Foreign exchange risk premia: from traditional to state-space analyses

📝 Abstract

This paper examines foreign exchange risk premia from simple univariate regressions to the state-space method. The adjusted traditional regressions properly figure out the existence and time-evolving property of the risk premia. Successively, the state-space estimations overall are quite rationally competent in examining the essence of time variability of the unobservable risk premia. To be more precise, the coefficients on the lagged estimated time-series are significant and the disturbance combined from the observation and transition equations in the state-space system, rational and premium errors, respectively, is statistically white noise. Such the two residuals are discovered to move oppositely with their covariance approaching zero suggested by the empirics. Besides, foreign exchange risk premia are projected and found significantly stationary at level and relatively volatile throughout time with some clustering. This volatility is however not quite dominant in the deviations of forward prediction errors.

💡 Analysis

This paper examines foreign exchange risk premia from simple univariate regressions to the state-space method. The adjusted traditional regressions properly figure out the existence and time-evolving property of the risk premia. Successively, the state-space estimations overall are quite rationally competent in examining the essence of time variability of the unobservable risk premia. To be more precise, the coefficients on the lagged estimated time-series are significant and the disturbance combined from the observation and transition equations in the state-space system, rational and premium errors, respectively, is statistically white noise. Such the two residuals are discovered to move oppositely with their covariance approaching zero suggested by the empirics. Besides, foreign exchange risk premia are projected and found significantly stationary at level and relatively volatile throughout time with some clustering. This volatility is however not quite dominant in the deviations of forward prediction errors.

📄 Content

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Foreign exchange risk premia:
from traditional to state-space analyses

Siwat Nakmai* 15 April 2016 Abstract This paper examines foreign exchange risk premia from simple univariate regressions to the state-space method. The adjusted traditional regressions properly figure out the existence and time-evolving property of the risk premia. Successively, the state-space estimations overall are quite rationally competent in examining the essence of time var- iability of the unobservable risk premia. To be more precise, the coefficients on the lagged estimated time-series are significant and the disturbance combined from the ob- servation and transition equations in the state-space system, rational and premium er- rors, respectively, is statistically white noise. Such the two residuals are discovered to move oppositely with their covariance approaching zero suggested by the empirics. Be- sides, foreign exchange risk premia are projected and found significantly stationary at level and relatively volatile throughout time with some clustering. This volatility is how- ever not quite dominant in the deviations of forward prediction errors.

Keywords: foreign exchange risk premia, univariate regressions, state-space modeling, Kalman filter

JEL classification: C20, C32, F31

1. Introduction In foreign exchange markets, there exist risk premia once forward rates differ from an- ticipations with the same horizon. Nevertheless, the risk premia are unobserved due to unobservable expectations. Hypothetically, they are temporally inherent in the linear dynamic system of forward pricing. To build up the system, it can be in a state-space representation, accounting for the unobservability and changeability in time of the var- iable of interest, which is the unseen risk premia in this paper. To proceed a risk-pre- mium state-space analysis, it may be more convincing to begin at a foundation. Thus, to do so, it is perhaps to understand and model the risk premia steadily from fundamentals, which are traditional-based univariate regressions, progressively to a generalized state- space approach with its Kalman-filter algorithm and log likelihood function. Accordingly, this risk-premium-analytic paper is outlined as background, theoretical framework, data descriptions and statistics, and empirics, respectively.

• Certified FRM, currently PhD economics candidate at Catholic University of Milan, Italy. E-mail: siwat.nakmai@unicatt.it

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2. Background In studying foreign exchange risk premia, Fama (1984) employed univariate regressions to explore the existence of time-variant risk premia. Later, Wolff (1987) identified and measured the risk premia in forward valuation via state-space constructions. He found that the state-space methodology is operative in grabbing the core of the time-series characters of the risk premia, which are also time persistent and prevailing in forward- error fluctuations. As Wolff (1987) simply and theoretically imposed that the covariance of rational and premium errors is zero, Cheung (1993) relaxed this assumption and suc- cessfully discovered that such non-zero covariance improved his modeling as obtaining larger maximum log likelihood values. He showed that the risk premia are stationary and highly persistent and the covariations between risk premia and unexpected cur- rency changes are negative. Along these, this paper attempts to go over foreign-ex- change-risk-premia analyses stage by stage. In doing so, Fama-related (1984) univariate regressions are done prior to conducting studies similar to Wolff (1987) and Cheung (1993). Pertaining to the sample, it is maybe better to take in hand currencies with their forward dynamics that have been significantly natural as long as possible up to the pre- sent time (i.e. almost fully floating and having considerably lengthy data series). With the US dollar (USD) as the domestic currency as usual, the foreign exchanges selected are one that is experienced, which is the Great British pound (GBP), and the other that is promising, which is the Hong Kong dollar (HKD). The former has been very well es- tablished in forwards market since January 1979. For the latter, Hong Kong is known as one of the largest financial hubs in Asia while its currency forwards have been more newly recognized since January 1996. Both are also considered ones of the most liquid and floating currencies for decades in financial markets globally.1

3. Theoretical framework Prior to analyzing foreign exchange risk premia in a state-space scheme, which is initi- ated upon their unobservable and time-varying characteristics, the relevant definitions and traditional-based structure are formerly considered in order to realize such unob- servability and time variation.

3.1 Traditional-based modeling Consistent with Fama (1984), rec

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