Robust portfolio optimization with a generalized expected utility model under ambiguity

This paper proposes a robust approach maximizing worst-case utility when both the distributions underlying the uncertain vector of returns are exactly unknown and the estimates of the structure of returns are unreliable. We introduce concave convex utility function measuring the utility of investors under model uncertainty and uncertainty structure describing the moments of returns and all possible distributions and show that the robust portfolio optimization problem corresponding to the uncertainty structure can be reformulated as a parametric quadratic programming problem, enabling to obtain explicit formula solutions, an efficient frontier and equilibrium price system. We would like to thank Prof. Zengjing Chen from School of Mathematics and System Sciences, Shandong University for helpful suggestions, and to thank the anonymous referee for valuable comments.     

Robust portfolio selection under downside risk measures

We investigate a robust version of the portfolio selection problem under a risk measure based on the lower-partial moment (LPM), where uncertainty exists in the underlying distribution. We demonstrate that the problem formulations for robust portfolio selection based on the worst-case LPMs of degree 0, 1 and 2 under various structures of uncertainty can be cast as mathematically tractable optimization problems, such as linear programs, second-order cone programs or semidefinite programs. We perform extensive numerical studies using real market data to reveal important properties of several aspects of robust portfolio selection. We can conclude from our results that robustness does not necessarily imply a conservative policy and is indeed indispensable and valuable in portfolio selection.     

Portfolio Selection with Quadratic Utility Revisited

Considering a simple portfolio selection problem by agents with quadratic utility, an apparently counterintuitive outcome results. When such a choice is over two assets that can be ordered in terms of riskiness, an agent that is more risk averse may optimally invest a larger portion of wealth in the riskier asset. It is shown that such an outcome is not counterintuitive, since for the portfolios from which agents optimally choose, a larger proportion of investment in the riskier asset leads to a less risky portfolio.     

Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, the estimated Markowitz portfolio rule and most of its extensions not only underperform the naive 1/N rule (that invests equally across N assets) in simulations, but also lose money on a risk-adjusted basis in many real data sets. In this paper, we propose an optimal combination of the naive 1/N rule with one of the four sophisticated strategies—the Markowitz rule, the Jorion (1986) rule, the MacKinlay and Pástor (2000) rule, and the Kan and Zhou (2007) rule—as a way to improve performance. We find that the combined rules not only have a significant impact in improving the sophisticated strategies, but also outperform the 1/N rule in most scenarios. Since the combinations are theory-based, our study may be interpreted as reaffirming the usefulness of the Markowitz theory in practice.     

An Improvement of the Parameter Certainty Equivalence Method in Portfolio Selection

This paper discusses an improvement of the Parameter Certainty Equivalence method in portfolio selection. Specifically, we derive methods of portfolio selection that are superior to the Parameter Certainty Equivalence method from the viewpoint of maximizing expected utility. We additionally derive such a method from the Bayesian approach.     

Portfolio optimization algorithms,simplified criteria,and security selection: A contrast and evaluation

The Markowitz full covariance model provides a general framework for analysis of the porfolio selection problem. Three alternative solution methodologies have been developed to facilitate normative applications, but this article shows that they lead to markedly different stock selection and portfolio weighting decisions. In sample-based applications, incompatibilities arise due to model misspecifications and different distributional assumptions, and from the interactive effects of estimation error, optimization model selection bias, and conflicting distributional assumptions.     

Binary switch portfolio

We propose herein a new portfolio selection method that switches between two distinct asset allocation strategies. An important component is a carefully designed adaptive switching rule, which is based on a machine learning algorithm. It is shown that using this adaptive switching strategy, the combined wealth of the new approach is a weighted average of that of the successive constant rebalanced portfolio and that of the 1/N portfolio. In particular, it is asymptotically superior to the 1/N portfolio under mild conditions in the long run. Applications to real data show that both the returns and the Sharpe ratios of the proposed binary switch portfolio are the best among several popular competing methods over varying time horizons and stock pools.     

The impact of global economic policy uncertainty on portfolio optimization: A Black–Litterman approach

This paper investigates the asymmetric impact of global economic policy uncertainty (GEPU) on global asset allocation. We employ the Double Asymmetric GARCH-MIDAS (DAGM) model to examine the asymmetric effect of GEPU shocks on long-term volatilities of global equities, bonds, commodities, clean energy and Bitcoin. The GEPU-based volatility is used as a proxy for the uncertainty of the investor’s views in the Black-Litterman (BL) framework. Empirical results show that the BL model with GEPU-based views yields higher out-of-sample risk-adjusted returns than other traditional benchmarks in most cases. The findings suggest that investors should consider the influence of GEPU when making portfolio decisions.