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Tracking error: a multistage portfolio model

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Abstract

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.

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References

  • Ammann, M., & Zimmermann, H. (2001). The relation between tracking error and tactical asset allocation (Working Paper, 09/01). WWZ Department of Finance.

  • Barone-Adesi, G., Giannopoulos, K., & Vosper, L. (1999). VaR without correlations for portfolios of derivative securities. The Journal of Future Markets, 19, 583–602.

    Article  Google Scholar 

  • Barro, D., & Canestrelli, E. (2005). Dynamic portfolio optimisation: Time decomposition using Maximum Principle with a scenario approach. European Journal of Operational Research, 163, 217–229.

    Article  Google Scholar 

  • Bawa, V. S. (1978). Safety first, stochastic dominance and optimal portfolio choice. Journal of Financial and Quantitative Analysis, 13, 255–271.

    Article  Google Scholar 

  • Birge, J. R., & Louveaux, F. (1997). Introduction to stochastic programming. New York: Springer.

    Google Scholar 

  • Browne, S. (1999). Beating a moving target: Optimal portfolio strategies for outperforming a stochastic benchmark. Finance and Stochastics, 3(3), 275–294.

    Article  Google Scholar 

  • Cesari, R., & Cremonini, D. (2003). Benchmarking portfolio insurance and technical analysis: a Monte Carlo comparison of dynamic strategies of asset allocation. The Journal of Economic Dynamics and Control, 27, 987–1011.

    Article  Google Scholar 

  • Clarke, R. C., Krase, S., & Statman, M. (1994). Tracking errors, regret and tactical asset allocation. The Journal of Portfolio Management, 20, 16–24.

    Google Scholar 

  • Connor, G., & Leland, H. (1995). Cash management for index tracking. Financial Analysts Journal, 51(6), 75–80.

    Article  Google Scholar 

  • Consiglio, A., & Zenios, S. A. (2001). Integrated simulation and optimization models for tracking international fixed-income indices. Mathematical Programming Serie B, 89, 311–339.

    Article  Google Scholar 

  • D’Ecclesia, R. L., Abaffy, J., Bertocchi, M., & Zenios, S. (2002). Modeling an indexed portfolio for the Italian market (Working Paper). University of Bergamo.

  • Dembo, R., & Rosen, D. (1999). The practice of portfolio replication, a practical overview of forward and inverse problems. Annals of Operations Research, 85, 267–284.

    Article  Google Scholar 

  • Dempster, M. A. H., & Thompson, G. W. P. (2002). Dynamic portfolio replication using stochastic programming. In M. A. H. Dempster (Ed.), Risk management: value at risk and beyond (pp. 100–128). Cambridge: Cambridge University Press.

    Google Scholar 

  • Franks, E. C. (1992). Targeting excess-of-benchmark returns. The Journal of Portfolio Management, 18(4), 6–12.

    Google Scholar 

  • Gaivoronski, A. A., Krylov, S., & van der Vijst, N. (2005). Optimal portfolio selection and dynamic benchmark tracking. European Journal of Operational Research, 163, 115–131.

    Article  Google Scholar 

  • Judd, K. L. (1999). Numerical methods in economics. Cambridge: MIT Press.

    Google Scholar 

  • Konno, H., & Yamazaki, H. (1991). Mean absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37, 519–531.

    Article  Google Scholar 

  • Larsen Jr., G. A., & Resnik, B. G. (1998). Empirical insights on indexing. The Journal of Portfolio Management, 25(1), 51–60.

    Google Scholar 

  • Mann, W. R. (1953). Mean value methods in iteration. Proceedings of the American Mathematical Society, 4, 506–510.

    Article  Google Scholar 

  • MSCI (1999). Euro Indices: Methodology & constituents. www.msci.com.

  • Ortega, A. J., & Leake, R. S. (1977). Discrete maximum principle with state constrained control. SIAM Journal on Control and Optimization, 15, 119–147.

    Article  Google Scholar 

  • Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., Mishchenko, E. F., & Brown, D. E. (1964). The mathematical theory of optimal processes. Oxford: Pergamon Press.

    Google Scholar 

  • Rockafellar, R. T., & Wets, R. B. J. (1991). Scenario and policy aggregation in optimization under uncertainty. Mathematics of Operations Research, 16, 119–147.

    Article  Google Scholar 

  • Rohweder, H. C. (1998). Implementing stock selection ideas: does tracking error optimization does any good?. The Journal of Portfolio Management, 24(3), 49–59.

    Article  Google Scholar 

  • Roll, R. (1992). A mean/variance analysis of tracking error. The Journal of Portfolio Management, 18(4), 13–22.

    Google Scholar 

  • Rudolf, M., Wolter, H.-J., & Zimmermann, H. (1998). A linear model for tracking error minimization. Journal of Banking and Finance, 23, 85–103.

    Article  Google Scholar 

  • Sethi, S. P., & Thompson, G. L. (2000). Optimal control theory: applications to management science and economics. Dordrecht: Kluwer Academic.

    Google Scholar 

  • Siegel, L. P. (2003). The research foundation of AIMR. Benchmarks and investment management. Charlottesville: AIMR.

    Google Scholar 

  • Worzel, K. J., Vassiadou-Zeniou, C., & Zenios, S. A. (1998). Integrated simulation and optimization models for tracking indices of fixed-income securities. Operations Research, 42, 223–232.

    Article  Google Scholar 

  • Ziemba, W. T. (2003). The research foundation of AIMR. The stochastic programming approach to asset, liability and wealth management. Charlottesville: AIMR.

    Google Scholar 

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Correspondence to Diana Barro.

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Barro, D., Canestrelli, E. Tracking error: a multistage portfolio model. Ann Oper Res 165, 47–66 (2009). https://doi.org/10.1007/s10479-007-0308-8

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  • DOI: https://doi.org/10.1007/s10479-007-0308-8

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