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This paper investigates the time-varying nature of expectation formation rules for institutional investors in the foreign exchange market. Using a dataset of survey expectations for four exchange rates, we first distinguish three different general rules. We find a momentum rule, a fundamental rule, and a rule that takes advantage of interest differentials between countries. Apart from heterogeneity in expectation formation rules, we show that the rules are time-varying conditional on a number of different factors, such as the sign of the most recent return, the forecast horizon, the distance to the PPP rate, and the extent to which the rule produces forecast errors vis-à-vis the market exchange rate.

Several foreign exchange market anomalies (e.g. excessive trade, momentum, forward premium puzzle) cannot be fully explained within the traditional framework. Also, non-fundamental strategies such as carry trade (Menkhoff et al., 2012a) and momentum (Menkhoff et al., 2012b) can be profitable. In addition, there is ample evidence of investors having expectations that are non-rational in the traditional sense, and also heterogeneous (Ito, 1990, Cavaglia et al., 1993, MacDonald and Marsh, 1996, Menkhoff et al., 2009, Jongen et al., 2012a and Jongen et al., 2012b). Several approaches have been suggested in the literature to address these issues. For example, the scapegoat approach (Bacchetta and van Wincoop, 2009 and Sarno and Valente, 2009) assumes that exchange rates can be explained by varying fundamentals over time. The learning approach (see e.g. Markiewicz, 2012 and De Grauwe and Markiewicz, 2013) poses that agents in the foreign exchange market behave as econometricians and attempt to learn the true data generating process from the empirical data. In this paper, we follow the behavioral finance literature and use survey data to test whether expectations are formed using heuristics, and whether the use of these heuristics is time-varying following the theoretical work of De Grauwe and Grimaldi (2006) and Spronk et al. (2013). The assumption of rational market participants with homogeneous expectations, once firmly rooted in financial theory, is losing ground in favor of alternative assumptions of agent behavior such as bounded rationality and heterogeneous expectations. Bounded rationality of market participants was already introduced by Simon (1957). In this framework it is assumed that agents are boundedly rational and that they use certain rules of thumb, heuristics, to form expectations about future asset prices. Various attempts have been made to determine what these rules of thumb are and how they are being used, ranging from theoretical models to lab experiments and survey analyses. The main theoretical contributions come from Frankel and Froot, 1987b and De Long et al., 1990 and Lux (1998). Frankel and Froot (1987b) develop a model with three types of actors: chartists (‘trend followers’), fundamentalists (‘model followers’) and portfolio managers. The portfolio manager is the only actor who buys and sells assets, and he receives input from the two other types. Therefore, he makes trades that can be seen as a weighted average between the chartist and the fundamentalist expectations. Lux' (1998) also makes this distinction between chartist and fundamentalist strategies. De Long et al. (1990) make a distinction between noise traders and sophisticated traders. In this model, the noise traders create a risky investment environment and are able to obtain excess returns without having access to inside information. Because of the presence of this group in the market, prices can deviate significantly from their fundamental value for longer periods of time. All of these authors explain various market anomalies and stylized facts with their models of investor behavior. The presence and behavior of different types of agents in financial markets has been examined in a number of ways. Schmalensee (1976) was one of the first to use experimental methods to reveal expectation formation processes for time series, in particular with respect to technical rules. De Bondt (1993) and Bloomfield and Hales (2002) use classroom experiments and find evidence of trend-following behavior, where Bloomfield and Hales (2002) also find support for the assumption in Barberis et al. (1998) that investors perceive past trend reversals as an indicator for the probability of future reversals even though they are aware of the random walk character. Hommes et al. (2005) illustrate coordination of expectations among participants in an experimental setting. As an alternative method to measure expectations, attempts have been made to directly measure investor expectations and expectation formation rules. To this end, both quantitative and qualitative surveys have been conducted. Taylor and Allen (1992) show, based on a questionnaire survey, that 90% of the foreign exchange dealers based in London use some form of technical analysis in forming expectations about future exchange rates, particularly for short-term horizons. The foreign exchange dealers further expressed that they see fundamental and technical analyses as complementary strategies for making forecasts and that technical analysis can serve as a self-fulfilling mechanism. Various quantitative surveys have been evaluated as well (among others, Ito, 1990, Cavaglia et al., 1993, MacDonald and Marsh, 1996, Branch, 2004 and Menkhoff et al., 2009). They all find heterogeneity in expectations, and most of them attribute this to extrapolative, regressive and adaptive expectations (for an overview, see Jongen et al., 2008). However, all these studies assume static and non-time-varying expectation formation. Branch (2004) investigates inflation expectations and finds that agents switch between different exogenously determined forecasting techniques (VAR, naïve and adaptive) based on the mean squared prediction errors of the strategies. This paper extends Branch (2004) by introducing dynamics in expectation formation strategies for financial markets, being the foreign exchange market, where feedback effects from expectations to realizations can be stronger than in the case of inflation. In addition, the forecasting rules are estimated endogenously. Whereas Branch (2004) optimizes the forecasting rules exogenously on realized inflation, we estimate the forecasting rules endogenously on the survey expectations. This approach allows for more flexibility in results as it does not presume consistency between expectations and realizations. In this paper we will further investigate this heterogeneity by testing three well-known foreign exchange forecasting strategies on a survey dataset with forecasts from foreign exchange analysts and large international banks. These strategies can be summarized as a momentum rule, a PPP rule and an interest parity rule. The choice for these three strategies is motivated partly by the academic literature on exchange rates and heterogeneous agents (see Spronk et al., 2013) and partly by evidence from industrial practice (see Pojarliev and Levich, 2008 and Pojarliev and Levich, 2010). We will advance the study of different types of agents in two ways. First, we introduce dynamics in the strategies by distinguishing between time-varying bandwagon versus contrarian expectations in the momentum strategies and by distinguishing between carry trade versus UIP expectations. Although, in general, it is acknowledged that the existence of such opposing beliefs could be hidden on an aggregated level because they even out, the distinction has, to the best of our knowledge, never been made when working with empirical data. Secondly, we will increase the dynamic nature of the model by allowing the agents to switch between different strategies based on forecasting accuracy with respect to the market exchange rate. These two additions, combined with the survey dataset, allow us to evaluate different currencies as well as different forecast horizons. Furthermore, the dataset has never been used for this purpose,1 thus making this paper a valuable extension to the existing literature on behavioral finance, expectation formation, exchange rate dynamics and survey data. We find evidence for the existence of all three strategies both when tested separately and when tested in a combined model, indicating that agents use these different strategies to form expectations about future returns. Moreover, we find dynamics in expectation formation in three different ways. First, agents hold opposing beliefs within different strategies and change these beliefs over time. Secondly, expectation formation is dynamic in the sense that the expectation formation rules change for different forecasting horizons. Carry trading and momentum are the main applied strategies for short-term forecasting, whereas PPP and UIP are predominantly used for long-term forecasting. Finally, the results show that agents attach time-varying weights to the different strategies based on the past performance of the strategies, especially for the long run forecast horizons. The remainder of this study is organized as follows. In Section 2, we describe the dataset, Section 3 contains the methodology used, and Section 4 contains the results. In Section 5, we give some concluding remarks and suggestions for further research.

In this paper, we used survey expectations for four exchange rates to evaluate the way in which investors form their expectations, building on the theoretical framework of the heterogeneous agent literature. To do this, we tested three different strategies on the disaggregated expectations: momentum trading, PPP trading and interest trading strategies. The momentum rule was divided into bandwagon and contrarian expectations, and the interest trading strategy was divided into UIP and carry trade expectations. These extensions to the basic models have shown to be a valuable improvement to the models. After testing the strategies separately and in a combined model the survey expectations were evaluated to determine whether agents switch between strategies over time. We obtained significant results for all strategies when tested separately and when tested in a combined model. This implies that investors use past changes, PPP rates and interest rates in forming their expectations. Momentum trading especially occurs for short horizons, whereas PPP trading is more common for longer horizons. The interest differential is used on all horizons but primarily for long-horizon forecasting. We find indications that agents have a stronger tendency to apply a carry trade (UIP) expectation at the shorter (longer) forecast horizon. Interestingly, there are also differences in expectations within different strategies. Some people expect past trends to continue and therefore positively extrapolate past returns into future forecasts (bandwagon). Other investors expect past trends to revert. There are investors who use the interest differential as a tool for carry trade; that is, they expect an appreciation of the currency of the high-interest-rate country. There are also investors who believe in UIP and therefore expect a depreciation of the currency of the high-interest-rate country. Furthermore, a long history of positive returns seems to influence investors when forming their expectations, making them more vulnerable to bandwagon expectations. A long history of undervaluation of an exchange rate can cause a loss of faith in reversion to the fundamental value. Not only do investors use different strategies to form their expectations, they also change the weights they assign to these strategies based on the past forecasting accuracy of the strategies. The weight assigned to the extrapolative strategy decreases for longer horizons, and investors put more weight on PPP rates in this case. Investors switch more for longer forecasting horizons. Switching mainly occurs between momentum traders and PPP traders. Our results further indicate that investors have deviating ways of forming expectations for the exchange rates that involve the Japanese yen. For the momentum and the PPP rules, we found surprising results that contradict earlier works as well as our empirical findings for the other exchange rates. This might suggest that Japan can be seen as a separate case. One of the reasons for this can be that Japan is an export economy and therefore the Japanese government actively intervenes in the foreign exchange market to maintain their trading competitiveness, which makes conventional rules less useful. Further research could explore this phenomenon. The results we presented in this paper are, on the one hand, a strong confirmation of theoretical statements and empirical findings from the behavioral finance literature. On the other hand, they are also an extension to the literature, as we have shown that there is also important heterogeneity within the strategies. Future research could investigate this heterogeneity and its implications for exchange rates. It would also be interesting to see whether these findings apply to other asset classes. Furthermore, applying the model to different time periods and/or focusing on different crises could provide better insight into the effect of heterogeneity and switching on crises and vice versa.