A Monte Carlo Method for Optimal Portfolios

Abstract

This paper proposes a new simulation‐based approach for optimal portfolio allocation in realistic environments with complex dynamics for the state variables and large numbers of factors and assets. A first illustration involves a choice between equity and cash with nonlinear interest rate and market price of risk dynamics. Intertemporal hedging demands significantly increase the demand for stocks and exhibit low volatility. We then analyze settings where stock returns are also predicted by dividend yields and where investors have wealth‐dependent relative risk aversion. Large‐scale problems with many assets, including the Nasdaq, SP500, bonds, and cash, are also examined.

Size and Value Anomalies under Regime Shifts

“…This concern is related to the prediction model's out-of-sample asset allocation performance, see Brennan, Schwartz, and Lagnado (1997), Campbell, Chan, and Viceira (2003) and Detemple, Garcia, and Rindisbacher (2003).…”

“…We solve the asset allocation problem by extending the Monte Carlo methods in Barberis (2000) and Detemple, Garcia, and Rindisbacher (2003) to the case with regime switching in returns. This allows us to treat the states as unobservable and to characterize investors' optimal portfolio weights under imperfect information about the current state.…”

Nonmyopic optimal portfolios in viable markets

“…Our paper is most closely related to the fundamental work by Detemple, Garcia, and Rindisbacher (2003) and Rindisbacher (2005, 2009), who were the first to use Malliavian calculus to derive general representations for intertemporal hedging demand with general utilities and a general multi-dimensional diffusion state variable. In our paper, the assumption that the market is viable leads to a particularly simple and intuitive representation of optimal portfolios and allows us to establish several important economic properties of the latter.…”

“…21 Monotonicity of optimal portfolios in risk aversion is also crucial for understanding the nature of risk-sharing in dynamic general equilibrium models. In fact, almost all existing papers on heterogeneous equilibria conjecture this monotonicity property and use it as the basis for their economic intuition, arguing that more-risk-averse agents will Pratt monotonicity result to a multi-period setting, neither in partial nor in general equilibrium.…”

Strategic Asset Allocation

“…To characterize the dynamic equilibrium portfolio policies in such a setting, one would need to resort to numerical methods, such as those proposed by Detemple, Garcia, and Rindisbacher (2003) and Cvitanic, Goukasian, and Zapatero (2003). We leave this for future work.…”