OPTIMAL INTERNATIONAL ACQUISITIONS
Published: 03/01/1975 | DOI: 10.1111/j.1540-6261.1975.tb03157.x
Michael Adler, Bernard Dumas
Deviations from Purchasing Power Parity in the Long Run
Published: 12/01/1983 | DOI: 10.1111/j.1540-6261.1983.tb03835.x
MICHAEL ADLER, BRUCE LEHMANN
This paper demonstrates that deviations from purchasing power parity reveal a remarkable and possibly startling consistency with martingale behavior during both fixed and flexible rate periods, for a wide variety of countries, and in both monthly and annual data. Since this pattern appears to be much more general than one would expect on the basis of models founded on international commodity arbitrage, the paper proposes an alternative explanation which instead relies on financial arbitrage in bonds as the underlying mechanism.
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.