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On horizon-consistent mean-variance portfolio allocation

Author

Listed:
  • Simone Cerreia-Vioglio

    (Università Bocconi)

  • Fulvio Ortu

    (Università Bocconi)

  • Francesco Rotondi

    (Università degli Studi di Padova
    Università Bocconi)

  • Federico Severino

    (Université Laval)

Abstract

We analyze the problem of constructing multiple buy-and-hold mean-variance portfolios over increasing investment horizons in continuous-time arbitrage-free stochastic interest rate markets. The orthogonal approach to the one-period mean-variance optimization of Hansen and Richard (Econometrica 55(3):587–613, 1987) requires the replication of a risky payoff for each investment horizon. When many maturities are considered, a large number of payoffs must be replicated, with an impact on transaction costs. In this paper, we orthogonally decompose the whole processes defined by asset returns to obtain a mean-variance frontier generated by the same two securities across a multiplicity of horizons. Our risk-adjusted mean-variance frontier rests on the martingale property of the returns discounted by the log-optimal portfolio and features a horizon consistency property. The outcome is that the replication of a single risky payoff is required to implement such frontier at any investment horizon. As a result, when transaction costs are taken into account, our risk-adjusted mean-variance frontier may outperform the traditional mean-variance optimal strategies in terms of Sharpe ratio. Realistic numerical examples show the improvements of our approach in medium- or long-term cashflow management, when a sequence of target returns at increasing investment horizons is considered.

Suggested Citation

  • Simone Cerreia-Vioglio & Fulvio Ortu & Francesco Rotondi & Federico Severino, 2024. "On horizon-consistent mean-variance portfolio allocation," Annals of Operations Research, Springer, vol. 336(1), pages 797-828, May.
  • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-022-04798-x
    DOI: 10.1007/s10479-022-04798-x
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    More about this item

    Keywords

    Return decomposition; Multiple horizons; Horizon consistency; Mean-variance frontier; Martingale pricing; Stochastic interest rates;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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