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A Downside Risk Analysis based on Financial Index Tracking Models

In: Stochastic Finance

Author

Listed:
  • Lian Yu

    (University of California, Department of Industrial Engineering and Operations Research)

  • Shuzhong Zhang

    (The Chinese University of Hong Kong Shatin, Department of Systems Engineering and Engineering Management)

  • Xun Yu Zhou

    (The Chinese University of Hong Kong Shatin, Department of Systems Engineering and Engineering Management)

Abstract

Summary This paper is mainly concerned with a single-stage financial index tracking problem under the downside risk constraint where short-selling is allowed. First, we formulate the portfolio selection model with the downside probability constraint to track the financial index. Due to the convexity of this problem, the optimal portfolio is derived analytically by applying the Karush-Kuhn-Tucker optimality conditions. Moreover, we extend the risk measure to higher order moment of the downside and study the corresponding portfolio optimization problem.

Suggested Citation

  • Lian Yu & Shuzhong Zhang & Xun Yu Zhou, 2006. "A Downside Risk Analysis based on Financial Index Tracking Models," Springer Books, in: A. N. Shiryaev & M. R. Grossinho & P. E. Oliveira & M. L. Esquível (ed.), Stochastic Finance, chapter 8, pages 213-236, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-28359-3_8
    DOI: 10.1007/0-387-28359-5_8
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