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.     

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 Term Structure of Real Rates and Expected Inflation

Changes in nominal interest rates must be due to either movements in real interest rates, expected inflation, or the inflation risk premium. We develop a term structure model with regime switches, time‐varying prices of risk, and inflation to identify these components of the nominal yield curve. We find that the unconditional real rate curve in the United States is fairly flat around 1.3%. In one real rate regime, the real term structure is steeply downward sloping. An inflation risk premium that increases with maturity fully accounts for the generally upward sloping nominal term structure.     

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.     

Currency futures-spot basis and risk premium

This paper explores the usefulness of currency futures-spot basis in predicting spot rate changes and currency futures returns. We conjecture that the currency risk premium may be an important component of the basis for long-maturity futures contracts, but may not be so for short-maturities. Thus, the basis of long-maturity contracts cannot predict the spot rate changes between now and maturity, rejecting uncovered interest rate parity (UIP), but can predict currency futures returns, which are solely determined by the risk premium. Conversely, the basis of the short-maturity contracts can predict the spot rate changes between now and maturity, validating the UIP, but cannot predict currency futures returns. Empirical tests support these conjectures for the Japanese, British, Swiss, and German currencies over the last two decades. The results are also consistent with Longstaff [Longstaff, F., 2000. The term structure of very short-term rates: new evidence for the Expectation Hypothesis. Journal of Financial Economics 58, 397–415], who shows that the Expectations Hypothesis holds at the very short end of the term structure of interest rates.     

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.     

Policy coordination and risk premium in foreign exchange markets for major EU currencies

This study investigates cointegration, policy coordination and the risk premium in foreign exchange markets for major EU currencies since the inception of the EMU in January 1999. The results show that only the krone and the pound are cointegrated with the euro. Tests of inflation convergence and analyses of reduced-form and structural VARs indicate that the cointegration evidence reflects the relatively stronger degree of monetary policy coordination and at least the de facto fixed exchange rate regime of Denmark and the U.K. with the EMU. Additionally, cointegration of spot exchange rates can be considered one of the factors that represent the time-varying risk premium due to its explanatory power for the return to forward speculation.     

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.     

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.     

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 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.     

Measuring the forward foreign exchange risk premium: multi-country evidence from unobserved components models

We investigate the nature of the foreign exchange risk premium for a wide range of currencies, using unobserved components models with exactly matched spot and forward exchange rate data. Significant time-variation of the risk premium is documented for most currencies. Our estimates indicate considerable persistence in the risk premium, and suggest that the variability of the risk premium is quite low relative to the variability of the forward forecast error.     

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.     

Optimal Portfolio Choices, House Risk Hedging and the Pricing of Forward House Transactions

This paper develops a utility indifference model for evaluating various prices associated with forward transactions in the housing market, based on the equivalent principle of expected wealth utility derived from the forward and spot real estate markets. Our model results show that forward transactions in the housing market are probably not due to house sellers?? and buyers?? heterogeneity, but to their demand for hedging against house price risk. When the imperfections of real estate markets and the risk preferences of market participants are taken into consideration, we are able to show that the idiosyncratic risk premium, which mainly depends on the participants?? risk preferences and the correlation between the traded asset and the real estate, is a remarkable determinant of house sellers?? and buyers?? forward reservation prices. In addition, we also find that the market clearing forward price usually will not converge toward the expected risk-neutral forward price. The sellers?? or buyers?? risk aversion degrees and market powers are also identified to play crucial roles in determining the clearing forward price.     

The Forward Premium in the Nord Pool Power Market

This article investigates the forward premium of futures contracts in the Nordic power market for the time period from January 2004 to December 2013. We find that futures prices are biased predictors of the subsequent spot prices and that there is a significant forward premium in the Nord Pool market, particularly during the winter and autumn. We analyze the impact from several factors on the forward premium. The spot price, and the deviation of water inflow from its usual level, positively affect the forward premium. The variance of the spot price also has a positive effect on the forward premium, but only for the contract closest to delivery.     

交易所国债期限风险溢价的实证研究

本文考察了上海证券交易所国债期限风险溢价的时间变化特征及决定因素。实证结果显示，债券剩余期限越长，平均风险溢价越高；通过对不同期限债券组合的风险溢价序列建立回归模型，发现长短期利差及风险溢价的前期值对中长期债券期限风险溢价的时变性具有明显的解释能力。     

The Forex Forward Puzzle: The Career Risk Hypothesis

We conjecture that the forward puzzle may reflect career risks. When professional investors observe public danger signals about a currency, they require a premium for holding it. We find evidence of this in Exchange Rate Mechanism rates. As deep discounts do signal danger, we next specify nonlinear variants of the Fama regression to capture this risk. We also decompose the forward premium into a long-memory trend and short-term component. We find empirical evidence for a career risk premium; risk is in fact dominant in the trend component while the short-term component loads more on expectations. All confidence intervals are calculated via Monte Carlo.     

The predictive performance of the currency futures basis for spot returns

This paper investigates the predictive performance of the futures basis in directly forecasting currency spot returns and compares it with that of the one-month forward basis. We consider the settle prices of both front-month and nearby-month continuous futures contracts and find that the futures basis exhibits statistically and economically significant in-sample and out-of-sample forecasting power, which clearly exceeds that of the well-known forward basis. The empirical results show that spot returns correspond negatively to both the front-month futures basis and nearby-month futures basis. Furthermore, the futures basis reveals substantial economic value for investors in terms of sizable and tangible portfolio gains, which are consistent with statistical measures. The difference in the forecasting ability of the futures basis and forward basis can be explained by the level of exposure to the time-varying risk premium. Finally, we find that impacts of the futures basis on spot returns vary with time and experienced substantial structural changes during the Global Financial Crisis.     

An Analysis of Intertemporal Pricing for Forward Foreign Exchange Contracts

An asset-pricing model with an unobservable time-varying risk premium is used to price forward foreign exchange contracts. Specifically, the term spectrum of forward foreign exchange contracts is examined in order to focus on country-specific and maturity-specific information. The testable restrictions imposed by the model are consistent with both cross-country and cross-maturity forward contracts except at the short end of the maturity spectrum for cross-country forward exchange rates. This indicates that the intertemporal model is relatively robust in valuing forward contracts of different maturities and for different exchange rates but that it may fail when there are significant short-term country-specific shocks.     

Can exchange rate volatility explain persistence in the forward premium?

The persistence of the forward premium has been cited both as evidence of the failure of the unbiasedness hypothesis and as rationale for the forward premium anomaly. This paper examines the recent proposition that forward premium persistence can be explained solely by the conditional variance of the spot rate. We provide theoretical and empirical evidence to challenge this proposition. Our empirical results are shown to be robust to the presence of structural breaks. A corollary of the results is that the ‘true’ risk premium contains a long memory component. This is non-standard and has implications for the construction of rational expectations models of the foreign exchange market.