Pricing Physical Assets Internationally

Transferring physical capital and transferring production and sales activities from one country to the other typically entails large adjustment costs. The model of this paper features two homogeneous stocks of physical capital located in two different countries separated by an ‘ocean.’ The two physical stocks are optimally invested in a random production process yielding real returns, consumed by local residents, or transferred abroad. Retro-fitting, transferring and re-building capital equipment, and increasing production and sales abroad either takes time (during which capital is idle) or consumes real resources. As a result, the price of capital-consumption goods located in one place is not equal to that of goods located in the other place. The stochastic process for this deviation from the Law of One Price (LOP) is obtained. By construction, this process is compatible with financial market efficiency and with the possibility of (costly) trade in commodities. Whereas empirical studies have found no evidence against the hypothesis that LOP deviations follow a martingale, the theoretical process which I find, exhibits mean reversion (as well as a fair degree of conditional hetero-scedasticity) when investors are risk averse.