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Non-fully invested derivative-free bond index replication

Author

Listed:
  • Iliya Markov
  • Rodrigue Oeuvray
  • Nils Tuchschmid

Abstract

The problem we address here is the replication of a bond benchmark when only a fraction of the portfolio is invested for the replication. Our methodology is based on a minimization of the tracking error subject to a set of constraints, namely (1) the fraction invested for the replication, (2) a no-short-selling constraint, and (3) a null-active-duration constraint, the last of which may be relaxed. The constraints can also be adapted to accommodate the use of interest rate and bond futures. Our main contribution, however, is our derivative-free approach to replication, which should prove very useful for managing assets when the use of derivatives is prohibited, for instance, by certain investors. We can, thus, still benefit from replicating a traditional investment in a bond index with a fraction of the portfolio according to our risk appetite. The rest of the portfolio can be invested in alpha-portable strategies. An analysis without the use of derivatives over the period from January 1, 2008 to October 3, 2011 shows that with 70–90 % invested for the replication, the annualized ex-ante tracking error can range from 0.41 to 0.07 %. We use principal component analysis to extract the main drivers of the size of the tracking error, namely, the volatility of and the differential between the yields in the objective function’s covariance matrix of spot rates. These results highlight our contribution of a generic and intuitive yet robust approach to bond index replication. Copyright Swiss Society for Financial Market Research 2013

Suggested Citation

  • Iliya Markov & Rodrigue Oeuvray & Nils Tuchschmid, 2013. "Non-fully invested derivative-free bond index replication," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(1), pages 101-124, March.
    • Handle: RePEc:kap:fmktpm:v:27:y:2013:i:1:p:101-124
    DOI: 10.1007/s11408-012-0201-6
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    References listed on IDEAS

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    More about this item

    Keywords

    Bond index replication; Derivatives; Tracking error; Optimization; C61; G11; G24;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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