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Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

Asset prices and exchange risk: Empirical evidence from Canada Lucie Samson ∗ Université Laval, 1025 av. des Sciences-Humaines, Pavillon J.-A. deSève, Québec, Québec, Canada C1V 0A6

a r t i c l e

i n f o

Article history: Received 29 June 2010 Received in revised form 27 September 2012 Accepted 28 September 2012 Available online 8 October 2012 Keywords: Asset pricing Risk premium Exchange risk Economic factors

a b s t r a c t Asset prices have been found to respond to unpredicted changes in macroeconomic variables in a number of studies. This paper focuses on the relationship between economic factors and the stock market for a small open economy, namely Canada. Exchange risk is observed to have a signiﬁcant impact on ﬁrm value in that country between 1971 and 2004. Inﬂation risk also played a non negligible role during the seventies and eighties. The role played by market risk is harder to ascertain. © 2012 Elsevier B.V. All rights reserved.

JEL classiﬁcation: G10 G11 G12 G15

1. Introduction Preference-free valuation models explain the behavior of asset returns through their link with relevant risk factors. These factors are those that cannot be diversiﬁed away. In some cases, the underlying risks are treated as unobserved and the time-varying expected returns are linked to the behavior of one or more latent variables. In other cases, observable macroeconomic economic variables are used as factors to capture some of the systematic risks present in the economy. Examples of these variables are the inﬂation rate, a market return index, a production index, a measure of aggregate consumption,

∗ Fax: +1 418 656 2707. E-mail address: [email protected] 0275-5319/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ribaf.2012.09.006

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the real rate of interest, and a measure of spread between a long and a short rate or between the return on risky and safe assets. Two approaches can be used to model the impact of economic variables on asset prices. On one hand, the factor loadings can be treated as constant over time and a simultaneously equation model can be estimated. When the risk factors are made explicit, the result is a highly constrained model. When they are left unspeciﬁed, the resulting latent variable model imposes fewer constraints, is not as easily rejected, but the source of risk cannot be identiﬁed. In the former case, the part of a return that is not explained by the factor realizations times their factor loading is simply the idiosyncratic risk associated with any given asset. Examples of this type of analysis are found in Ferson and Harvey (1991), Elton et al. (1995), and Harvey et al. (2002) among others. The obvious advantage of this procedure is that all equations are estimated simultaneously, so there is no errors-in-variables problem. The hypothesis of constant factor loadings over long periods of time can be too strong in some cases however. Fama and Macbeth (1973), Chen et al. (1986), Fama and French (1992), Shanken and Weinsten (2006), Virk (2012) and others use a cross-sectional procedure that presents the opposite problem. The loadings, the betas, are usually estimated from a series of rolling regressions, allowing them to vary over time, or from the entire sample period, implying that they are kept constant over time. The choice between the two procedures is often dictated by the length of the overall sample period, the rolling window method necessitating more observations. The betas are subsequently used as regressors in cross-sectional regressions to determine the size of various risk premia. Since the same data is used to generate the betas and estimate the risk premia, the commonly known errors-in-variables problem is then present and the standard errors associated with the premia are usually underestimated. The results presented in this paper combine both approaches, with speciﬁed risk factors, making it an interesting check on the robustness of our empirical ﬁndings. The Capital Asset Pricing Model (CAPM) identiﬁes the correlation between the return on any given asset j and the return on the market portfolio as the relevant factor in the determination of the associated risk premium. It has been observed in a number of papers that the market return is not always statistically signiﬁcant and/or important as a risk factor when other economic variables are considered simultaneously. In this paper, macroeconomic variables are introduced as risk factors along with the market return, with special emphasis on exchange risk factors since asset returns from a small open economy, Canada, are considered. The two approaches mentioned above are used. The Fama and Macbeth (1973) cross-sectional analysis is ﬁrst performed to identify factors that could be of importance as well as sub-periods where different macro variables might have played a signiﬁcant role. The simultaneous equation analysis is then performed with the chosen economic factors and sub-periods. The paper proceeds as follows. In the next section, the cross-sectional model is introduced and the estimation results are presented. Section 3 characterizes and reports results from the simultaneous model. Finally, conclusions are drawn in the last section. 2. Evaluating risk premia: a cross-sectional model In this section, a cross-sectional model, similar to the one proposed in Fama and Macbeth (1973), is presented. The estimation procedure is divided in two steps. In the ﬁrst stage of the analysis, the betas of the model, the multiple regression coefﬁcients related to a set of chosen variables, are generated using a rolling regressions method. The length of the rolling window is ﬁxed. In the second stage, the estimated betas themselves are used as regressors in a cross-section of returns of varying sizes. The corresponding risk premia are then estimated. The ﬁrst step can be described by the following set of time series regressions: Rit =

j

bji Zjt−1 + it

i = 1, . . . , K

(1)

where Rit is the period t return on portfolio i in excess of the risk free rate, the Zjt−1 ’s are the J information variables used to generate the betas, and it is the part of each excess return that is orthogonal to the proposed economic variables. There are K portfolio excess returns. A rolling window of pre-determined length N is used to generate a vector of betas for each time period. The informational

L. Samson / Research in International Business and Finance 28 (2013) 35–44

37

content of the economic variables is therefore renewed slowly, one observation at a time, allowing the estimated betas to vary over time. In the second step, the estimated ˇji ’s from Eq. (1), are used in a cross-section of returns, allowing the price of each factor to be assessed. A factor that is signiﬁcantly priced by the data has a corresponding statistically signiﬁcant risk premium. Therefore for each period , the following cross-section regression is performed: Rt = a0t +

j

ajt bjt + t

(2)

where R is a vector of size portfolio excess returns for period . The estimated aj is the risk premium associated with the corresponding period- beta. The error term is the part of each excess return that is uncorrelated with the constant and the identiﬁed risk factors. If a risk factor is priced, the associated estimated aj ’s will be statistically different from zero. The analysis is performed using monthly data from the Toronto Stock Exchange (TSE), from 1961:1 to 2004:12, a period of forty-four years. The data is regrouped into ten size portfolios. The individual returns used to form the ten size portfolios are obtained from the Canadian Financial Markets Research Center Database (CFMRC). When calculating the portfolio returns, the weight for each return is kept constant for the year at its June value. The returns are measured in excess of the 3-month Treasure bill rate, representing the risk free rate. The economic variables, the Z’s, used to generate the betas and estimate the risk premia are comparable to those presented in the existing literature.1 The return on the market portfolio (rM ), as measured by the value weighted return on the TSE, is considered since it is identiﬁed by the CAPM literature as a potentially important risk factor. Previous studies have found inﬂation and real interest rates to play a signiﬁcant role as well. The ﬁrst variable will be priced if it can have real effects via differing sensitivities or adjustment costs. The second variable summarizes the general state of investment opportunities. The measured inﬂation rate () is the percentage change in the consumer price index. The real interest rate (r) is the difference between the three-month Treasury bill rate and inﬂation. Since forty percent of the goods produced in Canada are sold abroad, and of those, eighty percent are directed towards the United States, a measure of foreign exchange rate risk is also introduced in the list of relevant economic variables. This variable is deﬁned as the absolute value of the changes in the bilateral Canada–US dollar exchange rate (F). A number of previous studies have found a moderate to signiﬁcant impact of exchange risk on ﬁrms’ value for various countries, assuming either asymmetric or symmetric exposure. See for example, Apergis et al. (2011), Doidge et al. (2006), Dominguez and Tesar (2006), Goldberg and Veitch (2010), Grifﬁn and Stulz (2001), Koutmos and Martin (2003), Kolari et al. (2008), Virk (2012), Zhao (2010) and others.2 Summary statistics for these variables are presented in Table 1. As expected the smallest size portfolio exhibits the highest average return, but with the corresponding highest standard deviation. The largest size portfolio is characterized by the opposite statistics. Among the economic and ﬁnancial risk factors, the market return is the most volatile, followed by the exchange rate variable. The real interest rate and the inﬂation rate are both relatively small and they have comparable standard deviations. The correlations (positive or negative) between these four variables are very small except for the real interest rate and the inﬂation rate, with a calculated value of −0.72.3 The ﬁrst pass of the estimation procedure requires that the length of the rolling window be speciﬁed when estimating Eq. (1). A ten year period, or 120 observations, was chosen. That choice was dictated by the fact that the period has to be long enough to generate meaningful betas, while not loosing

1

These variables were all obtained from the CANSIM database provided by Statistics Canada. Some studies have, on the other hand, found no or very little evidence of a priced exchange risk factor. Examples are Jorion (1991), Bartov and Bodnar (1994), Grifﬁn and Stulz (2001) and Anatolyev (2008). 3 No monthly consumption data is available for Canada, so this variable could not be included, even if the C-CAPM model would suggest it as a relevant risk factor. Chen et al. (1986) also introduced a production index variable in their list of economic factors. This series is available monthly, but not on a continuous basis for the entire period considered in this paper. 2

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L. Samson / Research in International Business and Finance 28 (2013) 35–44

Table 1 Descriptive statistics: returns and economic variables (1971:1–2004:12). Variable

Mean

Standard deviation

r1 r2 r3 r4 r5 r6 r7 r8 r9 r10 rM r F

2.905 1.656 1.150 0.915 0.864 0.865 0.716 0.872 0.899 0.850 0.984 0.183 0.875 0.405

9.173 6.553 6.065 5.297 5.147 4.885 4.935 4.862 4.809 4.267 4.867 0.415 0.720 0.421

r1 represents the monthly return for the smallest size portfolio and r10 is the return for the largest ﬁrms. The market return (rM ) is the value-weighted return on the TSE, (r) is the return on the 3-month Treasury bill less the inﬂation rate, (F) is the absolute value of the changes in the Canada-US dollars exchange rate, and () is the CPI inﬂation rate.

too many observations at the beginning of the sample period. Consequently, the starting date for the estimated betas is January 1971. Four betas per month are estimated this way, one for each risk factor. The second step of the procedure implies regressing a cross-section of returns on the betas for each time period, as shown in Eq. (2). Since only ten size portfolios were created (K = 10), due to the thinness of the Canadian market for small ﬁrms, it implies too few degrees of freedom. For that reason, a pooling of three consecutive months was done when estimating the risk premia, creating a dependent variable 30 observations long instead of 10 observations only. This procedure imposes that the estimated premia, the aj ’s, are constant over a three month period for each factor. Instead of 408 estimated values for each risk premium, this pooling of data implies that a third of that number, 136, is generated for the 1971:1–2004:12 period. A multi-factor analysis is performed since it has been shown in previous studies that a variable might show up as important when considered alone, but may be subsumed by other risk factors in a multivariate regression context. Table 2 reports summary statistics for the estimated premia. The top row of the table refers to the entire period while the next two rows report statistics related to two sub-samples. From this table, it appears that exchange risk has been present for the whole sample. The size of the estimated premium is stable over time, and in spite of the bias in the standard errors, it seems

Table 2 Estimated mean risk premia: cross-sectional model (1971:1–2004:12). Period

Constant

rM

r

F

1971:1–2004:12

−0.454 (4.059) [−1.305]

0.789 (30.06) [0.306]

0.209 (3.148) [0.775]

1.759 (3.542) [5.791]

0.921 (4.060) [2.644]

1971:1–1989:12

−0.425 (3.426) [−1.081]

−0.495 (18.49) [−0.233]

0.271 (3.294) [0.718]

1.716 (3.458) [4.327]

1.305 (5.210) [2.184]

1990:1–2004:12

−0.491 (4.771) [−0.798]

2.414 (40.35) [0.464]

0.131 (2.979) [0.340]

1.813 (3.674) [3.822]

0.433 (1.667) [2.014]

Estimates of risk premia are obtained from Eq. (2) for a cross-section of the ten size portfolios (maintaining the premia constant for three months each time), making 136 regressions. Means are calculated over the reported sample periods. Standard errors in parentheses and Fama and Macbeth t-statistics in brackets.

L. Samson / Research in International Business and Finance 28 (2013) 35–44 20

39

A

15

10

5

0

-5

-10 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

20

B

15

10

5

0

-5

-10

-15

-20 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004

Fig. 1. (A) Estimated exchange risk premium, (B) estimated inﬂation risk premium.

to play a signiﬁcant role. Inﬂation risk has been present mostly in the seventies and eighties, which corresponds to the period where central monetary authorities in many economies, including Canada, had to deal with fairly high and volatile inﬂation rates. By the end of the eighties, inﬂation was under control in Canada, dictating our choice of sub-sample. The market return premium seems to have become predominant in size in the nineties and the following years, but it is estimated with a lot of imprecision, causing it to be statistically insigniﬁcant. The support for the CAPM model is therefore very weak. The real interest rate does not show up as an important contributing risk factor with an estimated risk premium close to zero for the entire sample period. Since only the inﬂation and exchange premia have relatively high t-statistics for the whole sample period, only these two variables are reproduced in Fig. 1A and B. These two premia correspond to the estimated aj ’s in Eq. (2) associated with the inﬂation and exchange rate betas. As should be expected, they are both quite volatile. The volatility and mean value of the inﬂation premium have however decreased substantially after the eighties, while exchange rate risk does not seem to have changed much over time.

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L. Samson / Research in International Business and Finance 28 (2013) 35–44

3. Evaluating risk premia: a simultaneous equations model A simultaneous equations model with one pre-speciﬁed risk factor is presented and tested below. Since the previous analysis has identiﬁed a potential role for exchange risk during the entire sample period, this variable Ft is treated as the relevant observed risk factor. The proposed model is similar to the one presented in Ferson (1990). In the case of one observed risk factor, it is: Ft − Zt−1 ˛ = t

(3)

R1,t − Zt−1 ı − (Ft − Zt−1 ˛)˝1 = 1,t Ri,t − (Zt−1 ı)(˝1

−1

˝i ) − (Ft − Zt−1 ˛)˝i − i,t

(4) i = 2, . . . , K

(5)

In this system of equations, Ft is the foreign exchange risk factor, t is the factor realization which is orthogonal to the information set Zt−1 , and the ˝’s are the factor loadings of this realization in the excess return equations.4 Eq. (3) deﬁnes the conditional mean of the relevant state variable, Ft . As suggested by asset pricing models, it is the innovations in this state variable, the t ’s, that represent the relevant risk for investors. Eq. (3) is necessary to identify these innovations. They represent unexpected ﬂuctuations in Ft , those that are orthogonal to the information set Zt−1 . In this system, portfolio of size one is the reference asset and the other size portfolios are the test assets. The excess return on the reference portfolio is characterized by Eq. (4). This regression is a projection of the dependent variable on the innovations in Ft and on the information set. The rest of the system, embodied in Eq. (5), relates the mean of the reference asset to those of the test assets through the cross-equation restrictions present in the speciﬁed model. The well-known Generalized Method of Moments (GMM) procedure is used to carry out the estimations. This method implies deﬁning the following vector of orthogonality conditions: G(Xt, Zt−1, b) = H(Xt, b) × Zt−1

(6)

Where Xt is the data, Zt−1 is deﬁned above, b is the vector of parameter estimates and H(Xt , b) represents Eqs. (3)–(5). With a well speciﬁed model, at the true parameter vector b0 , it must be the case that: E[G(Xt, Zt−1, b0 )] = 0

(7)

The GMM procedure chooses the estimated coefﬁcients so as to be as close as possible to satisfying condition (7). The reported J-statistics in Table 3 and Table 4 are tests of the over-identifying restrictions implied by the model. As indicated by condition (7), they should be close to zero. They are distributed as Chi-squared statistics.5 Table 3 presents estimation results with the exchange rate variable as the only risk factor. The lagged exchange rate variable is included in the information set, Zt−1 , along with the other previously mentioned variables, namely the real interest rate, the market return and the inﬂation rate, to ensure that the realization of the risk factor is orthogonal to any relevant past information. This table indicates that, with a reported J-statistic(46) = 78.19 and a corresponding signiﬁcance level of 0.002, well below the usual ﬁve percent level, the model’s overidentifying restrictions are clearly rejected by the data when the entire sample period is considered. The factor loadings, the ˝’s, take plausible values however, and are statistically signiﬁcant. They indicate that small ﬁrms (portfolios 2, 3, etc.) may be more sensitive to exchange risk than larger ones (portfolios . . ., 9, 10). The assumption of constant loadings for the entire sample period could be too restrictive and may be causing the model’s rejection by the data. The estimations were therefore carried out for the two sub-samples discussed previously, 1971:1–1989:12 and 1990:1–2004:12. The signiﬁcance levels are greatly improved by this split in the sample even if the model’s restrictions are still rejected. The

4 If there are more than one explicit risk factors considered, Ft is replaced by an M-vector of risk factors, and there are K–M test assets remaining. 5 For more efﬁciency, the unpredicted component of exchange rate ﬂuctuations from equation (3) is used as an additional instrument. The degrees of freedom of the reported J-Statistics are adjusted accordingly.

L. Samson / Research in International Business and Finance 28 (2013) 35–44 Table 3 equations model: exchange Simultaneous Ri,t − (Zt−1 ı)(˝1 −1 ˝i ) − (Ft − Zt−1 ˛)˝i − i,t i = 2, . . ., K.

risk

factor,

Ft − Zt−1 ˛ = t ,

41

R1,t − Zt−1 ı − (Ft − Zt−1 ˛)˝1 = 1,t ,

Period: 1971:1–2004:12 ˛0 0.802 (0.082)

˛1 0.003 (0.006)

˛2 −0.205 (0.101)

˛3 0.257 (0.046)

˛4 −0.287 (0.117)

ı0 4.326 (0.797)

ı1 0.362 (0.074)

ı2 −3.083 (1.016)

ı3 0.144 (0.428)

˝3 ˝4 ˝5 ˝2 0.599 0.439 0.310 0.245 (0.066) (0.062) (0.054) (0.051) J-statistic(46): 78.19, signiﬁcance level: 0.002

˝6 0.188 (0.052)

˝7 0.178 (0.055)

˝8 0.163 (0.055)

˝9 0.129 (0.055)

˝10 0.100 (0.052)

˛3 0.201 (0.055)

˛4 0.291 (0.122)

ı0 4.808 (1.081)

ı1 0.275 (0.070)

ı2 −5.979 (1.301)

ı3 0.222 (0.574)

˝3 ˝4 ˝5 ˝2 0.748 0.566 0.546 0.427 (0.065) (0.063) (0.062) (0.058) J-statistic(46): 67.60, signiﬁcance level: 0.021

˝6 0.398 (0.064)

˝7 0.329 (0.067)

˝8 0.358 (0.071)

˝9 0.282 (0.068)

˝10 0.277 (0.067)

˛3 0.218 (0.058)

˛4 −0.912 (0.213)

ı0 2.850 (0.952)

ı1 0.601 (0.120)

ı2 0.054 (1.401)

ı3 0.027 (0.470)

˝2 ˝3 ˝4 ˝5 0.542 0.422 0.240 0.137 (0.083) (0.073) (0.060) (0.056) J-statistic(46): 63.44, signiﬁcance level: 0.045

˝6 0.090 (0.050)

˝7 0.090 (0.057)

˝8 0.088 (0.055)

˝9 0.024 (0.056)

˝10 −0.034 (0.052)

ı4 −4.615 (1.047)

Period: 1971:1–1989:12 ˛0 0.368 (0.087)

˛1 0.005 (0.006)

˛2 0.181 (0.098)

ı4 −4.974 (1.357)

Period: 1990:1–2004:12 ˛0 1.154 (0.116)

˛1 0.005 (0.009)

˛2 −0.767 (0.172)

ı4 −1.492 (1.350)

Standard errors in parentheses. Variables in Zt−1 are a constant and the lagged values of the market return, the real interest rate, the exchange rate variable and the inﬂation rate. The ˝’s are the sensitivity of each portfolio’s return to the factor’s realization (relative to portfolio one since, for identiﬁcation purposes, ˝1 = 1).

estimated loadings are generally larger and slightly more precisely estimated in the ﬁrst period. The reported signiﬁcance level is closer to the usual 5% level for the most recent sub-period however, leading almost to non-rejection of the proposed model. Since the standard errors are not biased when using this simultaneous procedure, the previous ﬁnding that exchange rate ﬂuctuations have been a priced risk factor appears to be robust. Rejection of the model’s restrictions implies however that this source of risk is not sufﬁcient to entirely determine the behavior of the analyzed excess returns during the period. The cross-sectional analysis presented in Section II indicated that inﬂation has potentially played an important role in the seventies and eighties, a period during which it was relatively high and volatile. The same analysis revealed that market exposure might, on the other hand, have been a more important contributing risk factor, even if quite imprecise, in the latter part of the sample period. Consequently, we checked for the presence of a statistically signiﬁcant second risk factor in those two sub-samples. Table 4 reports results of a two-factor model with inﬂation risk added to exchange rate risk for the 1971:1–1989:12 period, and the market return added as a second risk factor for 1990:1–2004:12.6 The exchange rate ﬂuctuations variable is present for both sub-periods since Table 3 has shown that, even if it cannot be the sole contributing risk factor, it has nevertheless signiﬁcantly

6 Estimations were also carried out for the entire period, 1971:1–2004:12, and the alternative sub-samples, for both factors, but did not converge.

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L. Samson / Research in International Business and Finance 28 (2013) 35–44

Table 4 Simultaneous equations model: two risk factors and two sub-periods. Exchange and inﬂation risk factors: 1971:1–1989:12 ˛0,F 0.416 (0.084)

˛1,F 0.012 (0.006)

˛2,F 0.285 (0.097)

˛3,F 0.087 (0.058)

˛4,F 0.301 (0.118)

˛0, 0.297 (0.066)

˛1, 0.001 (0.004)

˛2, 0.163 (0.080)

˛3, 0.018 (0.032)

˛4, 0.433 (0.084)

ı0,1 −0.822 (0.203)

ı1,1 0.054 (0.023)

ı2,1 −1.424 (0.668)

ı3,1 0.017 (0.306)

ı4,1 0.621 (0.490)

ı0,2 −0.946 (0.242)

ı1,2 0.073 (0.022)

ı2,2 −1.518 (0.629)

ı3,2 0.141 (0.329)

ı4,2 0.702 (0.496)

˝2,F 0.922 (0.250)

˝3,F 0.937 (0.244)

˝4,F 0.332 (0.229)

˝5,F 0.502 (0.225)

˝6,F 0.381 (0.214)

˝7,F 0.368 (0.231)

˝8,F 0.315 (0.232)

˝9,F 0.273 (0.246)

˝10,F 0.774 (0.246)

˝3, ˝4, ˝5, ˝2, 1.156 1.133 1.062 0.590 (0.258) (0.264) (0.215) (0.238) J-statistic(42): 39.06, signiﬁcance level: 0.601

˝6, 0.860 (0.240)

˝7, 0.541 (0.219)

˝8, 0.181 (0.246)

˝9, 0.005 (0.255)

˝10, −0.274 (0.344)

Exchange and market risk factors: 1990:1–2004:12 ˛0,F ˛1,F ˛2,F ˛3,F 1.059 −0.015 −0.633 0.215 (0.010) (0.176) (0.060) (0.118) ı1,1 ı2,1 ı3,1 ı0,1 0.691 0.983 3.083 1.048 (1.120) (0.456) (0.130) (0.164) ˝5,F ˝3,F ˝4,F ˝2,F −0.173 0.216 0.076 −0.081 (0.117) (0.125) (0.139) (0.118) ˝3,M ˝4,M ˝5,M ˝2,M 0.934 0.921 0.879 0.917 (0.055) (0.047) (0.046) (0.047) J-statistic(42): 64.23, signiﬁcance level: 0.015

˛4,F −0.570 (0.209) ı4,1 2.091 (1.098) ˝6,F −0.214 (0.132) ˝6,M 0.867 (0.048)

˛0,M −0.944 (0.655) ı0,2 −0.739 (0.375) ˝7,F −0.242 (0.144) ˝7,M 0.928 (0.043)

˛1,M 0.108 (0.071) ı1,2 0.510 (0.083) ˝8,F −0.221 (0.141) ˝8,M 0.916 (0.047)

˛2,M 0.116 (1.070) ı2,2 1.219 (0.895) ˝9,F −0.251 (0.125) ˝9,M 0.759 (0.047)

˛3,M 0.349 (0.266) ı3,2 0.706 (0.275) ˝10,F −0.314 (0.122) ˝10,M 0.763 (0.040)

˛4,M 2.599 (1.096) ı4,2 1.793 (0.829)

Standard errors in parentheses. Variables in Zt−1 are a constant and the lagged values of the market return, the real interest rate, the exchange rate variable and the inﬂation rate. The ˝’s are the sensitivity of each portfolio’s return to the factor’s realization (relative to portfolio one since, for identiﬁcation purposes, ˝1,E = 1, ˝1, = 1 and ˝1,M = 1).

impacted on excess returns. Portfolios one and two are the reference assets (with unconstrained ı parameters), and the other K-2 portfolios are the test assets. As shown in the top part of Table 4, adding inﬂation clearly improves the ﬁt of the model for the ﬁrst sub-period. The model’s restrictions are not rejected by the data and both factors are contributing to this good ﬁt. The factor loadings, the ˝’s, take plausible values and are generally statistically signiﬁcant. It appears from these estimation results that foreign exchange and inﬂation risks were both priced during the seventies and eighties, especially when small ﬁrms are considered.7 Once again, these results are generally in support of those presented in Table 2 with the cross-section methodology. The results for the second sub-period, with the market return as the additional risk factor, tell a different story. The model’s restrictions are rejected by the data. The ﬁt is worst than with exchange rate ﬂuctuations as the only risk factor. The loadings, however, indicate that the sensitivity to market risk may have been quite important during that period, while the role played by exchange risk is estimated with less precision. But, given the reported signiﬁcance level of 0.015, these coefﬁcients must be interpreted with care. Using the return on the Standard and Poor’s 500 as an alternative deﬁnition of market return, one implying perfect North American ﬁnancial integration, did not change

7 A notable exception is portfolio of size 10 composed of the largest Canadian ﬁrms, since the exchange rate factor loading (F ) increases for this excess return. This may reﬂect the fact that these ﬁrms represent a large percentage of across-the-border transactions.

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the basic results.8 No convergence or ﬂat rejection of the model’s restrictions was obtained for the two sub-samples (1971:1–1989:12 and 1990:1–2004:12) and the whole period. 4. Conclusion This paper has investigated the sources of risk present when pricing assets listed on the Toronto Stock Exchange, a market from a small open economy. Two methodologies commonly exploited in the literature were used, a Fama–Macbeth-type cross sectional model and a Ferson-type simultaneous equations with pre-speciﬁed factors model. The period under study extends from 1971:1 to 2004:12. The cross-sectional analysis revealed that exchange risk has affected the value of Canadian ﬁrms since the beginning of the ﬂoating exchange rate period in 1970. The important role played by this risk factor has stayed fairly stable over time. This result suggests that when looking at the costs and beneﬁts of a ﬂoating exchange rate regime, compared to a ﬁxed exchange rate regime or a monetary union, this impact should be taken into consideration. The cross-section analysis also revealed that inﬂation risk has also played a role in determining the price of assets, mostly in the seventies and eighties, a period of relatively high and volatile inﬂation in Canada. The simultaneous equations model conﬁrmed the important role played by exchange risk in determining asset returns in Canada. When combined with inﬂation risk, these two factors led to non-rejection of the models’ restrictions for the seventies and eighties sub-period. This result can be interpreted as meaning that, during this period, unexpected inﬂation and unexpected changes in the bilateral exchange rate were the two most important macroeconomic variables priced by the Canadian market. After the eighties, the exchange risk factor alone implied a nearly non-rejection the over-identifying restrictions of the model. Adding a market return variable as a second risk factor did not improve the ﬁt of the model implying that very little support was found for the CAPM. In summary, from the analysis performed in this paper, it can be concluded that exchange risk is the only factor, among those considered, that has been consistently priced by the stock market since the beginning of the ﬂexible exchange rate regime in Canada. References Anatolyev, S., 2008. A 10-year retrospective on the determinants of Russian stock returns. Research in International Business and Finance 22, 56–67. Apergis, N., Artikis, P., Sorros, J., 2011. Asset pricing and foreign exchange risk. Research in International Business and Finance 25, 308–328. Bartov, E., Bodnar, G.M., 1994. Firm valuation earnings, expectations, and the exchange-rate exposure effect. Journal of Finance 49, 1755–1785. Chen, N., Roll, R., Ross, S., 1986. Economic forces and the stock market. Journal of Business 59, 383–403. Doidge, C., Grifﬁn, J., Williamson, R., 2006. Measuring the economic importance of exchange rate exposure. Journal of Empirical Finance 13, 550–576. Dominguez, K.M.E., Tesar, L.L., 2006. Exchange rate exposure. Journal of International Economics 68, 188–218. Elton, E.J., Gruber, M.J., Blake, C.R., 1995. Fundamental economic variables expected returns, and bond fund performance. Journal of Finance 50, 1229–1256. Fama, E.F., French, K.R., 1992. The cross-section of expected stock returns. Journal of Finance 47, 427–465. Fama, E.F., Macbeth, J., 1973. Risk return and equilibrium: empirical tests. Journal of Political Economy 81, 607–636. Ferson, W.E., 1990. Are the latent variables in time-varying expected returns compensation for consumption risk? Journal of Finance 45, 397–429. Ferson, W.E., Harvey, C.R., 1991. The variations of economic risk premiums. Journal of Political Economy 99, 385–415. Goldberg, C.S., Veitch, J.M., 2010. Country risk and ﬁnancial integration: a case study of South Africa. Research in International Business and Finance 24, 138–145. Grifﬁn, J.M., Stulz, R.M., 2001. International competition and exchange rate shocks: a cross-country industry analysis of stock returns. Review of Financial Studies 14, 215–241. Harvey, C.R., Solnik, B., Zhou, G., 2002. What determines expected international asset returns. Annals of Economics and Finance 3, 249–298. Jorion, P., 1991. The pricing of exchange rate risk in the stock market. Journal of Financial and Quantitative Analysis 26, 363– 376.

8 For space consideration, these results are not reported here. Using a weighted TSE-SP500 aggregate return would not change the results since the SP500 would represent approximately 95% of the return.

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