On Time-Consistent Multi-Horizon Portfolio Allocation

46 Pages Posted: 10 May 2021

See all articles by Simone Cerreia-Vioglio

Simone Cerreia-Vioglio

Bocconi University - Department of Decision Sciences

Fulvio Ortu

Bocconi University - Department of Finance

Francesco Rotondi

Bocconi University - Department of Finance; University of Padua - Department of Mathematics "Tullio Levi-Civita"

Federico Severino

Université Laval; Université Laval - Faculty of Business Administration

Date Written: May 6, 2021

Abstract

We analyse the problem of constructing multiple mean-variance portfolios over increasing investment horizons in stochastic interest rate markets. The traditional one-period mean-variance optimal portfolios of Hansen and Richard (1987) require the replication of two payoffs. When several maturities are considered, different payoffs have to be replicated each time, with an impact on transaction costs. Using martingale decomposition techniques and introducing a family of risk-adjusted measures linked to increasing maturities, we provide an intertemporal version of the traditional orthogonal decomposition of asset returns. This allows us to construct a multi-horizon mean- variance frontier that is time-consistent and requires the replication of solely two payoffs for all horizons under consideration. When transaction costs are taken into account, our time-consistent mean-variance frontier may outperform the traditional mean-variance optimal strategies in terms of Sharpe ratio. Some interesting examples of this fact come from long-term contracts as life annuities.

Keywords: return decomposition, multiple horizons, time consistency, mean-variance frontier, martingale pricing, stochastic interest rates.

JEL Classification: G11, G12

Suggested Citation

Cerreia-Vioglio, Simone and Ortu, Fulvio and Rotondi, Francesco and Severino, Federico, On Time-Consistent Multi-Horizon Portfolio Allocation (May 6, 2021). Available at SSRN: https://ssrn.com/abstract=3841052 or http://dx.doi.org/10.2139/ssrn.3841052

Simone Cerreia-Vioglio

Bocconi University - Department of Decision Sciences ( email )

Via Roentgen 1
Milan, 20136
Italy

Fulvio Ortu

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Francesco Rotondi

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

University of Padua - Department of Mathematics "Tullio Levi-Civita"

Italy

Federico Severino (Contact Author)

Université Laval ( email )

Pavillon Palasis-Prince
2325 rue de la Terrasse
Québec, Quebec G1V 0A6
Canada

HOME PAGE: http://https://federicoseverino.org

Université Laval - Faculty of Business Administration ( email )

Canada

HOME PAGE: http://https://federicoseverino.org

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