When to Hedge Against Devaluation - Shapiro, Alan C.; Rutenberg, David P. (Management Science, 1974)
The treasurer of a multi-national corporation can hedge to protect his corporation against an impending currency devaluation or revaluation. He can cover a future period, τ, now, without covering any intervening periods, by selling the suspect currency forward for τ periods and buying it forward for τ − 1 periods. There are generally no external economies resulting from hedging for more than one period at a time so that the problem is formulated to analyze each period separately. The cost of hedging (for corporate sized amounts) appears to be linear so the hedging price for each period is treated as a constant. Given current costs, expectations of costs, and expectations of probable devaluations or revaluations, should the treasurer now contract to hedge a particular period or should he wait? (The aggregation of the past and current hedge decisions constitutes the intervals to be hedged now.) Each of these hedge or wait decisions is formulated as a dynamic program. This dynamic program fortunately distills down to a very simple decision rule of comparing the expected cost of hedging with a constant for that period when unhedging is permitted. Even when the spread between the buying and selling rates is significant, there will be a need to solve numerically a dynamic program for only a few of the periods. We present and analyse four situations: Hedging with no unhedging. Hedging with the option of unhedging later, but with a spread between buying and selling costs. Hedging in the face of a key event that will branch the probabilities. Hedging when there's a chance of more than one devaluation.