Conditional variance and the risk premium in the foreign exchange market

SSRN Electronic Journal, 2000

We investigate possible presence of time-varying risk premia in forward pound, yen, and Euro monthly exchange rates versus the US dollar over the last two decades. We study this issue using regression techniques and separately using a signal plus noise model. Our models account for time-varying volatility and non-normality in the observed series. Our regression model rejects the hypothesis that the forward rate is an unbiased predictor of future spot exchange rate, indicating the existence of time-varying risk premium under rational expectations. Our signal plus noise model reveals a time-varying risk premium component in yen and Euro. The same model provides evidence for the presence of risk premium in pound over a shorter sample period, though not over the entire sample. We conclude that risk premia exist, although we may fail to detect these for some currencies over specific time periods. Keywords Spot foreign exchange rates • Forward foreign exchange rates • Time-varying risk premium • Signal extraction • Non-normality • Volatility persistence JEL Classification F31 • C5 • G12 An earlier version of this paper authored by Prasad V. Bidarkota was circulated as, "Risk Premia in Forward Foreign Exchange Markets: A Comparison of Signal Extraction and Regression Methods".

2012

Using Consensus Economics survey data on experts' expectations, we aim to model the 3- and 12-month ahead ex-ante risk premia on the Yen/USD and the British Pound/USD exchange markets. For each market and at a given horizon, we show that the risk premium is well determined by the conditional expected variance of the change in the real exchange rate, agents' real net market position in assets and a constant composite risk aversion coefficient, as suggested by a two-country portfolio asset pricing model. The expected variance depends on the past values of the observed variance and the unobservable real net market position is estimated as a state variable using the Kalman filter methodology. We found that the trends of our estimated horizon-specific net market positions are consistent with the ones of the observed short term aggregate net market positions calculated using the U.S. Treasury International Capital System dataset. Moreover, we show that the ex-post premia tend to...

International Journal of Economics and Financial Issues, 2016

This paper empirically investigates the volatility dynamics of the EUR/USD forward premium via generalized autoregressive conditional heteroscedastic (GARCH-M) (1,1) and Glosten-Jagannathan-Runkle (GJR)-GARCH (1,1) and GJR-GARCH (1,1)-M models. Our empirical analysis is based on daily data related to the EUR/USD forward premiums. Our daily analysis reveals several results. Firstly, we confirm that the 9 month and 1 year forward premiums are explained in large part by their conditional variances. Secondly, according to the theoretical predictions of the asymmetric framework, we show that the conditional variances equations exhibit an asymmetry in the dynamics of the conditional variance only for the 9 months and 12 months horizons. Thirdly, for the 6 month, 9 month and 12 month forward premiums; the GJR-GARCH in mean effect is totally absent

2002

There is a huge literature on the existence of risk premia in the foreign exchange market and its influence in explaining the divergence between the forward exchange rate and the subsequently realised spot exchange rate. In this paper, we seek to model directly the risk premium as a mean-reverting diffusion process. This is done by making use of the spot-forward price relationship and assuming a geometric Brownian process for the spot exchange rate. We are able to obtain a stochastic differential equation system for the spot exchange rate, the forward exchange rate and the risk premium which we estimate using Kalman filtering techniques. The model is then applied to the French Franc/USD and Japanese Yen/USD exchange rates from 1 January 1990 to 31 December 1998. For both currencies our main findings show (i) the persistence of substantial positive time variation in the forward risk premium and its alternating regimes; and (ii) the presence of a term structure of the forward risk premia.

Journal of International Money and Finance, 1986

Fama (1984) analyzed the variability and the covariation of risk premiums and expected. rates of depreciation. We employ three statistical techniques that do not suffer from a potential bias in Fama's analysis, but we nevertheless confirm his findings. In contrast to his interpretation the results are not necessarily at variance with the 'predictions of a theoretical model of the risk premium. Increases in expected rates of depreciation of the dollar relative to five foreign currencies are positively correlated with increases in the expected profitability of purchasing these currencies in the forward market, and risk premiums have larger variances than expected rates of depreciation.

Journal of International Money and Finance, 1993

The hypothesis that the forward rate is an unbiased predictor of the future spot rate has been consistently rejected in recent empirical studies. This paper examines several sources of measurement error and misspecification that might induce biases in such studies. Although previous inferences are shown to be robust to a failure to construct true returns and to omitted variable bias arising from conditional heteroskedasticity in spot rates, we show that the parameters were not stable over the 1975-89 sample period. Estimation that allows for endogenous regime shifts in the parameters demonstrates that deviations from unbiasedness were more severe in the 1980s. (JEL F31). This paper reexamines the relation of the forward premium in the foreign exchange market to the expected rate of currency depreciation over the life of the forward contract. For at least ten years, empirical studies of this relation have regressed ex post rates of depreciation on a constant and the forward premium. Their null hypothesis is that the slope coefficient is one. Researchers have consistently found point estimates of the slope coefficient that are negative and that are often more than two standard errors from zero. Predicted currency depreciation is therefore very different from the forward premium whereas the unbiasedness hypothesis implies that they are equal.

2001

We provide new representations for the risk premium and expected exchange rate change. According to our representations they are a function of the term premium. In particular, we obtain that investors require higher interest rates on currencies expected to fall if the term premium is expected to stay constant. Moreover, our representations are such that the risk premium is very volatile and negatively correlated with the expected depreciation rate.

2003

Economists have long been perplexed by the negative relationship between short-run exchange-rate changes and interest differentials, known as the "forward premium puzzle." This paper develops an exchange-rate model that accounts for all of the notable empirical regularities associated with this puzzle. The model focuses on short-run exchange-rate dynamics, consistent with the short-run focus of the puzzle. This short-run focus, together with recent evidence on currency market microstructure, explains why the model incorporates a central role for flow demand and supply. In modeling speculative agents we note that, because of agency problems, short-term traders are encouraged to focus on profits rather than consumption. The model's clear analytic solutions show that risk premiums can be time varying and strongly negatively related to interest differentials. Simulations show that the volatility of exchange-rate returns exceeds the volatility of both interest differentials and forward premiums, and that exchange-rate persistence is quite low while that of expected excess returns is fairly high. Regression estimates using quarterly data for five currencies pr ovide strong support for the model, suggesting that currency microstructure may have macroeconomic relevance.

International Journal of Risk Assessment and Management, 2003

This paper investigates the relationship between the excess returns of foreign exchanges and the conditional volatility of domestic and foreign equity markets, based on a wide range of foreign currency market data. Utilising a VAR-GARCH-in-mean process to generate conditional variances, we find evidence to support the time varying, risk-premium hypothesis. Moreover, our evidence shows that the volatility evolution of stock returns displays not only a clustering phenomenon, but also a significant spillover effect. Given the fact that the correlation structure across markets is significant and time varying, investors and portfolio managers should continually assess this information and rebalance their portfolios over time to achieve optimal diversification.

2019

In this paper, we empirically examine time-varying risk premia in the Tunisian foreign exchange market by applying GARCH-M modeling to the TND/Euro and TND/USD parities for 1 to 12 months forecasting horizons. Our ultimate objective is to help better manage the parities and to help provide stability to a foreign exchange market where EMH is very weak. Our findings show 1) a heteroscedasticity of residuals for the TND/Euro (all forecasting horizons) and the TND/USD(for 1 month) indicating a lack of stability of their volatility; 2) a non-significant standard deviation of the risk premium against the presence of ARCH and GACH in all cases. On the other hand, the descriptive analysis of the risk premium and term premium variables show an asymmetric distribution. We used, therefore, the asymmetric GARCH model, E-GARCH. Our normality tests show, however, that the GARCH model neither allows for residuals smoothing nor improves the AIC.

Studies in Computational Finance, 2000

There is a huge literature on the existence of risk premia in the foreign exchange market and its influence in explaining the divergence between the forward exchange rate and the subsequently realised spot exchange rate. In this paper, we seek to model directly the risk premium as a mean-reverting diffusion process. This is done by making use of the spot-forward price relationship and assuming a geometric diffusion process for the spot exchange rate. We are able to obtain a stochastic differential equation system for the spot exchange rate, the forward exchange rate and the risk premium which we estimate using Kalman filtering techniques.

Review of Financial Studies, 1992

Review of International Economics, 2003

The hypothesis that the forward rate is an unbiased predictor of the future spot rate has been rejected in many empirical studies. The rejection of this hypothesis could occur because market behavior is inconsistent with rational-expectations or because there exists a risk premium. Equations describing the forward premium and the change in the exchange rate are estimated jointly, and tests of both the rationalexpectations and no-risk-premium hypotheses are conducted. Empirical estimates, obtained using quarterly data for the yen-dollar exchange rate, reject the rational-expectations hypothesis and suggest that there exists a time-varying risk premium.

2016

This paper empirically examines the interdependence between the foreign exchange forward premiums and the spot exchange return through a multivariate generalized autoregressive conditional heteroskedasticity type framework. The purpose of this study is to test the correlation sensitivity to shocks and the to capture the dynamic links between the EUR/USD 1, 3, 6, 9 and 12 months forward premiums and the spot exchange return. Our empirical analysis is based on daily data from. Our daily analysis reveals the presence of high correlations between the unconditional EUR/USD forward exchange premiums at different horizons and the possible effect of asymmetric shocks on the conditional variance. The estimation results show that the dynamic conditional correlations have a relatively small and insignificant autoregressive effect, in addition to the existence of significant correlation sensitivity to shocks.

2002