Time-varying exchange rate exposure and exchange rate risk pricing in the Canadian Equity Market

Economic Modelling 37 (2014) 451–463

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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod

Time-varying exchange rate exposure and exchange rate risk pricing in the Canadian Equity Market Mohammad Al-Shboul a,1, Sajid Anwar b,⁎ a b

Department of Accounting, Banking and Financial Sciences, College of Business Administration and Economics, Al-Hussein Bin Talal University, PO Box (20), Ma'an, 71111, Jordan School of Business, University of the Sunshine Coast, Maroochydore DC, QLD 4558, Australia

a r t i c l e

i n f o

Article history: Accepted 25 November 2013 Available online xxxx JEL classification: F31 G15 G10 C50 G12 G02 G01 E43

a b s t r a c t This paper aims to extend the existing literature on foreign exchange rate risk pricing. Unlike the existing studies on Canada, we use six alternative bilateral and one multilateral exchange rate proxies. Furthermore, using both a two-factor and a three-factor capital asset pricing model (CAPM), we test for the presence of a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. The estimated results based on both the ordinary least squares (OLS) and generalized least squares (GLS) estimation techniques confirm that exchange rate risk in the Canadian equity market is priced and that the pricing of this risk is timevarying. This result holds for all seven exchange rate proxies. Our empirical analysis also suggests the presence of a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. This relationship is found to be insensitive to variations in the world market return. © 2013 Elsevier B.V. All rights reserved.

Keywords: Foreign exchange risk Time-varying risk Exchange rate risk pricing Canadian equity market Rolling window regression Asset pricing Herding behavior Cointegration

1. Introduction Irrespective of whether or not a firm is involved in international business, foreign exchange rate fluctuations can affect its value. Investors who are not compensated for exchange rate risk expect a higher return and hedging becomes highly desirable. Since the work of Jorion (1991), a number of studies have attempted to test for the presence of exchange rate risk pricing in stock markets around the globe. However, the evidence provided by the exiting literature is mixed. This has led to substantial research in this area. Using an international version of the Capital Asset Pricing Model (CAPM), Jorion (1991) found that there was a link between the value of the US dollar and stock returns but exchange rate risk was not priced in the US stock market. Using a two factor asset pricing model, Loudon (1993a) reached the same conclusion for Australia where equity market ⁎ Corresponding author. Tel.: +61 7 5430 1222. E-mail addresses: [email protected] (M. Al-Shboul), [email protected] (S. Anwar). 1 Tel.: +962 3 217 9000x8343. 0264-9993/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.econmod.2013.11.034

returns were sensitive to exchange rate movements but exchange rate risk was not priced. Doukas et al. (1999) considered the case of Japan and concluded that exchange rate risk was priced in the Japanese equity market. The distinguishing feature of this study is time varying nature of the exchange rate risk premium. Using a conditional version of International CAPM (ICAPM) involving time varying risk, De Santis and Gérard (1998) found that foreign exchange rate risk was not priced in the US equity market. Dumas and Solnik (1995) conducted a multicountry study where both the conditional and unconditional versions of asset pricing models were considered and risk premiums were allowed to fluctuate over time. They found some evidence in support of exchange rate risk pricing. Dumas and Solnik concluded that ICAPM out performs the national version. Recent studies such as Saleem and Vaihekoski (2008) consider the case of Russia whereas Kodongo and Ojah (2011) consider the case of some African countries. The empirical studies in the area of exchange rate risk pricing can be divided into two groups. Group 1 includes studies that use unconditional multi-factor pricing models (e.g., Apergis et al., 2011; Carrieri and Majerbi, 2006; Chen et al., 1986; Choi et al., 1998; Di Iorio and Faff, 2002; Jorion, 1991; and Loudon, 1993b). These studies assume that

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exchange rate risk premium is constant over time. Even within this group, the empirical evidence is mixed. The second group includes studies that use conditional multi-factor asset pricing models. These studies assume that exchange rate risk premium varies over time. Generally speaking, studies in this group report evidence in favor of exchange rate risk pricing in some Asia-Pacific equity markets, such as Japan, Taiwan, and Australia (e.g., Brown and Otsuki, 1993; Chiang, 1991; Dumas and Solnik, 1995; Tai, 2003). In addition, empirical studies that consider the European equity markets found that exchange rate risk was priced in Finland, France, Eurozone and in Russia (e.g., Antell and Vaihekoski, 2007, 2012; Apergis et al., 2011; Korajczyk and Viallet, 1992; Saleem and Vaihekoski, 2008). Some multi-country studies (such as Bae et al., 2008; Groen and Balakrishnan, 2006; Guo et al., 2008) found evidence in favor of exchange rate risk pricing. However, generally speaking, the evidence provided by the existing studies is mixed and hence the literature in this area is continuously growing. While the issue of exchange rate risk pricing has been examined in the context of a number of countries, few studies have considered the case of the Canadian equity market. Recent studies on Canada include the work of Samson (2013) and Al-Shboul and Anwar (2014b). This paper aims to extend the existing literature in a number of ways. First, we utilize both multilateral and bilateral exchange rate factors. Specifically we use the Canadian exchange rate trade-weighted index (TWI) and the value of Canadian dollar against several foreign currencies – the US dollar (USD), Euro (EUR), Japanese Yen (JPY), British Pound (GBP), Chinese Yuan (CNY) and Mexican Peso (MXN) are used as proxies for exchange rates.2 Second, we examine the pricing of exchange rate risk phenomenon by means of a two-factor as well as a three-factor capital asset pricing model, which is an improvement over the existing Canadian studies. Third, we explore the issue of exchange rate risk pricing and the possibility of time-varying risk pricing by means of the Generalized Least Squares (GLS). Fourth, we conduct a full sample cointegration analysis to test for the presence of a stochastic trend among exchange rate risk pricing, herding behavior, term structure and the interest rate. The need for testing for the presence of a long-run relationship also arises from the fact that recent studies, such as Pastor and Stambaugh (2012), argue that stock investors may encounter more volatile stock prices over long horizons compared to short horizons. This follows from the fact that, in real life, values of population parameters are unknown and the estimated parameters can lead to imperfectly predictions of the conditional expected returns. This imperfect prediction of expected returns may be attributed to the fact that stock returns generally tend to exhibit mean reverting behavior in the long-run. In addition, as a result of the persistence in the expected returns, the variances of stock returns in long-run may surpass short-horizon variances (Berentsen et al., 2009). Finally, uncertainty in current returns resulting from the use of predicted parameters can contribute to an increase in variances over longer horizons. The choice of herding behavior, terms structure and the interest rate allows a wider analysis of the effects of both equity market (herding) and debt market instruments (interest rate and terms structure) on exchange rate risk pricing. While these three variables may be viewed as important determinants of the exchange rate risk pricing, focusing only on these variables is a limitation of our work. In real life, a number of fundamental factors also affect the price of exchange rate risk. Bailliu and King (2005, P. 8) suggest that macroeconomics factors can be unsuccessful in explaining the exchange rate risk exposure. The paucity of studies investigating the relationship between herd behavior of stock investors and exchange rate risk is one of the main motivations for our investigation of this issue. Recent studies, such as Russell (2012), suggest that the relationship between herding and exchange rate risk pricing has not been extensively examined in the existing literature. Kurz and Motolese (2001) argue that equity investors believe that the 2 The US, the UK, Euro zone, Mexico, China, and Japan are Canada's major trading partners.

herd behavior would influence the price of currency risk. They further argue that as investors are different in their levels of herding, they may also price exchange rate risk differently (Kurz and Motolese, 2001). Changes in interest rates and their term structure not only affect investor behavior but also the Canadian economy and hence it is useful to focus on the impact of these variables on exchange rate risk pricing. Changes in the dollar values are often driven by non-fundamental or speculative factors. Monetary policy, by neutralizing the impact of these factors, can be used to stabilize the economy. Finally, because of the unavailability of data and to limit the length of our study, we focus on only three variables. Based on weekly data on the largest 58 Canadian listed firms over the period 2003–2010, our empirical analysis indicates the presence of a time varying exchange rate risk exposure. In addition, we find evidence of exchange rate risk pricing in the Canadian equity market in terms of all foreign exchange rate proxies. This suggests that equity returns in Canada include a premium for fluctuations in exchange rates. Using all exchange rate proxies, we found exchange rate risk pricing in the Canadian equity market to be time-varying. Furthermore, using Johansen's approach to cointegration, we found that a long-run relationship exists among exchange rate risk pricing, herding behavior, term structure and the interest rate. This result holds when the exchange rate risk pricing is measured using both a two-factor and a three-factor capital asset pricing model. It can therefore be argued that the long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate in Canada is insensitive to the inclusion of a proxy for the world market return in the model. The rest of this paper is structured as follows. Section 2 contains a brief review of the related literature. Methodology is presented in Section 3. The empirical results are presented and discussed in Section 4. Section 5 concludes the paper. 2. Review of the related literature The issue of exchange rate risk pricing arises from the fact that the assumption of purchasing power parity (PPP) does not always hold in real life and hence equity investors from different countries are exposed to greater uncertainty. This situation arises due to the uncertainty associated with future exchange rate changes that can affect the expected returns on stocks. Exchange rate changes are yet another source of systematic risk that cannot be diversified away (see Bodnar et al., 1995 & 1996; Nance et al., 1993). As a result, capital market investors require additional return in the form of a risk premium. An exchange rate risk premium term is included in empirical models containing the return on an asset with an exchange rate risk factor. The inclusion of an exchange rate risk factor to the classical CAPM model allows one to investigate the issue of exchange rate risk pricing.3 The general issue of exchange rate risk pricing has been the subject of a large number of empirical studies. Most of these studies examine the issue of exchange rate risk pricing in developed countries. Early studies used the unconditional asset pricing model and the issue of time varying risk pricing was not investigated. For instance, using a multi-factor model, Chen et al. (1986) found that exchange rate risk was not priced in the U.S. stock market. Using both a two-factor and a multi-factor model, Jorion (1991) failed to find evidence of statistically significant exchange risk pricing in the U.S. stock market. Using data over the period of January 1975 to December 1984, Hamao (1988) found no evidence of exchange rate risk pricing in the Japanese equity market. In addition, after taking into account several Japanese macroeconomic factors, Hamao found that there was no difference in the overall performance of CAPM and Arbitrage Pricing Theory (APT) based 3 While this paper focuses on the issue of exchange rate risk pricing, a good analysis of pricing in other contexts can be found in Jindra and Walkling (2004), Eberhart (2005), Bartram (2007), Heng and Chan (2008), Daniels et al. (2009), Colla et al. (2012), Lel (2012), and Zhang (2012).

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empirical models of exchange rate exposure. Using an unconditional APT based empirical model, Brown and Otsuki (1993) found that exchange rate risk was not priced in the Japanese equity market. Loudon (1993b) found that exchange rate risk was not priced in the Australian equity market. This study is based on data from 1980 to 1991. Di Iorio and Faff (2002), using three versions of CAPM (a two-factor version, a zero-beta version and an orthogonalized version), reported that exchange rate risk was not priced in the Australian equity market during the full sample period of 1988–1998. However, some evidence of exchange rate risk pricing was found in periods of economic declines and during a secularly weak Australian dollar regime (i.e., during the sub-periods of 1990–1993 and 1997–1998). However, more recent studies are based on conditional asset pricing models where the exchange rate risk premium is allowed to vary over time. These studies have shown that exchange rate risk is priced at the aggregate stock market level in most developed countries. The seminal work of Dumas and Solnik (1995) is based on a conditional model involving covariance of assets with exchange rates as well as the traditional premium based on the covariance of the market portfolio. Such an approach allows for time-variation in risk premium associated with the exchange rate exposure. Based on the framework of Dumas and Solnik (1995), De Santis and Gérard (1998) developed a conditional model that can be used to examine the issue of exchange rate risk pricing. Their model is based on a modified version of the multivariate GARCH-in-Mean specification. De Santis and Gérard found that (i) exchange rate risk was priced in the equity markets of Germany, Japan, the U.K., and the U.S. and (ii) the risk premium was timevarying. They argued that unconditional models were unable to detect highly time-varying exchange rate risk. A large number of empirical studies have utilized De Santis and Gérard's framework. For example, in the case of Japan, Choi et al. (1998) found that exchange rate risk was priced in the Japanese stock market. In fact, Choi et al. reached the same conclusion using both a conditional and an unconditional model involving (i) the Yen/US dollar exchange rate and (ii) a trade-weighted exchange rate. In addition, they argued that the price of exchange rate risk is time-varying. Using data over the period of 1975–1995 and by making use of both unconditional and conditional multifactor asset pricing testing procedures, Doukas et al. (1999) found that exchange rate risk was priced in the case of multinationals and high-export Japanese firms and the price of exchange rate risk was time-varying. Using data from the European markets over the period of 1970 to 2004, Antell and Vaihekoski (2007) examined whether exchange rate risk is priced in the Finnish stock market. This study is based on an international conditional CAPM. They found that exchange rate risk was priced in the Finnish market but it was not time-varying. Antell and Vaihekoski (2012) used the same conditional ICAPM that was used in their 2007 study to investigate whether exchange rate risk is priced in the Finnish and Swedish stock markets. They concluded that exchange rate risk was not only priced in both stock markets but it was also time-varying. This study is based on data collected from 1970 to 2009. Saleem and Vaihekoski (2010) considered the pricing of exchange rate risk in the Russian stock market over the period from 1999 to 2009. They found that exchange rate risk was priced in the Russian stock market. The price of exchange rate risk was also found to be time-varying. Apergis et al. (2011) found that foreign exchange risk was priced in a cross section of the German stock returns over the period from 2000 to 2008. Furthermore, the exchange rate risk pricing was time-varying. The issue of exchange rate risk pricing has also been recently examined within the context of a number of multi-country studies. However, these studies are based on unconditional models where risk pricing is assumed to be constant over time. As far the studies on developed countries are concerned, using data over the period of 1999 to 2001, Bae et al. (2008) examined how economic and translation exposure components of the exchange rate risk are priced across four European and Asian

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economies (i.e., Australia, France, Japan, and the U.K). They found the exchange rate risk to be not only priced but also time-varying. While extending the work of Vassalou (2000), Kolari et al. (2008) found that exchange rate risk was priced and time-variant in the US equity markets. Within the context of emerging and developing economies, Carrieri and Majerbi (2006) used different specifications of unconditional model and assumed that exchange rate risk premium was constant over time for Argentina Brazil, Chile, Mexico, Greece, India, Korea, Thailand, and Zimbabwe. They found some evidence in favor of exchange rate risk pricing. This evidence contradicts the findings of early studies that used the same methodology and data from developed countries. Kodongo and Ojah (2011), using a multifactor unconditional asset pricing model, reported that foreign exchange risk was not priced in Africa's stock markets (Botswana, Egypt, Ghana, Kenya, Morocco, Nigeria and South Africa). Kodongo and Ojah assumed that exchange rate risk premium was constant over time. Within the context of Pacific-Basin stock markets, a number of studies allowed the exchange rate risk premium to be time-varying. For example, Tai (2003) examined time-varying exchange rate risk pricing in AsiaPacific forward exchange markets (i.e., Japan, Hong Kong, Singapore and Malaysia). Using monthly data from January 1986 to July 1998, Tai found the exchange rate risk pricing to be time-varying.4 While the existing literature has considered the issue of exchange rate risk pricing in a number of developed and developing countries, only a few studies have considered the case of Canada. Recent studies that have focused on Canada include Al-Shboul and Anwar (2014a,b) and Samson (2013). Using industry level data, Al-Shboul and Anwar (2014a) examined the issue of linear and non-linear exchange rate risk exposure in Canada. Using the Generalized Method of Moments (GMM) and GARCH-in-mean estimation techniques, Al-Shboul and Anwar (2014b) examined the possibility of time-varying exchange rate risk pricing and market segmentation in Canada's equity market. However, our earlier work is based on a three-factor conditional CAPM, where only two foreign exchange rate proxies are used. On the other hand, the present study makes use of GLS to estimate a twofactor as well as three-factor unconditional CAPM, where seven exchange rate proxies are used. In addition, using Johansen's cointegration methodology, this paper also investigates the presence of a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. Using monthly data over the period of January 1970 to December 2004, Samson (2013) investigated the impact of exchange rate and inflation risk on the value of Canadian firms. Samson concluded that exchange rate risk is consistently priced in the Canadian market since Canada adapted the flexible exchange rate system. Samson found the price of exchange rate risk in Canada to be stable. The issue of exchange rate risk in Canada has also been investigated by a few multi-countries studies. For example, Vassalou (2000) found that exchange risk and foreign inflation risk are priced in the 10 developed countries (Australia, Canada, France, Italy, Switzerland, the Netherlands, Japan, Germany, the UK, and the US). However, Vassalou did not focus on the time-varying nature of exchange rate risk pricing. Using data from January 1973 to December 2006, Moore and Wang (2014) found evidence of exchange rate risk pricing in some developed (the US, Australia, Canada, Japan and the UK) and emerging Asian markets (Indonesia, Malaysia, South Korea, the Philippines, Singapore, and Thailand). By making use of 33 industry portfolios from each of the G-7 stock markets, Roache and Merritt (2006) found evidence of exchange rate risk pricing in all countries. These multi-countries studies have not investigated the issue of time-varying exchange rate risk pricing. In this paper, using the unconditional model we investigate the 4 Other related studies include Malliaropulos (1997), Kasman and Ayhan (2008), Villavicencio (2008), Jiménez-Martín and Cinca (2010), Liang and Gao (2012) and Prat (2013).

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possibility of time-varying exchange rate risk pricing in the Canadian equity market. 3. Methodology and data In stage 1, we use a two-factor asset pricing model to examine whether the exchange rate risk is priced in the Canadian equity market. Specifically, the sensitivity of the firm rate of return to changes in an exchange rate factor is examined. As a starting point, we follow the traditional approach (see Jorion, 1991) as follows: Rit ¼ α 0 þ α 1i RLMt þ α 3i RFXt þ ξit

ð1Þ

where Rit is the stock return of firm i; RLMt is the return on the local market portfolio; RFXt is the return on an exchange rate (i.e., the traded weighted index or one of the six individual hard currencies); and ξit is the error term. The estimated value of the coefficient α3i measures the exposure of firm i to changes in the value of the Canadian dollar. If the exchange rate is measured in the units of the Canadian currency per unit of a foreign currency or an index of foreign currencies, a positive value of the estimated α3i suggests that depreciation of Canadian dollar increases the value of the firm. However, if the estimated coefficient is negative then appreciation of Canadian dollar increases the value of the firm. In stage 2, a three-factor asset pricing model is used to examine whether exchange rate risk is priced in the Canadian equity market. This model is an extension of Eq. (1), where the world stock market return has been taken into account. Rit ¼ α 0 þ α 1i RLMt þ α 2i RWMt þ α 3i RFXt þ εit

ð2Þ

where RWMt is the return on the world market portfolio and εit is the error term. Following Rosenberg (1973) and Cooley and Prescott (1976), we apply a time-varying test of exchange rate risk exposure. This involves estimation of Eqs. (1) and (2) for each firm using a 50 rolling window regression, which allows us to obtain the best estimates of the parameters of Eqs. (1) and (2). The rolling window regression is also used to test for time-varying exposure.5 The use of time-varying estimation technique allows the exposure coefficients to evolve stochastically over time. Such an approach can be applied to time series models with parameter instability (see Engle and Watson, 1987 and Stock and Watson, 1998). As the cross-sectional exposure parameter α3i, in both Eqs. (1) and (2) has a time index, the cross-sectional average of the exposure coefficients for each exchange rate risk proxy is plotted against time to show the time-varying results. The time-varying parameters follow a random walk without drift (Pierdzioch and Kizys, 2011). The random walk provides a simple empirical model of the dynamic behavior of the regression coefficients and contains constant coefficients as a special case (Engle and Watson, 1987; Garbade, 1977). Recent studies such as (Kim et al., 2001; Kizys and Pierdzioch, 2007; and Pierdzioch and Kizys, 2011) have used the random walk model to analyze the implications of time-varying parameters. The estimated standard errors are corrected for autocorrelation and heteroskedasticity using Newey– West procedure. Based on Eqs. (1) and (2), we also tested the hypothesis that exchange rate risk is priced in the Canadian equity market. In the case of a two factor model, the pricing of exchange rate risk is examined by estimating Eq. (3) as follows: α 0i ¼ δ0 þ δ1 α 1i þ δ3 α 3i þ ηi

ð3Þ

5 Other studies that have used rolling regression to estimate the change in Okun's coefficient over time include Moosa (1997), Perman and Tavera (2005), Knotek (2007) and Pierdzioch and Kizys (2011).

where α3i is the cross-sectional average of the exposure coefficients of a specific exchange rate; α1i is the cross-sectional average of the local market risk exposure coefficients and ηi is the usual error term. These cross-sectional averages in Eq. (3) are based on the results of rolling window estimates obtained from Eq. (1). Eq. (3) is estimated using both OLS and GLS. Using the estimated parameters of the three-factor model, i.e., Eq. (2), the issue of exchange rate risk pricing can be examined by means of Eq. (4) as follows: α 0i ¼ δ0 þ δ1 α 1i þ δ2 α 2i þ δ3 α 3i þ ς i

ð4Þ

where α3i is the cross-sectional average of the world market risk exposure coefficients and, ςi, is the error term. All variables in Eq. (4) are the cross-sectional averages of the parameters obtained from rolling window estimation of Eq. (2). Eq. (4) is estimated using both OLS and GLS. 3.1. Data The data was sourced from the Canadian stock exchange database, which includes the largest 58 listed firms. Weekly data starting from the beginning of 2003 to the end of December 2010 is used in this study. The results of the Augmented Dickey–Fuller (ADF) test are shown in Table 1. The results of unit root testing suggest that the data series are stationary. In addition, the data series are also tested for autocorrelation. The hypothesis that no serial correlation exists is cannot be rejected at lags 1, 5, 10 and 20. The estimated coefficients of the autoregressive lags continue to decline as the number of lags increases. The return on share prices of the firms included in our sample, the return on the Toronto stock market index (S&P/TSX-Composite index) and the return on the world stock market index (S&P 500) were obtained from the Datastream International. Other relevant data such as the returns on trade-weighted exchange-rate index (TWI) (the Canadian-dollar effective Return Index – CERI), the bilateral foreign exchange rate of the Canadian dollar with respect to six individual hard currencies (USD, AUD, JPY, EUR, CNY, MXN), and risk free rate of interest (13-week Treasury Notes) were obtained from the Bank of Canada database. 4. Empirical results A summary of the descriptive statistics of the variables used (the average of stock returns of all firms, stock market index return and the return on the foreign exchange rate proxies) in this paper is reported in Table 1. 4.1. Exchange rate risk exposure The exchange rate risk exposure using the two-factor and the threefactor models is estimated using OLS rolling window regression technique. The rolling window regression technique involving 50 observations (step size = 1) is used. Once the exposure coefficients are estimated, the cross-sectional exposure coefficients are calculated by taking the cross-sectional average of the coefficients of each firm for each foreign exchange rate proxy. The cross-sectional average of the exposure, for each foreign exchange rate, is plotted against time to see if these coefficients vary over time. Fig. (1) suggests that the crosssectional exposure coefficients vary across time. This implies that variations in exchange rates affect the firm values and these effects vary across time. The results of the cross-sectional average of the rolling window exposures of the three-factor model are shown in Fig. 2. The estimated coefficients, plotted against time, exhibit variation over time, which suggests the presence of a time-varying exposure

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Table 1 Descriptive statistics

Ave Rit RLMt RWMt RTWI,t RUSD,t REUR,t RJPY,t RGBP,t RCNY,t RMXN,t

N

Mean

St. Dev

Min

Max

AR(1)

AR(5)

AR(10)

AR(20)

ADF

KPSS

417 417 417 417 417 417 417 417 417 417

0.002 0.002 0.001 0.001 0.001 0.002 0.002 0.001 0.001 0.002

0.024 0.026 0.026 0.014 0.015 0.014 0.021 0.014 0.015 0.017

−0.164 −0.175 −0.201 −0.054 −0.058 −0.057 −0.12 −0.055 −0.063 −0.081

0.108 0.128 0.114 0.058 0.051 0.047 0.075 0.068 0.058 0.123

−0.033 −0.088 −0.059 −0.02 0.003 0.013 −0.08 0.046 −0.032 −0.159

0.028 0.065 0.076 −0.026 −0.022 −0.086 0.027 −0.063 −0.001 0.021

−0.102 0.057 0.019 0.005 −0.026 0.027 0.060 0.066 0.08 −0.013

−0.042 0.036 0.064 0.053 0.059 −0.014 −0.046 0.085 0.060 0.071

−7.39*** −7.21*** −7.37*** −8.32*** −7.81*** −9.82*** −8.14*** −9.32*** −7.85*** −8.79***

0.083 0.071 0.096 0.060 0.054 0.066 0.046 0.039 0.080 0.063

This Table shows the summary of the descriptive statistics, the estimated autocorrelation coefficients and the results of stationarity testing for all variables using ADF and KPSS tests. The maximum lag length of 17 for KPSS test was chosen based on the Schwert criterion. The critical values of KPSS test are as follows: 10%: 0.119; 5%: 0.146; 2.5%: 0.176; 1%: 0.216). The null hypothesis (i.e., H0) is that the variable is trend stationary. Ave is the average return on stocks; RLMt and RWMt, respectively, are local and world stock market returns; RCNY,t, REUR,t, RGBP,t, RJPY,t, RJPY,t, RUSD,t, RMXN,t and RTWI,t, respectively, are the bilateral and trade weighted foreign exchange rate proxies; ***, **, and * respectively refer to significance at the 1%, 5% and 10% level.

with respect to each foreign exchange rate. Generally speaking, the inclusion of the world market index in the original two-factor model has not affected the results of the time-varying test and the

Cross-sectional average of exchange rate exposure estimated using TWI

1.5

presence of exchange rate exposure. This suggests that Canadian firms are affected by changes in exchange rates differently over time.

Cross-sectional average of exchange rate exposure estimated using USD 1.5 1

1

0.5

0.5 0

0 -0.5

1

41 81 121 161 201 241 281 321 361

1

Cross-sectional average of exchange rate exposure estimated using EUR 1

41 81 121 161 201 241 281 321 361

-0.5

Cross-sectional average of exchange rate exposure estimated using JPY 1

0.5 0.5 0 1

41 81 121 161 201 241 281 321 361

-0.5

0 1

41 81 121 161 201 241 281 321 361

-0.5

-1

Cross-sectional average of exchange rate exposure estimated using GBP

Cross-sectional average of exchange rate exposure using CNY

1

1.5

0.5

1 0.5

0 1

41 81 121 161 201 241 281 321 361

-0.5

0

-1

-0.5

1

41 81 121 161 201 241 281 321 361

Cross-sectional average of exchange rate exposure estimated using MXN 1 0.5 0 1

41 81 121 161 201 241 281 321 361

-0.5 -1 Fig. 1. Time-varying cross-sectional average of exchange rate exposures—the two-factor model. Note: The sample size is measured along the horizontal axis.

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Cross-sectional average of exchange rate exposure using TWI 1.5

Cross-sectional average of exchange rate exposure using USD

1.5

1

1

0.5

0.5 0

0 -0.5

1

41 81 121 161 201 241 281 321 361

-0.5

Cross-sectional average of exchange rate exposure using EUR

1

41 81 121 161 201 241 281 321 361

Cross-sectional average of exchange rate exposure using JPY

1 1 0.5

0.5 0 -0.5

1

41 81 121 161 201 241 281 321 361

-1

0 1

41 81 121 161 201 241 281 321 361

-0.5 Cross-sectional average of exchange rate exposure using GBP

1

Cross-sectional average of exchange rate exposure using CNY

1.5 1

0.5

0.5 0 1

41 81 121 161 201 241 281 321 361

0 1

41 81 121 161 201 241 281 321 361

-0.5

-0.5

Cross-sectional average of exchange rate exposure using MXN 1

0.5 0 -0.5

1

41 81 121 161 201 241 281 321 361

-1 Fig. 2. Time-varying cross-sectional average of exchange rate exposures—the three-factor model. Note: The sample size is measured along the horizontal axis.

4.2. Pricing of the exchange rate risk Using OLS, both the two and three-factor exchange rate risk pricing models (i.e., Eqs. (3) and (4)) are estimated. The rolling window regression technique of 50 observations (step size = 1) is implemented, where the number of rolling windows for the full sample period is 321. The estimated pricing coefficients (i.e., δ3), in Eq. (3), for each individual exchange rate proxy are plotted against time in Fig. 3. A visual examination of the estimated coefficients of exchange rate risk pricing suggests time-varying risk pricing in Fig. 3. The results using a three-factor model are shown in Fig. 4. Just like Fig. 3, we report time-varying evidence of the pricing of exchange rate risk using all foreign exchange rate proxies. The rolling window regression technique was used to estimate the pricing coefficients δ3 for each individual exchange rate proxy. Fig. 4 suggests that the coefficients of exchange rate risk pricing vary over time. In other words, there is clear evidence of time-varying risk pricing. In this section, we report the results of GLS estimation. The GLS technique has higher power as compared to the traditional OLS approach. In addition, GLS allows one to test the cross-sectional restrictions imposed by the model through a likelihood ratio test. This latter test can be used to find out whether the multi-factor model provides a reasonable fit for the data. The estimated results are shown in Table 2. The estimated coefficient of δ3 is statistically significant in the case of all exchange rate proxies. Table 2 shows that exchange rate risk is priced in the Canadian equity market and it is negative. All estimated

values of the Chi-square test statistic reported in Table 2 are highly significant suggesting that the model is adequately specified and fits the data well. Table 3 contains the results of the exchange rate pricing tests for the three-factor model. The estimated asymptotic t-values are reported underneath the corresponding estimated parameter values. These results indicate that, in terms of all currencies, foreign exchange rate risk is priced in the Canadian equity market. These results are similar to those presented in Table 2. Generally speaking, these results are consistent with Carrieri and Majerbi (2006) who reported evidence of significant exchange rate risk pricing. However, our results contradict the findings of Chen et al. (1986), Jorion (1991) and Kodongo and Ojah (2011). We also tested the hypothesis that all pricing coefficients are jointly equal to zero but this hypothesis was strongly rejected. This suggests that adding a proxy for the world market risk does not affect our original results reported in Table 2. However, the estimated values of the Chi-square test statistic reported in Table 3 are highly significant, which suggests that the three-factor model is a useful tool for the analysis of the exchange rate risk pricing phenomenon. The results presented in Table 3 are not very different from those presented in Table 2. Most estimated exchange rate risk pricing coefficients are significant and negative in the case of all exchange rate proxies. The negative sign suggests that Canadian firms earn higher return as they are exposed to negative exchange rate risk. In summary, the results

M. Al-Shboul, S. Anwar / Economic Modelling 37 (2014) 451–463

Currency risk pricing using TWI

Currency risk pricing using USD

0.01

0.02 0.01

0 1

41

81 121 161 201 241 281

0

-0.01

-0.01

1

41 81 121 161 201 241 281

-0.02

-0.02

Currency risk pricing using Euro

Currency risk pricing using JPY

0.02

0.04

0.01

0.02 0

0 -0.01

457

1

41

81 121 161 201 241 281

1

41

81 121 161 201 241 281

-0.02 -0.04

-0.02

Currency risk pricing using GBP

Currency risk pricing using CNY

0.02

0.01

0.01 0 1

0 1

41

81

121 161 201 241 281

-0.01 -0.02

41

81 121 161 201 241 281

-0.01 -0.02

Currency risk pricing using MXN 0.04 0.02 0 1

41

81 121 161 201 241 281

-0.02 Fig. 3. Time-varying foreign exchange rate pricing—the two-factor model. Rit = α0i + α1iRLWt + α3iRFXt + εit. α0 = δ0 + δ1α1i + δ3α3i + ηi. δ0i is the cross-sectional average of the rolling window regression of intercept coefficients estimated using Eq. (3). δ1i is the cross-sectional average of the rolling window regression of the local market risk pricing coefficients estimated using Eq. (3). δ3i is the cross-sectional average of the rolling window regression exchange rate risk pricing coefficients estimated using Eq. (3).

presented in this section suggest that Canadian investors do price the foreign exchange rate risk. 4.3. Cointegration test In this section, we first show the relationship between the exchange rate risk pricing and each of the three variables of interest (i.e., herding behavior, term structure and the interest rate) by graphical means. This is followed by testing for cointegration among all four variables using Johansen's methodology. However, before reporting our empirical results, we first report diagnostic testing results in Table 4. All variables appear to exhibit high variability, which reflects time-varying nature of the exchange rate risk pricing in terms of all exchange rate proxies. The results of J–B (Jarque–Bera) test suggest that the distribution of all variables is non-normal. We also tested for stationarity by using the augmented Dickey–Fuller (ADF) unit root test (Dickey and Fuller, 1981) and the KPSS unit root test (Kwiatkowski et al., 1992). In the case of the ADF unit root test, based on Akaike information criterion (AIC), the optimal lag length of p = 2 was selected. The results of ADF presented in Table 4 suggest the presence of non-stationarity. However, the first differences were found to be stationary. The relationship between the estimated exchange rate risk pricing coefficients and each of the three variables (i.e., herding, term structure and interest rate) is shown in different panels of Figs. 5 and 6. Herding

behavior of stock investors is considered one of the variables affecting exchange rate risk pricing. Herding means that investors blindly follow the actions of each other in buying and selling stocks. The reasons for herding include the fact that investors tend to protect their portfolios from changes in stock prices, downside risk and exchange rate risk in particular (Russell, 2012). Based on Chang et al. (2000), we measure herding by the absolute deviation of stock return from the stock market return. Herding is detected when the absolute deviation increases at a decreasing rate. The reason for using this variable is the existence of heterogeneity of beliefs in financial markets. The existing literature in this area suggests that dispersion of such beliefs arises due to information asymmetry (Frankel and Rose, 1995; Jongen et al., 2008). All market participants do not hold identical information. Generally speaking, different market participants hold different information but part of the information is common among all market participants. In other words, part of the information held is public, whereas the rest is private. Kurz and Motolese (2001) argue that structure of market expectations can give rise to differences in information and its interpretation. Because stock market investors are different in their levels of herding, they may price exchange rate risk differently. In Fig. 5, we report a scatter plot of the GLS estimation based exchange rate risk pricing coefficients (for each of the seven exchange rate proxies) based on a two-factor model. The regression line shown in the scatter plot captures the correlation between exchange rate risk

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Currency risk pricing using TWI

0.01

Currency risk pricing using USD

0.02

0 1

41

81 121 161 201 241 281

0

-0.01

1 -0.02

-0.02 Currency risk pricing using Euro

Currency risk pricing using JPY

0.02

0.04

0.01

0.02 0

0 -0.01

41 81 121 161 201 241 281

1

41 81 121 161 201 241 281

-0.02

-0.02

1

41 81 121 161 201 241 281

-0.04 Currency risk pricing using GBP

Currency risk pricing using CNY

0.01

0.01

0

0 1

1

41 81 121 161 201 241 281

-0.01

-0.01

-0.02

-0.02

41 81 121 161 201 241 281

Currency risk pricing using MXN

0.03 0.02 0.01 0 1

41 81 121 161 201 241 281

-0.01 Fig. 4. Time varying foreign exchange rate pricing—the three-factor model. Rit = α0 + α1iRLMt + α2iRWMt + α3iRFXt + εit. α0 = δ0 + δ1α1i + δ2α2i + δ3α3i + ηi. δ0i is the cross-sectional average of the rolling window regression intercept coefficients estimated using Eq. (4). δ1i is the cross-sectional average of the rolling window regression market risk pricing coefficients estimated using Eq. (4). δ2i is the cross-sectional average of the rolling window regression world market risk pricing coefficients estimated using Eq. (4). δ3i is the cross-sectional average of the rolling window regression exchange rate risk pricing coefficients estimated using Eq. (4).

pricing and herding for all exchange rate proxies (see panel (a) of Fig. 5). This correlation presents a stochastic trend. A similar stochastic trend is observed in the case of the three-factor model as shown in panel (a) of

Fig. 6. Because the exchange rate risk exposure follows a random walk, it is possible for the results of the unit root tests to show a stochastic trend. As the exposure might have a stochastic trend, the pricing of the

Table 2 GLS estimation of the two-factor model

Table 3 GLS estimation of the three-factor model

Rit = α0 + α1iRLWt + α3iRFXt + εit

Rit = α0 + α1iRLMt + α2iRWMt + α3iRFXt + εit.

α0 = δ0 + δ1α1i + δ3α3i + ηi.

TWI USD JPY EUR GBP MXN CNY

α0 = δ0 + δ1α1i + δ2α2i + δ3α3i + ηi. 2

δ0

δ1

δ3

χ (2)

0.004*** (12.765) 0.003*** (7.741) 0.003*** (8.129) 0.001* (1.722) 0.001*** (3.007) −0.001 (−1.443) 0.004*** (14.277)

−0.001*** (−2.800) 0.001 (0.873) −0.001 (−1.115) 0.001* (1.762) 0.002*** (3.490) 0.004*** (4.791) −0.001*** (−3.123)

−0.005*** (−15.648) −0.004*** (−10.171) −0.003*** (−7.679) −0.003*** (−6.091) −0.007*** (−18.354) −0.002*** (−3.175) −0.004*** (−14.959)

383.286***

TWI

210.050***

USD

124.980***

JPY

65.339***

EUR

394.739***

GBP

39.877***

MXN

341.224***

CNY

This Table reports the GLS results of exchange rate risk pricing for each foreign exchange rate proxy as in Eq. (3). The pricing model uses the cross-sectional average of the rolling window regression estimated parameters of the three-factor model of Eq. (1). ***, **, and * respectively represent significance at the 1%, 5%, and 10% level.

δ0

δ1

δ2

δ3

χ2(2)

0.005*** (11.042) 0.003*** (4.714) 0.003*** (9.938) 0.002*** (4.390) 0.001*** (4.929) −0.001** (−2.174) 0.004*** (8.229)

−0.003*** (−4.244) 0.000 (0.319) −0.002*** (−3.937) 0.000 (−0.389) 0.002*** (3.557) 0.004*** (5.352) −0.001** (−2.003)

−0.001*** (−2.532) 0.001 (1.463) 0.000 (−1.283) 0.002*** (5.352) 0.002*** (5.413) 0.003*** (5.968) −0.001** (−1.948)

−0.006*** (−14.137) −0.004*** (−6.633) −0.005*** (−10.072) −0.005*** (−11.215) −0.009*** (−25.695) −0.004*** (−6.143) −0.004*** (−9.081)

315.875*** 117.394*** 169.390*** 188.341*** 741.792*** 74.850*** 147.269***

This Table reports the GLS results of exchange rate risk pricing for each foreign exchange rate proxy as in Eq. (4). The pricing model uses the cross-sectional average of the rolling window regression estimated parameters of the three-factor model of Eq. (2). ***, **, and * respectively represent significance at the 1%, 5%, and 10% level.

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459

Table 4 Diagnostic testing of the pricing coefficients, herding, term structure and interest rate Variable

Obs

Mean

Std.

Min

Max

J–B χ2(2)

AR(1)

Panel (a): Exchange rate risk pricing coefficient series from the two-factor model TWI 319 −0.005 0.004 −0.016 0.008 35.75*** USD 319 −0.005 0.005 −0.017 0.009 9.964*** JPY 319 −0.004 0.007 −0.024 0.023 41.67*** EUR 319 −0.001 0.005 −0.011 0.011 13.48*** GBP 319 −0.005 0.005 −0.015 0.010 16.97*** MXN 319 0.002 0.007 −0.014 0.021 23.74*** CNY 319 −0.005 0.004 −0.017 0.007 21.13***

0.983*** 0.988*** 0.961*** 0.978*** 0.974*** 0.991*** 0.983***

Panel (b): Exchange rate risk pricing coefficient series from the three-factor model TWI 319 −0.005 0.004 −0.018 0.006 74.01*** USD 319 −0.004 0.004 −0.018 0.010 12.16*** 319 −0.004 0.007 −0.024 0.018 57.39*** JPY EUR 319 −0.001 0.004 −0.011 0.015 12.46*** GBP 319 −0.005 0.004 −0.016 0.007 10.64*** MXN 319 0.002 0.007 −0.007 0.022 58.24*** CNY 319 −0.005 0.004 −0.019 0.007 56.40***

0.976*** 0.982*** 0.967*** 0.975*** 0.959*** 0.991*** 0.979***

Panel (c): Determinants of risk pricing Herding 319 0.000 0.005 Term structure 319 0.002 0.163 Interest rate 319 −0.002 0.041

−0.024 −1.566 −0.177

0.025 1.261 0.152

301.3*** 109.8*** 96.77***

−0.169*** −0.120** −0.097**

AR(5)

AR(20)

AR(40)

0.841*** 0.847*** 0.755*** 0.769*** 0.817*** 0.894*** 0.828***

0.094*** −0.018*** 0.208*** 0.074*** 0.398*** 0.465*** 0.062***

−0.482*** −0.321*** −0.106*** 0.125*** 0.212*** 0.169*** −0.547***

0.779*** 0.807*** 0.793*** 0.736*** 0.749*** 0.909*** 0.796***

0.071*** −0.056*** 0.229*** 0.087*** 0.403*** 0.487*** 0.055*** −0.013*** −0.073*** 0.072***

0.094** −0.017** 0.006**

ADF

ADF 1st diff

KPSS 1st diff

−1.535 −0.920 −2.512 −1.617 −3.164** −1.387 −1.510

−12.54*** −7.92*** −16.29*** −9.34*** −11.14*** −8.55*** −11.39***

0.036 0.031 0.041 0.032 0.078 0.047 0.036

−0.426*** −0.251*** −0.215*** −0.100*** 0.118*** 0.115*** −0.475***

−1.958 −1.258 −2.339 −1.643 −2.876** −1.258 −1.713

−12.55*** −9.56*** −14.85*** −10.45*** −13.93*** −12.14*** −11.97***

0.033 0.030 0.042 0.035 0.066 0.053 0.038

0.027*** 0.067*** 0.003***

−21.09*** −20.05*** −19.59***

−11.73*** −12.16*** −13.16***

0.063 0.092 0.073

This Table shows the summary of the descriptive statistics and diagnostic testing results for the risk pricing coefficients for all currencies for both models as well as herding, term structure and interest rate. We test for autocorrelation of the order AR(1) to AR(40). The normality test is performed by using Jarque–Bera (J–B) test where H0: normality. The stationarity is tested by means of the ADF and KPSS tests. Based on the Schwert criteria a maximum lag length of 16 for KPSS test was selected. The critical values of KPSS test are as follows: 10%: 0.119; 5%: 0.146; 2.5%: 0.176; 1%: 0.216). The null hypothesis tested is that H0: the variable is trend stationary. The results of ADF test for unit root are interpolated by MacKinnon et al. (1999) approximate technique. The critical values of ADF are −3.455:1%; −2.877:5%; −2.570:10%. The number of observations is 319. ***, **, and * respectively refer to significance at the 1%, 5% and 10% level.

exchange rate risk may also have a similar trend. In addition, if there is a substantial increase in international trade, the results of the unit root test would also exhibit a stochastic trend. Stock investors herd for protection from changes in stock prices. Due to the presence of the exchange rate risk, investors require additional return, which increases stock trading and the end result is a stochastic trend. We also plot the relationship between the exchange rate risk pricing coefficients for all currencies and the term structure of interest rate. It is well-known that an increase in interest rate differential leads to appreciation of the domestic currency, which results in an increase in the cost of capital (Dornbusch, 1976). However, a decrease in interest differential reduces the cost of borrowing which promotes economic growth. Increase in the rate of economic growth contributes to increase in international trade and therefore an increase in exposure to exchange rate risk. The increase in exchange rate risk encourages stock investors to price this risk. Schmukler and Serven (2002) have shown that interest rate differentials vary substantially over time. Since changes in the interest rate differentials may cause changes in exchange rate risk exposure, one can also expect changes in the pricing of exchange rate risk. In panel (b) of Figs. 5 and 6, the relationship between the term structure and pricing shows a stochastic trend and exchange rate risk pricing is negatively associated with the term structure. The relationship between exchange rate risk pricing and the interest rate is also plotted in panel (c) of Figs. 5 and 6. In general, interest rate and pricing coefficients are negatively related and their relationship exhibits a stochastic trend. In order to check for robustness of the observed stochastic trend, we tested for the presence of a long run relationship among all four variables (i.e., the rolling window estimates of the exchange rate risk pricing coefficients, herding behavior, terms structure and the interest rate). The results of the ADF test reported in Table 4 suggest that almost all variables are non-stationary in levels and therefore it makes sense to test for the presence of a cointegrating relationship. The test statistic used is the Johansen's (1988) trace test of cointegration for the joint null hypothesis that there is no long-run relationship (noncointegration) among all the four variables.

In Table 5, the results of the cointegration test are reported.6 We used a likelihood ratio test to select the optimal lags for each of the estimated series of pricing coefficients. Based on the 5% level of significance, a maximum of four lags was allowed. In addition, we considered the case of a linear trend. The results of Johansen's trace test suggest that the four variables are cointegrated. In other words, there is a long-run relationship among these variables and hence there is evidence of a common stochastic trend among all the four variables. Table 5 shows that this result holds in the case of all exchange rate proxies. Furthermore, Table 5 also shows that when the world market return proxy is taken into account (i.e., when the three-factor model is used), the results are similar to those reported for the two-factor model. It can therefore be argued that the long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate is insensitive to fluctuations in the world market return.

5. Conclusion Using a two-factor (and also a three-factor) unconditional capital asset pricing model, this paper examines whether (i) the exchange rate risk is priced in the Canadian equity market, (ii) the pricing of exchange rate risk varies over time, and (iii) there is a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. Unlike the existing studies, we use six alternative bilateral exchange rates (the Chinese Yuan, Euro, the UK pound, Japanese Yen, Mexican Peso and the US dollar) and one multilateral (trade weighted index) exchange rate proxies. The sample consists of monthly data on 58 largest Canadian firms over the period 2003 to 2010. The foreign exchange risk exposure is estimated using rolling window regression on both the two and three-factor models. The three factor model is found to be more reliable. 6 For robustness, the long run relationship was also tested using Autoregressive Distributed Lags (ARDL) bounds testing procedure developed by Pesaran et al. (2001). The results were qualitatively similar to those found from Johansen's test. The ARDL bounds testing results are available from authors upon request.

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a) Exchange rate risk pricing coefficients

b) Exchange rate risk pricing coefficients and term structure

c) Exchange rate risk pricing coefficients and interest rate

Fig. 5. The relationship between exchange rate risk pricing and herding, term structure and interest rate using the two-factor model. Panel a: Exchange rate risk pricing coefficients (vertical axis) and herding (horizontal axis). Panel b: Exchange rate risk pricing coefficients and term structure. Panel c: Exchange rate risk pricing coefficients and interest rate.

Empirical investigation based on ordinary least squares and generalized least squares technique reveals that foreign exchange rate risk is priced in the Canadian equity market. This conclusion

holds in the case of all seven exchange rate proxies. The estimated pricing coefficients are negative and significant indicating that Canadian firms achieve lower returns when exchange rate exposure

M. Al-Shboul, S. Anwar / Economic Modelling 37 (2014) 451–463

461

a) Exchange rate risk pricing coefficients (vertical axis) and herding (horizontal axis) Pricing coefficients of CNY and herding

Pricing coefficients of MXN and herding

0.02

0.02

0

0

Pricing coefficients of MXN and herding

Pricing coefficients of EUR and herding

0.04

0.02

0.02 0.04 0.02

0

-0.02 -0.04

0.05

-0.05

Pricing coefficients of GBP and herding

Pricing coefficients of JPY and herding

0.05

0.05

0

-0.02 -0.04

0.04 0.02

0

0

-0.02 -0.04 -0.02

Pricing coefficients of TWI and herding

0.05 0

-0.02 -0.04

-0.05

0.04 0.02

-0.02 -0.04 -0.02

0

0 0

0 0.04 0.02

-0.02

-0.02

0.04 0.02

0

0

0.04 0.02

0

-0.02 -0.04 -0.05

-0.05

b) Exchange rate risk pricing coefficients and term stucture Pricing coefficients of CNY and term structure

Pricing coefficients of USD and term structure

0.02

0.02

0

0

Pricing coefficients of EUR and term structure

Pricing coefficients of MXN and term structure

0.02

0.04 0.02

2

0

-2

2

0

0 0

-2 2

-0.02

0

-0.02

-0.02

Pricing coefficients of GBP and term structure

Pricing coefficients of JPY and term structure

0.01

2

0

-2

-2 -0.02

Pricing coefficients of TWI and term structure

0.02

0.05

0 2

0

0

0

-2 -0.01

2

0

-2

2

-0.05

-0.02

0

-2 -0.02

c) Exchange rate risk pricing coefficients and Interest rate Pricing coefficients of CNY and interest rate

0.2

Pricing coefficients of USD and interest rate

0.02

0.02

0

0

0

-0.2

0.2

0

Pricing coefficients of GBP and interest rate

0

0.2

0

0

0 0.2

0 -0.02

0.2 -0.2

0

-0.2 -0.02

Pricing coefficients of CNY and interest rate

0.05

0 -0.2

-0.05

-0.2

0.05

0 0.2

0.02

0.02

Pricing coefficients of JPY and interest rate

0.05

Pricing coefficients of EUR and interest rate

0.04

-0.02

-0.02

Pricing coefficients of MXN and interest rate

0 -0.2

-0.05

0.2

0

-0.2 -0.05

Fig. 6. The relationship between exchange rate pricing and herding, term structure and interest rate using the three-factor model. Panel a: Exchange rate risk pricing coefficients (vertical axis) and herding (horizontal axis). Panel b: Exchange rate risk pricing coefficients and term stucture. Panel c: Exchange rate risk pricing coefficients and Interest rate.

increases. By making use of Johansen's cointegration approach, we also tested for the presence of a long-run relationship among exchange rate risk pricing, herding behavior, term structure and the interest rate. Using all seven exchange rate proxies, we found that within the context of both the two-factor and the three-

factor models, a cointegrating relationship exists among all variables. This suggests that the presence of a long-run relationship among exchange rate pricing, herding behavior, terms structure and the interest rate is insensitive to fluctuations in the world market return.

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Table 5 The results of Johansen Cointegration Test Hypothesized No. of CE(s)

Eigenvalue

Trace Statistic

0.05 Critical Value

Prob.⁎⁎

Three-factor model TWI None ⁎ At most 1 ⁎ At most 2 ⁎ At most 3 ⁎ USD None ⁎ At most 1 ⁎ At most 2 ⁎ At most 3 ⁎ JPY None ⁎ At most 1 ⁎ At most 2 ⁎ At most 3 ⁎ EUR None ⁎ At most 1 ⁎ At most 2 ⁎ At most 3 ⁎ GBP None ⁎ At most 1 ⁎ At most 2 ⁎ At most 3 ⁎ MXN None ⁎ At most 1 ⁎ At most 2 ⁎ At most 3 ⁎ CNY None ⁎ At most 1 ⁎ At most 2 ⁎ At most 3 ⁎

Eigenvalue

Trace Statistic

0.05 Critical Value

Prob.⁎⁎

Two-factor model

0.229 0.176 0.159 0.027

204.051 122.820 62.507 8.4297

47.857 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0037

0.228 0.173 0.159 0.027

203.491 122.162 62.534 8.501

47.857 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0035

0.231 0.171 0.168 0.037

209.952 127.796 69.110 11.747

47.857 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0006

0.231 0.171 0.164 0.038

209.436 127.068 68.262 12.039

47.857 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0005

0.227 0.187 0.162 0.027

208.826 128.310 63.495 8.386

47.856 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0038

0.227 0.186 0.161 0.027

208.551 127.771 63.343 8.430

47.857 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0037

0.233 0.171 0.160 0.040

208.764 125.608 67.071 12.852

47.856 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0003

0.232 0.170 0.158 0.041

207.921 125.238 66.851 12.995

47.856 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0003

0.221 0.171 0.157 0.027

198.297 120.355 61.7616 8.355

47.856 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0038

0.220 0.170 0.157 0.027

198.425 120.475 62.086 8.519

47.856 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0035

0.233 0.178 0.167 0.026

209.411 126.450 65.131 8.146

47.857 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0043

0.233 0.178 0.164 0.026

209.126 125.990 64.487 8.164

47.857 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0043

0.231 0.173 0.159 0.027

204.207 121.906 62.535 8.444

47.856 29.798 15.495 3.842

0.0000 0.0000 0.0000 0.0037

0.231 0.171 0.158 0.028

203.722 121.350 62.518 8.558

47.856 29.798 15.495 3.8415

0.0000 0.0000 0.0000 0.0034

The Table presents the results of Johansen cointegration test through Eigenvalue and Trace test for the null hypothesis that there is no long run relationship between the four variables: the exchange rate risk pricing series, herding, interest rate, and term structure. The unrestricted cointegration rank test (Trace) is used. The maximum lags interval used (in first differences): 1 to 4. ⁎ Denotes rejection of the null hypothesis at the 0.05 level. ⁎⁎ MacKinnon et al. (1999) p-values.

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