Asset Pricing in a Production Economy with Incomplete Information
Published: 06/01/1986 | DOI: 10.1111/j.1540-6261.1986.tb05043.x
JÉRÔME B. DETEMPLE
This paper analyzes an economy in which investors operate under partial information about technology‐relevant state variables. It is shown that for Gaussian information structures under incomplete observations, the consumer's problem can be transformed into an equivalent program with a completely observed state: the conditional expectation of the underlying unobservable state variables. A consequence of this transformation is that classic results in finance remain valid under an appropriate reinterpretation of the state variables.
On the Optimal Hedge of a Nontraded Cash Position
Published: 03/01/1988 | DOI: 10.1111/j.1540-6261.1988.tb02594.x
MICHAEL ADLER, JÉRÔME B. DETEMPLE
In this paper, we focus on the optimal demand for futures contracts by an investor with a logarithmic utility function who attempts to hedge a nontraded cash position. When the analysis is conducted in the “cash‐commodity‐price” space, we show that the value function associated with the Bernoulli investor program is not additively separable, thus suggesting that this investor hedges against shifts in the opportunity set as represented by the commodity price. By establishing the equivalence between the cash formulation of the problem and the wealth formulation, we are able to analyze the problem in the “wealth‐commodity‐price” space. In this space, we show the additive separability of the value function when the futures settlement price process is perfectly locally correlated with the commodity price process. The demand for futures in this instance is composed of (a) a mean‐variance term and (b) a minimum‐variance component that is a classic feature of models with nontraded assets. Since the first‐best (nonmyopic) optimum is attained, however, the deviation from a mean‐variance demand should not be interpreted as the expression of a nonmyopic behavior but rather as an attempt to restore a first‐best optimum. On the other hand, when the correlation between the futures price and the underlying commodity price is imperfect, in general, the value function does not separate additively, the first‐best solution cannot be attained, and the optimal futures trading strategy involves a hedging term against shifts in the opportunity set.
A Monte Carlo Method for Optimal Portfolios
Published: 02/12/2003 | DOI: 10.1111/1540-6261.00529
Jérôme B. Detemple, Ren Garcia, Marcel Rindisbacher
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.