Home Foster-Hart optimization for currency portfolios
Article
Licensed
Unlicensed Requires Authentication

Foster-Hart optimization for currency portfolios

  • Tetsuo Kurosaki ORCID logo EMAIL logo and Young Shin Kim
Published/Copyright: October 23, 2018

Abstract

We examine the effectiveness of Foster-Hart optimization for currency portfolios. Compared to stock trading, short selling is quite common in currency trading. Combining long and short positions leads to maintaining positive expected portfolio returns. Foster-Hart optimization is more applicable to currency portfolios than to stock portfolios because the Foster-Hart risk measure is not defined for the gamble whose expected returns are negative. Our sample portfolio consists of ten European currencies. For time series analysis, we employ a generalized autoregressive conditional heteroscedasticity (GARCH) model with multivariate normal tempered stable (MNTS) distributed residuals in order to capture fat-tailedness, skewness, and asymmetric interdependence of exchange rate dynamics. Statistical tests indicate that the model is recommendable among the candidate models. We establish that Foster-Hart optimization is more profitable than standard techniques in this context.

JEL Classification: C13; C22; C52; C61; G11

Acknowledgements

We appreciate Professor Svetlozar Rachev for his continuous guidance and encouragements throughout the process of writing this paper. The opinions, findings, conclusions or recommendations expressed in this paper are our own and do not necessarily reflect the views of the Bank of Japan. Also, all remaining errors are entirely our own.

References

Acerbi, C., and B. Szekely. 2014 Backtesting Expected Shortfall. Working paper, MSCI, URL https://www.msci.com/documents/10199/22aa9922-f874-4060-b77a-0f0e267a489b.Search in Google Scholar

Anand, A., T. Li, T. Kurosaki, and Y. S. Kim. 2016. “Foster-Hart Optimal Portfolios.” Journal of Banking & Finance 68: 117–130.10.1016/j.jbankfin.2016.03.011Search in Google Scholar

Anand, A., T. Li, T. Kurosaki, and Y. S. Kim. 2017. “The Equity Risk Posed by the Too-Big-to-Fail Banks: A Foster-Hart Estimation.” Annals of Operations Research 253: 21–41.10.1007/s10479-016-2309-ySearch in Google Scholar

Barndorff-Nielsen, O. E., and S. Z. Levendorskii. 2001. “Feller Processes of Normal Inverse Gaussian Type.” Quantitative Finance 1: 318–331.10.1088/1469-7688/1/3/303Search in Google Scholar

Barndorff-Nielsen, O. E., and N. Shephard. 2001 Normal Modified Stable Processes. Department of Economics Discussion Paper Series 72, University of Oxford, URL https://ora.ox.ac.uk/objects/uuid:d22c00b1-7854-4385-9b25-be31b5cc3790.Search in Google Scholar

Berkowitz, J. 2001. “Testing Density Forecasts, with Applications to Risk Management.” Journal of Business & Economic Statistics 19: 465–474.10.1198/07350010152596718Search in Google Scholar

Bollen, N. P. B., S. F. Gray, and R. E. Whaley. 2000. “Regime Switching in Foreign Exchange Rates: Evidence from Currency Option Prices.” Journal of Econometrics 94: 239–276.10.1016/S0304-4076(99)00022-6Search in Google Scholar

Bollerslev, T. 1986. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics 31: 307–327.10.1016/0304-4076(86)90063-1Search in Google Scholar

Bonilla, C. A., R. Romero-Meza, and M. J. Hinich. 2007. “GARCH Inadequacy for Modelling Exchange Rates: Empirical Evidence from Latin America.” Applied Economics 39: 2529–2533.10.1080/00036840600707316Search in Google Scholar

Brooks, C., and M. J. Hinich. 1998. “Episodic Nonstationarity in Exchange Rates.” Applied Economics 5: 719–722.10.1080/135048598354203Search in Google Scholar

Christoffersen, P. F. 1998. “Evaluating Interval Forecasts.” International Economic Review 39: 841–862.10.2307/2527341Search in Google Scholar

Engle, R. 1982. “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica 50: 987–1007.10.2307/1912773Search in Google Scholar

Fabozzi, F. J., S. M. Focardi, and P. N. Kolm. 2006. Financial Modeling of the Equity Market: From CAPM to Cointegration. New Jersey: John Wiley & Sons, Inc.Search in Google Scholar

Foster, D. P., and S. Hart. 2009. “An Operational Measure of Riskiness.” Journal of Political Economy 117: 785–814.10.1086/644840Search in Google Scholar

Kim, Y. S., S. T. Rachev, M. L. Bianchi, and F. J. Fabozzi. 2008. “Financial Market Models with Lévy Processes and Time-Varying Volatility.” Journal of Banking & Finance 32: 1363–1378.10.1016/j.jbankfin.2007.11.004Search in Google Scholar

Kim, Y. S., S. T. Rachev, M. L. Bianchi, and F. J. Fabozzi. 2010. “Computing VaR and AVaR in Infinitely Divisible Distributions.” Probability and Mathematical Statistics 30: 223–245.10.2139/ssrn.1400965Search in Google Scholar

Kim, Y. S., S. T. Rachev, M. L. Bianchi, I. Mitov, and F. J. Fabozzi. 2011. “Time Series Analysis for Financial Market Meltdowns.” Journal of Banking & Finance 35: 1879–1891.10.1016/j.jbankfin.2010.12.007Search in Google Scholar

Kim, Y. S., R. Giacometti, S. T. Rachev, F. J. Fabozzi, and D. Mignacca. 2012. “Measuring Financial Risk and Portfolio Optimization with a Non-Gaussian Multivariate Model.” Annals of Operations Research 201: 325–343.10.1007/s10479-012-1229-8Search in Google Scholar

Kurosaki, T., and Y. S. Kim. 2013a. “Mean-CoAVaR Optimization for Global Banking Portfolios.” Investment Management and Financial Innovation 10: 15–20.Search in Google Scholar

Kurosaki, T., and Y. S. Kim. 2013b. “Systematic Risk Measurement in the Global Banking Stock Market with Time Series Analysis and CoVaR.” Investment Management and Financial Innovation 10: 184–196.Search in Google Scholar

Leiss, M., and H. H. Nax. 2018. “Option-Implied Objective Measures of Market Risk.” Journal of Banking & Finance 88: 241–249.10.1016/j.jbankfin.2017.11.017Search in Google Scholar

Markowitz, H. 1952. “Portfolio Selection.” Journal of Finance 7: 77–91.10.12987/9780300191677Search in Google Scholar

Markowitz, H. 1959. Portfolio Selection Efficient Diversification of Investments. New York: John Wiley & Sons, Inc.Search in Google Scholar

Rachev, S. T., S. V. Stoyanov, and F. J. Fabozzi. 2008. Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures. New Jersey: John Wiley & Sons, Inc.Search in Google Scholar

Rachev, S. T., R. D. Martin, B. Racheva, and S. Stoyanov. 2009. “Stable ETL Optimal Portfolios and Extreme Risk Management.” in Risk Assessment, edited by G. Bol, S. T. Rachev, and R. Würth, 235–262. Heidelberg: Physica-Verlag HD.10.1007/978-3-7908-2050-8_11Search in Google Scholar

Rachev, S. T., Y. S. Kim, M. L. Bianchi, and F. J. Fabozzi. 2011. Financial Models with Lévy Processes and Volatility Clustering. New Jersey: John Wiley & Sons, Inc.10.1002/9781118268070Search in Google Scholar

Riedel, F. and T. Hellmann. 2015. “The Foster-Hart Measure of Riskiness for General Gambles.” Theoretical Economics 10: 1–9.10.3982/TE1499Search in Google Scholar

Shao, B. P., S. T. Rachev, and Y. Mu. 2015. “Applied Mean-ETL Optimization in Using Earnings Forecasts.” International Journal of Forecasting 31: 561–567.10.1016/j.ijforecast.2014.10.005Search in Google Scholar

Sharpe, W. T. 1966. “Mutual Fund Performance.” Journal of Business 39: 119–138.10.1086/294846Search in Google Scholar


Supplementary Material

The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/snde-2017-0119).


Published Online: 2018-10-23

©2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 24.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/snde-2017-0119/html?lang=en
Scroll to top button