Handbook of Exchange Rates

15.4 Parameter Uncertainty in Bayesian Asset Allocation

The asset allocation literature typically assumes that investors make optimal decisions with full knowledge of the true parameters of the model. In practice, model parameters have to be estimated, and if there is estimation error, the resulting allocation will be suboptimal. This gives rise to estimation risk in applications of the plug-in method, which replaces the true parameter values by their estimates. In contrast, the Bayesian approach to asset allocation integrates estimation risk into the analysis and deals with parameter uncertainty by assuming that the investor evaluates her expected utility under the predictive distribution, which is determined by historical data and the prior, but does not depend on the parameter estimates.

We consider an investor who takes into account volatility and correlation timing but is uncertain about the parameters of the model. The Bayesian portfolio choice literature argues that in the presence of parameter uncertainty, the unknown objective return distribution in the expected utility maximization should be replaced with the investor's subjective posterior return distribution reflecting the information contained in the historical data and the investor's prior beliefs about the parameters. Use of predictive distributions was pioneered by Zellner and Chetty (1965) and it was used, among others, by Barberis (2000), Kandel and Stambaugh (1996), and Kan and Zhou (2007). These studies demonstrate ...