.