Colombo Business Journal - SSRN papers

Faculty of Management & Finance

Colombo Business Journal

University of Colombo

Vol. 01, No. 02 - February 2008 (13-23)

Colombo Business Journal International Journal of Theory & Practice

Evidence for Sign Asymmetry of Exchange Rate Exposure Prabhath Jayasinghe Department of Business Economics, Faculty of Management & Finance, University of Colombo, Sri Lanka

Abstract This paper attempts to find evidence for sign asymmetry of exchange rate exposure. An extended classification of the sources of asymmetry has been introduced in place of somewhat incomplete classification suggested by previous studies. In addition, a new measure is suggested in order to estimate the overall impact of incorporating sign asymmetry. The study results in several important findings: (a) there is evidence for the presence of sign asymmetry; (b) as it can work in either direction, it is not appropriate to make generalizations like incorporating sign asymmetry always leading to more/less exchange rate exposure; and (c) the exposure coefficients estimated by the models that do not capture sign asymmetry are likely to under/overestimate the exposure to exchange rate risk. Key Words: Asymmetric Exchange Rate Exposure; GARCH; Pricing to Market; Hysteresis; Hedging

1. Introduction The augmented market model that is frequently used to estimate exchange rate exposure implies that the impact of exchange rate changes on firm value is symmetric1. Such a relationship implicitly assumes that firms are passive agents and their strategic planning process is not influenced by the direction of macroeconomic changes. In reality, firms respond to macroeconomic changes in such a way that the relevant beneficial effects are exploited and the adverse effects are mitigated. As such, it would be hard to imagine that they would respond to local currency appreciations and depreciations in a similar manner. The implication is that exchange rate exposure may be asymmetric between appreciations and depreciations. In addition, though there are studies that attempt to capture exchange rate exposure asymmetries, there seems to be a dearth of studies which examine the overall impact of incorporating asymmetries. Many studies comment on their results in a conjectural manner without employing a proper measure to evaluate this effect.

1

Following Adler and Dumas (1984) and some later extensions such as Jorion (1990), exchange rate exposure is commonly estimated using the following augmented market model specification: ri , t   0   m rm , t   x rx , t   i , t where ri , t is return on firm i’s stock at time t; rm , t is return on market portfolio; rx , t is percentage change in exchange rate;  mi is firm i’s market beta;  x is firm i’s exchange rate exposure coefficient (also known as exposure beta or exposure coefficient).

P. Jayasinghe / Colombo Business Journal - Vol. 01, No. 02, February 2008

2

In this paper, the Koutmos and Martin (2003) framework of estimating sign asymmetry of exchange rate exposure is enhanced by adding a few new features. First, an enhanced classification for the sources of sign asymmetry is introduced. Second, a new measure to evaluate the overall impact of incorporating sign asymmetry is suggested. Third, a thick tailed distribution is used to address the problem of leptokurtosis of financial data. A sample of 80 Japanese firms is used to find the evidence for sign asymmetry and the overall impact of incorporating the same. The rest of the paper is organized as follows. Section 2 examines the sources of asymmetric exchange rate exposure. Section 3 presents a brief literature review. In Section 4, the existing framework is expanded in a more appropriate set up. The data is described in Section 5. Section 6 reports the major empirical findings. Concluding remarks are contained in Section 7.

2. Sources of the Sign Asymmetry of Exchange Rate Exposure In general, asymmetries in exchange rate exposure stem from the microeconomic behaviour of firms. There are a few behavioural characteristics of firms with which one can explain the asymmetric nature of exchange rate exposure. These characteristics include pricing-to-market (PTM), hysteretic behaviour and hedging.

2.1 Pricing-to-market behaviour of firms2 Among others, Froot and Klemperer (1989), Knetter (1994), Krugman (1987), and Marston (1990) propose the concept of PTM to explain the asymmetric nature of export pricing. Basically, there are two relevant concepts: volume constraints and market share maximization. Behaviour under volume constraints: Export quotas and inadequate investments in marketing capacity are examples for volume constraints. In the face of these “bottlenecks”, even if the foreign price decreases, a firm cannot get the benefits of a reduction in price because it cannot increase the supply effectively to meet the demand. Therefore, an exporter who operates under volume constraints cannot increase profits by passing-through the benefits of depreciation to foreign buyers. If local currency depreciates, such a firm may increase its mark-ups by increasing the local price and may keep the foreign price unchanged in order to clear the market. This PTM behaviour increases their profits drastically. On the other hand, when local currency appreciates there is no such constraint and the firm may not price-to-market, but pass-through the appreciation of local currency to foreign prices. As a result, the increase in profits during a depreciation of local currency is greater than the decrease in profits during an appreciation of it. Figure 1, which shows the changes in profit against the changes in exchange rate per given time period, explains this mechanism in a highly simplified context. Exchange rate is expressed as local currency price of foreign currency (i.e. an increase in the index implies a depreciation). Assume that the firm’s initial profit-exchange rate combination is represented by the origin. Under ceteris paribus conditions, the firm may pass-through a local currency appreciation and the resultant profit change for the exchange rate change  a is represented by  b . However, if there is a local currency depreciation, due to volume constraints, the same firm may price-to-market, meaning that for a similar change in exchange rate (i.e. a ) there would be a higher increase in profits represented by c . Apparently, c  b . This means that the average exchange rate exposure of a firm that adopts PTM strategy under volume constraints may be higher than the average exchange rate exposure of a firm that does not behave so.

2

For illustrations of these sources, let us consider a producer of export goods who uses only domestic resources. More realistically, even the prices of local inputs are affected by exchange rate changes although the objective of this assumption is to abstract from it.


3

% change in profit c -a

b

a -b

% change in exchange rate

Figure 1: The relationship between exchange rate changes and the profits of an exporter who faces volume constraints

Market share maximizing behaviour: In order to build up their market share, firms may passthrough local currency depreciations to foreign markets by decreasing the foreign prices. Driven by the market share maximization objective, they may not increase their mark-ups, but merely maintain them in the face of local currency depreciations. However, this process does not reverse symmetrically when local currency appreciates. On such occasions, with the intention of securing/protecting the market share and avoiding the dumping attempts by competitors, firms may price-to-market by reducing their mark-ups and try to keep their foreign prices unaffected. As such, the decrease in profits during appreciations is greater than the increase in profit during depreciations (Koutmos and Martin, 2003). Figure 2 explains this phenomenon. The firm may pass-through the benefits of a local currency depreciation to the buyers. The resultant profit change for the exchange rate change a is represented by b . However, if there is a local currency appreciation, in order to secure its existing market share, the same firm may price-to-market, meaning that for a similar change in exchange rate % change in profit

b -a a -b


-c

Figure 2: The relationship between exchange rate changes and the profits of an exporter with market share maximization objective


4

(i.e.  a ) there would be a higher decrease in profit represented by  c . Apparently  c   b . This means that the average exchange rate exposure of a firm that adopts PTM strategy with market share maximization may be higher than the average exchange rate exposure of a firm that does not behave so. 2.2 Hysteresis Hysteretic models of trade developed in Baldwin (1988) and Dixit (1989) and Baldwin and Krugman (1989) have also some insights towards asymmetric exchange rate exposure. For instance, if a depreciation of local currency persists for a considerably lengthy period, a number of new exporting firms (both local and foreign) may enter the market to make the advantage of weakened local currency. Therefore, the profits of the existing exporting firms may not increase to the extent that would occur, if the new entrants had not entered. However, if this period of depreciation is followed by a period of appreciation, then the same process may not occur in the opposite direction symmetrically. Given the sunk costs that have already been incurred, new firms are not in a position to simply quit the market. These firms are more likely to stay in the market with meagre profit margins or even with losses during such periods of appreciation. This mechanism, known as the hysteretic behaviour of firms, is also a possible source of asymmetric exchange rate exposure. The reduction in profits during appreciations is larger than the increase in profit during depreciations. % change in profit

b -a a

-c


-b

Panel A: An exporter % change in profit

b a -a

-c -b

Panel B: An importer

Figure 3: Reduction in exposure through hedging


5


2.3 Hedging Basically, firms may be engaged in two types of hedging: financial hedging and hedging through real options. Financial hedging represents firms’ purchase of financial instruments such as currency options with the intention of hedging against adverse exchange rate changes. The term real options refers to “all types of operating or strategic flexibility … [including] the ability of a firm to shift production location or factors of production, to shift marketing activities between sales markets and market segments, and to shift level of competitive rivalry” (Andren, 2001, p. 6). Firms’ desire to exploit opportunities and avoid adverse effects in response to various macroeconomic changes is well reflected in their hedging behaviour. Since hedging activities provide both downside protection and opportunities to exploit upside potential, they are intrinsically asymmetric in nature. For instance, an exporter who has already shipped goods but has not received payment denominated in foreign currency in return may hedge through a financial instrument against local currency appreciations. However, he is more than happy to accept local currency depreciations. This feature is common to real hedging as well. If the switching cost does not exceed the benefit, an exporting firm that usually buys its inputs from domestic producers may turn to foreign suppliers when local currency appreciations. Therefore, the firm’s exposure related to that particular activity during local currency appreciations is less than the exposure that would occur, if it had not engaged in real hedging. Panels A and B in Figure 3 depict, respectively, the resultant reduction in exposure of an exporter and an importer due to hedging strategies.

3. Evidence for Asymmetric Exposure Based on the theoretical evidence that export pricing is asymmetric, Kanas (1997) performs a test for asymmetric economic exposure. The study cites empirical evidence for an asymmetric effect in exposure. Miller and Reuer (1998) use real and financial option theory and the concept of PTM to explain the exposure asymmetries. Di Iorio and Faff (1999) make an attempt to capture both magnitude and sign asymmetries in exposure. To this end, they differentiate large depreciations from large appreciations. The study reports mixed results for exposure and exposure asymmetries. Andren (2001), a study that estimates the asymmetric exposure to the changes in various macroeconomic variables such as exchange rate, interest rate and inflation rate, employs two separate models to incorporate sign and magnitude asymmetries. The study cites evidence for the asymmetric economic exposure. Partly attributing the difficulty in detecting exchange rate exposure in earlier studies to the negligence of conditional heteroskedasticity, Koutmos and Martin (2003) propose a GARCH-type model to capture sign asymmetry of exchange rate exposure. The model uses the following mean equation with a dummy-type variable to differentiate appreciations from depreciations.

ri ,t   0   1 rm ,t  (  2   3 Dsign )rx ,t   i ,t

(1)

where Dsign  1 if rx ,t  0 and 0 otherwise3. They argue that the statistical significance of  3 in the above specification provides a direct test for sign asymmetry of exposure.  2 and  3 can be either negative or positive depending on whether the firm in question is an exporter or an importer.

3

The other variables in Equation 3 are similar to those mentioned in footnote 1.


6

Table 1 Sources of sign asymmetry of exchange rate exposure

3  0

3  0

3  0

2  0

2  0

2  0

(i)

(ii)

(iii)

PTM with MSM

PTM with MSM

PTM with MSM

objective or Hysteresis (Net Exporters)

objective or Hysteresis (Net Exporters)

objective (Net importers)

(iv)

(v)

(vi)

Symmetric exposure

No exposure

Symmetric exposure

(Net exporters)

(Net exporters or importers)

(Net importers)

(vii)

(viii)

(ix)

PTM under VC or

PTM under VC or

Asymmetric hedging

Asymmetric hedging (Net exporters)

Asymmetric hedging (Net importers)

(Net importers)

__________________________________________________________________________________ PTM – pricing-to-market; MSM – market share maximization; VC – volume constraints Source: Koutmos and Martin (2003)

Accordingly, there may be a number of possible combinations of  2 and  3 . Table 1 shows the relationship between these combinations and the possible sources of sign asymmetry. Solakoglu (2005) and Muller and Verschoor (2006) use Koutmos and Martin (2003) model outlined above in order to inquire into asymmetric exchange rate exposure in a set of Turkish and US firms, respectively. Though the exposure asymmetries are not examined in the way that it is done by the above studies, there are several studies that pay attention to non-linear exposure effects. In addition to the exchange rate changes, Priestley and Odegaard (2002) include squared values of exchange rate changes in the augmented market model. Griffin and Stulz (2001) report that various non-linear measures of exchange rate changes do not help in modelling exposure. Bartram (2002) also includes a number of convex and concave non-linear functional forms of exchange rate changes as determinants. Only the convex specifications are found to be having a significant impact on returns. Though there are several studies that attempt to capture exchange rate exposure asymmetries, the overall impact of incorporating such asymmetries seems to have largely been left unexamined. Moreover, there is no consensus on the matter whether incorporating asymmetries would lead to large/significant exposure coefficients or small/insignificant exposure coefficients. For instance, Di Iorio and Faff (1999, p. 134) implicitly assume that taking asymmetries into account would lead to an increase in overall exposure when they state that “… asymmetric payoffs lead one to hypothesize that exchange rate exposure may display an asymmetric behaviour and it is for this reason that previous studies may not have uncovered overwhelming evidence of exchange rate sensitivity of equity securities”. On the contrary, classifying PTM as a particular form of hedging called pricing flexibility, Carter et al. (2003) argue that taking asymmetries into account would lead to significant reduction in a firm’s exchange rate exposure.


7

4. Incorporating Asymmetric Exposure: Extension of the Existing Framework In this section, the Koutmos and Martin (2003) model is extended by adding a few important features to it. First, their classification of sources of sign asymmetry is reconsidered. Second, a criterion is suggested to measure the overall impact of incorporating asymmetries on exchange rate exposure. Finally, in order to address the issue of the leptokurtic behaviour of financial time series, residuals are assumed to follow an appropriate thick-tailed distribution. 4.1 Sign asymmetry of exchange rate exposure Although Koutmos and Martin (2003) provide a promising framework to capture sign asymmetry of exchange rate exposure, their classification is somewhat incomplete for a few reasons. First, in explaining the PTM behaviour of firms, it neglects the role played by the elasticity of the demand. For instance, although mark-ups decrease during appreciations under PTM strategy, it is difficult to draw the conclusion that profits will also decrease. Decrease/increase of profits may be largely dependent on whether the demand is elastic or not. When a firm, that is driven by the market share maximization objective, prices-to-market, it reduces the local currency price in order to accommodate the appreciation and keeps the foreign price unaffected. Suppose that demand for this good is relatively elastic. A price increase might have caused a drastic decrease in the quantity demanded and the firm would have realized less profit, if it did not adopt PTM strategy. In this case, the firm’s exposure to exchange rate changes is less under PTM strategy than pass-through (PT) strategy4. This means that, under PTM with market share maximization, for a firm with a product whose demand is relatively more elastic, the decrease in profit during appreciations is less than the increase in profit during depreciations. In other words, the firm is less exposed to exchange rate changes during appreciations than during depreciations. On the other hand, when the demand for a product is relatively inelastic, the price increase would cause a relatively small reduction in demand, if it did not adopt the PTM strategy. In other words, the firm would have been better off, if it passed-through the appreciation to foreign prices. On such an occasion, a firm’s exposure to exchange rate changes is higher under PTM strategy than PT strategy. As such, under PTM strategy, the exposure of a firm that exports a product % change in profit

b -a

Elastic demand

-c -b

a


-d Inelastic demand

Figure 4: Reconsidering the relationship between exchange rate changes and the profits of an exporter with market share maximization objective

4

Although a firm may, or happen to, use a proper mix of these two strategies in reality, for simplicity, let us assume that they may select either PTM or PT.


8

with relatively inelastic demand is higher during appreciations than during depreciations. Thus, whether profits would increase to a lesser degree during depreciation periods than decrease in appreciation periods depends on the demand elasticity of the product in question. These two possibilities are shown in Figure 4. For  a change in exchange rate during an appreciation, whether the change in profit will be  c or  d is dependent on the elasticity of the demand for the product. Koutmos and Martin (2003 ) do not take demand elasticity into account and conclude that PTM with market share maximising objective may essentially lead to more exposure during appreciations than depreciations. Due to the negligence of the role of elasticity, PTM with market share maximization objective is confined only to cases (i) and (ii) in Table 1. However, such a classification is possible, only if the demand for the good in question is relatively inelastic. For instance, if the demand is sufficiently elastic and  2   3 , exposure during depreciation is larger than the exposure during appreciations and this case is represented by (vii) in Table 1. Second, in Table 1, (iii) is allocated to net importers. However, when the two coefficients bear opposite signs, whether we can unambiguously identify the firm as a net importer is dependent on the magnitudes of the coefficients. For instance, if  2  0 and  3  0 , but  2   3 , although it still belongs to case (iii), it is not clear whether the firm is a net importer or exporter. During appreciations, the combined effect (   2   3 ) is positive as in the case of exporters. However, during depreciations, the effect (   2 ) is negative and displays the features of an importer. This is not merely a theoretical possibility. In our sample, we found many cases in favour of this argument. Third, due to the above ambiguity, the source of exposure asymmetry of such a firm is inconclusive. In addition, whether such a firm is more exposed during appreciations or depreciations is dependent on the magnitudes of  2 and (  2   3 ) . If  2  (  2   3 ) , then the firm is more exposed to exchange rate changes during depreciations. On the other hand, if  2  (  2   3 ) , the firm is more exposed during appreciations. When these facts are taken into account, possible sources of sign asymmetry associated with the nine combinations in Table 1 can be summarized in a slightly different format (for the convenience of presentation) as it is done in Table 2.

4.2 Overall impact of incorporating sign asymmetry Undoubtedly, investigating the statistical significance of individual exposure parameters such as

 2 and  3 in Koutmos and Martin (2003) model represented by Equation 1 is useful in strategic decision making. For instance, information on the sign and the significance of  3 for a particular firm offers some insights into managing its risk in the face of asymmetric exposure of its operating cash flows to exchange rate changes. We suggest that the evaluation of the overall impact of incorporating asymmetries is also equally important. Although individual coefficients are significant, each coefficient may bear different signs and may offset one another leaving an insignificant overall impact of exchange rate changes on firm’s operating cash flows. Usually, it is this overall impact of exposure that the firms are eventually concerned about. As such, in addition to the individual exposure coefficients such as  2 and  3 , there must be another reliable measure that might show the overall impact of asymmetries on exchange rate exposure. We assume that this overall impact of sign


9

Table 2 Sources of sign asymmetry of exchange rate exposure: an extension of Koutmos and Martin (2003) classification ______________________________________________________________________________________ Signs of parameters Net exporter/importer Source of asymmetry ______________________________________________________________________________________ (i)  2

 0 ; 3  0

Net exporters

(ii)  2

 0 ; 3  0

Net exporters

(iii)

 2  0 ; 3  0

PTM with MSM objective (if demand is relatively inelastic) Hysterisis PTM with MSM objective (if demand is relatively inelastic) Hysterisis

Net importers, if

PTM with VC

3  2 (iv)

-do-

Scenario1:

importers, if

Inconclusive

-do-

Scenario 2:

3  2

(v)

-do-

 2  ( 2   3 )

Net exporters or

 2  ( 2   3 )

Inconclusive (vi)  2

 0 ; 3  0

Net exporters

Symmetric exposure

(vii)  2

 0 ; 3  0

Net exporters or

No exposure

(viii)  2

 0 ; 3  0

Net importers

Symmetric exposure

Net exporters, if

PTM under VC

(ix)  2

 0 , 3  0

importers

3  2

Asymmetric hedging PTM with MSM objective (if demand is relatively elastic)

(x)

-do-

Net importers

Scenario 1:

or importers, if

Inconclusive

-do-

Scenario 2:

3  2

(xi)

-do-

 2  ( 2   3 )

 2  ( 2   3 )

Inconclusive (xii)  2

 0 ; 3  0

Net importers

(xiii)  2

 0 ; 3  0

Net importers

PTM with MSM objective (demand may be relatively elastic or inelastic) Asymmetric hedging PTM with MSM objective (demand may be

relatively elastic or inelastic) Asymmetric Hedging ______________________________________________________________________________________ PTM – pricing-to-market; MSM – market share maximization; VC – volume constraints

10


asymmetry on exposure is represented by the combination of the two individual coefficients

(  2   3 ) . Therefore, to measure the overall impact of incorporating sign asymmetry, one has to check whether this “combined exposure coefficient” is significantly different from zero. The use of financial and real options basically leads to less exposure of a firm’s profits to exchange rate changes. On the contrary, hysteresis, PTM under volume constraints and PTM with market share maximization objective (with a product whose demand is relatively inelastic) may increase the overall exchange rate exposure. Viewed from this perspective, whether incorporating asymmetries would lead to large/significant combined exposure coefficients or small/insignificant combined exposure coefficients should be dependent on: (a) the source of asymmetry in question; and (b) in what proportions a firm is engaged in the activities that give rise to asymmetries. 4.3. Considering Koutmos and Martin (2003) Model in a more appropriate set up Following Adler and Dumas (1984), we assume that a firm’s market value is a reasonable proxy to its future operating cash flows. The implication is that all current and future changes in firm’s profits in response to macroeconomic changes are reasonably reflected in the changes in its stock prices. In such a context, the exchange rate exposure of a firm can be estimated by regressing the changes in firm value on exchange rate changes (Adler and Dumas, 1984). Among others, Bodner and Wong (2003) show the necessity of the inclusion of market returns as a regressor in such an estimation equation to avoid the component of spurious correlation between stock returns and exchange rate changes. The inclusion of market returns is also warranted as it largely helps to overcome omitted variable bias in the regression. To obtain precise parameter estimates through removing non-linear dependencies, the relevant mean equation is augmented with a simple generalized autoregressive conditional heteroskedasticity (GARCH) structure suggested by Bollerslev (1986). As a remedy to the issue of the leptokurtosis associated with many financial time series, the residuals from the relevant mean equation are assumed to be asymptotically t-distributed. More specifically, we suggest the following parsimonious univariate GARCH(1,1)-t model: m

ri ,t   0,i   1,i rm ,t  (  2,i   3,i Dsign )rx ,t    4,i ,t l ri ,t l   i ,t i  1,2,...n

(2)

l 1

1

z i ,t   i ,t hi ,t

2

(3)

 t I t 1 ~ f  t | I t 1  hi ,t  c0,i  ai  t21  bi hi ,t 1

(4)

where the definition of most of the variables and parameters in mean equation 2 remain the same as those mentioned in footnote 1. Dsign  1 if rx ,t  0 and zero otherwise.  i ,t | I t 1 denotes the random shock at time t given all available information at time (t-1). As denoted by f . , residuals from mean equation 2 are assumed to follow a t-distribution with  degrees of freedom, mean 0 and conditional variance hi ,t . Standardized errors denoted by z i are assumed to be independently and identically distributed with mean 0 and variance 1. And, m number of lag terms of the dependent variable is included to avoid autocorrelation among residuals. Usual non-negativity constraints like c  0 ,

11


a  0 , b  0 together with (a  b)  1 must hold for the conditional variance to be positive and stationary. Student’s t-test is used to check the validity of the null hypotheses  2  0 and  3  0 . The combined exposure coefficient (  2   3 ) reflects the overall impact of incorporating asymmetries (i.e. the degree and the direction of exchange rate exposure when sign asymmetry is taken into account). Wald test is employed to examine the validity of the null hypothesis (  2   3 )  0 against the alternative (  2   3 )  0 . Assuming that the residuals of the suggested univariate model are t-distributed, the conditional log-likelihood of residual vector  t at time t can be defined as follows: 2 1   2       2    t / ht      t  ln   ln   ln    2  ln h  ln 1       t 2  2  2  2  2  

  (5)  

where  is the vector of parameters to be estimated. The log-likelihood function of the sample is obtained as L  

   T

t

t 1

where T is the total number of observations. The parameter vector of

the model is estimated by maximizing L with respect to  using BHHH algorithm. 5. Data and Preliminary Statistics The data set consists of 80 Japanese firms in two industrial sectors: 42 firms from Automobile and Parts sector and 38 firms from Electronics and Electrical Equipment sector. These sectors are selected for the study due to their high international involvement as exporters/importers. The selection criterion for the firms to be included in the sample was the firm size that is reasonably proxied by their annual sales. Firms whose average total annual sales exceed Y 40,000,000,000 for the period 2000 - 2003 have been selected. Market portfolio is assumed to be represented by Nikkei 225, the overall stock index in Japan. All stock returns and market returns are expressed in yen. A trade-weighted yen exchange rate, compiled by the Bank of England and the base year of which is 1990, is used. Exchange rate is expressed as the local currency price of foreign currency. Following most of the previous studies, nominal exchange rates have been used. All data is extracted from DataStream. We use daily and weekly data from June 1989 through May 2004. As such, the number of observations for daily and weekly samples are 3910 and 783, respectively. As for weekly data, in order to reduce biases, prices/rates on every Wednesday are taken into account. Continuously compounded returns and exchange rate changes are calculated as follows:

R r j , t  ln  

j ,t

R

j ,t  1

  * 100 

j  i , x, m

(6)

where R j ,t and R j ,t 1 are the closing values of stock prices/exchange rates for period t and t  1 respectively; i is return on ith stock; x is changes in exchange rate and m is return on market portfolio. Ljung-Box test for returns and squared returns (performed for 20 lags) indicate the existence of linear and non-linear dependencies in the return series in all four samples. Especially, the test statistic

12


for squared returns is a three-figure number for more than 90 percent of the 160 return series. As evidenced by ARCH-LM test results, there exists conditional heteroskedasticity in the return series in all four samples except only in 2 cases which were found in weekly data sample from the electronics and electrical equipment sector. These pre-estimation findings strongly support the use of a GARCHtype model for the estimation of exchange rate exposure. In addition, the basic statistics of the majority of the series show excess kurtosis which justifies the assumption that residuals are asymptotically t-distributed.

6. Empirical Findings and Discussion For comparison, we estimate two versions of the model suggested by Equations 2 through 4. While the GARCH structure remains unchanged for both versions, the mean equations for the two versions are as follows: Model 1:

m

ri ,t   0,i   1,i rm ,t  (  2,i   3,i Dsign )rx ,t    4,i ,t l ri ,t l   i ,t

(2)

l 1

Model 2:

m

ri ,t   0,i   1,i rm ,t   2,i rx ,t    4,i ,t l ri ,t l   i ,t

(7)

l 1

Model 1 contains the mean equation of the suggested model and is represented by Equation 2. Model 2 which does not capture the sign asymmetry of exchange rate exposure is considered as the benchmark case. We use both daily and weekly data to see whether return horizon matters in determining the sign asymmetry of exchange rate exposure. Prior to the analysis of the estimation results, it would be more appropriate to investigate the adequacy of the model from which the estimates have been obtained. For diagnostic purposes, we used the Ljung-Box test performed for 20 lags using both standardized residuals and squared standardized residuals. Results of the former indicate that the Ljung-Box statistic is well below the relevant critical value in all 160 cases in the four samples. The same test for squared standardized residuals reveal that the statistic is less than the relevant critical value in 148 out of 160 cases. Even in the case of the other 12 series, Ljung-Box statistic is far smaller than the same statistic of the relevant return series. These results imply that the suggested model adequately captures both linear and nonlinear dependencies. This guarantees the precision of the exchange rate exposure parameters estimated.

6.1 Overview of Results Table 3 provides us with an overview of the results obtained from Model 2. In daily data sample, 11 out of 80 (13.75%) firms show sign asymmetry. 15 out of 80 (18.75%) firms in the sample possess at least one significant individual coefficient (i.e. either  2 or  3 ). 21 out of 80 (26.25%) firms are significantly exposed to exchange rate changes in terms of the combined exposure coefficient

(  2   3 ) (see last column in Panel A). In weekly data sample, 5 out of 80 (6.25%) firms in the total sample show evidence for the existence of sign asymmetry. 17 out of 80 (21.75%) firms have at least one significant individual coefficient. Combined exposure coefficient is significant in 16 out of 80 (20%) cases included in the total sample (see last column in Panel B). 6.2 Tracing the sources of sign asymmetry Results from the suggested model can be used to trace the relevant sources of the sign asymmetry. Table 4 classifies the firms in both daily and weekly data samples based on the signs and the

13


magnitudes of individual coefficients  2 and  3 . A large percentage of firms in the sample does not show evidence for exchange rate exposure. It is apparent that 65 (81.25%) firms in the daily data Table 3 Overview of results Panel A: Daily data _________________________________________________________________________ Coefficient Automobile Electronics Total _______________________________________________________________________ (1) Sign asymmetry (  3 )

05

(11.90)

06

(15.79)

11

(13.75)

(2) Main (  2 )

06

(14.28)

02

(5.26)

08

(10.00)

(3) Any a (  2 or

3 )

08

(19.04)

07

(18.42)

15

(18.75)

(4) Overall b (  2

 3 )

09

(21.43)

12

(31.58)

21

(26.25)

________________________________________________________________________ Panel B: weekly data ________________________________________________________________________ Asymmetry Automobile Electronics Total ________________________________________________________________________ (1) Sign asymmetry (  3 )

03

(7.14)

02

(5.26)

05

(6.25)

(2) Main (  2 )

08

(19.05)

07

(18.42)

15

(18.75)

(3) Any a (  2 or  3 )

09

(21.43)

08

(21.05)

17

(21.25)

4) Overall b (  2

10

(23.81)

06

(15.79)

16

(20.00)

 34 )

__________________________________________________________________________________ a

or

 3 ; b Significance of the combined coefficient

 2  0 , 3  0 ;

Wald test is used to test the null hypothesis

Significance of any type of exposure represented by coefficients

( 2

  3 );

t-test is used to test null hypotheses

( 2   3 )  0 ;

2

Level of significance used is 5%; Figures within parentheses in Automobile, Electronics and Total

columns show the significant number of cases as percentages of 42, 38 and 80, respectively.

sample and 63 (78.25%) firms in the weekly data sample are not significantly exposed when exposure is measured in terms of the individual coefficients  2 and  3 (see row (vii)). 4 (5%) firms in daily data sample and 12 (15.00%) firms in the weekly data sample do not possess asymmetries, even though they are significantly exposed (see rows (vi) and (viii)). Only a few firms (13.75% in daily data sample and 6.25% in weekly data sample) show sign asymmetry and the main sources of the asymmetry of these firms are summarized in Table 5. 6.3 Overall impact of incorporating sign asymmetry The overall impact of incorporating sign asymmetry on exchange rate exposure coefficient is assumed to be represented by the combined exposure coefficient (  2   3 ) . Table 6 compares the results obtained from the suggested model (which accommodates sign asymmetry) and the model which does not take sign asymmetry into account. The numbers shown against Model 1 and Model 2

14


are the number of cases in which the null hypotheses of (  2   3 )  0 in Model 1 and  2  0 in Model 2 are rejected, respectively. The numbers within parentheses express the number of such cases (i.e. the number of significantly exposed firms) as a percentage of the total number of firms in each sector. Apparently, daily and weekly data show two different trends. Table 4 Sources of sign asymmetry: a classification of firms based on the signs and magnitudes of

 2 and  3

________________________________________________________________________________________ Type of Features Exporter/ Daily data ___ Weekly data______ Exposure Importer Auto Elect Total Auto Elect Total ___________________________________________________________________________________ (i)

 2  0 ; 3  0

Net exporters

-

-

-

-

-

-

(ii)

 2  0 ; 3  0

Net exporters

02

05

07

-

01

01

(iii)

2  0 ; 3  0

Net importers

-

-

-

-

-

-

2  0 ; 3  0

Net exporters

03

01

04

01

-

01

3  2

or importers

-

-

-

-

-

-

3  2 (iv)

 2  ( 2   3 ) (v)

2  0 ; 3  0

Net exporters

3  2

or importers

 2  ( 2   3 ) (vi)

2  0 ; 3  0

Net exporters

02

01

03

05

05

10

(vii)

2  0 ; 3  0

Net exporters

34

31

65

33

30

63

or importers (viii)

2  0 ; 3  0

Net importers

01

-

01

01

01

02

(ix)

2  0 , 3  0

Net exporters

-

-

-

-

-

-

2  0 , 3  0

Net importers

-

-

-

01

01

02

3  2

or importers

-

-

-

-

-

-

3  2 (x)

 2  ( 2   3 ) (xi)

2  0 , 3  0

Net importers

3  2

or importers

 2  ( 2   3 ) (xii)

2  0 ; 3  0

Net importers

-

-

-

01

-

01

(xiii)

2  0 ; 3  0

Net importers

-

-

-

-

-

-

__________________________________________________________________________________


15

The number of significant cases in daily data sample increases when the asymmetry is incorporated. However, in weekly data sample, the number of significant cases seems to decrease. An important factor to be focused on is the change in the composition of firms when sign asymmetry is taken into account. Table 5 Sources of sign asymmetry: a summary _____________________________________________________________________________________ Type of Net exporter/ Sources of Asymmetry No. of firms Exposure Net importer Daily Weekly _____________________________________________________________________________________ (ii) Net exporter PTM with MSM (inelastic demand) 07 01 Hysteresis (iv)

Net exporter or importer

Inconclusive

04

01

(x)

Net importer or importer

Inconclusive

00

02

(xii)

Net importer

PTM with MSM (inelastic or inelastic 00 01 demand) Hedging _____________________________________________________________________________________ PTM – pricing-to-market; MSM – market share maximization; VC – volume constraints

Table 7 helps us have a closer look at the same phenomenon. Column 1 of Table 7 shows the number of firms that are significantly exposed to exchange rate changes when sign asymmetry is neglected (measured in terms of Model 2). Column 5 shows the number of significantly exposed firms when sign asymmetry is incorporated (measured in terms of Model 1). Columns 2, 3 and 4 reveal the black box between the numbers appearing at the two ends represented by Model 2 and Model 1. Column 2 indicates the number of firms whose significant exposure to exchange rate changes remain unchanged even after the asymmetry is incorporated. The criterion used here is the acceptance of both alternative hypotheses of  2  0 in Model 2 and (  2   3 )  0 in Model 1. Column 3 indicates the number of firms that are significantly exposed to exchange rate changes as long as the sign asymmetry is neglected, but no longer exposed when the asymmetry is incorporated. Relevant criterion is given by the acceptance of the alternative of  2  0 in Model 2 and the null of

(  2   3 )  0 in Model 1. Finally, Column 4 indicates the number of firms that are not significantly exposed when sign asymmetry is neglected, but become exposed when asymmetry is taken into account (the criterion being the acceptance of the null of  2  0 in Model 2 and the alternative of

(  2   3 )  0 in Model 1). A careful look at the daily data sample reveal that, though the percentage (and the number) of firms that are exposed to exchange rate changes roughly remains unchanged when asymmetry is incorporated, the composition of the firms do change. Only a part of the initial group of firms that showed exposure remains in the group as significantly exposed firms when asymmetries are taken into account (see Column 2 in Panel A). Significance of the exposure coefficient decays in the case of another part of the group (Column 3 of Panel A). More interestingly, significance of the exposure coefficient of a new group of firms improves (Column 4 of Panel A). The number of firms whose exposure becomes statistically insignificant is greater than the number of

16


firms whose exposure becomes statistically significant, hence the increase of the total percentage of significantly exposed firms. Panel B reveals that the results in weekly data sample are largely similar, though the trend is in the opposite direction. Although the number (and the percentage) of significantly exposed firms decreases when sign asymmetry is incorporated, that does not mean a part of the same group of firms who were significantly exposed to exchange rate changes will remain as significant cases. As in the case of daily data sample, exposure of a part of the initial group becomes insignificant and a new group of firms become significantly exposed. Unlike in the daily data sample, the latter group is smaller than the former group, hence the decrease of the total percentage of significantly exposed cases. These results suggest that it is not sensible to make generalizations (as documented in some previous studies) of the sort that the incorporation of asymmetries will lead to more/less exchange rate exposure. It can work in either direction as some sources result in more exposure (e.g. PTM with volume constraints) and yet another set of sources may result in less exposure (e.g. hedging). We conjecture that whether the negligence of sign asymmetry may under- or over-estimate the true exposure is dependent on the underlying sources of asymmetry. More specifically, it may be dependent on firm-specific factors such as a firm’s financial and real hedging activities, its marketing strategies, in what proportions it is engaged in activities that give rise to exposure asymmetries etc. If the same firm is engaged in both export and import activities with multiple objectives and multiple behavioural patterns in various markets (this is the case with most MNCs) 5, the issue becomes really complicated because the exposure effects brought about by various sources may offset and/or reinforce one another. Table 6 Exposure in terms of Models 1 and 2 ___________________________________________________________________________________ Model used Automobile Electronics Total ___________________________________________________________________________________ Panel A: daily data Model 2 (without sign asymmetry)

06 (14.29)

10 (26.32)

16 (20.00)

Model 1 (with sign asymmetry)

09 (21.43)

12 (31.58)

21 (26.25)

14 (33.33)

14 (36.84)

28 (35.00)

Panel B: weekly data Model 2 (without sign asymmetry)

Model 1 (with sign asymmetry) 10 (23.81) 06 (15.79) 16 (20.00) __________________________________________________________________________________

5

For instance, a Japanese MNC may export to US and a number of other countries; use both domestic and imported inputs from a number of countries; face quota (volume constraints) in the US market; try to secure/enhance its market share in a number of other countries; use financial hedging as an exporter and importer; produce through its subsidiaries overseas and for the same reason may be engaged in real options through the same network.

17

P. Jayasinghe / Colombo Business Journal - Vol. 01, No. 02, February 2008 Exchange rate exposure without sign asymmetry and with sign asymmetry are assumed to be represented by

2  0

and

(  2   3 )  0 , respectively; t-test is used to check the null hypothesis  2  0 while Wald

test is used to test the null hypotheses

(  2   3 )  0 ; Level

of significance used is 5%; Figures within

parentheses in Automobile, Electronics and Total columns show the number of cases as percentages of 42, 38 and 80, respectively

Table 7 The relationship between the significance of exposure coefficients and incorporating sign asymmetry

__________________________________________________________________________________ Sector

No. of significant cases when asymmetries are neglected

When asymmetries are taken into account ________________________________________ no. of cases no. of cases no. of cases that remains whose whose significant significance significance decays improves

i.e.  2  0

i.e.

i.e.

i.e.

No.of significant cases when asymmetries are taken taken into account i.e.

in Model 2

 2  0 and

 2  0 but

 2  0 but

( 2  3 )  0

( 2  3 )  0

( 2  3 )  0

( 2  3 )  0

in Model 1

(1) (2) (3) (4) (5) _________________________________________________________________________________________ Panel A: daily data Automobile 06 03 03 06 09 Electronics 10 06 04 06 12 Total 16 09 07 12 21 Panel B: weekly data Automobile 14 07 07 03 10 Electronics 14 05 09 01 06 Total 28 12 16 04 16 ________________________________________________________________________________________ Exchange rate exposure without asymmetries and with asymmetries are assumed to be represented by

2  0

and

(  2   3 )  0 , respectively; t-test is used to check the null hypothesis  2  0 while Wald test is used to check the null hypotheses

(  2   3 )  0 ; Level of significance used is 5%.

7. Conclusions Using the conventional exposure equation augmented with a dummy variable and a simple GARCH(1,1) structure, this paper makes an attempt to find evidence for sign asymmetry of exchange rate exposure. The classification of the sources of sign asymmetry has been extended, as Koutmos and Martin (2003) classification seems to be somewhat incomplete. In addition, a new measure, namely “combined exposure coefficient”, has been introduced in order to estimate the overall impact of incorporating sign asymmetry. Residuals are also assumed to be asymptotically t- distributed. There are a few important findings. First, we show that measuring overall impact of asymmetries in terms of combined coefficient (  2   3 ) is as important as measuring the individual components of asymmetries represented by  2 and  3 . This is mainly due to the fact that the presence/absence of


18

the latter does not necessarily guarantee the presence/absence of the former. We observe that the individual coefficients sometimes offset one another leaving an insignificant overall impact. There are also cases in which the individual coefficients reinforce the impact of one another, thus making the overall impact significant. As such, it is not appropriate to make generalizations like “taking asymmetries into account always leads to large/significant exposure coefficients or small/insignificant exposure coefficients”. Our empirical findings reveal that this can occur in either direction. We conjecture that whether the exposure increases or decreases as a result of accommodating asymmetries may be dependent on the sources of asymmetries and in what proportions a firm is engaged in those sources. Second, we cite empirical evidence for the existence of sign asymmetry of exchange rate exposure among the firms in the two Japanese industrial sectors selected. Third, the need for an extension of the classification of the sources of sign asymmetry arises for a few reasons. For instance, in the context of the market share maximizing objective of the firms, the fact that incorporating sign symmetry may lead to more/less exposure is dependent on whether the demand for the product in question is elastic or not. Furthermore, a firm cannot be classified as an importer/exporter using the sole criterion whether  2 is negative/positive. The suggested classification of the sources of sign asymmetry is supported by data. Fourth, the exposure coefficients estimated by the models that do not capture sign asymmetry are likely to under/overestimate the exposure to exchange rate risk. Finally, both daily and weekly data have been used to see whether return horizon matters in determining the sign asymmetry of exchange rate exposure. Results reveal that the arguments of sign asymmetry raised and tested for daily data are, though to a somewhat different degree, applicable to weekly data as well. References Adler, M. & Dumas, B. (1984). Exposure to Currency Risk: Definition and Measurement. Financial Management, 13, 41-50. Andren, N. (2001). Is Macroeconomic Exposure Asymmetric? Working Paper, Department of Business Administration, Lund University. Baldwin, R. (1988). Hysteresis in Import Prices: the Beachhead Effect. American Economic Review, 78, 773-785. Baldwin, R. & Krugman, P. (1989). Persistent Trade Effects of Large Exchange Rate Shocks. Quarterly Journal of Economics, 104 (4), 635-654. Bartram, S. (2002). Linear and Nonlinear Foreign Exchange Rate Exposures of German Nonfinancial Corporations. Working Paper, Graduate School of Management, Lancaster University. Bodnar, G. M. & Wong, M. F. H. (2003). Estimating Exchange Rate Exposures: Issues in Model Structure. Financial Management, Spring, 35-67. Bollerslev, T. (1986). A Generalized Conditional Autoregressive Heteroskedasticity. Journal of Econometrics, 31, 307-327. Carter, D. A., Pantzalis, C. & Simkins, B. J. (2003). Asymmetric Exposure to Foreign-Exchange Risk: Financial and Real Option Hedges Implemented by U.S. Multinational Corporations. Working Paper, Department of Finance, College of Business Administration, Oklahoma State University. Di Iorio, A. & Faff, R. (1999). An Analysis of Asymmetry in Foreign Currency Exposure of the Australian Equities Market. Journal of Multinational Financial Management, 10, 133-59. Dixit, A. (1989). Entry and Exit Decisions under Uncertainty. Journal of Political Economy, 97, 620638.


19

Froot, K. A. &. Klemperer, P. D. (1989). Exchange Rate Pass-through When Market Share Matters. Economic Review, 79, 637-654. Griffin, J. M. & Stulz, R. M. (2001). International Competition and Exchange Rate Shocks: A Cross Country Industry Analysis of Stock Returns. The Review of Financial Studies, 14 (1), 215241. Jorion, P. (1990). The Exchange Rate Exposure of U. S. Multinationals, Journal of Business, 63, 331345. Kanas, A. (1997). Is Economic Exposure Asymmetric between Long-run Depreciations and Appreciations? Testing Using Cointegration Analysis. Journal of Multinational Financial Management, 7, 27-42. Knetter, M. M. (1994). Is Export Price Adjustment Asymmetric? Evaluating the Market Share and Marketing Bottlenecks Hypotheses. Journal of International Money and Finance, 14, 491-510. Koutmos, G. & Martin, A. D. (2003). Asymmetric Exchange Rate Exposure: Theory and Evidence. Journal of International Money and Finance, 14, 747-62. Krugman, P. (1987). Pricing to Market When the Exchange Rate Changes, In S. W. Arndt & S. W. Richardson (Eds.), Real Financial Linkages among Open Economies, Cambridge: MIT Press. Marston, R. C. (1990). Pricing to Market in Japanese Manufacturing, Journal of International Economics, 29, 217-236. Miller, K. D. & Reuer, J. J. (1998). Asymmetric Corporate Exposures to Foreign Exchange Rate Changes. Strategic Management Journal, 19, 1183-1191. Muller, A. & Verschoor, W. (2006). Asymmetric Foreign Exchange Risk Exposure of US Multinationals. Journal of Empirical Finance, 13, 495-518. Priestley, R. & Odegaard, B. A. (2002). Linear and Nonlinear Exchange Rate Exposure and the Price of Exchange Rate Risk. Working Paper, Department of Financial Economics, Norwegian School of Management. Solakoglu, M. N. (2005). Exchange Rate Exposure and Firm-Specific Factors: Evidence from Turkey. Journal of Economic and Social Research, 7 (2) 35-46.