“Dynamic Speculative Attacks”

Christophe Chamley

IED Discussion Paper 119, March 2002

Fixed exchange parities are well known to be vulnerable to coordinated speculative attacks. From the speculators’ perspective, participation in a speculative attack is akin to making choices in a coordination game: if a sufficient number attack, a devaluation ensues and profits accrue to the attackers. If not, then the exchange parity stays and the attackers lose money. Most of the literature on coordinated speculative attacks has focused on the role of self-fulfilling expectations in determining which of the two equilibrium outcomes (crisis or stability) will be realized. Surprisingly, this literature has failed to produce a theory of expectations formation and change that may reveal in a more satisfying manner, the role of fundamental factors such as market capital, the rate of information transmission, and central bank policy variables in altering the probability of speculative attacks.

Chamley’s paper presents a tractable model of speculation in an exchange rate band regime that explicitly models the process of expectations-formation in such markets. In this dynamic model, speculators are free to choose the time at which they wish to change their currency portfolio. By delaying any portfolio adjustment, therefore, speculators can learn whether there is sufficient capital in the market for a successful attack. They do this through an observation of the fluctuation of the exchange rate within the

band. The paper, therefore, models expectation formation and change in a very natural manner by incorporating the trade-off that exists at the individual level, between attacking early and earning a premium (when the price of foreign currency is lower), and delaying for more information. The availability of an option to wait, observe, and learn is exploited by the speculators in a very intuitive manner. Chamley shows that as the time horizon of the market increases, the amount of speculation increases in any period for any set of initial conditions. Thus the probability of a successful attack increases as the opportunity for learning increases.

Chamley goes on to analyze the impact of alternate defense policies that a central bank may adopt in such a market. By widening the band of fluctuation, the bank lowers the ex-ante probability that the speculative capital in the market can induce a devaluation. This makes speculators more cautious by increasing the option value of delay, thereby slowing down the learning process. This policy can therefore be one way of trying to prevent a speculative attack. Indeed some of the European central banks, notably France, did just this in 1993 and managed to stop the attack. Chamley also demonstrates that an anticipated exchange rate stabilization policy makes an exchange rate more vulnerable to an attack. Interestingly, however, by trading in a non-predictable manner, the central bank can prevent speculators from coordinating an attack.