روحیه و تمایلات غیرانسانی در بازار ارز

It is traditionally assumed in finance models that the fundamental value of an asset is known with certainty. In this paper we depart from that assumption. We propose a simple model of the exchange rate in which agents have biased and unbiased beliefs about the fundamental rate. We show that such a model produces waves of optimism and pessimism unrelated to the underlying fundamental value. In addition, the model shows that in a world characterized by the existence of heterogeneous beliefs about the fundamental, exchange rate movements can be remarkably complex even if only fundamentalist traders operate in the market.

Beliefs are important forces, not only in everyday life, but also in financial markets. Changes in beliefs shape events even if there is no change in the objective forces affecting reality. Economists have long recognized this in the past. Keynes (1964), for example, wrote about ‘animal spirits’ influencing reality and creating waves of optimism and pessimism. More recently, Kindelberger (2005) in his celebrated study ‘Manias, panics and crashes’ analyzed the way in which agents develop beliefs and how these beliefs move stock prices. Beliefs also matter in the foreign exchange market. A few years ago two sets of beliefs emerged about the fundamental value of the U.S. dollar. The first set was represented, among others, by Obstfeld and Rogoff (2005) and Obstfeld (2005). According to this view the large current account deficits of the U.S. observed since the second half of the 1990s were unsustainable. A major decline in the value of the dollar would be the consequence of adjusting the current account balance to a sustainable level. These authors estimated that restoring the balance in U.S., European and Asian current accounts would imply a 30% depreciation of the dollar against the Euro and a 35% depreciation against a basket of Asian currencies respectively. It turned out later that these authors were right, but at that time there were also other beliefs about the fundamental value of the dollar. One was developed by Hausmann and Sturzenegger (2006). In this alternative view there did not arise a problem of sustainability. These authors detected ‘Dark Matter’ in the international financial markets, i.e. attributes present in certain assets (the U.S. dollar in this case) that could not properly be measured. Corrected for the amount of ‘dark matter’ these authors came to the conclusion that there was in fact no net foreign US debt, and thus that the dollar was correctly priced. Similar differences in beliefs about other exchange rates have been observed. For example, economists disagree about the fundamental value of the Renminbi against the dollar and other currencies. There can be little doubt that these differing beliefs about the fundamental value of currencies are realities that can affect the market exchange rates. In this paper we develop a systematic analysis of beliefs in the foreign exchange market. Traders in our model have divergent beliefs about the value of the fundamental exchange rate. They form their expectations adaptively and interact with each other selecting the trading strategy that is most profitable. Put differently, traders in our model develop beliefs about the underlying fundamental value of the exchange rate, but they are willing to change these beliefs and switch to another one if the latter turns out to be more useful (profitable). Thus traders are willing to learn about the world in a ‘trial and error’ fashion. In this way we introduce an evolutionary type of discipline, so as to avoid that ‘anything can happen’. That is, trading strategies are not just selected in an ad hoc way but according to a disciplining algorithm, which is consistent with the idea of utilitarianism, whereby the most useful beliefs are favored. We deviate from the rational expectations paradigm for several reasons. First, rational expectations implies that agents have full knowledge of the underlying model, whatever its complexity, and that they know the objective probability distribution of all exogenous shocks. In such an environment there is no room for divergent beliefs about the underlying fundamentals.1 Second, there is a large body of evidence showing that humans are boundedly rational. Broadly speaking, psychologists divide our actions between two types: intuitive and rational. A large amount of studies suggest that many of our actions correspond to the first type and therefore they are spontaneous rather than deliberate and rational (Epstein, 2003, Gilbert, 2002 and Wilson, 2002). Furthermore, Tversky and Kahneman (1974) show that humans base a large share of their decisions on a limited number of simple heuristic rules. All together this suggests that people tend to use fast associative thinking instead of spending a large amount of time in making effortful rational decisions. This means that traders might make systematic mistakes, particularly so under situations of uncertainty. At the same time however, making decisions based on heuristics allows humans to save large amounts of computational time. Using adaptive expectations does not mean, however, that we move into a world of irrationality. As mentioned in the previous paragraph, the second, rational dimension of human behavior is given its due role in our model. Traders are willing to learn from their mistaken beliefs in an evolutionary fashion. They adjust their behavior dropping their mistaken beliefs in favor of newer ones when the latter outperforms the former. Our paper belongs to the heterogeneous agent literature that has developed over the last years (Brock and Hommes, 1997, Brock and Hommes, 1998, Chiarella, 1992 and Chiarella and He, 2002; De Grauwe and Grimaldi, 2006a and De Grauwe and Grimaldi, 2006b; Frankel and Froot, 1986, Frankel and Froot, 1990 and Lux and Marchesi, 1999). Only a few papers in this literature however model the uncertainty about fundamentals in a systematic way: De Grauwe and Rovira Kaltwasser (2007), Diks and Dindo (2008), Manzan and Westerhoff (2005), Rovira Kaltwasser (2010), Westerhoff (2003). Also in Heitger (2010) there is an interesting treatment of fundamentalist traders with different degrees of risk aversion as well different perception levels of the excess return of assets.2 We begin with a very simple model of the exchange rate, which is extended later. The model deviates from the standard chartist-fundamentalist approach by assuming that no trend followers participate in the market but only traders following a fundamentalist rule. We show in this very simple setup how cycles of optimism and pessimism emerge in the foreign exchange market, even in the absence of innovations to the true fundamental. The remaining of the paper is organized as follows: in Section 2 we present the basic theoretical model of the exchange rate, in Section 3 we extend the basic setup by allowing traders who observe the underlying fundamental without any bias. In Section 4 we augment the model by including trend followers. Section 5 offers a brief analysis of the statistical properties of the data generated by the model in a noisy environment and Section 6 concludes.

In this paper we have presented a parsimonious heterogeneous agent model of the foreign exchange market. The main features of the model are that traders, who do not know the underlying value of the fundamental, form beliefs about its value. In the simplest version of the model we assumed two types of beliefs, an optimistic and a pessimistic one. Traders then switch between these two beliefs depending on how well these beliefs perform in forecasting the change in the exchange rate. Thus our model combines simple heuristics with a learning mechanism based on trial and error. We showed that this simple model generates cyclical movements of optimism and pessimism even if the fundamental does not fluctuate. These endogenous waves of optimism and pessimism are an emergent property of the model and can be interpreted as a mechanism aimed at discovering the true fundamental. We then extend the model by adding traders who have unbiased views about the fundamental exchange rate, and traders who use trend chasing (chartist) rules. Adding these rules maintains the cycles of optimism and pessimism but makes these more complex and unpredictable. The model developed in this paper assumes that the fundamental exchange rate is exogenously given. This implies that the movements in the market exchange rate do not feedback into the fundamental exchange rate. This is a simplifying assumption that in future research should be relaxed. There are reasons to believe that movements in the exchange rate also affect real variables, e.g. exports and imports, the current account and savings-investment decisions. These real effects in turn affect the fundamental value of the exchange rate. The model offers an intuitive explanation for both the disconnect and excess volatility puzzles. Additionally, it is capable of replicating the widely observed phenomenon that exchange rate returns are not normally distributed, but on the contrary exhibit fat tails. Although it is outside the scope of the present paper, our analysis allows us to make a tentative suggestion about the role of monetary policy in stabilizing (or destabilizing) the exchange rate. In an environment in which monetary policies are stable and predictable there will be less uncertainty about the underlying fundamental of the exchange rate. As a result, the belief bias will tend to be smaller, thereby reducing the power of waves of optimism and pessimism in driving the exchange rate. Obviously, more research will have to be done to analyze the importance of monetary policies in stabilizing the exchange rate. Our model is based on the assumption of bounded rationality. Findings from psychology and brain sciences suggest that there are two interacting cognitive processes at work in our brains. The first one is based on intuition and emotion and it is therefore fast and automatic. The second one is based on explicit reasoning. It can be called the rational process and it is slow and requires effort. Our model has this dual structure. Traders follow simple heuristics (e.g. extrapolating past changes), which belong to the first process. These simple rules are subject to the second, the rational evaluation process, which interacts with the first process in that it selects the rules that perform best. This dual decision making process creates remarkably complex movements of the exchange rate when implemented in a model of interacting agents. Furthermore, the interactions between traders not only lead to complex dynamics in the exchange rate, they are also key to understand the emergence of fat tailed distributed exchange rate returns.