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.     

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.     

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.     

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.     

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 Efficiency of the Canadian-U.S. Exchange Market under the Assumption of no Risk Premium

The efficiency of the Canadian-U.S. exchange market for the current float is examined more extensively than previously. Semi-strong-form tests which admit the lagged spot rate as a predictor are considered in addition to the standard weak-form test. These stronger tests reject the joint null hypothesis of an efficient exchange market and no risk premium for the period ending in October 1976, although not for the entire period. For almost every year the current spot rate provided a better forecast of the future spot rate than did the current forward rate.     

PREDICTIVE POWER OF THE TERM STRUCTURE IN AUSTRALIA IN THE LATE 1980'S: A NOTE

The Market Expectations Theory of the Term Structure of Interest Rates is tested using Wednesday yields on 13 week and 26 week treasury notes and 90 and 180 day bank accepted bills for the period 3 December 1986 to 13 March 1991 obtained from the Reserve Bank of Australia. In ordinary least squares regression based tests the Market Expectations Theory of the Term Structure of Interest Rates is accepted for bank accepted bills but rejected for treasury notes. Augmented Dickey Fuller unit root tests provide evidence of non-stationarity in the variables; a possibility often ignored in Australian studies. Although the unit root tests are generally consistent with the existence of one unit root, residual based cointegration tests between the forward rate and spot rate are not consistent with cointegration. This suggests that the prior expectations theory results may be a result of spurious regression. Perhaps a more complex model is required, coupled with tests which take account of non-stationary time series.     

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.     

Efficiency tests with overlapping data: an application to the currency options market

This paper presents the results of an empirical study into the efficiency of the currency options market. The methodology derives from a simple model often applied to the spot and forward markets for foreign exchange. It relates the historic volatility of the underlying asset to the implied volatility of an option on the underlying at a specified prior time and then proceeds to test obvious hypotheses about the values of the coefficients. The study uses panel regression to address the problem of overlapping data which leads to dependence between observations. It also uses volatility data directly quoted on the market in order to avoid the biases which may occur when ‘backing out’ volatility from specific option pricing models. In general, the evidence rejects the hypothesis that the currency option market is efficient. This suggests that implied volatility is not the best predictor of future exchange rate volatility and should not be used without modification: the models presented in this paper could be a way of producing revised forecasts.     

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.     

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.     

Forward interest rate premium and asymmetric adjustment: Evidence from 16 countries

This paper examines the ability of the forward premium to provide an unbiased estimate of the future spot rate allowing for potential asymmetries. Extant evidence suggests that forward rates provide a biased predictor of future spot rates. Examining the forward premium for 16 countries, only for 2 countries does the linear expectations hypothesis holds. For the remaining countries, results generally support the view that the larger the forward premium the better a predictor for future spot rates it is, however, this result is not unique across all countries. Furthermore, although the asymmetric model improves data fit over the linear model, only in four cases does the model support an unbiased predictor interpretation. Further research is therefore required to understand the nature of this relationship, not least given the importance of correctly priced forward and long rates in terms of expected returns to future investments and the conduct of monetary policy.     

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.     

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.     

A Variance-Ratio Test of Random Walks in Foreign Exchange Rates

The separate variance-ratio tests under homoscedasticity and heteroscedasticity both provide evidence rejecting the random walk hypothesis, using five pairs of weekly nominal exchange rate series over the period from August 7, 1974 to March 29, 1989. The rejections cast doubt on the random walk hypothesis in exchange rates, which has received support in the existing literature. Furthermore, since the rejections are robust to heteroscedasticity, they suggest autocorelations of weekly increments in the nominal exchange rate series, which may be consistent with the exchange rate overshooting or undershooting phenomenon.     

Random walk and efficiency tests in the Asia-Pacific foreign exchange markets: Evidence from the post-Asian currency crisis data

This paper empirically tests the random walk and efficiency hypothesis for 12 Asia-Pacific foreign exchange markets. The hypothesis is tested using individual as well as panel unit root tests and two variance-ratio tests. The study covers the high (daily) and medium (weekly) frequency post-Asian crisis spot exchange rate data from January 1998 to July 2007. The inferential outcomes do not differ substantially between the unit root tests and the variance-ratio tests when using daily data but differ significantly when using weekly data. With the daily data, both types of unit root tests identify unit root components for all the series and two variance-ratio tests provide the evidence of martingale behavior for majority of the exchange rates tested. With the weekly data, panel unit root tests identify unit root component for the exchange rates and, the unit root tests on a single series basis identify unit root component for 10 foreign exchange markets. However, the variance-ratio tests reject the martingale null for the majority of the exchange rates when using weekly data.     

Foreign exchange,fractional cointegration and the implied–realized volatility relation

Almost all relevant literature has characterized implied volatility as a biased predictor of realized volatility. In this paper we provide new time series techniques to investigate the validity of this finding in several foreign exchange options markets, including the Euro market. First, we develop a new fractional cointegration test that is shown to be robust to both stationary and non-stationary regions. Second, we employ both intra-day and daily data to measure realized volatility in order to assess the relevance of data frequency in resolving the bias. Third, we use data on implied volatility traded on the market. In contrast to previous studies, we show that the frequency of data used for measuring realized volatility within a fractionally cointegrating framework is important for the results of unbiasedness tests. Significantly, for many popular exchange rates, the use of intra-day rather than daily data affects the emergence of a different bias, as the possibility of a fractionally integrated risk premium admits itself!     

Central bank intervention and the volatility of foreign exchange rates: evidence from the options market

This paper tests the effects of central bank intervention on the ex ante volatility of $/DM and $/yen exchange rates between 1985 and 1991. In contrast to previous research which employed GARCH estimates of conditional volatility, we estimate ex ante volatility using the implied volatilities of currency option prices. We also control for the effects of other macroeconomic announcements. We find little support for the hypothesis that central bank intervention decreases expected exchange rate volatility. Instead, central bank intervention is generally associated with a positive change in ex ante exchange rate volatility, or with no change.     

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.     

Arbitrage, Risk Premium, and Cointegration Tests of the Efficiency of Futures Markets

This article provides a new perspective on the efficiency of futures markets in a cointegration framework. Under the conventional risk premium hypothesis, if futures and spot prices are non-stationary, they must be cointegrated if futures markets are efficient. Alternatively, the cost-of-carry model implies that there should be a cointegration relationship among spot prices, futures prices and interest rates assuming all the series contain a unit root. Market efficiency further implies specific parameter restrictions under these two models. Using data on the futures markets for gold, silver, palladium and platinum, this article first establishes that interest rates, spot and futures prices are unit root non-stationary. The evidence on cointegration is somewhat mixed: the gold futures market is consistent with the cost-of-carry model, and the silver futures market satisfies the risk premium hypothesis, but the evidence for the other two markets is inconclusive.