EMS exchange rate expectations and time-varying risk premia

Transcription

1 Economics Letters 60 (1998) EMS exchange rate expectations and time-varying ris premia a b c,d, * Frederic G.M.C. Nieuwland, Willem F.C. Verschoor, Christian C.P. Wolff a Algemeen Burgerlij Pensioenfonds, Heerlen, The Netherlands b De Nationale Investeringsban, The Hague, The Netherlands c Limburg Institute of Financial Economics (LIFE), Maastricht University, P.O. Box 616, 600 MD Maastricht, The Netherlands d CEPR, London, UK Received 8 January 1998; accepted 7 May 1998 Abstract In this paper we examine exchange ris premia employing a survey dataset of EMS exchange rates. We are able to test a ris premium model directly, i.e. without having to rely on the rational expectations assumption. Our results indicate that time-varying ris premia are present in almost all cases and that a GARCH-in-mean specification for the premium is often appropriate Elsevier Science S.A. All rights reserved. Keywords: Exchange rates; EMS; Ris premia; survey data JEL classification: F31 1. Introduction One of the well-estabished empirical regularities in the financial economics literature is the finding that the forward discount is a biased predictor of the future change in the exchange rate. The rejection of forward maret efficiency is generally attributed to irrational expectations and time-varying ris premia. See, e.g., Franel and Froot (1987); Cavaglia et al. (1994). Alternative methodologies have been explored in the literature to model and measure time-varying ris premia. In an interesting contribution Domowitz and Haio (1985) proposed a model in which ris premia are embedded in an autoregressive conditional heterosedasticity (ARCH) framewor. Their approach is conditional on the hypothesis that the forward exhange maret is efficient or rational. In this paper we study European Monetary System (EMS) currency marets. We model ris premia using an approach that builds on the Domowitz and Haio analysis. Our approach implements a survey database of exchange rate expectations, covering a wide range of EMS exchange rates. The principal benefit of employing such data is that one obtains a direct measure of agent s beliefs. Whereas the Domowitz and Haio study proceeds conditional on the assumption that expectations are rational, we are able to test the ris premium model directly, based on observed expectations. Our survey dataset is described in detail in Cavaglia et al. (1993), (1994). *Corresponding author. Tel.: ; fax: ; c.wolff@berfin.unimass.nl / 98/ $ Elsevier Science S.A. All rights reserved. PII: S (98)0018-1

2 35 F.G.M.C. Nieuwland et al. / Economics Letters 60 (1998) The paper is organized as follows. In Section we briefly describe the survey dataset. In Section 3 the methodology is explained. The empirical results are presented in Section 4 and our conclusions in Section 5.. The survey data From 1986 through 1991, Business International Corporation conducted a monthly survey of exchange rate expectations covering five European currencies relative to the Deutschmar, which were published in its Cross Rates Bulletin. For publication purposes, survey participants were ased a few days prior to the end of the month to fax 3, 6 and 1 month-ahead expectations of currencies with projections being made from the beginning of the following month. Thus, for instance, the 3, 6 and 1 month-ahead expected French franc/ German mar rates recorded on December 7th, 1990, reflect slightly longer forecast horizons as they represent the spot rates expected for April 1st, 1991, July 1st, 1991, and January nd, 199, respectively. The dates when the surveys were conducted were recorded, as well as the spot and 3, 6, and 1 month forward rates on that particular day. 3. Measuring time-varying ris premia: methodology In order to test whether the existence of time-varying ris premia is the economically important reason for rejection of forward maret efficiency, the following equation is often fitted in the literature [see Franel and Froot (1987); Cavaglia et al. (1994)]: ES S 5 a 1 b(f S ) 1 (1) t t1 t t,t1 t t where St is the natural logarithm of the spot exchange rate, Ft,t1 is the logarithm of the forward rate at t for delivery at t1. and ES t t1 is the expectation of St1 which is formed at time t. The null hypothesis of perfect substitutability implies that a 50 and b 51. Under the hypothesis that the correlation of the ris premium with the forward discount is zero, b will equal 1. Fitting Eq. (1) to the data by ordinary least squares, appropriately adjusting standard errors to reflect the overlapping nature of the data, we find for our sample (results not shown) that the joint hypothesis a 50 and b 51 as well as the simple hypothesis b 51 are rejected in almost all cases. Thus, variation in the forward discount for EMS currencies reflects a statistically significant degree of variation in the ris premium. Diagnostic checs on the residuals of the even regression equations reveal the presence of conditional heterosedasticity in the residual t, at the longer forecast horizons. This evidence contrasts with the results of Domowitz and Haio, who found no significant ARCH effects, except for the case of the Japanese Yen. Based on the utility optimizing models with money growth by Lucas (198), Domowitz and Haio presented an international asset pricing model in which the ris premium is a function of the conditional variances of domestic and foreign money supplies. We use their model as a starting point to model EMS exchange ris premia, but in the light of the apparent irrationality of expectations on the part of maret participants, we do not impose rational expectations but, instead, test the model directly on the basis of our survey data.

3 The model we study is the following: F.G.M.C. Nieuwland et al. / Economics Letters 60 (1998) ES S 5 RP 1 b (F S ) 1 () t t1 t t 1 t,t1 t t t 0 t RP 5 b 1uh (3) ui N(0,h ) (4) t t1 t t 0 1 t11 g1h t1 h 5 a 1 a (5) Eqs. () (5) represent a GARCH-in-mean model of the ris premium, RP. The specification is slightly more general than Domowitz and Haio (1985), who study an ARCH-in mean model. The conditional volatility of t, h t, plays a dual role: it also enters the ris premium specification in Eq. (). Our choice for a GARCH(1,1) specification in Eq. (5) is inspired by the Nieuwland et al. (1994) results, which indicate that this specification gives a parsimoneous and adequate representation of time series of EMS exchange rates. t 4. Empirical results We estimate the model using the Berdt, Hall, Hall and Hausman algorithm to maximize the lielihood function associated with the model. All calculations were performed with the software pacage GAUSS. Maximum lielihood estimates of the parameters and their heterosedasticityconsistent asymptotic standard errors are reported in Table 1. It is interesting to note in Table 1 that the coefficient u, which was always insignificant in the Domowitz and Haio study, is statistically significant here in a number of cases, lending some support to the ris premium specification. In addition, the results provide a fairly consistent rejection of the hypothesis b 51 (no time-varying ris premia), suggesting significant variation in the ris premium. This conclusion also differs from Domowitz and Haio, who found significant variation in the ris premium for only two out of five currencies in their sample. The GARCH(1,1) specification is supported in a number of cases by significant a and g estimates. Note that in the case of the Italian 1 1 lira/german mar exchange rate the coefficient estimates of a 1g are greater than one in all three 1 1 cases, indicating high persistence in volatility shocs. This may be due to shifts in monetary regimes which affect the level of the unconditional variances. (See Lamoureux and Lastrapes, 1990.) 5. Conclusions In this paper we examined EMS exchange ris premia over the period. We extended the analysis of Domowitz and Haio (1985) using survey data in order to avoid relying on expectational rationality on the part of maret participants. Our results indicate that time-varying ris premia were present in almost all cases and that the time-varying premia can be accounted for by our GARCH-in-

4 354 F.G.M.C. Nieuwland et al. / Economics Letters 60 (1998) Table 1 Maximum lielihood estimates of the model in Eqs. () (5). January 1st, 1986 September 1st, 1991 b0 b1 u a 0(?10 ) a1 g1 L.L. 3 months BF/ DM *** *** (0.0051) (0.1064) (0.5486) (0.003) (0.5036) (0.3598) DG/ DM ** * ** *** 3.46 (0.003) (0.771) (0.391) (0.0003) (0.0000) (0.0507) FF/ DM * *** (0.0066) (0.1673) (1.4011) (0.0005) (0.0700) (0.0000) IL/ DM *** *** *** *** (0.0063) (0.4408) (0.054) (0.0013) (0.003) (0.133) SP/ DM ** 0.819*** *** * *** (0.0037) (0.1798) (0.90) (0.0003) (0.0000) (0.075) 6 months BF/ DM *** ***.18*** ** *** 8.5 (0.005) (0.0371) (0.991) (0.0007) (0.0714) (0.0566) DG/ DM *** * *** * *** (0.007) (0.1445) (0.5177) (0.0005) (0.103) (0.185) FF/ DM ** (0.0189) (0.1770) (.3751) (0.007) (0.130) (0.780) IL/ DM *** *** 0.736*** (0.0130) (0.18) (0.5179) (0.0010) (0.146) (0.0684) SP/ DM *** ** (0.0085) (0.1383) (0.3474) (0.0073) (0.767) (0.0885) 1 months BF/ DM *** 0.888*** ** 0.781** (0.0058) (0.1101) (0.940) (0.0039) (0.3534) (0.0000) DG/ DM *** (0.0071) (0.347) (0.9379) (0.0013) (0.6647) (0.4368) FF/ DM 0.004** *** (0.0114) (0.134) (1.154) (0.0097) (0.349) (1.3983) IL/ DM *** *** *** (0.0076) (0.0873) (0.1705) (0.006) (0.534) (0.150) SP/ DM 0.015*** 0.653*** *** *** (0.0044) (0.0655) (0.117) (0.0000) (0.0000) (0.0051) *, **, ***, denote significance at the 10%, 5%, and 1% level for the hypotheses b 50, b 51, a 50, a 50, or g 50, respectively. Note: Heterosedasticity-consistent standard errors of the coefficients are given in parentheses. Abreviations: L.L., log-lielihood values; BF, Belgian franc; DG, Dutch guilder; DM, German mar; FF, French franc; IL, ltalian lira; SP, Spanish peseta. mean specification in a number of cases. The results basically contrast with those of Domowitz and Haio, who found only minimal support for their specification for a different set of currencies. References Cavaglia, S., Verschoor, W.F.C., Wolff, C.C.P., Further evidence on exchange rate expectations. Journal of International Money and Finance 1,

5 F.G.M.C. Nieuwland et al. / Economics Letters 60 (1998) Cavaglia, S., Verschoor, W.F.C., Wolff, C.C.P., On the biasedness of forward foreign exchange rates: Irrationality or ris premia?. Journal of Business 67, Domowitz, I., Haio, C.S., Conditional variance and the ris premium in the foreign exchange maret. Journal of International Economics 19, Franel, J.A., Froot, K.A., Using survey data to test propositions regarding exchange rate expectations. American Economic Review 77, Lamoureux, C.G., Lastrapes, W.D., Persistence in variance, structural change and the GARCH model. Journal of Business and Economic Statistics 8, Lucas, R.E., 198. Interest rates and currency prices in a two-country world. Journal of Monetary Economics 10, Nieuwland, F.G.M.C., Verschoor, W.F.C., Wolff, C.C.P., Stochastic trends and jumps in EMS exchange rates. Journal of International Money and Finance 13,