A comment on: “The solution to the forward-bias puzzle”

Pippenger (2011) recently proposed a solution to the longstanding forward-bias puzzle. He argues that the puzzling estimates obtained using the standard equation for the efficient markets hypothesis are due to omitted variable bias. He identifies the missing variables as the future change in the forward exchange rate and the future interest differential. When these are added to the standard equation, he finds a one-to-one relationship between the future change in the spot rate and the forward premium. However, we argue that his equation can only test covered interest parity and offers no insight into the forward-bias puzzle.     

An explanation of the forward premium 'puzzle'

Existing literature reports a puzzle about the forward rate premium over the spot foreign exchange rate. The premium is often negatively correlated with subsequent changes in the spot rate. This defies economic intuition and possibly violates market efficiency. Rational explanations include non-stationary risk premia and econometric mis-specifications, but some embrace the puzzle as a guide to profitable trading.
We suggest there is really no puzzle. A simple model fits the data: forward exchange rates are unbiased predictors of subsequent spot rates. The puzzle arises because the forward rate, the spot rate, and the forward premium follow nearly non-stationary time series processes. We document these properties with an extended sample and show why they give the delusion of a puzzle.     

Forward and spot exchange rates

There is a general consensus that forward exchange rates have little if any power as forecasts of future spot exchange rates. There is less agreement on whether forward rates contain time varying premiums. Conditional on the hypothesis that the forward market is efficient or rational, this paper finds that both components of forward rates vary through time. Moreover, most of the variation in forward rates is variation in premium, and the premium and expected future spot rate components of forward rates are negatively correlated.     

Behavioural asymmetries in the G7 foreign exchange market

This paper examines the exchange rate disconnect puzzle of Obstfeld and Rogoff (2000) from a behavioural perspective. It provides evidence on the existence of substantial asymmetries in the underlying loss preferences for the difference between the spot and forward nominal exchange rates between the G7 countries for one-week and four-week forecast horizons. We further perform forecast breakdown tests in forward markets during the Greek and the Portuguese sovereign debt crisis, and then re-estimate the loss preferences showing a mean-reverting transition from optimism to pessimism and vice versa. Finally, we attribute the evolution of preferences to economic fundamentals and risk indexes and find that together with significant endogenous dynamics, variables such as growth and deficit differentials, interest rate and legal risk assert some significant impact on asymmetry. This new set of information suggests that the puzzle could have its roots on an underlying asymmetric loss function that reflects variability in preferences over exchange rate movements due to a variety of episodes in economic fundamentals.     

Testing the unbiasedness hypothesis of foreign exchange rates and the analysis of transformations

Recent researchers have utilized various functional forms for testing the hypothesis that the forward rate is an unbiased predictor of future spot rates in foreign exchange markets. We compare a large number of these functional forms for a similar time period and test their consistency with the data for five major currencies. Our results imply that certain functional form models may be inappropriate for some currencies. Researchers must, therefore, be cautious of misspecification due to erroneous functional forms when testing the unbiased forward rate hypothesis.     

An Examination of Uncovered Interest Rate Parity in Segmented International Commodity Markets

We examine the effect of segmented commodity markets on the relation between forward and future spot exchange rates in a dynamic economy. We calculate the slope coefficient in our theoretical economy from regressing exchange rate changes on forward premia. With reasonable parameter values, the slope coefficient is less than unity. However, even for extreme parameters the slope is not less than zero, as found in the data. A negative slope coefficient in a nominal version of the model requires the covariance between monetary shocks and relative output shocks to be significantly negative, in contrast to the covariance in the data.     

The forward rate unbiasedness hypothesis reexamined: evidence from a new test

Under conditions of risk neutrality and rational expectations in the foreign exchange market, there should be a one-to-one relationship between the forward rate and the corresponding future spot rate. However, cointegration-based tests of the unbiasedness hypothesis of the forward rate have produced mixed findings. In order to exploit significant cross-sectional dependencies, we test the unbiasedness hypothesis using a new multivariate (panel) unit-root test, the Johansen likelihood ratio (JLR) test, which offers important methodological advantages over alternative standard panel unit-root tests. When applied to a data set of eight major currencies in the post-Bretton Woods era, the JLR test provides strong and robust evidence in support of a unitary cointegrating vector between forward and corresponding future spot rates. However, the orthogonality condition is satisfied only for three major currencies.     

Expectations in the German hyperinflation reconsidered

Data on forward foreign exchange rates during the German hyperinflation after World War I provide direct observations of expected changes in the spot rate. Although levels of these forward rates seem to be efficient predictors of the spot rate, the predicted changes in the spot rate are biased downward substantially and do not meet the specific conditions of rationality. Indeed, the bias in the forward rate predictions is similar to bias in adaptive expectations of the spot rate. The behavior of the forward rate can be rationalized as a gradual market adaptation to a new regime of volatile and escalating inflation, reasonably represented by adaptive expectations. The strict definition of rational expectations needs to be broadened to allow for the difficulty of distinguishing between permanent and transitory shocks.     

Floating exchange rates,expectations and new information

This paper analyzes the relationship between forward exchange rates, future spot rates and new information. A stochastic model of exchange rate determination is used to formally show how unanticipated changes in the exchange rate determinants (or ‘news’) affect the spot rate. The empirical analysis indicates that ‘new information’ plays an important role in explaining the market forecasting error, or difference between the spot rate and the forward rate, determined in the previous period.     

EMPIRICAL ANALYSIS ON THE PREDICTORS OF FUTURE SPOT RATES

This paper examines the issue of the prediction of future spot rates by applying the seemingly unrelated regression technique to four major currencies using data from January 1974 to September 1982. The empirical evidence indicates that current spot rates provide a better prediction of future spot rates than do current forward rates. In further rolling subsample studies, the estimated coefficients for current forward rates (or spot rates) are found to be sensitive to the new information. An important implication of this paper is that since the estimated coefficients vary over time, the underlying pattern of the generated coefficients should be extrapolated and incorporated into the exchange rate predictions.     

The information in the Mexican term structure of interest rates: capital market implications

This paper employs the term structure approach to examine Mexican security markets during the recent period of political and economic turmoil. We investigate the characteristics of these markets and the forecast applicability of the pure expectations hypothesis to interest rates in Mexico. We find that both forward rates and spot rate spreads are found to have significant forecasting ability for future spot rates for Mexico. Both forecasting approaches suggest greater predictive ability during the period of higher interest rates and general economic volatility (1995–1996) than the more stable economic environment of the early 1990s (1991–1994).     

The forward market in emerging currencies: Less biased than in major currencies

Many studies have replicated the finding that the forward rate is a biased predictor of the future change in the spot exchange rate. Usually the forward discount actually points in the wrong direction. But, at least until recently, those studies applied only to advanced economies and major currencies. We apply the same tests to a sample of 14 emerging market currencies. We find a smaller bias than for advanced country currencies. The coefficient is on average positive, i.e., the forward discount at least points in the right direction. It is never significantly less than zero. To us this suggests that a time-varying exchange risk premium may not be the explanation for traditional findings of bias. The reasoning is that emerging markets are probably riskier; yet we find that the bias in their forward rates is smaller. Emerging market currencies probably have more easily-identified trends of depreciation than currencies of advanced countries.     

The forward exchange rate and the prediction of the future spot rate: Empirical evidence

This paper examines the characteristics and evaluates the record of the forward exchange rate as a predictor of the future spot rate of three European currencies during the recent period of floating rates. The forward rate (for 1, 3 and 6 months) is compared to a simple predictor of ‘no change’ extrapolations (i.e., a Martingale model) by the use of Theil's inequality ratios. Theil's measures are then applied to assess the relative importance of the various sources of the forward's prediction errors, and the efficiency of the forecast is tested. The results show that the forward rate, while generally producing unbiased forecasts, fails to track the fluctuations in future spot rates and poorly reflects their variations. Further, it does not perform better than the current spot rate in predicting the future spot rate for all the examined forecast leads. Thus its usefulness for the purpose of business decisions is questioned.     

Forward Foreign Exchange Rates,Expected Spot Rates,and Premia: A Signal-Extraction Approach

In this paper, we implement a methodology to identify and measure premia in the pricing of forward foreign exchange that involves application of signal-extraction techniques from the engineering literature. Diagnostic tests indicate that these methods are quite successful in capturing the essence of the time-series properties of premium terms. The estimated premium models indicate that premia show a certain degree of persistance over time and that more than half the variance in the forecast error that results from the use of current forward rates as predictors of future spot rates is accounted for by variation in premium terms. The methodology can be applied straightforwardly to the measurement of unobservables in other financial markets.     

Tests of the hypothesis of the existence of risk premium in the foreign exchange market

This paper tests for a risk premium in the foreign exchange market. The null hypothesis of the test is the random walk hypothesis in the foreign exchange market. The alternative hypothesis is that biases of current spot rates (or forward rates) from future spot rates are systematically related to a set of economic variables on which a risk premium may depend. This paper provides firm evidence for a risk premium in the foreign exchange market. The risk premium explains 10–20% of the total variance in future spot rates when the US dollar/mark quarterly rates are used. The magnitudes are smaller (less than 10%) for monthly rates.     

Unbiasedness of the Forward Exchange Rates

This paper derives an error correction model under the assumption that the spot and the forward rates are cointegrated, the first difference of forward rates is stationary, and the first order autocorrelation in the forecast error is allowed. When tests of the unbiasedness hypothesis are conducted with an error correction model using generalized methods of moments [GMM], the unbiasedness hypothesis cannot be rejected. Furthermore, the multivariate GMM estimation supports the hypothesis of unbiasedness of the forward exchange rates and the absence of a risk premium in the foreign exchange markets.     

Temporal Patterns in Foreign Exchange Returns and Options

Although the foreign exchange market is believed to be one of the most efficient financial markets in the world, there is significant evidence that technical analysis is profitable in this market. In this study we investigate the ability of information from the options market to supplement the commonly used information on past prices to predict temporal patterns in foreign exchange returns. We find that strategies using information from at-the-money options were more consistently profitable than the commonly used strategies based on only historical spot exchange rates (past prices). Consequently, options appear to contain information regarding future spot exchange rate movements.     

Common Stochastic Trends in a System of Exchange Rates

Univariate tests reveal strong evidence for the presence of a unit root in the univariate time-series representation for seven daily spot and forward exchange rate series. Furthermore, all seven spot and forward rates appear to be cointegrated; that is, the forward premiums are stationary, and one common unit root, or stochastic trend, is detectable in the multivariate time-series models for the seven spot and forward rates, respectively. This is consistent with the hypothesis that the seven exchange rates possess one long-run relationship and that the disequilibrium error around that relationship partly accounts for subsequent movements in the exchange rates.     

Forward exchange market unbiasedness: the case of the Australian dollar since 1984

This paper implements a robust statistical approach to regression with non-stationary time series. The methods were recently developed in other work and are briefly exposited here. They allow us to perform regressions in levels with non-stationary time series data, they accommodate data distributions with heavy tails and they permit serial dependence and temporal heterogeneity of unknown form in the equation errors. With these features the methods are well suited to applications with frequently sampled exchange rate data, which generally display all of these empirical characteristics. Our application here is to daily data on spot and forward exchange rates between the Australian and US dollars over the period 1984–1991, following the deregulation of the Australian foreign exchange market. We find big differences between the robust and the non-robust regression outcomes and in the associated statistical tests of the hypothesis that the forward rate is an unbiased predictor of the future spot rate. The robust tests reject the unbiasedness hypothesis but still give the forward rate an important role as a predictor of the future spot rate.     

THE RESPONSE OF FORWARD EXCHANGE RATES TO INTEREST RATE FORECASTING ERRORS

This paper examines the effects of interest rate news on changes in forward foreign exchange rates. Virtually none of the errors in forecasting forward exchange rates are explained by interest rate forecasting errors. The results are consistent with a conjecture that the forward exchange rate is not an estimate of the expected spot exchange rate.