Abstract
The forward premium anomaly refers to the fact that changes in spot exchange rates are negatively related to interest rate differentials between home and foreign countries, which is contrary to the predictions of the uncovered interest rate parity (UIRP). We propose a regression model of the interest rate differentials across countries (known as carry trade) adjusted for a time-varying exchange rate risk premium which can explain the anomaly and provide forecasts of exchange rate changes in accordance to the theory. The proposed model is based on estimates of the exchange rate risk premium implied by a simple and empirically attractive two-country affine term structure model with global and local factors. We also show that the forecasting power of the model compares favorably to the random walk model of exchange rates, considered as benchmark in the literature.
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Notes
Alternative theories include the following: peso problems due to missed regime shifts by investors (see Evans and Karen 1995), exchange rate stabilization monetary policy rules smoothing out exchange rate changes (see McCallum 1994), sticky prices yielding time-varying real exchange rate deviations from the PPP (purchasing power parity) (see, e.g., see Meese and Rogoff 1988, and more recently Boudoukh et al. 2016) and measurement errors combined with small magnitudes of interest rate differentials, see, e.g., Lothian and Wu (2011).
See Dai and Singleton (2002).
Note that the common factor structure of x1t and x2t across countries allows us to retrieve local factors \(x_{3t}^{(j)}\) based on the spreads of interest rates \(R_{t}^{(h)}(\tau )-R_{t}^{(f)}(\tau )\), for τ = {τ1,τ2}, by inverting the following relationships:
$$ \begin{array}{@{}rcl@{}} R_{t}^{(h)}(\tau_{1})-R_{t}^{(f)}(\tau_{1})&=&A^{(h)}(\tau_{1})-A^{(f)}(\tau_{1})+D_{3}^{(h)}(\tau_{1})x_{3t}^{(h)}-D_{3}^{(f)}(\tau_{1})x_{3t}^{(f)} \\ R_{t}^{(h)}(\tau_{2})-R_{t}^{(f)}(\tau_{2})&=&A^{(h)}(\tau_{2})-A^{(f)}(\tau_{2})+D_{3}^{(h)}(\tau_{2})x_{3t}^{(h)}-D_{3}^{(f)}(\tau_{2})x_{3t}^{(f)} \end{array} $$Then, given \(x_{3t}^{(h)}\) and \(x_{3t}^{(f)}\), we can retrieve x1t and x2t by also inverting (6), for τ1 and τ2.
For Germany, we have used the euro conversion rate of the Deutsche Mark (DM) (i.e., 1.95583) to participate in the EMS to calculate the series of the currency rate of this country with respect to USD after the introduction of Euro as the single currency in 1999. See also Diez de los Rios and Sentana (2011).
Note that Eurocurrency deposits are essentially zero-coupon bonds whose payoffs at maturity are the principal plus the interest payment. Eurocurrency deposit rates are used in many studies testing the predictions of the UIRP (see, e.g., Olmo and Pilbeam2011).
Note that ℘t(τ) constitutes a good proxy of the exchange rate risk premium implied by interest rate differential \(R_{t}^{(h)}(1)-R_{t}^{(f)}(1)\), for a small maturity τ and interval of time. This regression model corresponds to Eq. 9 - see Ahn (2004), and it is in the spirit of the regression models of Tzavalis (2003), and Argyropoulos and Tzavalis (2019) adjusting the term spread of interest rates for risk premium effects in order to forecast future changes in short-term interest rates or inflation rate changes, respectively.
This method has been suggested in the term structure of interest rates literature to capture the effects of the risk premium on the term spread in forecasting future short-term interest rates by Driffill et al. (1997).
Note that, for models M1 and M2, the DM test statistic is based on the forecast loss function \(d_{t+j}=\left (u_{t+j}^{(M1)}\right )^{2}-\left (u_{t+j}^{(M2)}\right )^{2}\). Given dt+j, DM is defined as \(DM=\left (\frac {1}{T-T_{0}}{\sum }_{j=T_{0}+1}^{T}d_{t+j}\right ) \hat {\sigma _{d}}^{1/2}\), where T0 is the initial, in-sample window of the sample and \(\hat {\sigma _{d}}\) is the long-run variance of dt+j, which can be consistently estimated based on Newey and West (1987) estimator.
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We thank James Payne (the editor) and three anonymous referees for very helpful comments on an earlier version of the paper. We acknowledge financial support provided by the operational program “Human Resources Development, Education and Lifelong Learning” co-financed by the European Union (European Social Fund) and Greek national funds. Also, we would like to thank Thanasis Stengos and participants at the C.R.E.T.E. conference 2018, for useful comments on an earlier version of the paper. The views expressed in this paper are those of the author and do not necessarily reflect the views or policies of the IMF, its Executive Board, or IMF management.
Appendix
Appendix
In this appendix, we present descriptive statistics, including correlation coefficients among interest rates \(R_{t}^{(j)}(\tau )\), for maturity intervals τ = {1, 3, 6, 12} months, and risk premium ℘t(τ) across all countries j (see Tables 5, 6 and 7). Figure 1 graphically presents the estimates of ℘t(τ).
Exchange rate risk premium ℘t(τ)
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Argyropoulos, E., Elias, N., Smyrnakis, D. et al. Can country-specific interest rate factors explain the forward premium anomaly?. J Econ Finan 45, 252–269 (2021). https://doi.org/10.1007/s12197-020-09509-5
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DOI: https://doi.org/10.1007/s12197-020-09509-5
Keywords
- UIRP
- Two-country affine term structure model
- Forward premium anomaly
- Exchange rate forecasting
- Expectations hypothesis