RDP 9307: Explaining Forward Discount Bias: Is it Anchoring? 1. Introduction

The short-run behaviour of floating exchange rates has baffled economists for at least a decade. Along with the apparent inability of structural models of the exchange rate to outperform a random-walk (Meese and Rogoff (1983)) probably the best documented and most enduring puzzle is the bias of the forward discount as an estimate of the future exchange rate change. This paper provides a possible explanation for this bias.

If foreign exchange market participants are rational and risk-neutral and transaction costs in the market are small enough to be ignored, then the forward discount should be an unbiased estimate of the future exchange rate change. The overwhelming empirical evidence of forward discount bias is therefore a rejection of this joint hypothesis.^[1]

There are four possible interpretations of the failure of this joint hypothesis. The first is that there is a time-varying risk premium required to hold assets denominated in different currencies. However, a model which incorporates risk premia and explains the bias of the forward discount has proven elusive (see, for example, Hodrick (1987), Cumby (1988), Baillie and Bollerslev (1990) and Froot (1990)). Furthermore, theory-based estimates of risk premia turn out to be very small indeed (see Frankel (1985), Frankel (1988) and Engel (1992)).

The second interpretation is that the sample used to test the joint hypothesis has been too small – either because of peso problems (Rogoff (1979), Krasker (1980)) or because rational agents need time to learn the true model of their economic environment (Lewis (1989)). But this interpretation seems increasingly strained the longer forward discount bias manifests itself in the data, and recent extensive evidence (Frankel and Chinn (1991)) shows no sign of its disappearance.

A third possibility (Baldwin (1990)) is that small transaction costs combined with uncertainty can lead to an interest rate differential matched neither by a risk premium nor by an expected exchange rate change. Interest rate differentials within a small band do not set in motion the capital flows that would close the gap because transaction costs render the moving of capital sub-optimal. However, this analysis (which assumes the full rationality of market participants) seems inconsistent with results from surveys of market participants' expectations.

The final possible interpretation is that the foreign exchange market is not efficient. This is the interpretation we explore in this paper.^[2] In particular, we examine the consequences for the exchange rate of the presence of market participants whose exchange rate expectations are directly influenced by the value of the forward exchange rate.

We justify this focus on the forward exchange rate by drawing on the work of cognitive psychologists. In Section 2 of the paper, we report some of this work and argue that the forward exchange rate fits very closely psychologists' definition of an ‘anchor’ for exchange rate expectations. For brevity, we describe foreign exchange market participants whose expectations are influenced by the value of the forward rate as ‘anchored traders’.

The paper presents a stochastic version of Dornbusch's 1976 sticky-price model in which two types of risk-averse traders, anchored and rational, jointly determine the exchange rate. The anchored traders use the forward rate as the anchor for their expectations, but they also have a view of the appropriate level of the exchange rate (and if the exchange rate is not at that level, their expectations adjust from the anchor).^[3] By contrast, the rational traders understand the true nature of the foreign exchange market, how the anchored traders behave, as well as the proportion of market wealth managed by them. As a consequence, the rational traders have unbiased expectations of the future path of the exchange rate.

The traders manage the funds of ‘investors’ who are assumed to base their investment decisions on the traders' relative performance over an exogenously specified finite horizon. The equilibrium proportion of anchored traders in the market is determined endogenously assuming a decision rule for investors based on the probability that the anchored traders' chosen portfolio out-performs the rational traders' portfolio over the investors' horizon.

The vast majority of future short-run movements in the exchange rate are unpredictable and hence, in particular, are unrelated to the value of the current forward discount.^[4] This fact plays a key role in the model. It implies that the advantage gained from correctly understanding the relation between the forward discount and the spot exchange rate is not great. As a consequence, even when examined over quite long horizons, the anchored traders often out-perform the rational traders simply by chance. Provided investors have (even quite long) finite horizons over which they compare the relative performance of the traders, a significant proportion of anchored traders survive in the market in the long-run.

The model explains two puzzling features of the foreign exchange market. Firstly, it predicts forward discount bias in the direction consistently observed in foreign exchange markets. And secondly, it predicts that market participants' average exchange rate expectations are strongly correlated with the forward discount, as has been documented by Froot and Frankel (1989) and Frankel and Chinn (1991).

The paper proceeds as follows. Section 2 reviews some of the psychological evidence on anchoring and provides more detail on the puzzles in the foreign exchange market on which we focus. Section 3 explains why the presence of anchored traders in the market can help explain these puzzles. Section 4 presents a stochastic version of the Dornbusch (1976) sticky-price model in which risk-averse rational and anchored traders jointly determine the exchange rate. Data on interest rate differentials and exchange rate volatility are used in Section 5 to calibrate the model. This section also proposes a closure for the model which allows endogenous determination of the proportion of anchored traders in the market. Numerical results are presented which suggest that the model is empirically relevant and that it generates several of the empirical regularities described in the literature. Finally, we examine a potentially serious simplification in the model. Section 6 concludes.

Footnotes

See, for example, Hodrick (1987), Goodhart (1988) and Frankel and Chinn (1991). [1]

Froot and Thaler (1990) are also drawn to this interpretation. They suggest that forward discount bias may be a consequence of some market participants responding sluggishly to changes in the interest differential. But again, it is hard to see how this analysis is consistent with the results of surveys of market participants' expectations (see later). [2]

The importance of assuming that the anchored traders respond to changes in the current exchange rate will become apparent when we describe the model in Section 4. [3]

See, for example, Dornbusch (1980), Meese and Rogoff (1983), Cumby and Obstfeld (1984), Obstfeld (1985), Frankel and Meese (1987) and Campbell and Clarida (1987). Clarida and Taylor (1993) provide a dissenting view, though it is based on only a short run of out-of-sample testing. [4]