CVaR Models with Selective Hedging for International Asset Allocation∗

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 model’s 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.