Robust Portfolio Optimization with Applications in Currencies and Private Equity

Abstract

This dissertation presents new insights and variations of the Robust Counterpart problem defined by Ben-Tal and Nemirovski. These models are applied to a set of practical portfolio problems.

First, we focus on the uncertainty set. We establish the volume to compare solutions of the same original problem, but with differing sizes. Using various shapes, we generate and compare robust currency carry trade strategies. In order to combine previous strategies, we build a hidden Markov model to classify carry trade performance under economic regimes. Backtests results on the major developed world currencies show that our dynamic strategy can outperform benchmark carry trade indexes, by a 8.5% increase in annual returns and 13% decrease in ulcer.

Second, we present a methodology to find less conservative robust solutions by applying transformations on the original problem. The transformations aim to group uncertain and correlated parameters into fewer constraints. We test the methodology in a multistage portfolio problem, using a factor-based market and exchange traded funds prices. Simulations show that allocation strategies using this methodology are in fact less conservative than solutions without it. Portfolios present lower cash holding ratios and higher final values at most risk aversion levels.

Third, we apply the previous methodology in a portfolio problem that includes private equity investments in the pool of assets. We model private equity as investments with uncertain future commitments and distributions flows. Investments in this area are considered highly illiquid and can produce cash flow burdens on the sponsoring organization. Employing the same previous data set for liquid assets and using historical cash flows information, we construct allocation strategies with alternative risk aversion levels. Simulation results depict that only more conservative strategies can avoid liquidity issues. In those cases, including private equity assets increase annual return by 5% to 7% without increasing risk.