RDP 9103: The Failure of Uncovered Interest Parity: Is it Near-Rationality in the Foreign Exchange Market? 1. Introduction

Uncovered interest parity is one of the linchpins of modern exchange rate theory. It follows from the joint hypothesis that the foreign exchange market is efficient, that traders are risk-neutral and that transaction costs are negligible. However, uncovered interest parity is overwhelmingly rejected by empirical evidence.^[1]

There are four possible interpretations of the failure of this joint hypothesis. The first, and most widely accepted, is that there is a time-varying risk premium^[2] required to hold a portfolio of assets denominated in a range of currencies. A model which incorporates risk premia and performs well empirically has, however, proven elusive (see for example, Hodrick (1987), Cumby (1988) and Baillie and Bollerslev (1990)). Furthermore, theory-based estimates of risk premia turn out to be very small indeed (see Frankel (1985), Frankel (1988) and Smith and Gruen, (1989)).

A second possibility is that the joint hypothesis fails because of a small sample bias or ‘peso problem’. The suggestion here is that investors rationally estimate the ex ante probabilities of events which, if they occur, will have a significant impact on the real return from their portfolio. During the period under study, if the events do not occur with a frequency consistent with their estimated probabilities, it will incorrectly appear that the investor's behaviour was irrational.

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.

The final possible interpretation of the rejection of uncovered interest parity is that the foreign exchange market is not efficient. This is the interpretation we explore in this paper.

We consider the returns available to a representative risk-averse fund-manager who maximizes a function of mean and variance of end-period wealth. The investor chooses the shares held in different currencies by examining interest rates and expected changes in the exchange rate. We discover that, in terms of expected utility, the investor loses very little by exhibiting certain types of ‘near-rational’ behaviour (see Akerlof and Yellen (1985) for a definition of near-rational). If we then allow for the possibility of small transaction costs, the benefits of being fully rational are even smaller.

Initially, we assume that the investor responds immediately to all new information which affects expected utility. We assume that new information arrives weekly. We then explore three deviations from this strategy.

In the text of the paper, we estimate the cost of changing the portfolio shares infrequently rather than every time new information becomes available. In the Appendix, we examine two further examples of near-rationality. In these examples we assume that investors either:

1. take account of the expected returns available in different countries and the variability of those returns but ignore the covariances between them, or
2. make small mistakes in forming expectations of exchange rate changes.

We estimate the expected utility cost of each of these types of near-rational behaviour using interest rate and exchange rate data over the period 1983–1989. The main contribution of the paper is to show that the cost of sluggishly adjusting portfolio shares over periods of relevance to tests of uncovered interest parity is very small indeed. We conclude that there are no strong grounds for expecting that the agents who engage in such behaviour will be driven from the market. This provides a potential explanation for the failure of uncovered interest parity.

Footnotes

See Hodrick (1987) and Goodhart (1988) for international evidence with a range of currencies, or Smith and Gruen (1989) for the Australian/US exchange rate. [1]

The term ‘risk premium’ is often used loosely to mean the excess return demanded by investors to compensate them for the ‘risk’ of an exchange rate depreciation. We use the term in its technical sense. For a given expectation of the return on an asset, the risk premium is the excess return required because of the expected volatility of the return and its expected correlation with the returns on other assets. [2]