On horizon-consistent mean-variance portfolio allocation

Simone Cerreia-Vioglio (), Fulvio Ortu (), Francesco Rotondi () and Federico Severino ()
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Simone Cerreia-Vioglio: Università Bocconi
Fulvio Ortu: Università Bocconi
Francesco Rotondi: Università degli Studi di Padova
Federico Severino: Université Laval

Annals of Operations Research, 2024, vol. 336, issue 1, No 26, 797-828

Abstract: 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.

Keywords: Return decomposition; Multiple horizons; Horizon consistency; Mean-variance frontier; Martingale pricing; Stochastic interest rates (search for similar items in EconPapers)
JEL-codes: G11 G12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-022-04798-x

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