Static Fund Separation of Long Term Investments

38 Pages Posted: 25 Jun 2011 Last revised: 27 Mar 2012

See all articles by Paolo Guasoni

Paolo Guasoni

Dublin City University - School of Mathematical Sciences; Boston University - Department of Mathematics and Statistics

Scott Robertson

Questrom School of Business, Boston University

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Date Written: June 25, 2011

Abstract

This paper proves a class of static fund separation theorems, valid for investors with a long horizon and constant relative risk aversion, and with stochastic investment opportunities. An optimal portfolio decomposes as a constant mix of a few preference-free funds, which are common to all investors. The weight in each fund is a constant that may depend on an investor's risk aversion, but not on the state variable, which changes over time. Vice versa, the composition of each fund may depend on the state, but not on the risk aversion, since a fund appears in the portfolios of different investors.

We prove these results for two classes of models with a single state variable, and several assets with constant correlations with the state. In the linear class, the state is an Ornstein-Uhlenbeck process, risk-premia are affine in the state, while volatilities and the interest rate are constant. In the square root class, the state follows a square root diffusion, expected returns and the interest rate are affine in the state, while volatilities are linear in the square root of state.

Keywords: fund separation, long horizon, portfolio choice

JEL Classification: G11, G12

Suggested Citation

Guasoni, Paolo and Robertson, Scott, Static Fund Separation of Long Term Investments (June 25, 2011). Boston U. School of Management Research Paper, No. 2011-15, Available at SSRN: https://ssrn.com/abstract=1872320 or http://dx.doi.org/10.2139/ssrn.1872320

Paolo Guasoni (Contact Author)

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

HOME PAGE: http://www.guasoni.com

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Scott Robertson

Questrom School of Business, Boston University ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

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