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Aggregate and disaggregate measures of the foreign exchange risk premium
International Review of Economics and Finance 11 (2002) 57 – 84
Aggregate and disaggregate measures of the foreign exchange risk premium$ Dionysios Chionisa, Ronald MacDonaldb,* a
Department of Economics, University of Thessaly, Argonafton and Fillelinon, Volos 38221, Greece Department of Economics, University of Strathclyde, 100 Cathedral Street, Glasgow G4 OLN, UK
b
Received 7 December 2000; received in revised form 11 December 2000; accepted 23 January 2001
Abstract Using a disaggregate survey database, this paper reexamines the issue of the existence of a timevarying risk premia in three foreign exchange markets. Previous research on this topic has utilised a consensus measure of the risk premium, based on the rational expectations assumption, and is not supportive of the existence of such a premium. In contrast, this paper reports compelling evidence in favour of time-varying risk premia for the British pound (BP), German mark (DM), and Japanese yen (JY) exchange rates. In particular, we demonstrate that consensus measures of the risk premium mask the existence of risk because of the importance of heterogeneous expectations. D 2002 Elsevier Science Inc. All rights reserved. JEL classification: F31; G12 Keywords: Exchange risk premia; Survey data
1. Introduction The failure to uncover a statistically significant risk premium in foreign exchange markets has become something of a stylised fact in the international finance literature (see, for
$ The authors are grateful to two anonymous referees for their helpful comments on an earlier draft of this paper. * Corresponding author. Tel.: +44-141-548-3861; fax: +44-141-552-5589. E-mail address: [email protected] (R. MacDonald).
1059-0560/02/$ – see front matter D 2002 Elsevier Science Inc. All rights reserved. PII: S 1 0 5 9 - 0 5 6 0 ( 0 1 ) 0 0 0 9 6 - X
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example, Engle, 1995). Thus, although the common finding that the forward exchange rate is a biased predictor of the future exchange rate is often interpreted as evidence in favour of a time-varying risk premia (see, for example, Fama, 1984), researchers who have empirically modelled the risk premium report only limited success. For example, a number of researchers have used ARCH-based models (see Domowitz & Hakkio, 1985), the latent variable class of models (see Hansen & Hodrick, 1983), and the portfolio balance approach (see Frankel, 1993) and reported, at best, only limited evidence that foreign exchange risk premia are related to ‘fundamentals’. However, all of these works, including the interpretation of the biasedness finding, is predicated on the assumption that agents form their expectations rationally. However, if they do not, or if there is some sort of ‘expectational failure’, such as a ‘peso’ effect (Krasker, 1980), then these tests may not have established that unbiasedness does indeed reflect a risk premium and, more fundamentally, the measure of risk used may be wrong. In this paper, we propose using survey expectational data to establish an independent risk premium measure (independent, that is, of the assumption of rationality) for three key currencies, namely, the US dollar bilaterals of the German mark (DM), British pound (BP), and Japanese yen (JY). Other researchers have begun to use survey data for this purpose (see Giorgianni, 1997; MacDonald & Marsh, 1996).1 In addition to exploiting a new data set for this purpose, our work, in contrast to these other studies, involves looking at various levels of disaggregation of the risk premium. In particular, the nature of our data set, supplied by Consensus Economics of London, allows us to go from the overall international market mean, to a country mean, to aggregation at the sectoral level (such as banking or securities companies) down to the behaviour of the individual risk premium. This, of course, is only a worthwhile activity if the participants in the data display heterogeneous behaviour, a feature of our data set which has, in fact, already been established by Chionis and MacDonald (1997) and MacDonald and Marsh (1996). The outline of the remainder of this paper is as follows. In the next section, we present a brief discussion of issues relating to the definition of the foreign exchange risk premium. In Section 3, we discuss our data set and provide a preliminary analysis of the data. Empirical results based on an ARCH-in-mean modelling framework are presented in Section 4. The paper closes with a concluding section.
2. The foreign exchange market risk premium The foreign exchange risk premium is the amount required by a risk-averse investor to compensate her for taking a position in a foreign asset whose characteristics are identical 1 There is a fairly large literature that exploits aggregate (i.e., mean) survey data to test the rationality of survey expectations and the existence of time-varying risk premia (see, for example, Cavaglia, Verschoor, & Wolff, 1993; Chinn & Frankel, 1994; Dominguez, 1986; Frankel & Froot, 1987; MacDonald, 1990; MacDonald & Torrance, 1988, 1990). A more limited literature uses disaggregate survey data to investigate the existence of heterogeneity amongst survey expectations (see Chionis & MacDonald, 1997; Ito, 1990; MacDonald & Marsh, 1994, 1996).
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in all respects to an equivalent domestic asset, apart from its currency of denomination. It is normally defined as: lt ¼ ð fttþk st Þ ðsetþk st Þ,
ð1Þ
ftt + k
denotes the period t forward rate with a maturity date where lt denotes the risk premium, in period t + k (henceforth this shall be denoted as ft ), ste+ k denotes the spot exchange rate expected to prevail in period t + k, conditional on information available in period t, st denotes the period t spot rate, and all variables are expressed in natural logarithms. The first term in parenthesis in Eq. (1) is the forward premium, while the second term is the expected change in the exchange rate (for future reference, it is worth noting that Eq. (1) implies the risk premium can be defined more succinctly as: ft ste+ k ). The expectation pertaining to the spot exchange rate is a subjective expectation. The traditional approach to defining lt has involved assuming that the subjective exchange rate expectation equals the expectation conditional on information available in period t; that is, expectations are rational. This assumption may be expressed as (Eq. (2)): setþk ¼ E½stþk j It , stþk ¼ setþk þ htþk ,
ð2Þ
where, of variables not previously defined, E denotes the mathematical expectations operator, It is the information set on which agents base their expectations, and h is a forecast error, orthogonal to the information set. The ‘rational’ risk premium is therefore defined as ft st + k + ht + k and we label this ltre. Practically all of the extant research on the foreign exchange risk premium has involved this measure (see, for example, Domowitz & Hakkio, 1985; Frankel, 1979; Hansen & Hodrick, 1983), although it is important to note this it is not the only measure that could be derived on the basis of the rational expectations assumption.2 The approach adopted in this paper, however, involves using survey-based expectations to define the risk premium. This gives an alternative definition of the risk premium, labeled ltsu, which we believe is a more direct measure of this premium, since it should capture the expectations of agents who are ‘close to the market’. The measured period-by-period mean value3 of the survey expectation is defined as stsue + k . For a variety of reasons, such as the imperfect synchronisation of survey responses and the use of a consensus response (mean or median), which is extracted from only a fraction of market participants, it is unlikely that the mean survey expectation will be identically equal to the ‘true’ subjective expectation value, ste+ k . In common with researchers who have tested various expectational properties of survey data (see, for example, Frankel & Froot, 1987), we assume that the measured expected value is equal to the ‘true’ value plus a random measurement error (Eq. (3)): e ssue tþk ¼ stþk þ jtþk ,
ð3Þ
where jt + k is the survey forecast or measurement error. This implies that ltsu is given by ft stsue + k + jt + k Having access to the individual expectations of survey respondents 2
We are grateful to an anonymous referee for making this point. This is the mean of the cross-section at each point in time defined as the mean of the log of the individual expectation. 3
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Table 1 Unit root tests on the actual and expected variables (a) Spot rate D
L DM JY BP
t
t trend
t
t trend
1.99 0.48 1.86
2.37 2.15 2.52
7.22 5.10 6.67
7.19 5.27 6.65
(b) Forward rate D
L DM JY
t
t trend
t
t trend
2.13 0.53
2.07 3.01
7.20 7.00
7.10 6.90
(c) Expected spot rates DM
JY
BP
Country
t
t trend
t
t trend
t
t trend
MUK MCAN MFRA MGER MITL MJAP MUSA MBAN MSEC MIND
2.56 2.67 2.66 2.56 2.53 1.40 0.47 0.96 2.03 2.01
2.62 2.66 3.02 2.75 2.65 1.44 0.77 0.23 3.04 2.93
0.67 0.42 0.64 0.64 0.79 0.63 0.45 1.37 2.86 2.22
2.97 2.68 2.54 2.33 3.1 2.9 2.72 2.06 2.93 2.17
1.95 1.85 1.95 1.87 1.44 1.65 2.75 1.61 0.58 1.03
2.78 2.52 1.86 2.82 2.45 2.65 1.86 1.97 1.67 2.81
(d) Expected spot changes DM
JY
BP
Country
t
t trend
t
t trend
MUK MCAN MFRA MGER MITL MJAP MUSA MBAN MSEC MIND
13.4 17.2 18.1 12.9 9.5 31.5 12.1 12.1 17.4 27.5
42.4 18.0 28.0 22 15.2 40 56 20.8 35.2 33.2
9.7 17.8 10.4 10.1 14.5 15.8 6.7 20.4 16.3 18.3
37.7 35.7 25.03 20.08 36.9 41.8 3.96 34.2 45.8 38.8
t
t trend
25.3 35.4 36.7 39.5 31.1 35.7 29.5 29.6 35.1 37.2 38.1 38.8 33.9 36.2 29.6 29.7 36.9 40.1 30.4 30.8 (continued on next page)
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Table 1 (continued ) (e) The forward and risk premia Forward premium
Risk premium
t
t trend
2.95 4.63 3.86
3.20 5.44 6.71
t
t trend
DM survey RP 4.35 6.20 DM RERP 5.80 5.56 JY survey RP 4.16 7.58 JY RERP 4.50 4.55 BP survey RP 5.17 5.92 BP RERP 4.69 4.37 Of terms not defined in the text, the number in the columns headed t and t trend are, respectively, the estimated t ratios from an ADF equation when a constant and a constant plus a time trend are included as the deterministic variables. The 5% critical values for constant and time trend are, respectively, 2.79 and 3.09 (source Fuller, 1981). Column headings L and D denote, respectively, levels and first differences. DM JY BP
allows us to define the risk premium for each individual (or subgroups of individuals) in our survey as Eq. (4): i,sue
lt
i,sue ¼ ft stþk þ jitþk ,
ð4Þ
where the superscript i denotes individual i. One key issue in defining the rational expectations risk premium is that it is modeldependent: the econometrician has to make some assumption about the conditioning information set and a particular empirical result may be driven by a mismatch between the information set used by forecasters and that used by the econometrician. The use of survey data to measure expectations means that there is no difference between the investor’s and the econometrician’s information sets.
3. Data sources, time series properties, and some empirical regularities The survey data set that we exploit is constructed by the Consensus Forecasts of London. Since October 1989 Consensus Forecasts have surveyed and published the exchange rate forecasts of economists, foreign exchange dealers, and executives in over 150 companies and institutions in the G-7 nations. The companies surveyed, who remain the same over time, are mainly commercial and investment banks, but industrial corporations and forecasting agencies were also polled. The responders return a fax on the first Monday of each month containing their point forecasts of dollar–sterling, Deutschemark–dollar, and yen–dollar exchange rates, 3 and 12 calendar months ahead. Since the response rate is less than perfect, in the work that follows we constrain our analyses to a subset of the total panel (in particular, a balanced panel of 60 individuals). The time series dimensions of our data set are from October 1989 to March 1995.
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From the disaggregate data, we have constructed a number of aggregate indicators or means. In particular, the mean across forecasters located in the same nation — the country mean — will be denoted by the country mnemonic, preceded by ‘M’ (i.e., MUK is the UK mean; the other means, which should be self-explanatory, are MGER, MFRA, MITL, MJAP, MUSA, and MCAN). Additionally, we have estimated the properties of the mean for the three different groups of activities represented in our data set: MBAN is the mean of the banks, MSEC is the mean of the securities companies, and MIND is the mean of nonfinancial industries. Finally, our data on spot and forward exchange rates are collected from Datastream International and have been carefully aligned with the survey data. As a preliminary exercise, we used augmented Dickey–Fuller (ADF) tests to check the orders of integration of each of the series used in our econometric tests, and these are reported in Table 1. In sum, we find that the levels of variables — spot rates, expected spot rates, and forward rates — are nonstationary, but become stationary after first differencing (or quasidifferencing in the case of the forward premium and expected change in the exchange rate). The various measures of the risk premium are all stationary in levels. This essentially confirms the prediction of theoretical models of the risk premium (see, for example, Hodrick, 1987) and the findings of others using alternative data sets (see, for example, Frankel & Froot, 1989; MacDonald & Torrance, 1988). In Figs. 1–3, the forward premia (indicated by FP) for each of the three currencies is plotted against the corresponding rational risk premia, ltre. We note that the pattern here is
Fig. 1. DM rational risk premium and the forward premium.
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Fig. 2. BP rational risk premium and the forward premium.
very similar to that highlighted in many other papers: the forward premia are relatively constant around zero, while the rational risk premium risk premia are relatively volatile (this finding is confirmed in a statistical sense by our descriptive statistics, noted below). Of more interest, perhaps, is an answer to the question: how volatile are survey risk premia compared to their rational counterparts? The answer is portrayed in Figs. 4–6, where ltre is plotted against ltsu. It is clear from these figures that the rational risk premia are much more volatile
Fig. 3. JY rational risk premium and the forward premium.
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Fig. 4. DM rational- and survey-based risk premia.
than the survey-based counterparts, a finding confirmed in Table 2 where the variance of the rational risk premium is larger in every case than its survey-based counterpart. The source of this greater instability is revealed in Figs. 7–9 where, across the three currencies, the rational expected change in the exchange rate is more volatile than its survey-based counterpart, a finding which is again confirmed in Table 2 by the estimated sample variances. Given the discussion in Section 2, we interpret this as evidence that the rational-based risk premium is a much noisier proxy of the true risk premium than its survey-based counterpart. The disaggregate nature of our data set enables us to push our preliminary exploration of foreign exchange risk premia further, by comparing rational risk premia with individual risk premia and the risk premium defined for a particular sector (banks and securities). Consider Figs. 10–12, generated for the DM: in Fig. 10, the rational risk premium,
Fig. 5. BP rational- and survey-based risk premia.
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Fig. 6. JY rational- and survey-based risk premia.
RERPDM, is plotted against the survey risk premia defined for banks, RPBANKDM, and securities RPSECDM; in Fig. 11, RERPDM is plotted against RPBANKDM and the risk Table 2 Descriptive statistics for consensus variables and individual risk premia Dste + 3 Panel A: DM Mean 0.005 8.7e 005 s2 Ku 0.48 (.44) Q16 126 (.000)
fpt + 3
lsu t
lre t
Dst + 3
lt B18
lt B25
0.002 0.002 0.0089 0.006 0.21 0.214 8.8e 006 8.6e 005 0.00819 0.000851 0.0011 0.0007 0.59 (.356) 0.068 (.91) 0.437 (.495) 0.432 (.500) 0.53 (.408) 0.91 (.886) 231 (.00) 92.42 (.000) 89.5 (.000) 85.06 (.00) 76.2 (.000) 151.2 (.000)
Panel B: JY Mean 0.0004 0.0006 0.00088 0.0061 0.006 0.003 0.0018 s2 7.7e 005 3.4e 006 0.000145 0.00035 0.00034 0.00033 0.00032 Ku 0.148 (.817) 0.78 (.223) 7.26 (.000) 0.179 (.780) 0.173 (.786) 1.57 (.139) 0.059 (.925) Q16 173 (.000) 94 (.000) 121.84 (.000) 61.23 (.000) 61.9 (.000) 43.53 (.000) 234.9 (.000) Panel Mean s2 Ku Q16
C: BP 0.004 0.004 0.0007 4.7e 005 9.5e 006 8.66e 005 0.60 (.34) 2.01 (.001) 6.42 (.000) 22.21 (.136) 137 (.00) 39.18 (.001)
0.00181 0.0032 62.94 (.000) 60.62 (.000)
0.0014 0.0009 32.9 (.000) 60.63 (.000)
0.003 0.005 0.00033 0.000182 1.57 (.139) 0.472 (.461) 43.53 (.000) 140 (.000)
Of variables not defined in the text, lt B18 and lt B25 denote the individual risk premia of individual 18 and 25, respectively. s2 indicates the sample variance, Ku is the statistic of kurtosis Q16 is the Ljung – Box Q statistics for the 16 correlation coefficients and numbers in parentheses are the significance levels.
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Fig. 7. DM rational- and survey-based expected exchange rate changes.
premium defined for individual 18 (from the banking sector); in Fig. 12, RERPDM is again plotted against RPBANKDM and the risk premium defined for individual 25 (from the banking sector). This sequence of figures is repeated for the BP (Figs. 13–15) and for the JY (Figs. 16–18). The general thrust of these figures is that, across the three currencies, individual risk premia seem to contain a similar degree of volatility to the rational risk premia and for the JY there is some evidence that the sectoral risk premia also exhibit similar volatility (although not necessarily with the same sign). This finding is confirmed, in a statistical sense, in Table 2 where we see that the variance of the risk premia for two
Fig. 8. BP rational- and survey-based expected exchange rate changes.
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Fig. 9. JY rational- and survey-based expected exchange rate changes.
representative individuals (B18 and B25) are more volatile than the survey consensus measure and closer to the rational risk premia. It would seem therefore that the aggregate measures of the survey-based risk premia actually mask, or average out, much of the heterogeneity and richness of the individual survey expectations. This is consistent with studies that report important elements of heterogeneity in the kind of survey data used in this paper (see, for example, Chionis & MacDonald, 1997; MacDonald & Marsh, 1996).
Fig. 10. DM rational risk premium and risk premia for banks and securities.
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Fig. 11. DM rational risk premium and risk premia for banks and individual 18.
In Figs. 19–21, we present the first 17 autocorrelations of the rational risk premium for our three currencies, while in Figs. 22 – 24 the corresponding (mean) survey risk premia autocorrelations are noted. The striking contrast between these two sets of graphs is that the survey-based measures of the risk premia all tend have more persistence than their rational counterparts and to generate, with one exception, only positive autocorrelations. Interestingly, however, the disaggregate survey risk premia give a rather different picture as indicated in Fig. 25, which contains the autocorrelation functions of a representative selection of eight
Fig. 12. DM rational risk premium and risk premia for banks and individual 25.
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Fig. 13. BP rational risk premium and risk premia for banks and securities.
individual risk premia. Here the pattern is one of positive autocorrelations up to Month 5, followed by a sequence of insignificant negative autocorrelations down to Period 17. In addition to what we have already noted, several features of the aggregate time series properties of the data, as summarised in Tables 2–8, are worth commenting on. In accordance with previous findings using the rational expectations assumption, the unconditional variance of the survey expected exchange rate change is many times more variable than the variance of the forward premium. This is so irrespective of the consensus measure referred to. Further, both for the individual markets and for the means, the unconditional variance of the expected exchange rate change are large relative to the unconditional variance of the average. The fourth moments of the forward premium and the expected exchange rate changes suggest that the distributions deviate from normality. In most cases, the null hypothesis of a normal distribution is rejected. Finally, the magnitude of variances
Fig. 14. BP rational risk premium and risk premia for banks and individual 18.
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Fig. 15. BP rational risk premium and risk premia for banks and individual 25.
Fig. 16. JY rational risk premium and risk premia for banks and securities.
is similar across countries and across sectors, although there are one or two exceptions (for example, the mean of the US forecasters produces a much larger variance than any of the other country means).4
4
An anonymous referee has pointed out that the volatility of the rational risk premium may simply be a function of the use of the ex-post realisation of the spot rate rather than the assumption of rationality. While agreeing with this point, we would note that our measure of the rational risk premium is the most commonly used in the literature.
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4. Empirical modelling of the survey-based risk premium As we noted in Section 2, the availability of disaggregate survey data allows us to define a risk premium for each individual in our survey database and also for parti-
Fig. 17. JY rational risk premium and risk premia for banks and individual 18.
Fig. 18. JY rational risk premium and risk premia for banks and individual 25.
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Fig. 19. Autocorrelation function for DM rational risk premium.
cular groupings, or categories, such as banks and the insurance sector. We propose modelling these disaggregate risk premia using an ARCH(1)-M multivariate model of
Fig. 20. Autocorrelation function for BP rational risk premium.
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Fig. 21. Autocorrelation function for JY rational risk premium.
the following form: sei,tþ1 st ¼ li,t þ bi,0 ð ft st Þ þ ei,tþ1 ,
ð5Þ
lit ¼ ai þ bi,1 hi,tþ1 , ei,tþ1 j It N ð0,h2tþ1 Þ, h2tþ1 ¼ gi,0 þ gi,1 e2i,tþ1 þ gi,2 ðHetÞ2tþ1 : where the subscript i denotes firm- or individual-specific variables, Het stands for the heterogeneity, defined as the individual’s standard deviation from the mean value of all forecasters, the time index t + 1 indicates that this is a dispersion measure of survey expectations for t + 1 exchange rates, based upon time t information, and It is the information set available to investors at time t. The information matrix for the ARCH-M model is not block diagonal between b, on the one hand, and g on the other. This has two implications for
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Fig. 22. Autocorrelation function for DM survey risk premium.
the estimation methods. First, the model has to be estimated simultaneously, and not recursively, and secondly, the feasible GLS and one-step efficient estimation techniques that work for other ARCH models cannot be used. Maximum likelihood methods are therefore used to estimate the model.5 Domowitz and Hakkio (1985) have demonstrated how the ARCH class of model can be used to estimate a representative agent model of the risk premium. Here we simply posit this model as a useful and tractable way of capturing the effect of heterogeneity on individual risk premia. Before presenting the results of our analysis, we should note that since the response rate to the survey is less than perfect, we constrain our ARCH analysis to a subset of the total panel examined in the first part of this work. Specifically, we fit an ARCH-M to 51 individual forecasts for the DM, 46 for the BP, and 55 for the JY individuals (where the individuals are drawn from the banking and security sectors). The results from our ARCH modelling are summarised in Table 9a and b for the DM, Table 10a and b for BP, and Table 11a and b for the JY. In general terms, these results seem to 5
In order to incorporate the moving average error structure implied by the overlapping nature of our data set, we used the Broyden, Fletcher, Goldfarb, and Shanno algorithm to estimate the model. This algorithm facilitates the construction of standard errors, robust to both serial correlation and moving average errors.
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Fig. 23. Autocorrelation function for BP survey risk premium.
Fig. 24. Autocorrelation function for JY survey risk premium.
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Fig. 25.
provide strong support for the predictions of the theoretical model developed in Section 3. In particular, for the DM there are 28 out of 34 instances in the banking sector in which the heterogeneity term enters with a statistically significant coefficient and 13 out of 17 in the security industry. Similarly, for the BP, the corresponding ratios are 22 out of 25 for banks and 19 out of 21 for the security industry, while for the JY there are 23 significant out of 28 for the banking sector and 23 out of 27 for the security sector. It would seem therefore that the difference in heterogeneity is equally important across the two sectors. It is worth noting that when the heterogeneity term is excluded from the above model, the conditional heteroscedastic structure is significant in 97% of cases. However, with the heterogeneity included, the hetersoscedasticity becomes insignificant in most cases. It would seem then that the major part of the conditional volatility’s momentum,6 which other number of researchers have also found in foreign exchange markets, is explicable in terms of heterogeneous expectations. Not surprisingly, perhaps, in all cases in which the heterogeneity term is statistically significant it enters with a positive sign, indicating that an increase in heterogeneity increases the conditional volatility and subsequently the risk premium.
6 We test for the existence of conditional heteroscedastic structure in the forecasting residuals by applying an LM test statistic. In 97% of the cases, we can reject the null of no-conditional heteroscedasticity.
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Table 3 DM 3-month forecasts: expected exchange rate changes, per country mean MUK
MCAN
MFRA
MGER
MITA
MJAP
MUSA
Mean 0.006 0.0008 0.007 0.006 0.004 0.003 0.004 s2 0.00012 0.0001 9.52e 005 0.0001 0.0001 0.0001 7.83e 005 Ku 0.441 (.491) 9.12 (.000) 0.616 (.336) 0.22 (.730) 0.377 (.556) 0.527 (.410) 0.533 (.40) Q16 181 (.000) 18.93 (.217) 87 (.000) 123 (.000) 140 (.000) 41.8 (.000) 34.8 (.005) The mnemonics in the column headings are consensus, or mean values (M), for the United Kingdom (UK), Canada (CAN), France (FRA), Germany (GER), Italy (ITA), Japan (JAP), and the United States of America (USA). See Table 2 for other definitions. Table 4 DM 3-month forecasts: expected exchange rate changes, group mean Mean s2 Ku Q16
MBAN
MIND
MSEC
0.005 0.0001 0.33 (.602) 151 (.00)
0.005 0.0001 0.07 (.902) 30.56 (.015)
0.054 8.3e 005 0.31 (.61) 109 (.000)
The mnemonics in the column headings are consensus, or mean values (M) for key groups within the total panel, namely the banking sector group (BAN), nonfinancial industries (IND), and the mean of the securities companies (SEC).
In their estimates of the ARCH-M model for rational expectations-defined risk premia, Domowitz and Hakkio (1985) report rather weak results for the statistical significance of the risk premium in the unbiasedness equation. Our results present much clearer evidence for the existence of such a premium, especially when disaggregate data are considered. Thus, in the Table 5 JY 3-month forecasts: expected exchange rate changes, per country mean MUK
MCAN
MFRA
MGER
MITA
MJAP
MUSA
Mean 0.0007 0.002 0.001 0.002 0.0010 0.0005 0.09 s2 0.0001 6.8e 005 0.0001 0.0001 0.0001 6.2e005 0.17 Ku 0.47 (.461) 0.191 (.765) 0.148 (.171) 0.19 (.758) 1.37 (.031) 0.538 (.401) 18.1 (.00) Q16 219 (.000) 51.7 (.000) 142 (.000) 150 (.000) 162 (.000) 126 (.000) 38.0 (.001) See Table 3 for definitions. Table 6 JY 3-month forecasts: expected exchange rate changes, group mean Mean s2 Ku Q16 See Table 4 for definitions.
MBAN
MIND
MSEC
.005 0.0003 0.737 (.274) 56 (.00)
0.001 0.0001 96.7 (.08) 96 (.000)
0.0003 5.2e 005 0.49 (.44) 98.16 (.000)
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Table 7 BP 3-month forecasts: expected exchange rate changes, per country mean MUK
MCAN
MFRA
MGER
MITA
MJAP
MUSA
Mean 0.0047 0.002 0.006 0.006 0.218 0.11 0.007 s2 6.5e 005 5.7e 005 6.6e 005 6.2e 005 0.001 0.0001 8.6e 005 Ku 0.55 (.38) 0.28 (.66) 0.15 (.808) 0.55 (.38) 1.06 (.096) 5.4 (.000) 0.11 (.86) Q16 42.9 (.000) 29.7 (.019) 33.9 (.005) 29.9 (.018) 225 (.000) 16.8 (.397) 18.33 (.304) See Table 3 for definitions.
Table 8 BP 3-month forecasts: expected exchange rate changes, group mean Mean s2 Ku Q16
MBAN
MIND
MSEC
0.003 0.0002 2.52 (.0001) 31.8 (.010)
0.0029 0.0001 1.16 (.068) 35.3 (.003)
0.003 5.0e 005 0.58 (.365) 18.90 (.273)
See Table 4 for definitions.
case of the DM and BP, in 52–60% of cases we found the conditional variance to be statistically significant, although for the JY the number is smaller—24% in the banking sector and 30% in the security industry. Evaluating the performance of subgroups, we find that in the vast majority of the French-based institutions the risk premium is not significantly different from zero, while the British-based institutions produce weak results regarding the risk premium of the BP. Again, a notable feature of these results is the almost identical influence of the risk premium in the forecasting patterns of the bank and security sectors. The fluctuations between negative and positive values of the risk premium (see columns labeled Risk) is in accordance with the findings of Domowitz and Hakkio and the theoretical model proposed by Stockman (1980). The majority of the negative signs imply that the effect of the risk premium is to push estimates of the standard coefficient of b above 1; a positive value indicating an overreaction to available information. The vast majority of positive signs are concentrated in the security industry’s forecasting patterns, especially for the DM and the JY. For the JY and DM, 67% and 65% of individual’s risk premia enter with a positive sign; in the case of BP, the ratio approaches 30%.7
5. Conclusions In this paper, we have reexamined the importance of risk premia in foreign exchange markets using a disaggregate multicountry exchange rate survey database. The availability of 7
As a robustness check on the results presented in this section, we reestimated all of the models using a GARCH process. The results were qualitatively similar to those generated using the ARCH-in-mean model and are therefore not reported here.
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Table 9 Summary of results for ARCH modelling (currency: DM) Heter (a) Sector: banks B13 B25 B35 C1 C12 C15 C2 F11 F16 F9 G10 G11 G12 G13
Forward
Risk
B13
C12 C15
F16 F4 F9 G10 G12 G15
G18
B25 B35 C1 C12 C15 C2
F16
G11 G12 G15 G18
G19 G2 G22 G23 G3 G4 G5 G8 I5 I6 J9 U15 U19 U18 82% Total: 34 (b) Sector: securities B18 B27 B29 B30 B4 B8
G22 G23
G2 G22 G23
G5 I1 I5 I6
G8 I1
U15 U19 U18 56%
U15 U19 U18 56%
B18 B27 B29
B18 B27 B29 B30
B8
+ Heter
Risk
B13 B25 B35 C1 C12 C15 C2 F10 F11 F16 F4 F9 G10 G11 G12 G13
B13 B25 B35 C1 C12 C15 C2 F10 F11
G18 G19 G2 G22 G23 G3 G4 G5 G8 I1 I5 I6 J2 J9 U15 U19 U18 97%
G18
B18 B27 B29 B30 B4 B8
G10 G11 G12
G2 G23 G3 G5 I1
J2 J9 U15 U19 U18 68%
B18
B4 B8 (continued on next page)
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Table 9 (continued) Heter (b) Sector: securities B9 C3 F12 F2 G5 J20 J3
Forward
Risk
+ Heter
B9 C3 C4
B9 C3 C4 F12
B9 C3 C4 F12 F2 G5
F2 G5 J20 J3
Risk
C3
G5
J20 U1
J3 U1 U24 88%
U24 88% 65% 59% 35% Total: 17 The column headed Heter lists those individuals who produce a statistically significant coefficient of heterogeneity in the ARCH model listed as Eq. (5). The letters B, C, F, G, I, J, and U denote the country in which the forecaster is based (Britain, Canada, France, Germany, Italy, Japan, and the US, respectively). The column marked Forward lists those individuals for whom the forward premium is statistically significant while in Risk those individuals producing a statistically significant coefficient on the risk premium are recorded. Those individuals for which the heterogeneity term is positive are recorded in the column labeled + Heter, while those in Risk have a statistically significant negative sign on the risk premium.
survey data offers an independent measure of foreign exchange market participants’ expectations of the exchange rate. In summary form, our work clearly indicates that studying the behaviour of agents in disaggregate terms produces very different results to aggregate studies that rely on the assumption of rationality. More specifically, we have found that although rational risk premia are noisier than consensus measures of survey risk premia, individual risk premia based on survey data show a degree of volatility that is closer to that of rational risk premia. We attribute the difference between individual survey premia and consensus measures to the existence of heterogeneity in the individual data that essentially cancels out in the mean. Furthermore, when an ARCH-M model was used to model individual risk premia a large number of the risk premium terms were statistically significant and, interestingly, the heterogeneity term removed much of the momentum in the conditional volatility. The evidence in favour of a risk premium is, however, less clear-cut when the consensus value is used. So essentially our findings confirm the importance of heterogeneity in foreign exchange markets noted by Chionis and MacDonald (1997), Ito (1990), and MacDonald and Marsh (1996), although these papers focussed on expectational processes rather than risk premia. We believe that the existence of such heterogeneity is supportive of the market microstructure view of the operation of foreign exchange markets (see, for example, Goodhart, Ito, & Payne, 1996; Lyons, 1995). The main conclusion of this paper is that the failure of other researchers to uncover a risk premium is due in large measure to the use of a consensus measure of risk. What comes out
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81
Table 10 Summary of results for ARCH modelling (currency: BP) Heter
Forward
(a) Sector: banks B25 B13 C15 C1 F4 F12 F10 F5 F10 G10 G11 G12 G13 G2 G22 G3 G4 C5 G8 I1 I2 I5 88% Total: 25 (b) Sector: securities B30 B27 B22 B2 B18 B14 B12 B9 B8 B4 B35 C18 C12 C4
Risk
+ Heter
B25
B25 B13 C15 C1 F4 F12 F10 C5 F5 F10 G10 G11 G12 G13 G15 G2 G22 G3 G4 G5 G8 I1 I2 I5 J2 100%
C15 C1 F12 F10 C5 F10 G10 G11 G12
G2 G22 G4
G4 G8 I2
8%
J2 60%
B30
B2 B14 B9 B8 B4
C12 C4 G19
B35 C18 C12
B30 B27 B22 B2 B18 B14 B12 B9 B8 B4 B35 C18 C12 C4 G19
Risk
B13 C15 C1 F4
C5 F5
G12 G13 G15 G22 G3 G4 G8 I1 I2 I5 J2 68%
B30 B27
B18 B14 B9 B8 B35
C12 G19 (continued on next page)
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Table 10 (continued) Heter (b) Sector: securities G9 I6 J20 U1
Forward
Risk
+ Heter
Risk
G9 I6 J20
G9 I6 J20 U1 U24 100%
G9 I6 U1 U24 70%
+ Heter
Risk
B13 B25 B27 B9 C1 F10 F16 F4 F5 F9 G8 G5 G4 G3 G22 G20 G15 G13 G12 G10 I1 I5 J9
B13
U1
95% 25% Total: 21 See Table 9a for definitions.
52%
Table 11 Summary of results for ARCH modelling (currency: JY) Heter (a) Sector: bank B13 B25 B27 B9 F10 F16 F4 F5
Forward B13 B25 B27
F5
G8 G5 G4 G3
Risk
B27
F5 G8 G4 G22
G20 G15 G12 G10 I1 I5 J9 J2 J17 J11 J13 82% Total: 28
G12 G10 I1
G10
J9
J17
28%
24%
J17 J11 J13 93%
F16 F5 F9 G8
G3
G13 G12 I1 I5 J9 J2 J18 J17
50% (continued on next page)
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83
Table 11 (continued) Heter (b) Sector: securities B18 B2 B29 B30 B35 C12 C3 C4 C5 F12 G9 G19 G11 I6 J6 J4 J16 J15 J1
Forward
Risk
B18 B2 B29 B30 C12
C4 F12 G9
J4
J4
J16
J16
+ Heter B18 B2 B29 B30 B35 C12 C18 C3 C4 C5 F12 G9 G19 G11 I6 J6 J4 J3 J16 J15 J1
U8 U30 U24 U19 U15 U1 U1 85% 30% Total: 27 See Table 9a for definitions.
U19
30%
Risk
B2
C12 C18
G11 J6
J15 U8
U30 U24 U19 U15 U1 96%
U19 U1 33%
clearly from the present work is that because the consensus essentially averages out heterogeneity it means that any tests for the existence of risk premia based on consensus expectations are unlikely to be successful.
References Cavaglia, S., Verschoor, W. F. C., & Wolff, C. (1993). Further evidence on exchange rate expectations. Journal of International Money and Finance, 12, 78 – 98. Chinn, M., & Frankel, J. (1994). Patterns in exchange rate forecasts for twenty-five currencies. Journal of Money Credit and Banking, 26, 757 – 770.
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Chionis, D., & MacDonald, R. (1997). Some tests of market microstructure hypotheses in the foreign exchange market. Journal of Multinational Financial Management, 7, 223 – 229. Dominguez, K. (1986). Are foreign exchange forecasters rational? New evidence from survey data. Economics Letters, 21, 277 – 281. Domowitz, I., & Hakkio, G. (1985). Conditional variance and the risk premium in the foreign exchange market. Journal of International Economics, 19, 47 – 66. Engle, C. (1995). The forward discount anomaly and the risk premium: a survey of recent evidence (Working Paper 5312). National Bureau of Economic Research. Fama, E. (1984). Forward and spot exchange rates. Journal of Monetary Economics, 14, 319 – 328. Frankel, J. A. (1979). Test of rational expectations in the forward exchange market. Southern Journal of Economics, 1093 – 1101. Frankel, J. A. (1993). Monetary and portfolio-balance models of the determination of exchange rates. In J. Frankel (Ed.), On exchange rates (pp. 95 – 116). Cambridge: MIT Press. Frankel, J., & Froot, K. (1987). Using survey data to test standard proportions regarding exchange rate expectations. American Economic Review, 77, 133 – 153. Fuller, W.A. (1976). Introduction to statistical time series methods. New York: Wiley. Giorgianni, L. (1997). Foreign exchange risk premium. Does fiscal policy matter? Evidence from Italian data (Working Paper 39). International Monetary Fund. Goodhart, C., Ito, T., & Payne, R. (1996). A study of the Reuters D2000-2 Dealing System. In J. A. Frankel, G. Galli, & A. Giovannini (Eds.), The microstructure of foreign exchange markets (pp. 87 – 96). Chicago: Chicago University Press. Hansen, L. P., & Hodrick, R. J. (1983). Risk averse speculation in the forward foreign exchange market: an econometric analysis of linear models. In J. A. Frenkel (Ed.), Exchange rates and international macroeconomics (pp. 101 – 123). Chicago: Chicago University Press. Hodrick, R. (1987). The empirical evidence on the efficiency of forward and futures markets. London: Harwood. Ito, T. (1990). Foreign exchange rate expectations: micro survey data. American Economic Review, 80, 434 – 449. Krasker, W. S. (1980). The peso problem in testing the efficiency of forward exchange markets. Journal of Monetary Economics, 6, 269 – 276. Lyons, R. (1995). Tests of microstructural hypotheses in the foreign exchange market. Journal of Financial Economics, 39, 321 – 351. MacDonald, R. (1990). Are foreign exchange market forecasters ‘rational’? Some survey based tests. The Manchester School, 58, 229 – 241. MacDonald, R., & Marsh, I. (1994). Combining exchange rate forecasts: what is the optimal consensus measure? Journal of Forecasting, 13, 313 – 332. MacDonald, R., & Marsh, I. (1996). Currency forecasters are heterogeneous; confirmation and consequences. Journal of International Money and Finance, 15, 665 – 685. MacDonald, R., & Torrance, T. S. (1988). On risk, rationality and excessive speculation in the Deutschemark – US dollar exchange market: some evidence using survey data. Oxford Bulletin of Economics and Statistics, 50, 107 – 123. MacDonald, R., & Torrance, T. S. (1990). Expectations formation and risk in four foreign exchange markets. Oxford Economic Papers, 42, 544 – 561. Stockman, A. (1980). A theory of exchange rate determination. Journal of Political Economy, 88, 673 – 698.
Aggregate and disaggregate measures of the foreign exchange risk premium$ Dionysios Chionisa, Ronald MacDonaldb,* a
Department of Economics, University of Thessaly, Argonafton and Fillelinon, Volos 38221, Greece Department of Economics, University of Strathclyde, 100 Cathedral Street, Glasgow G4 OLN, UK
b
Received 7 December 2000; received in revised form 11 December 2000; accepted 23 January 2001
Abstract Using a disaggregate survey database, this paper reexamines the issue of the existence of a timevarying risk premia in three foreign exchange markets. Previous research on this topic has utilised a consensus measure of the risk premium, based on the rational expectations assumption, and is not supportive of the existence of such a premium. In contrast, this paper reports compelling evidence in favour of time-varying risk premia for the British pound (BP), German mark (DM), and Japanese yen (JY) exchange rates. In particular, we demonstrate that consensus measures of the risk premium mask the existence of risk because of the importance of heterogeneous expectations. D 2002 Elsevier Science Inc. All rights reserved. JEL classification: F31; G12 Keywords: Exchange risk premia; Survey data
1. Introduction The failure to uncover a statistically significant risk premium in foreign exchange markets has become something of a stylised fact in the international finance literature (see, for
$ The authors are grateful to two anonymous referees for their helpful comments on an earlier draft of this paper. * Corresponding author. Tel.: +44-141-548-3861; fax: +44-141-552-5589. E-mail address: [email protected] (R. MacDonald).
1059-0560/02/$ – see front matter D 2002 Elsevier Science Inc. All rights reserved. PII: S 1 0 5 9 - 0 5 6 0 ( 0 1 ) 0 0 0 9 6 - X
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example, Engle, 1995). Thus, although the common finding that the forward exchange rate is a biased predictor of the future exchange rate is often interpreted as evidence in favour of a time-varying risk premia (see, for example, Fama, 1984), researchers who have empirically modelled the risk premium report only limited success. For example, a number of researchers have used ARCH-based models (see Domowitz & Hakkio, 1985), the latent variable class of models (see Hansen & Hodrick, 1983), and the portfolio balance approach (see Frankel, 1993) and reported, at best, only limited evidence that foreign exchange risk premia are related to ‘fundamentals’. However, all of these works, including the interpretation of the biasedness finding, is predicated on the assumption that agents form their expectations rationally. However, if they do not, or if there is some sort of ‘expectational failure’, such as a ‘peso’ effect (Krasker, 1980), then these tests may not have established that unbiasedness does indeed reflect a risk premium and, more fundamentally, the measure of risk used may be wrong. In this paper, we propose using survey expectational data to establish an independent risk premium measure (independent, that is, of the assumption of rationality) for three key currencies, namely, the US dollar bilaterals of the German mark (DM), British pound (BP), and Japanese yen (JY). Other researchers have begun to use survey data for this purpose (see Giorgianni, 1997; MacDonald & Marsh, 1996).1 In addition to exploiting a new data set for this purpose, our work, in contrast to these other studies, involves looking at various levels of disaggregation of the risk premium. In particular, the nature of our data set, supplied by Consensus Economics of London, allows us to go from the overall international market mean, to a country mean, to aggregation at the sectoral level (such as banking or securities companies) down to the behaviour of the individual risk premium. This, of course, is only a worthwhile activity if the participants in the data display heterogeneous behaviour, a feature of our data set which has, in fact, already been established by Chionis and MacDonald (1997) and MacDonald and Marsh (1996). The outline of the remainder of this paper is as follows. In the next section, we present a brief discussion of issues relating to the definition of the foreign exchange risk premium. In Section 3, we discuss our data set and provide a preliminary analysis of the data. Empirical results based on an ARCH-in-mean modelling framework are presented in Section 4. The paper closes with a concluding section.
2. The foreign exchange market risk premium The foreign exchange risk premium is the amount required by a risk-averse investor to compensate her for taking a position in a foreign asset whose characteristics are identical 1 There is a fairly large literature that exploits aggregate (i.e., mean) survey data to test the rationality of survey expectations and the existence of time-varying risk premia (see, for example, Cavaglia, Verschoor, & Wolff, 1993; Chinn & Frankel, 1994; Dominguez, 1986; Frankel & Froot, 1987; MacDonald, 1990; MacDonald & Torrance, 1988, 1990). A more limited literature uses disaggregate survey data to investigate the existence of heterogeneity amongst survey expectations (see Chionis & MacDonald, 1997; Ito, 1990; MacDonald & Marsh, 1994, 1996).
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59
in all respects to an equivalent domestic asset, apart from its currency of denomination. It is normally defined as: lt ¼ ð fttþk st Þ ðsetþk st Þ,
ð1Þ
ftt + k
denotes the period t forward rate with a maturity date where lt denotes the risk premium, in period t + k (henceforth this shall be denoted as ft ), ste+ k denotes the spot exchange rate expected to prevail in period t + k, conditional on information available in period t, st denotes the period t spot rate, and all variables are expressed in natural logarithms. The first term in parenthesis in Eq. (1) is the forward premium, while the second term is the expected change in the exchange rate (for future reference, it is worth noting that Eq. (1) implies the risk premium can be defined more succinctly as: ft ste+ k ). The expectation pertaining to the spot exchange rate is a subjective expectation. The traditional approach to defining lt has involved assuming that the subjective exchange rate expectation equals the expectation conditional on information available in period t; that is, expectations are rational. This assumption may be expressed as (Eq. (2)): setþk ¼ E½stþk j It , stþk ¼ setþk þ htþk ,
ð2Þ
where, of variables not previously defined, E denotes the mathematical expectations operator, It is the information set on which agents base their expectations, and h is a forecast error, orthogonal to the information set. The ‘rational’ risk premium is therefore defined as ft st + k + ht + k and we label this ltre. Practically all of the extant research on the foreign exchange risk premium has involved this measure (see, for example, Domowitz & Hakkio, 1985; Frankel, 1979; Hansen & Hodrick, 1983), although it is important to note this it is not the only measure that could be derived on the basis of the rational expectations assumption.2 The approach adopted in this paper, however, involves using survey-based expectations to define the risk premium. This gives an alternative definition of the risk premium, labeled ltsu, which we believe is a more direct measure of this premium, since it should capture the expectations of agents who are ‘close to the market’. The measured period-by-period mean value3 of the survey expectation is defined as stsue + k . For a variety of reasons, such as the imperfect synchronisation of survey responses and the use of a consensus response (mean or median), which is extracted from only a fraction of market participants, it is unlikely that the mean survey expectation will be identically equal to the ‘true’ subjective expectation value, ste+ k . In common with researchers who have tested various expectational properties of survey data (see, for example, Frankel & Froot, 1987), we assume that the measured expected value is equal to the ‘true’ value plus a random measurement error (Eq. (3)): e ssue tþk ¼ stþk þ jtþk ,
ð3Þ
where jt + k is the survey forecast or measurement error. This implies that ltsu is given by ft stsue + k + jt + k Having access to the individual expectations of survey respondents 2
We are grateful to an anonymous referee for making this point. This is the mean of the cross-section at each point in time defined as the mean of the log of the individual expectation. 3
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Table 1 Unit root tests on the actual and expected variables (a) Spot rate D
L DM JY BP
t
t trend
t
t trend
1.99 0.48 1.86
2.37 2.15 2.52
7.22 5.10 6.67
7.19 5.27 6.65
(b) Forward rate D
L DM JY
t
t trend
t
t trend
2.13 0.53
2.07 3.01
7.20 7.00
7.10 6.90
(c) Expected spot rates DM
JY
BP
Country
t
t trend
t
t trend
t
t trend
MUK MCAN MFRA MGER MITL MJAP MUSA MBAN MSEC MIND
2.56 2.67 2.66 2.56 2.53 1.40 0.47 0.96 2.03 2.01
2.62 2.66 3.02 2.75 2.65 1.44 0.77 0.23 3.04 2.93
0.67 0.42 0.64 0.64 0.79 0.63 0.45 1.37 2.86 2.22
2.97 2.68 2.54 2.33 3.1 2.9 2.72 2.06 2.93 2.17
1.95 1.85 1.95 1.87 1.44 1.65 2.75 1.61 0.58 1.03
2.78 2.52 1.86 2.82 2.45 2.65 1.86 1.97 1.67 2.81
(d) Expected spot changes DM
JY
BP
Country
t
t trend
t
t trend
MUK MCAN MFRA MGER MITL MJAP MUSA MBAN MSEC MIND
13.4 17.2 18.1 12.9 9.5 31.5 12.1 12.1 17.4 27.5
42.4 18.0 28.0 22 15.2 40 56 20.8 35.2 33.2
9.7 17.8 10.4 10.1 14.5 15.8 6.7 20.4 16.3 18.3
37.7 35.7 25.03 20.08 36.9 41.8 3.96 34.2 45.8 38.8
t
t trend
25.3 35.4 36.7 39.5 31.1 35.7 29.5 29.6 35.1 37.2 38.1 38.8 33.9 36.2 29.6 29.7 36.9 40.1 30.4 30.8 (continued on next page)
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Table 1 (continued ) (e) The forward and risk premia Forward premium
Risk premium
t
t trend
2.95 4.63 3.86
3.20 5.44 6.71
t
t trend
DM survey RP 4.35 6.20 DM RERP 5.80 5.56 JY survey RP 4.16 7.58 JY RERP 4.50 4.55 BP survey RP 5.17 5.92 BP RERP 4.69 4.37 Of terms not defined in the text, the number in the columns headed t and t trend are, respectively, the estimated t ratios from an ADF equation when a constant and a constant plus a time trend are included as the deterministic variables. The 5% critical values for constant and time trend are, respectively, 2.79 and 3.09 (source Fuller, 1981). Column headings L and D denote, respectively, levels and first differences. DM JY BP
allows us to define the risk premium for each individual (or subgroups of individuals) in our survey as Eq. (4): i,sue
lt
i,sue ¼ ft stþk þ jitþk ,
ð4Þ
where the superscript i denotes individual i. One key issue in defining the rational expectations risk premium is that it is modeldependent: the econometrician has to make some assumption about the conditioning information set and a particular empirical result may be driven by a mismatch between the information set used by forecasters and that used by the econometrician. The use of survey data to measure expectations means that there is no difference between the investor’s and the econometrician’s information sets.
3. Data sources, time series properties, and some empirical regularities The survey data set that we exploit is constructed by the Consensus Forecasts of London. Since October 1989 Consensus Forecasts have surveyed and published the exchange rate forecasts of economists, foreign exchange dealers, and executives in over 150 companies and institutions in the G-7 nations. The companies surveyed, who remain the same over time, are mainly commercial and investment banks, but industrial corporations and forecasting agencies were also polled. The responders return a fax on the first Monday of each month containing their point forecasts of dollar–sterling, Deutschemark–dollar, and yen–dollar exchange rates, 3 and 12 calendar months ahead. Since the response rate is less than perfect, in the work that follows we constrain our analyses to a subset of the total panel (in particular, a balanced panel of 60 individuals). The time series dimensions of our data set are from October 1989 to March 1995.
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From the disaggregate data, we have constructed a number of aggregate indicators or means. In particular, the mean across forecasters located in the same nation — the country mean — will be denoted by the country mnemonic, preceded by ‘M’ (i.e., MUK is the UK mean; the other means, which should be self-explanatory, are MGER, MFRA, MITL, MJAP, MUSA, and MCAN). Additionally, we have estimated the properties of the mean for the three different groups of activities represented in our data set: MBAN is the mean of the banks, MSEC is the mean of the securities companies, and MIND is the mean of nonfinancial industries. Finally, our data on spot and forward exchange rates are collected from Datastream International and have been carefully aligned with the survey data. As a preliminary exercise, we used augmented Dickey–Fuller (ADF) tests to check the orders of integration of each of the series used in our econometric tests, and these are reported in Table 1. In sum, we find that the levels of variables — spot rates, expected spot rates, and forward rates — are nonstationary, but become stationary after first differencing (or quasidifferencing in the case of the forward premium and expected change in the exchange rate). The various measures of the risk premium are all stationary in levels. This essentially confirms the prediction of theoretical models of the risk premium (see, for example, Hodrick, 1987) and the findings of others using alternative data sets (see, for example, Frankel & Froot, 1989; MacDonald & Torrance, 1988). In Figs. 1–3, the forward premia (indicated by FP) for each of the three currencies is plotted against the corresponding rational risk premia, ltre. We note that the pattern here is
Fig. 1. DM rational risk premium and the forward premium.
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63
Fig. 2. BP rational risk premium and the forward premium.
very similar to that highlighted in many other papers: the forward premia are relatively constant around zero, while the rational risk premium risk premia are relatively volatile (this finding is confirmed in a statistical sense by our descriptive statistics, noted below). Of more interest, perhaps, is an answer to the question: how volatile are survey risk premia compared to their rational counterparts? The answer is portrayed in Figs. 4–6, where ltre is plotted against ltsu. It is clear from these figures that the rational risk premia are much more volatile
Fig. 3. JY rational risk premium and the forward premium.
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Fig. 4. DM rational- and survey-based risk premia.
than the survey-based counterparts, a finding confirmed in Table 2 where the variance of the rational risk premium is larger in every case than its survey-based counterpart. The source of this greater instability is revealed in Figs. 7–9 where, across the three currencies, the rational expected change in the exchange rate is more volatile than its survey-based counterpart, a finding which is again confirmed in Table 2 by the estimated sample variances. Given the discussion in Section 2, we interpret this as evidence that the rational-based risk premium is a much noisier proxy of the true risk premium than its survey-based counterpart. The disaggregate nature of our data set enables us to push our preliminary exploration of foreign exchange risk premia further, by comparing rational risk premia with individual risk premia and the risk premium defined for a particular sector (banks and securities). Consider Figs. 10–12, generated for the DM: in Fig. 10, the rational risk premium,
Fig. 5. BP rational- and survey-based risk premia.
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65
Fig. 6. JY rational- and survey-based risk premia.
RERPDM, is plotted against the survey risk premia defined for banks, RPBANKDM, and securities RPSECDM; in Fig. 11, RERPDM is plotted against RPBANKDM and the risk Table 2 Descriptive statistics for consensus variables and individual risk premia Dste + 3 Panel A: DM Mean 0.005 8.7e 005 s2 Ku 0.48 (.44) Q16 126 (.000)
fpt + 3
lsu t
lre t
Dst + 3
lt B18
lt B25
0.002 0.002 0.0089 0.006 0.21 0.214 8.8e 006 8.6e 005 0.00819 0.000851 0.0011 0.0007 0.59 (.356) 0.068 (.91) 0.437 (.495) 0.432 (.500) 0.53 (.408) 0.91 (.886) 231 (.00) 92.42 (.000) 89.5 (.000) 85.06 (.00) 76.2 (.000) 151.2 (.000)
Panel B: JY Mean 0.0004 0.0006 0.00088 0.0061 0.006 0.003 0.0018 s2 7.7e 005 3.4e 006 0.000145 0.00035 0.00034 0.00033 0.00032 Ku 0.148 (.817) 0.78 (.223) 7.26 (.000) 0.179 (.780) 0.173 (.786) 1.57 (.139) 0.059 (.925) Q16 173 (.000) 94 (.000) 121.84 (.000) 61.23 (.000) 61.9 (.000) 43.53 (.000) 234.9 (.000) Panel Mean s2 Ku Q16
C: BP 0.004 0.004 0.0007 4.7e 005 9.5e 006 8.66e 005 0.60 (.34) 2.01 (.001) 6.42 (.000) 22.21 (.136) 137 (.00) 39.18 (.001)
0.00181 0.0032 62.94 (.000) 60.62 (.000)
0.0014 0.0009 32.9 (.000) 60.63 (.000)
0.003 0.005 0.00033 0.000182 1.57 (.139) 0.472 (.461) 43.53 (.000) 140 (.000)
Of variables not defined in the text, lt B18 and lt B25 denote the individual risk premia of individual 18 and 25, respectively. s2 indicates the sample variance, Ku is the statistic of kurtosis Q16 is the Ljung – Box Q statistics for the 16 correlation coefficients and numbers in parentheses are the significance levels.
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Fig. 7. DM rational- and survey-based expected exchange rate changes.
premium defined for individual 18 (from the banking sector); in Fig. 12, RERPDM is again plotted against RPBANKDM and the risk premium defined for individual 25 (from the banking sector). This sequence of figures is repeated for the BP (Figs. 13–15) and for the JY (Figs. 16–18). The general thrust of these figures is that, across the three currencies, individual risk premia seem to contain a similar degree of volatility to the rational risk premia and for the JY there is some evidence that the sectoral risk premia also exhibit similar volatility (although not necessarily with the same sign). This finding is confirmed, in a statistical sense, in Table 2 where we see that the variance of the risk premia for two
Fig. 8. BP rational- and survey-based expected exchange rate changes.
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Fig. 9. JY rational- and survey-based expected exchange rate changes.
representative individuals (B18 and B25) are more volatile than the survey consensus measure and closer to the rational risk premia. It would seem therefore that the aggregate measures of the survey-based risk premia actually mask, or average out, much of the heterogeneity and richness of the individual survey expectations. This is consistent with studies that report important elements of heterogeneity in the kind of survey data used in this paper (see, for example, Chionis & MacDonald, 1997; MacDonald & Marsh, 1996).
Fig. 10. DM rational risk premium and risk premia for banks and securities.
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Fig. 11. DM rational risk premium and risk premia for banks and individual 18.
In Figs. 19–21, we present the first 17 autocorrelations of the rational risk premium for our three currencies, while in Figs. 22 – 24 the corresponding (mean) survey risk premia autocorrelations are noted. The striking contrast between these two sets of graphs is that the survey-based measures of the risk premia all tend have more persistence than their rational counterparts and to generate, with one exception, only positive autocorrelations. Interestingly, however, the disaggregate survey risk premia give a rather different picture as indicated in Fig. 25, which contains the autocorrelation functions of a representative selection of eight
Fig. 12. DM rational risk premium and risk premia for banks and individual 25.
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Fig. 13. BP rational risk premium and risk premia for banks and securities.
individual risk premia. Here the pattern is one of positive autocorrelations up to Month 5, followed by a sequence of insignificant negative autocorrelations down to Period 17. In addition to what we have already noted, several features of the aggregate time series properties of the data, as summarised in Tables 2–8, are worth commenting on. In accordance with previous findings using the rational expectations assumption, the unconditional variance of the survey expected exchange rate change is many times more variable than the variance of the forward premium. This is so irrespective of the consensus measure referred to. Further, both for the individual markets and for the means, the unconditional variance of the expected exchange rate change are large relative to the unconditional variance of the average. The fourth moments of the forward premium and the expected exchange rate changes suggest that the distributions deviate from normality. In most cases, the null hypothesis of a normal distribution is rejected. Finally, the magnitude of variances
Fig. 14. BP rational risk premium and risk premia for banks and individual 18.
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Fig. 15. BP rational risk premium and risk premia for banks and individual 25.
Fig. 16. JY rational risk premium and risk premia for banks and securities.
is similar across countries and across sectors, although there are one or two exceptions (for example, the mean of the US forecasters produces a much larger variance than any of the other country means).4
4
An anonymous referee has pointed out that the volatility of the rational risk premium may simply be a function of the use of the ex-post realisation of the spot rate rather than the assumption of rationality. While agreeing with this point, we would note that our measure of the rational risk premium is the most commonly used in the literature.
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4. Empirical modelling of the survey-based risk premium As we noted in Section 2, the availability of disaggregate survey data allows us to define a risk premium for each individual in our survey database and also for parti-
Fig. 17. JY rational risk premium and risk premia for banks and individual 18.
Fig. 18. JY rational risk premium and risk premia for banks and individual 25.
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Fig. 19. Autocorrelation function for DM rational risk premium.
cular groupings, or categories, such as banks and the insurance sector. We propose modelling these disaggregate risk premia using an ARCH(1)-M multivariate model of
Fig. 20. Autocorrelation function for BP rational risk premium.
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Fig. 21. Autocorrelation function for JY rational risk premium.
the following form: sei,tþ1 st ¼ li,t þ bi,0 ð ft st Þ þ ei,tþ1 ,
ð5Þ
lit ¼ ai þ bi,1 hi,tþ1 , ei,tþ1 j It N ð0,h2tþ1 Þ, h2tþ1 ¼ gi,0 þ gi,1 e2i,tþ1 þ gi,2 ðHetÞ2tþ1 : where the subscript i denotes firm- or individual-specific variables, Het stands for the heterogeneity, defined as the individual’s standard deviation from the mean value of all forecasters, the time index t + 1 indicates that this is a dispersion measure of survey expectations for t + 1 exchange rates, based upon time t information, and It is the information set available to investors at time t. The information matrix for the ARCH-M model is not block diagonal between b, on the one hand, and g on the other. This has two implications for
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Fig. 22. Autocorrelation function for DM survey risk premium.
the estimation methods. First, the model has to be estimated simultaneously, and not recursively, and secondly, the feasible GLS and one-step efficient estimation techniques that work for other ARCH models cannot be used. Maximum likelihood methods are therefore used to estimate the model.5 Domowitz and Hakkio (1985) have demonstrated how the ARCH class of model can be used to estimate a representative agent model of the risk premium. Here we simply posit this model as a useful and tractable way of capturing the effect of heterogeneity on individual risk premia. Before presenting the results of our analysis, we should note that since the response rate to the survey is less than perfect, we constrain our ARCH analysis to a subset of the total panel examined in the first part of this work. Specifically, we fit an ARCH-M to 51 individual forecasts for the DM, 46 for the BP, and 55 for the JY individuals (where the individuals are drawn from the banking and security sectors). The results from our ARCH modelling are summarised in Table 9a and b for the DM, Table 10a and b for BP, and Table 11a and b for the JY. In general terms, these results seem to 5
In order to incorporate the moving average error structure implied by the overlapping nature of our data set, we used the Broyden, Fletcher, Goldfarb, and Shanno algorithm to estimate the model. This algorithm facilitates the construction of standard errors, robust to both serial correlation and moving average errors.
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Fig. 23. Autocorrelation function for BP survey risk premium.
Fig. 24. Autocorrelation function for JY survey risk premium.
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Fig. 25.
provide strong support for the predictions of the theoretical model developed in Section 3. In particular, for the DM there are 28 out of 34 instances in the banking sector in which the heterogeneity term enters with a statistically significant coefficient and 13 out of 17 in the security industry. Similarly, for the BP, the corresponding ratios are 22 out of 25 for banks and 19 out of 21 for the security industry, while for the JY there are 23 significant out of 28 for the banking sector and 23 out of 27 for the security sector. It would seem therefore that the difference in heterogeneity is equally important across the two sectors. It is worth noting that when the heterogeneity term is excluded from the above model, the conditional heteroscedastic structure is significant in 97% of cases. However, with the heterogeneity included, the hetersoscedasticity becomes insignificant in most cases. It would seem then that the major part of the conditional volatility’s momentum,6 which other number of researchers have also found in foreign exchange markets, is explicable in terms of heterogeneous expectations. Not surprisingly, perhaps, in all cases in which the heterogeneity term is statistically significant it enters with a positive sign, indicating that an increase in heterogeneity increases the conditional volatility and subsequently the risk premium.
6 We test for the existence of conditional heteroscedastic structure in the forecasting residuals by applying an LM test statistic. In 97% of the cases, we can reject the null of no-conditional heteroscedasticity.
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Table 3 DM 3-month forecasts: expected exchange rate changes, per country mean MUK
MCAN
MFRA
MGER
MITA
MJAP
MUSA
Mean 0.006 0.0008 0.007 0.006 0.004 0.003 0.004 s2 0.00012 0.0001 9.52e 005 0.0001 0.0001 0.0001 7.83e 005 Ku 0.441 (.491) 9.12 (.000) 0.616 (.336) 0.22 (.730) 0.377 (.556) 0.527 (.410) 0.533 (.40) Q16 181 (.000) 18.93 (.217) 87 (.000) 123 (.000) 140 (.000) 41.8 (.000) 34.8 (.005) The mnemonics in the column headings are consensus, or mean values (M), for the United Kingdom (UK), Canada (CAN), France (FRA), Germany (GER), Italy (ITA), Japan (JAP), and the United States of America (USA). See Table 2 for other definitions. Table 4 DM 3-month forecasts: expected exchange rate changes, group mean Mean s2 Ku Q16
MBAN
MIND
MSEC
0.005 0.0001 0.33 (.602) 151 (.00)
0.005 0.0001 0.07 (.902) 30.56 (.015)
0.054 8.3e 005 0.31 (.61) 109 (.000)
The mnemonics in the column headings are consensus, or mean values (M) for key groups within the total panel, namely the banking sector group (BAN), nonfinancial industries (IND), and the mean of the securities companies (SEC).
In their estimates of the ARCH-M model for rational expectations-defined risk premia, Domowitz and Hakkio (1985) report rather weak results for the statistical significance of the risk premium in the unbiasedness equation. Our results present much clearer evidence for the existence of such a premium, especially when disaggregate data are considered. Thus, in the Table 5 JY 3-month forecasts: expected exchange rate changes, per country mean MUK
MCAN
MFRA
MGER
MITA
MJAP
MUSA
Mean 0.0007 0.002 0.001 0.002 0.0010 0.0005 0.09 s2 0.0001 6.8e 005 0.0001 0.0001 0.0001 6.2e005 0.17 Ku 0.47 (.461) 0.191 (.765) 0.148 (.171) 0.19 (.758) 1.37 (.031) 0.538 (.401) 18.1 (.00) Q16 219 (.000) 51.7 (.000) 142 (.000) 150 (.000) 162 (.000) 126 (.000) 38.0 (.001) See Table 3 for definitions. Table 6 JY 3-month forecasts: expected exchange rate changes, group mean Mean s2 Ku Q16 See Table 4 for definitions.
MBAN
MIND
MSEC
.005 0.0003 0.737 (.274) 56 (.00)
0.001 0.0001 96.7 (.08) 96 (.000)
0.0003 5.2e 005 0.49 (.44) 98.16 (.000)
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Table 7 BP 3-month forecasts: expected exchange rate changes, per country mean MUK
MCAN
MFRA
MGER
MITA
MJAP
MUSA
Mean 0.0047 0.002 0.006 0.006 0.218 0.11 0.007 s2 6.5e 005 5.7e 005 6.6e 005 6.2e 005 0.001 0.0001 8.6e 005 Ku 0.55 (.38) 0.28 (.66) 0.15 (.808) 0.55 (.38) 1.06 (.096) 5.4 (.000) 0.11 (.86) Q16 42.9 (.000) 29.7 (.019) 33.9 (.005) 29.9 (.018) 225 (.000) 16.8 (.397) 18.33 (.304) See Table 3 for definitions.
Table 8 BP 3-month forecasts: expected exchange rate changes, group mean Mean s2 Ku Q16
MBAN
MIND
MSEC
0.003 0.0002 2.52 (.0001) 31.8 (.010)
0.0029 0.0001 1.16 (.068) 35.3 (.003)
0.003 5.0e 005 0.58 (.365) 18.90 (.273)
See Table 4 for definitions.
case of the DM and BP, in 52–60% of cases we found the conditional variance to be statistically significant, although for the JY the number is smaller—24% in the banking sector and 30% in the security industry. Evaluating the performance of subgroups, we find that in the vast majority of the French-based institutions the risk premium is not significantly different from zero, while the British-based institutions produce weak results regarding the risk premium of the BP. Again, a notable feature of these results is the almost identical influence of the risk premium in the forecasting patterns of the bank and security sectors. The fluctuations between negative and positive values of the risk premium (see columns labeled Risk) is in accordance with the findings of Domowitz and Hakkio and the theoretical model proposed by Stockman (1980). The majority of the negative signs imply that the effect of the risk premium is to push estimates of the standard coefficient of b above 1; a positive value indicating an overreaction to available information. The vast majority of positive signs are concentrated in the security industry’s forecasting patterns, especially for the DM and the JY. For the JY and DM, 67% and 65% of individual’s risk premia enter with a positive sign; in the case of BP, the ratio approaches 30%.7
5. Conclusions In this paper, we have reexamined the importance of risk premia in foreign exchange markets using a disaggregate multicountry exchange rate survey database. The availability of 7
As a robustness check on the results presented in this section, we reestimated all of the models using a GARCH process. The results were qualitatively similar to those generated using the ARCH-in-mean model and are therefore not reported here.
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Table 9 Summary of results for ARCH modelling (currency: DM) Heter (a) Sector: banks B13 B25 B35 C1 C12 C15 C2 F11 F16 F9 G10 G11 G12 G13
Forward
Risk
B13
C12 C15
F16 F4 F9 G10 G12 G15
G18
B25 B35 C1 C12 C15 C2
F16
G11 G12 G15 G18
G19 G2 G22 G23 G3 G4 G5 G8 I5 I6 J9 U15 U19 U18 82% Total: 34 (b) Sector: securities B18 B27 B29 B30 B4 B8
G22 G23
G2 G22 G23
G5 I1 I5 I6
G8 I1
U15 U19 U18 56%
U15 U19 U18 56%
B18 B27 B29
B18 B27 B29 B30
B8
+ Heter
Risk
B13 B25 B35 C1 C12 C15 C2 F10 F11 F16 F4 F9 G10 G11 G12 G13
B13 B25 B35 C1 C12 C15 C2 F10 F11
G18 G19 G2 G22 G23 G3 G4 G5 G8 I1 I5 I6 J2 J9 U15 U19 U18 97%
G18
B18 B27 B29 B30 B4 B8
G10 G11 G12
G2 G23 G3 G5 I1
J2 J9 U15 U19 U18 68%
B18
B4 B8 (continued on next page)
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Table 9 (continued) Heter (b) Sector: securities B9 C3 F12 F2 G5 J20 J3
Forward
Risk
+ Heter
B9 C3 C4
B9 C3 C4 F12
B9 C3 C4 F12 F2 G5
F2 G5 J20 J3
Risk
C3
G5
J20 U1
J3 U1 U24 88%
U24 88% 65% 59% 35% Total: 17 The column headed Heter lists those individuals who produce a statistically significant coefficient of heterogeneity in the ARCH model listed as Eq. (5). The letters B, C, F, G, I, J, and U denote the country in which the forecaster is based (Britain, Canada, France, Germany, Italy, Japan, and the US, respectively). The column marked Forward lists those individuals for whom the forward premium is statistically significant while in Risk those individuals producing a statistically significant coefficient on the risk premium are recorded. Those individuals for which the heterogeneity term is positive are recorded in the column labeled + Heter, while those in Risk have a statistically significant negative sign on the risk premium.
survey data offers an independent measure of foreign exchange market participants’ expectations of the exchange rate. In summary form, our work clearly indicates that studying the behaviour of agents in disaggregate terms produces very different results to aggregate studies that rely on the assumption of rationality. More specifically, we have found that although rational risk premia are noisier than consensus measures of survey risk premia, individual risk premia based on survey data show a degree of volatility that is closer to that of rational risk premia. We attribute the difference between individual survey premia and consensus measures to the existence of heterogeneity in the individual data that essentially cancels out in the mean. Furthermore, when an ARCH-M model was used to model individual risk premia a large number of the risk premium terms were statistically significant and, interestingly, the heterogeneity term removed much of the momentum in the conditional volatility. The evidence in favour of a risk premium is, however, less clear-cut when the consensus value is used. So essentially our findings confirm the importance of heterogeneity in foreign exchange markets noted by Chionis and MacDonald (1997), Ito (1990), and MacDonald and Marsh (1996), although these papers focussed on expectational processes rather than risk premia. We believe that the existence of such heterogeneity is supportive of the market microstructure view of the operation of foreign exchange markets (see, for example, Goodhart, Ito, & Payne, 1996; Lyons, 1995). The main conclusion of this paper is that the failure of other researchers to uncover a risk premium is due in large measure to the use of a consensus measure of risk. What comes out
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Table 10 Summary of results for ARCH modelling (currency: BP) Heter
Forward
(a) Sector: banks B25 B13 C15 C1 F4 F12 F10 F5 F10 G10 G11 G12 G13 G2 G22 G3 G4 C5 G8 I1 I2 I5 88% Total: 25 (b) Sector: securities B30 B27 B22 B2 B18 B14 B12 B9 B8 B4 B35 C18 C12 C4
Risk
+ Heter
B25
B25 B13 C15 C1 F4 F12 F10 C5 F5 F10 G10 G11 G12 G13 G15 G2 G22 G3 G4 G5 G8 I1 I2 I5 J2 100%
C15 C1 F12 F10 C5 F10 G10 G11 G12
G2 G22 G4
G4 G8 I2
8%
J2 60%
B30
B2 B14 B9 B8 B4
C12 C4 G19
B35 C18 C12
B30 B27 B22 B2 B18 B14 B12 B9 B8 B4 B35 C18 C12 C4 G19
Risk
B13 C15 C1 F4
C5 F5
G12 G13 G15 G22 G3 G4 G8 I1 I2 I5 J2 68%
B30 B27
B18 B14 B9 B8 B35
C12 G19 (continued on next page)
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Table 10 (continued) Heter (b) Sector: securities G9 I6 J20 U1
Forward
Risk
+ Heter
Risk
G9 I6 J20
G9 I6 J20 U1 U24 100%
G9 I6 U1 U24 70%
+ Heter
Risk
B13 B25 B27 B9 C1 F10 F16 F4 F5 F9 G8 G5 G4 G3 G22 G20 G15 G13 G12 G10 I1 I5 J9
B13
U1
95% 25% Total: 21 See Table 9a for definitions.
52%
Table 11 Summary of results for ARCH modelling (currency: JY) Heter (a) Sector: bank B13 B25 B27 B9 F10 F16 F4 F5
Forward B13 B25 B27
F5
G8 G5 G4 G3
Risk
B27
F5 G8 G4 G22
G20 G15 G12 G10 I1 I5 J9 J2 J17 J11 J13 82% Total: 28
G12 G10 I1
G10
J9
J17
28%
24%
J17 J11 J13 93%
F16 F5 F9 G8
G3
G13 G12 I1 I5 J9 J2 J18 J17
50% (continued on next page)
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Table 11 (continued) Heter (b) Sector: securities B18 B2 B29 B30 B35 C12 C3 C4 C5 F12 G9 G19 G11 I6 J6 J4 J16 J15 J1
Forward
Risk
B18 B2 B29 B30 C12
C4 F12 G9
J4
J4
J16
J16
+ Heter B18 B2 B29 B30 B35 C12 C18 C3 C4 C5 F12 G9 G19 G11 I6 J6 J4 J3 J16 J15 J1
U8 U30 U24 U19 U15 U1 U1 85% 30% Total: 27 See Table 9a for definitions.
U19
30%
Risk
B2
C12 C18
G11 J6
J15 U8
U30 U24 U19 U15 U1 96%
U19 U1 33%
clearly from the present work is that because the consensus essentially averages out heterogeneity it means that any tests for the existence of risk premia based on consensus expectations are unlikely to be successful.
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