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.     

Testing the forward rate unbiasedness hypothesis during the 1920s

This paper reexamines the forward rate unbiasedness hypothesis (FRUH) during the 1920s and it contributes to the literature as follows: first, it utilizes a database that includes currencies not studied before, as well as the 3 month forward rates; second, it applies three different approaches to test for cointegration and it shows that the choice of the technique is not of crucial importance; third, it tests for the temporal stability of the cointegration results; finally, it tests for the existence of the FRUH in the short run, by means of error correction models, whereas previous studies focused on cointegrated vectors only. Our analysis shows that for countries that did not undergo major financial turmoil during that period, there exists more favorable evidence for the FRUH.     

The spot–forward relationship revisited: an ERM perspective

We re-examine the relationship between spot and forward exchange rates using Hansen's stability tests for co-integrating equations. Two numeraire currencies are used: the DM as the ERM's nth currency and the US$ as a ‘control’. The striking feature is that while the spot–forward relationship displays broad stability against the dollar, precisely the opposite is true against the DM. We investigate whether this result can be interpreted as evidence that the ERM target zones lacked credibility. Using the general-to-specific modelling framework, we develop dynamic relationships that can be readily used to interpret the source of the Hansen instability. Our results also have implications for the appropriate way to test the unbiasedness of the forward exchange rate.     

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.     

Spot and forward volatility in foreign exchange

This paper investigates the empirical relation between spot and forward implied volatility in foreign exchange. We formulate and test the forward volatility unbiasedness hypothesis, which may be viewed as the volatility analogue to the extensively researched hypothesis of unbiasedness in forward exchange rates. Using a new dataset of spot implied volatility quoted on over-the-counter currency options, we compute the forward implied volatility that corresponds to the delivery price of a forward contract on future spot implied volatility. This contract is known as a forward volatility agreement. We find strong evidence that forward implied volatility is a systematically biased predictor that overestimates movements in future spot implied volatility. This bias in forward volatility generates high economic value to an investor exploiting predictability in the returns to volatility speculation and indicates the presence of predictable volatility term premiums in foreign exchange.     

The Forward Exchange Rate Bias Puzzle Is Persistent: Evidence from Stochastic and Nonparametric Cointegration Tests

An important puzzle in international finance is the failure of the forward exchange rate to be a rational forecast of the future spot rate. We document that even after accounting for nonstationarity, nonnormality, and heteroskedasticity using parametric and nonparametric tests on data for over a quarter century, U.S. dollar forward rates for the major currencies (the British pound, Japanese yen, Swiss franc, and the German mark) are generally not rational forecasts of future spot rates. These findings deepen the forward exchange rate bias puzzle, especially as these markets are the most liquid foreign exchange markets with very low trading costs.     

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.     

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.     

Currency crisis and the forward discount bias: Evidence from emerging economies under breaks

This paper investigates the effects of two financial crises (the 1997 Asian currency crisis and the 2000 Turkish financial crisis) on the forward discount bias in 14 emerging-market economies using a robust two-stage procedure. This unique sample of less researched currencies displays: (i) high persistence in forward discount equations; and (ii) varying variance ratios between changes in exchange rates and the forward premium. The findings provide new insights into the forward discount puzzle: financial crises exert considerable power on the forward discount bias and uphold the forward rate unbiasedness hypothesis (FRUH) by reverting the negative sign into positive.     

Does the forward premium puzzle disappear over the horizon?

This paper provides the first comprehensive study of the horizon effect in tests of the forward rate unbiasedness hypothesis. It estimates Fama regressions employing 1-month through to 10-year horizon data for the five most heavily traded US dollar currency pairs pre-crisis 1980–2006. In contrast with extant studies, it fully deals with the econometric problems of long horizon regressions by means of a novel heteroskedastic- and autocorrelation-consistent bootstrap. The regression results confirm a clear horizon effect in that the slope coefficient approaches unity as the forward contract maturity is extended. The puzzle disappears at the 3-year horizon and beyond for all currencies.     

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.     

Market microstructure effects of government intervention in the foreign exchange market

As asymmetric information model of the bid - ask spread is developedfor a foreign exchange market subject to occasional governmentinterventions. Traditional tests of the unbiasedness of theforward rate as a predictor of the future spot rate are shownto be inconsistent when the rates are measured as the averageof their respective bid and ask quotes. Larger bid - ask spreadson Fridays are documented. Reliable evidence of asymmetric bid- ask spreads for all days of the week, albeit more pronouncedon Fridays, are presented. The null hypothesis that the forwardrate is an unbiased predictor of the future spot rate continuesto be rejected. The regression slope coefficients increase towardunity, however, indicating a less variable risk premium.     

Cross‐sectional Restrictions on the Spot and Forward Term Structures of Interest Rates and Panel Unit Root Tests

In this paper we examine the stationarity of all the rates comprising the USD, GBP, DM and JPY spot and forward term structures. Instead of focussing on short maturity interest rates, as most other papers do, we perform a detailed analysis of the whole range of spot and forward interest rates of the 4 main currencies. We investigate the issue of stationarity within the framework of an equilibrium interest rate model such as Vasicek (1977), that defines the cross-sectional and time series properties that interest rates of various maturities must satisfy. We show that within a one-factor interest rate model, such as Vasicek, all interest rates are restricted to exhibit the same mean reverting behaviour. This restriction allows us to apply more powerful panel unit root tests. This methodology increases considerably the number of observations available and as a result the power of the unit root tests. The higher power of these tests allows us to demonstrate that there does exist mean reversion on the spot and forward US interest rates and the forward DM and GBP interest rates.     

The Unbiasedness Hypothesis in the Freight Forward Market: Evidence from Cointegration Tests

The current paper investigates the unbiasedness hypothesis of Forward Freight Agreement (FFA) prices in the freight over-the-counter (OTC) forward market trades. Cointegration techniques are employed to examine the hypothesis. The results indicate that: FFA prices one and two months before maturity are unbiased predictors of the realised spot freight rates for all investigated shipping routes; three months FFA prices for panamax Pacific routes are unbiased predictors of spot prices, while FFA prices for panamax Atlantic routes are found to be biased predictors of spot prices. This diverse evidence suggests that the validity of the unbiasedness hypothesis depends on the specific characteristics of the market under investigation, the selected trading route and the time to maturity of the contract. JEL classification G13, G14, C32     

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.     

Cointegration and forward and spot exchange rate regressions

We investigate the relationship between cointegration models of the current spot exchange rate, s_t, and the current forward rate, f_t, and cointegration models of the future spot rate, s_t+1, and f_t and the implications of this relationship for tests of the forward rate unbiasedness hypothesis (FRUH). We show that simple models of cointegration between s_t and f_t imply complicated models of cointegration between s_t+1 and f_t. Consequently, standard methods are often inappropriate for modeling the cointegrated behavior of (s_t+1, f_t)′ and we show that the use of such methods can lead to erroneous inferences regarding the FRUH.     

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.     

Resuscitating real interest rate parity: new evidence from panels

This paper considers the real interest rate parity (RIRP) in OECD countries applying a sequential panel selection (SPS) method on alternative panel unit-root tests. Our approach exploits the enhanced power of panels to uncover evidence of stationarity, but also identifies the exact countries for which the RIRP holds in a panel. Moreover, we construct real interest rate measures using alternative approaches, including a Markov regime-switching procedure, which is consistent with the forward-looking nature of inflation expectations formation. Considering US as the benchmark economy, we produce strong evidence of stationarity in real interest rate differentials, which resuscitates RIRP, especially given the inconclusive results in the related literature. Our results are robust to different panel unit-root tests, measures of inflation expectations, and interest rate maturities. The RIRP appears quite resilient in the face of the global financial crisis and the low real interest rate environment after the great recession. The SPS allows to calculate half-lives, which avoid the pitfalls of over/underestimating the speed of adjustment and are lower as compared to the typical estimates in the literature.     

FORWARD RISK PREMIA AND THE MATURITY OF CONTRACTS: A NOTE

This paper examines the behavior of the risk premium component of currency forward rates. Analyzing forward rates of one, two and three-month maturity, we find that the power of forward rate as a predictor of future spot rate decreases with the length of contract maturity. Further, we find that the proportion of the variance of the forward premium which is due to the variation of the risk premium is larger than the proportion due to the expected spot rate change for all currencies except for the Canadian dollar. This proportion also increases with the length of maturity.     

IS THE TOKYO SPOT FOREIGN EXCHANGE MARKET CONSISTENT WITH THE EFFICIENT MARKET HYPOTHESIS?

Recent Studies in the area of foreign exchange market efficiency have employed time series analysis to test for the absence of long-run equilibrium or cointegration relationships among the exchange rates for the major currencies. Cointegration directly violates the weak form of the Efficient Market Hypothesis in a speculative efficient market (Granger, 1986). In this study, we address the efficiency of the Tokyo spot foreign exchange market while updating the test procedures developed by Phillips and Ouliaris (1990), Johansen and Juselius (1990) and Johansen (1991). Cointegration is found to be absent, showing that the Tokyo spot market is consistent with the efficient market hypothesis.