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Tracking a Financial Benchmark Using a Few Assets

Author

Listed:
  • David D. Yao

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Shuzhong Zhang

    (Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China)

  • Xun Yu Zhou

    (Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China)

Abstract

We study the problem of tracking a financial benchmark---a continuously compounded growth rate or a stock market index---by dynamically managing a portfolio consisting of a small number of traded stocks in the market. In either case, we formulate the tracking problem as an instance of the stochastic linear quadratic control (SLQ), involving indefinite cost matrices. As the SLQ formulation involves a discounted objective over an infinite horizon, we first address the issue of stabilizability. We then use semidefinite programming (SDP) as a computational tool to generate the optimal feedback control. We present numerical examples involving stocks traded at the Hong Kong and New York Stock Exchanges to illustrate the various features of the model and its performance.

Suggested Citation

  • David D. Yao & Shuzhong Zhang & Xun Yu Zhou, 2006. "Tracking a Financial Benchmark Using a Few Assets," Operations Research, INFORMS, vol. 54(2), pages 232-246, April.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:2:p:232-246
    DOI: 10.1287/opre.1050.0260
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    References listed on IDEAS

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    1. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    2. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
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    Cited by:

    1. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2018. "Index tracking model, downside risk and non-parametric kernel estimation," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 103-128.
    2. Huang, Jinbo & Li, Yong & Yao, Haixiang, 2022. "Partial moments and indexation investment strategies," Journal of Empirical Finance, Elsevier, vol. 67(C), pages 39-59.
    3. van Staden, Pieter M. & Forsyth, Peter A. & Li, Yuying, 2024. "Across-time risk-aware strategies for outperforming a benchmark," European Journal of Operational Research, Elsevier, vol. 313(2), pages 776-800.

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