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Robust Optimization of Currency Portfolios

Author

Listed:
  • Raquel J. Fonseca
  • Steve Zymler
  • Wolfram Wiesemann
  • Berc Rustem

Abstract

We study a currency investment strategy, where we maximize the return on a portfolio of foreign currencies relative to any appreciation of the corresponding foreign exchange rates. Given the uncertainty in the estimation of the future currency values, we employ robust optimization techniques to maximize the return on the portfolio for the worst-case foreign exchange rate scenario. Currency portfolios differ from stock only portfolios in that a triangular relationship exists among foreign exchange rates to avoid arbitrage. Although the inclusion of such a constraint in the model would lead to a nonconvex problem, we show that by choosing appropriate uncertainty sets for the exchange and the cross exchange rates, we obtain a convex model that can be solved efficiently. Alongside robust optimization, an additional guarantee is explored by investing in currency options to cover the eventuality that foreign exchange rates materialize outside the specified uncertainty sets. We present numerical results that show the relationship between the size of the uncertainty sets and the distribution of the investment among currencies and options, and the overall performance of the model in a series of backtesting experiments.

Suggested Citation

  • Raquel J. Fonseca & Steve Zymler & Wolfram Wiesemann & Berc Rustem, 2009. "Robust Optimization of Currency Portfolios," Working Papers 012, COMISEF.
  • Handle: RePEc:com:wpaper:012
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    References listed on IDEAS

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    1. Levy, Haim & Sarnat, Marshall, 1978. "Exchange Rate Risk and the Optimal Diversification of Foreign Currency Holdings," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 10(4), pages 453-463, November.
    2. Glen A. Larsen, Jr. & Bruce G. Resnick, 2000. "The Optimal Construction of Internationally Diversified Equity Portfolios Hedged Against Exchange Rate Uncertainty," European Financial Management, European Financial Management Association, vol. 6(4), pages 479-514.
    3. Steil, Benn, 1993. "Currency Options and the Optimal Hedging of Contingent Foreign Exchange Exposure," Economica, London School of Economics and Political Science, vol. 60(240), pages 413-431, November.
    4. Glen, Jack & Jorion, Philippe, 1993. " Currency Hedging for International Portfolios," Journal of Finance, American Finance Association, vol. 48(5), pages 1865-1886, December.
    5. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2002. "CVaR models with selective hedging for international asset allocation," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1535-1561, July.
    6. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2008. "A dynamic stochastic programming model for international portfolio management," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1501-1524, March.
    7. Shawky, Hany A. & Kuenzel, Rolf & Mikhail, Azmi D., 1997. "International portfolio diversification: a synthesis and an update," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 7(4), pages 303-327, December.
    8. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    9. Levy, Haim & Sarnat, Marshall, 1970. "International Diversification of Investment Portfolios," American Economic Review, American Economic Association, vol. 60(4), pages 668-675, September.
    10. Eun, Cheol S & Resnick, Bruce G, 1988. " Exchange Rate Uncertainty, Forward Contracts, and International Portfolio Selection," Journal of Finance, American Finance Association, vol. 43(1), pages 197-215, March.
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    Cited by:

    1. Raquel Fonseca & Wolfram Wiesemann & Berç Rustem, 2012. "Robust international portfolio management," Computational Management Science, Springer, vol. 9(1), pages 31-62, February.
    2. Nonthachote Chatsanga & Andrew J. Parkes, 2016. "International Portfolio Optimisation with Integrated Currency Overlay Costs and Constraints," Papers 1611.01463, arXiv.org.

    More about this item

    Keywords

    robust optimization; portfolio optimization; currency hedging; second-order cone programming;

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