Long-Term Asset Allocation under Time-Varying Investment Opportunities: Optimal Portfolios with Parameter and Model Uncertainty

Abstract

We study the implications of predictability on the optimal asset allocation of ambiguity averse long-term investors. We analyze the term structure of the multivariate risk-return trade-off in a VAR model under full consideration of parameter uncertainty, and we decompose the predictive covariance along different sources of risk/uncertainty. We calibrate the model to real returns of US stocks, US long-term government bonds, cash, real-estate and gold using term spread and dividend yields as additional predictive variables. While over short periods the model-implied conditional covariance structure of asset-class returns determines the optimal allocation, we find that over longer horizons the optimal asset allocation is significantly influenced by the covariance structure induced by estimation errors. As a consequence, the ambiguity averse long-term investor tilts her portfolio not simply toward the global minimum-variance portfolio but shrinks portfolio weights toward a seemingly inefficient portfolio which shows maximum robustness against estimation errors. Most interestingly, we find that even though time diversification of stock returns vanishes after consideration of estimation errors, real long-term bond returns are even more affected, making stocks an important asset class for the ambiguity averse long-term investor.