Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models. This paper was accepted by David Simchi-Levi, finance.

A remark on some extensions of the mean-variance portfolio selection models

Quantitative risk management techniques should prove their efficacy when financially turbulent periods are about to occur. Along the common saying “who needs an umbrella on a sunny day?”, a theoretical model is really helpful when it carries the right suggestion at the proper time, that is when markets start behaving hecticly. The beginning of the third decade of the 21st century carried along a turmoil that severely affected worldwide economy and changed it, probably for good. A consequent and plausible research question could be this: which financial quantitative approaches can still be considered reliable? This article tries to partially answer this question by testing if the mean-variance selection model (Markowitz [16], [17]) and some of his refinements can provide some useful hints in terms of portfolio management.

Decision Making in Real Estate: Portfolio Approach

An investment policy is suggested about assets on real estate markets. Such analysis recommends investments in non-financial assets and optimization of the results from such decisions. The formalization of the investment policy is based on the portfolio theory for asset allocation. Two main criteria are applied for the decision making: return and risk. The decision support is based on Mean-Variance portfolio model. A dynamical and adaptive investment policy is derived for active portfolio management. Sliding procedure in time with definition and solution of a set of portfolio problems is applied. The decision defines the relative value of the investment to which real estates are to be allocated. The regional real estate markets of six Bulgarian towns, which identify the regions with potential for investments, are compared. The added value of the paper results in development of algorithm for a quantitative analysis of real estate markets, based on portfolio theory.

Time Series Clustering for Robust Mean-Variance Portfolio Selection: Comparison of Several Dissimilarity Measures

This paper shows how to create a robust portfolio selection with time series clustering by using some dissimilarity measure. Based on such dissimilarity measures, stocks are initially sorted into multiple clusters using the Partitioning Around Medoids (PAM) time series clustering approach. Following clustering, a portfolio is constructed by selecting one stock from each cluster. Stocks having the greatest Sharpe ratio are selected from each cluster. The optimum portfolio is then constructed using the robust Fast Minimum Covariance Determinant (FMCD) and robust S MV portfolio model. When there are a big number of stocks accessible for the portfolio formation process, we can use this approach to quickly generate the optimum portfolio. This approach is also resistant to the presence of any outliers in the data. The Sharpe ratio was used to evaluate the performance of the portfolios that were created. The daily closing price of stocks listed on the Indonesia Stock Exchange, which are included in the LQ-45 indexed from August 2017 to July 2018, was utilized as a case study. Empirical study revealed that portfolios constructed using PAM time series clustering with autocorrelation dissimilarity and a robust FMCD MV portfolio model outperformed portfolios created using other approaches.

Optimal Portfolio Choice with Estimation Risk: No Risk-Free Asset Case

We propose an optimal combining strategy to mitigate estimation risk for the popular mean-variance portfolio choice problem in the case without a risk-free asset. We find that our strategy performs well in general, and it can be applied to known estimated rules and the resulting new rules outperform the original ones. We further obtain the exact distribution of the out-of-sample returns and explicit expressions of the expected out-of-sample utilities of the combining strategy, providing not only a fast and accurate way of evaluating the performance, but also analytical insights into the portfolio construction. This paper was accepted by Tyler Shumway, finance.

Personalized Robo-Advising: Enhancing Investment Through Client Interaction

Automated investment managers, or robo-advisors, have emerged as an alternative to traditional financial advisors. The viability of robo-advisors crucially depends on their ability to offer personalized financial advice. We introduce a novel framework in which a robo-advisor interacts with a client to solve an adaptive mean-variance portfolio optimization problem. The risk-return tradeoff adapts to the client’s risk profile, which depends on idiosyncratic characteristics, market returns, and economic conditions. We show that the optimal investment strategy includes both myopic and intertemporal hedging terms that reflect the dynamic risk profile of the client. We characterize the optimal portfolio personalization via a tradeoff faced by the robo-advisor between receiving information from the client in a timely manner and mitigating behavioral biases in the communicated risk profile. We argue that the optimal portfolio’s Sharpe ratio and return distribution improve if the robo-advisor counters the client’s tendency to reduce market exposure during economic contractions when the market risk-return tradeoff is more favorable. This paper was accepted by David Simchi-Levi, stochastic models and simulation.