Bayesian Asset Allocation and U.S. Domestic Bias

U.S. investors hold much less international stock than is optimal according to mean–variance portfolio theory applied to historical data. We investigated whether this home bias can be explained by Bayesian approaches to international asset allocation. In comparison with mean–variance analysis, Bayesian approaches use different techniques for obtaining the set of expected returns by shrinking the sample means toward a reference point that is inferred from economic theory. Applying the Bayesian approaches to the field of international diversification, we found that a substantial home bias can be explained when a U.S. investor has a strong belief in the global mean–variance efficiency of the U.S. market portfolio, and in this article, we show how to quantify the strength of this belief. We also found that one of the Bayesian approaches leads to the same implications for asset allocation as the mean–variance/tracking-error criterion. In both cases, the optimal portfolio is a combination of the U.S. market portfolio and the mean–variance-efficient portfolio with the highest Sharpe ratio. The benefits of international diversification have been the subject of a controversial and ongoing debate in recent decades. According to standard mean–variance portfolio theory, an internationally diversified equity portfolio has risk–return characteristics that are preferable to those of a domestic-only benchmark portfolio. The behavior of investors, however, is often inconsistent with this normative theory. For example, U.S. investors hold much less non-U.S. stock than portfolio theory predicts should be optimal: According to mean–variance analysis, U.S. investors should allocate 30–40 percent of portfolio wealth to non-U.S. equities, but the actual allocation is 8–10 percent. This discrepancy is known as the “home bias puzzle.”To explain the home bias puzzle, some researchers have applied approaches other than mean–variance analysis, such as behavioral finance or nonexpected utility theory. Surprisingly little effort has been made to investigate approaches that are consistent with mean–variance analysis and that might establish a link between normative and descriptive research on international diversification. The key is to focus on the estimation of the input parameters for mean–variance optimization.The most crucial input for asset allocation is the set of expected returns. Expected returns can be estimated from historical returns, derived from a forecasting model, or inferred from an asset-pricing model. In each case, a substantial amount of uncertainty is attached to the estimates. The problem with mean–variance analysis is that it uses only a single set of estimates: Asset allocation is based only on sample means, in the case of identically and independently distributed data, or on personal judgments about the future performance of asset classes. Furthermore, estimated expected returns are treated as if they were true values. A better approach would be to assess the information content of the various information sources and combine them into a single estimate, which is the basic idea of Bayesian statistics.Bayesian inference combines extra-sample, or prior, information with sample returns. The sample means are shrunk toward a reference point that is inferred from economic theory. We investigated whether three Bayesian approaches can explain the home bias of U.S. investors. In the first approach, the mean–variance-efficient portfolio with the highest Sharpe ratio, which is called the tangency portfolio, is shrunk toward the minimum-variance portfolio. In the second approach, the tangency portfolio is shrunk toward the market portfolio. The prior expected returns are inferred from the capital asset pricing model, and the shrinkage effect depends on the degree of sample information in the data and the investor's confidence in the pricing model. In the third model, historical returns are discarded as worthless for estimating expected returns and the investor is allowed to express subjective views about future expected returns. These views and the investor's level of conviction determine the extent of deviation from the market portfolio. In addition to evaluating the three Bayesian approaches, we investigated the mean–variance/tracking-error (MVTE) criterion, under which an investor is concerned not only with expected portfolio return and its variance but also with regret aversion—the risk of underperforming a benchmark portfolio (U.S. equities in our case). Interestingly, the Bayesian approach of shrinking toward the market portfolio led to conclusions similar to those based on portfolios formed under the MVTE criterion.In our empirical study, we found that a substantial home bias can be explained when a U.S. investor has both a strong belief in the global mean–variance efficiency of the U.S. market portfolio and a high aversion to falling behind the U.S. market portfolio. (In this article, we also show how to quantify the strength of this belief.) We also found that the current level of the home bias can be justified whenever regret aversion is significantly greater than risk aversion. Furthermore, the results held qualitatively for non-U.S.-based investors.Finally, to assess the potential of various approaches for adding value in tactical asset allocation, we conducted an out-of-sample study to compare the risk-adjusted performance of the Bayesian approaches with the risk-adjusted performance of mean–variance analysis. We found mixed results. The Bayesian approaches proved to be superior to mean–variance tangency portfolios that rely on sample means, and the Bayesian portfolios exhibited higher risk-adjusted returns and lower turnover. The Bayesian approaches were not found to be systematically superior to heuristic strategies, however, such as the market portfolio or the minimum-variance portfolio. Thus, the empirical results confirm the well-known fact that accurately estimating expected returns from historical returns alone is hard.