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.

On horizon-consistent mean-variance portfolio allocation

Cerreia-Vioglio, Simone;Ortu, Fulvio;Severino, Federico
In corso di stampa

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.
In corso di stampa
2022
Cerreia-Vioglio, Simone; Ortu, Fulvio; Rotondi, Francesco; Severino, Federico
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4062484
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