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.     

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.     

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.     

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.     

Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets

Spot power prices are volatile and since electricity cannot be economically stored, familiar arbitrage-based methods are not applicable for pricing power derivative contracts. This paper presents an equilibrium model implying that the forward power price is a downward biased predictor of the future spot price if expected power demand is low and demand risk is moderate. However, the equilibrium forward premium increases when either expected demand or demand variance is high, because of positive skewness in the spot power price distribution. Preliminary empirical evidence indicates that the premium in forward power prices is greatest during the summer months.     

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.     

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.     

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.     

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 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.     

Forward exchange rates in general equilibrium

This paper develops a two-country, overlapping-generations model of an economy with a forward market in foreign exchange. The equilibrium forward rate exhibits the conventional decomposition into the expected future spot rate, a convexity term and a risk premium. Unlike partial equilibrium models, however, the model expresses these terms as functions of the primitive structural parameters of the economy. It thus provides insights into the structure of the premium which may facilitate interpretation of empirical studies of the forward markets. In particular, it suggests that time-varying risk premia may arise from changes in the distribution of wealth between countries over time.     

The Relation Between Default-Free Interest Rates and Expected Economic Growth Is Stronger Than You Think

The relation between default-free interest rates and expected economic growth is substantially stronger than suggested by extant literature. Futures-implied Treasury bill yield spreads are more highly correlated with future real consumption, investment, and GNP growth than spot spreads. This stronger relation arises because using futures removes a component of the spot term structure that covaries negatively with real economic growth. Treasury forward rates from spot bills contain a premium for the risk that short-sellers will default. This risk premium is negatively related to expected economic growth.     

An Option-Pricing Approach to the Costs of Export Credit Insurance

This article investigates the relationship between a debtor country's external financial indicators and the costs associated with the insurance of export credits to that country. For this purpose a stylized model of export credit insurance (ECI) is developed, the central idea being that ECI is similar to a contingent claim such as a European put option. Thus, tools from option pricing theory were used to calculate the price of ECI, implying that not only the current financial position but also the volatility of the changes in that position determine such costs. The empirical results of a statistical analysis of the premium rates for ECI, applied by a private export credit insurer to seventy-seven developing countries during 1993, provide some support for these hypotheses. In particular, the reserves-over-imports ratio of a debtor country and the volatility of the rates of change of this ratio appear to contribute significantly to the premium rates that apply to that country. Thus, the article provides evidence that option pricing parameters do play role in practical insurance pricing, even if this pricing is not explicitly based on these parameters. Premium rates are set as if an underlying option market operated. Thus, the trade of countries with volatile external financial positions is saddled with higher costs than that of countries with more stable positions.     

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.     

Implicit Inflation and Risk Premiums in the Brazilian Fixed Income Market

The breakeven inflation, the differential between nominal and real yields of bonds, is often used as a predictor of future inflation. The model presented here decomposes this interest rate differential into a risk premium and implicit inflation using a parametric formulation based on no-arbitrage conditions using nominal and indexed yield curves in Brazil, via an affine model of the Nelson–Siegel family. The measures of implicit inflation obtained from the model are shown to be unbiased estimators of future inflation for short horizons and carry some information for long horizons, and the model forecasts are superior to market surveys.     

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.     

Modelling the Currency Forward Risk Premium: A New Perspective

In this paper we seek to develop a new approach to the time series analysis of foreign exchange risk premia. We do so by assuming a geometric Brownian process for the spot exchange rate and expressing the no-arbitrage spot-forward price relationship under the historical probability measure. We are thereby able to obtain a stochastic differential equation system linking the spot exchange rate, the forward exchange rate and the risk premium (modelled directly as a mean-reverting diffusion process) which we estimate using Kalman filtering techniques. We are able to use observations at a range of frequencies since the framework we set up does not involve overlapping observations. The model is then applied to the French Franc/USD, DEM/USD, GBP/USD, and Japanese Yen/USD exchange rates from 1 January 1990 to 31 December 1998. For all currencies we find evidence that the forward risk premium is stationary and exhibits substantial positive time variation.     

Pricing Efficiency and Arbitrage in the Bitcoin Spot and Futures Markets

This study examines the pricing efficiency for the leading cryptocurrency, Bitcoin using spot prices and all CBOE and CME futures contracts traded from January 2018 to March 2019. We find that the futures basis provide some predictive power for future changes in the spot price and in the risk premium. However, the basis of Bitcoin is a biased predictor of the future spot price changes. Cointegration tests also demonstrate that futures prices are biased predictors of spot prices. Deviations from no-arbitrage between spot and futures markets are persistent and widen significantly with Bitcoin thefts (hacks, frauds) as well as alternative cryptocurrency issuances.     

Spot rates,forward rates and exchange market efficiency

This paper examines the relationship between forward exchange rates and subsequently observed spot rates. No evidence is found for a liquidity premium on forward exchange, indicating that the forward rate can be used as a proxy of the market's expectations and that open exchange positions involve little systematic risk. It is also shown that forward exhange is priced as if the exchange rate could be characterized by a diffusion process with a trend, although there is some evidence such a process does not adequately characterize the exchange rate in all cases.     

The expectations hypothesis: New hope or illusory support?

Recent studies of the expectations hypothesis of the term structure (EHTS) find evidence in favor of the EHTS using post 1980s US data. This has been attributed to the relative macro stability of this period and greater market efficiency. Using a panel of forecasts for 3-month interest rates for ten countries we test separately for EHTS and rational expectations. Assuming rational expectations holds we find support for the EHTS is illusory due to an off-setting time-varying term premia and non-rational expectations. Previous forecast-based studies suggest biased expectations tend to reinforce the effect of a time varying term premium. This change can be understood in the context of Fama’s (2006) argument that markets tend to underestimate future spot rates during periods of long-run increases and overestimate during declines.