Nikolas Topaloglou

CVaR models with selective hedging for international asset allocation

Abstract We develop an integrated simulation and optimization framework for multicurrency asset allocation problems. The simulation applies principal component analysis to generate scenarios depicting the discrete joint distributions of uncertain asset returns and exchange rates. We then develop and implement models that optimize the conditional-value-at-risk (CVaR) metric. The scenario-based optimization models encompass alternative hedging strategies, including selective hedging that incorporates currency hedging decisions within the portfolio selection problem. Thus, the selective hedging model determines jointly the portfolio composition and the level of currency hedging for each market via forward exchanges. We examine empirically the benefits of international diversification and the impact of hedging policies on risk–return profiles of portfolios. We assess the effectiveness of the scenario generation procedure and the stability of the models results by means of out-of-sample simulations. We also compare the performance of the CVaR model against that of a model that employs the mean absolute deviation (MAD) risk measure. We investigate empirically the ex post performance of the models on international portfolios of stock and bond indices using historical market data. Selective hedging proves to be the superior hedging strategy that improves the risk–return profile of portfolios regardless of the risk measurement metric. Although in static tests the MAD and CVaR models often select portfolios that trace practically indistinguishable ex ante risk–return efficient frontiers, in successive applications over several consecutive time periods the CVaR model attains superior ex post results in terms of both higher returns and lower volatility.

A dynamic stochastic programming model for international portfolio management

We develop a multi-stage stochastic programming model for international portfolio management in a dynamic setting. We model uncertainty in asset prices and exchange rates in terms of scenario trees that reflect the empirical distributions implied by market data. The model takes a holistic view of the problem. It considers portfolio rebalancing decisions over multiple periods in accordance with the contingencies of the scenario tree. The solution jointly determines capital allocations to international markets, the selection of assets within each market, and appropriate currency hedging levels. We investigate the performance of alternative hedging strategies through extensive numerical tests with real market data. We show that appropriate selection of currency forward contracts materially reduces risk in international portfolios. We further find that multi-stage models consistently outperform single-stage models. Our results demonstrate that the stochastic programming framework provides a flexible and effective decision support tool for international portfolio management.

Testing for Stochastic Dominance Efficiency

We consider consistent tests for stochastic dominance efficiency at any order of a given portfolio with respect to all possible portfolios constructed from a set of assets. We justify block bootstrap approaches to achieve valid inference in a time series setting. The test statistics are computed using linear and mixed integer programming formulations. Monte Carlo results show that the bootstrap procedure performs well in finite samples. The empirical application reveals that the Fama and French market portfolio is first and second-order stochastic dominance efficient, although it is mean–variance inefficient.

Controlling Currency Risk with Options or Forwards

We consider alternative means for controlling currency risk exposure in actively-managed international portfolios. We extend multi-stage stochastic programming models to incorporate decisions for optimal selection of forward contracts or currency options for hedging purposes. We adapt a valuation procedure to price currency options consistently with discrete distributions of exchange rates that are used in the context of the stochastic programming model. We empirically assess the comparative eectiveness of alternative decision strategies through extensive numerical tests. Besides individual put options, we also consider trading strategies that involve combinations of options, and contrast them with optimal choices of forward contracts. We compare the alternative strategies both in static tests — in terms of their risk-return profiles — as well as in dynamic backtesting simulations using market data in a rolling horizon basis. We find that optimally selected currency forward contracts yield superior results in comparison to single protective puts per currency. However, option-trading strategies with suitable payos can improve performance in terms of higher portfolio returns. Moreover, we demonstrate that a multistage (dynamic) stochastic programming model consistently outperforms its single-stage (myopic) counterpart and yields incremental benefits.

Stochastic Bounds for Portfolio Analysis

A stochastic bound is a portfolio which stochastically dominates all alternatives in a reference portfolio set instead of a single alternative portfolio. An approximate bound is a portfolio which comes as close as possible to this ideal. To identify and analyze exact or approximate bounds, feasible approaches to numerical optimization and statistical inference are developed based on Linear Programming and subsampling. The use of reference sets and stochastic bounds is shown to improve investment performance in representative applications to enhanced benchmarking using equity industry rotation and equity index options combinations.

Optimal Privatization Portfolios in the Presence of Arbitrary Risk Aversion

We consider the global portfolio of privatized state assets from 1985 to 2012 in the non-parametric decision-making context of Stochastic Dominance Efficiency for broad classes of investor preferences. We estimate all possible portfolios in the context of Strategic vs. non-Strategic and Cyclical vs. non-Cyclical asset allocations that dominate the market benchmark and provide a complete efficiency ranking. The optimal solutions are computed using linear and mixed integer programming formulations. Dominant portfolios tend to overweight non-Cyclical and non-Strategic assets, while rotation may take place across business cycles. Bayesian investment style return attribution analysis, based on Monte Carlo Integration, suggests that Growth drives returns during the first business cycle, rotating to a balanced mix of styles with Size and Debt Leverage during the second business cycle and finally to Size during the last business cycle. Value is found to be the least influential style in all periods.