This study was partially supported by the ERC (278295), NSF (DMS-0807994, DMS-1109047), SFI (07/MI/008, 07/SK/M1189, 08/SRC/FMC1389), and FP7 (RG-248896). We thank Bernard Dumas and Hao Xing for useful comments.
STATIC FUND SEPARATION OF LONG-TERM INVESTMENTS
Article first published online: 2 NOV 2012
© 2012 Wiley Periodicals, Inc.
How to Cite
Guasoni, P. and Robertson, S. (2012), STATIC FUND SEPARATION OF LONG-TERM INVESTMENTS. Mathematical Finance. doi: 10.1111/mafi.12017
- Article first published online: 2 NOV 2012
- Manuscript received June 2011; final revision received August 2012.
- portfolio choice;
- fund separation;
- long horizon
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 the state.