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 INFORMATIONAL CONTENT OF FORWARD RATES: FURTHER EVIDENCE

Using single-equation estimation techniques, researchers have generally found that forward rates have little ability to predict future spot rates. In this paper, Generalized Least Squares is used to estimate simultaneously the forecastive ability of multiple forward rates. It is discovered that current forward rates significantly predict future spot rates for various rate maturities up to twelve months ahead. Also found are instances in which the Treasury bill market does not conform to the weak form of market efficiency.     

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.     

On the informational content of spot and forward exchange rates

In foreign exchange markets, efficiency tests have typically been applied to the forward rate on the argument that the forward rate should be a good proxy for the unobservable market expectations of future spot rates. The present study offers innovations in two directions. First we utilize a data set which consists of daily observations on spot and forward exchange rates. This allows us to match the forward contract with the exact settlement date and to create a large number of non-overlapping data sets. Second, and more importantly, we show that in general the current spot rate is a ‘better’ predictor of the future spot rate than is the current forward rate of appropriate maturity.     

The information in the term structure

This paper presents a regression approach to measuring the information in forward interest rates about time varying premiums and future spot interest rates. Like earlier work, the regressions identify variation in the expected premiums on longer-maturity Treasury bills. The more novel evidence concerns the forecasts of future spot rates in forward rates. The regressions provide evidence that the one-month forward rate has power to predict the spot rate one month ahead. During periods preceding 1974, forward rates have reliable forecast power for one-month spot rates up to five months in the future.     

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 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.     

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.     

Spot and forward rates in the Canadian treasury bill market

The efficiency of the Canadian Treasury bill market is examined with data on spot and forward rates of return. Over the period from 7/62 to 3/79, the bill market has been efficient in the sense that it correctly uses the information contained in past spot rates in assessing the expected future spot rate and in determining the forward rate. Moreover, the forward rate is found to contain some information about future spot rates above and beyond that in past spot rates.     

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.     

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.     

Forward rates as predictors of future spot rates

When adjusted for variation through time in expected premiums, the forward rates of interest that are implicit in Treasury Bill prices contain assessments of expected future spot rates of interest that are about as good as those that can be obtained from the information in past spot rates. Moreover, in setting bill prices and forward rates, the market reacts appropriately to the negative autocorrelation in monthly changes in the spot rate and to changes through time in the degree of this autocorrelation. This evidence is consistent with the market efficiency proposition that in setting bill prices, the market correctly uses the information in past spot rates.     

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.     

The Behavior of Interest Rates

The evidence in Fama and Bliss (1987) that forward interestrates forecast future spot interest rates for horizons beyonda year repeats in the out-of-sample 1986–2004 period.But the inference that this forecast power is due to mean reversionof the spot rate toward a constant expected value no longerseems valid. Instead, the predictability of the spot rate capturedby forward rates seems to be due to mean reversion toward atime-varying expected value that is subject to a sequence ofapparently permanent shocks that are on balance positive tomid-1981 and on balance negative thereafter.     

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.     

The bias of tests for a risk premium in forward exchange rates

The pure expectations theory of unbiased forward exchange rates predicts that the slope coefficient in a regression of the change in the spot rate on the difference between the current forward and spot rates should equal unity. In the recent empirical work by Fama, the estimates of this coefficient turn out to be negative in all regressions for nine major industrialized nations. This paper demonstrates that under the expectations theory, the sampling distribution of the regression estimator of this coefficient is upward-biased relative to unity and strongly skewed to the right. The likelihood of negative values is essentially zero. Thus, the estimator is biased in a direction opposite to what is observed. Since the observed estimates lie far out in the thin left-hand tail of the estimator's sampling distribution, the evidence against the hypothesis of unbiased forward rates is much stronger than previously believed.     

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).     

Do forecast errors or term premia really make the difference between long and short rates?

Forward rates in the term structure of interest contain predictions of future spot rates plus (possibly) term premia. Realized spot rates contain predicted spot rates plus forecast errors. Under rational expectations forecast errors are not predictable. By forecasting spot rates using publicly available information, bounds on the variation of forecast errors, and term premia are obtained. For one-month treasury bill rates, one to two thirds of the variation in the difference between forward rates and realized spot rates is due to variation in term premia.     

Spot versus forward speculation and hedging: A diagrammatic exposition

It has recently been recognized that the controversial implication of the Modern Theory of Forward Exchange, that the forward rate can differ from the rate required for interest parity, no longer holds when speculators are allowed to choose between spot and forward speculation. This paper shows this result within the diagrammatic apparatus usually used to describe the Modern Theory. The paper also shows the effect of importers and exporters choosing between spot and forward hedging. It is observed that when either speculators or traders can choose between money market and forward speculation/hedging, forward rates equal interest parity rates. The diagram can be adapted to consider borrowing-lending spreads etc.     

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.