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<p>In this paper we consider the problem of hedging a portfolio of ZC bonds aiming to get a return close to a targeted one relative to a liability. For the time evolution of the YTM interest rate curve we assume a dynamic factor model. Moreover we adopt the criterium of minimum variance of the spread between the portfolio and liability returns under a generalized duration matching constraint in order to achieve an optimal portfolio choice, as proposed in Borup et al. (in: Immunization in the Treasury market with consistent term structure dynamics, SSRN. 2022. <a href="https://doi.org/10.2139/ssrn.4164195">https://doi.org/10.2139/ssrn.4164195</a>). We prove that, under non negativity constraints on the portfolio weights, the previous selection procedure might be unfeasible. More precisely, our unfeasibility result holds under a set of minimal hypothesis on the factor loadings which we show are verified by the Nelson–Siegel family. We also discuss an example for which the optimal portfolios can be easily determined, the shown instance clearly highlights how the shape of the factor loadings may influence the possibility of achieving an optimal hedge without short-selling.</p>

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An analysis of short selling restrictions in factor model based portfolio immunization

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  • 发表日期：

    2025年10月6日

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  • F. Manzini,
  • A. Ramponi,
  • S. Scarlatti

摘要

In this paper we consider the problem of hedging a portfolio of ZC bonds aiming to get a return close to a targeted one relative to a liability. For the time evolution of the YTM interest rate curve we assume a dynamic factor model. Moreover we adopt the criterium of minimum variance of the spread between the portfolio and liability returns under a generalized duration matching constraint in order to achieve an optimal portfolio choice, as proposed in Borup et al. (in: Immunization in the Treasury market with consistent term structure dynamics, SSRN. 2022. https://doi.org/10.2139/ssrn.4164195). We prove that, under non negativity constraints on the portfolio weights, the previous selection procedure might be unfeasible. More precisely, our unfeasibility result holds under a set of minimal hypothesis on the factor loadings which we show are verified by the Nelson–Siegel family. We also discuss an example for which the optimal portfolios can be easily determined, the shown instance clearly highlights how the shape of the factor loadings may influence the possibility of achieving an optimal hedge without short-selling.