1

Time-varying betas of sectoral returns to market returns and

exchange rate movements

Hyunjoo Kim and R. Scott Hacker

Department of Economics

Jönköping International Business School (JIBS)

P.O.Box 1026 SE-551 Jönköping, Sweden

Abstract

The time-varying behavior of the market and exchange risk sensitivities of the U.S. sectoral

returns are estimated using random walk process in connection with the Kalman filter. As a

whole, it is observable that the market risks shrink over longer time-horizons. As regards

exchange risk, the findings are consistent with the notion that high US returns will induce a

greater capital inflow into the US stock market and thereby cause an appreciation of the US

dollar. The exchange rate risks appear to be declining with longer time horizons, in some cases

resulting ultimately in a negative relationship between the US dollar and the industry returns.

This is consistent with the idea that the effect of a US dollar appreciation on competitiveness of

US exports becomes stronger with the larger time horizons.

1. Introduction

The objective of this paper is to investigate the time-varying behavior of beta of the industry

returns in the U.S. stock market to market returns and to exchange rate movements. An

empirical beta pricing model, where industry-specific conditional betas measure sensitivity to

market and the global risk factors, is formulated. From here and onwards, betas and sensitivities

are used interchangeably. These sensitivities are measured for various industries at the

supersectoral level for the 1995 – 2010 period and are measured at different time horizons. This

investigation allows us to consider various relevant issues, as listed below.

The first issue is how exchange rate movements are associated with industry returns after

controlling for movements in the market premium (the market return minus the risk-free return).

The returns performance in reaction to exchange rate change should be different in different

industries, with one expectation being that industries with substantial US production and heavy

involvement in exports should be negatively affected by appreciation of the US dollar due to loss

of competitiveness. For industries with substantial multinational involvement the opposite is true

due to the gain in competitiveness for subsidiaries outside the US, although the appreciation

causes foreign revenues in dollar terms to diminish for the same amount sold, which could then

be reflected in lower returns in dollar terms. The value of intermediate goods from abroad also

has an impact on how the exchange rate affects industry returns, with industries relying more

heavily on non-US intermediate goods being positively affected by a dollar appreciation as

foreign inputs appear cheaper in US dollars.

2

Exchange rate relationships with industry returns get further complicated by a causal relationship

opposite to that considered in the previous paragraph. For example if an industry‘s stock prices

show a strong upward trend while those in other industries are flat, investors from outside the

US will be induced to invest in the industry with the growing returns, putting upward pressure

on the dollar. By this means, a positive relationship between an industry‘s returns and the value

of the dollar may be observed.

If exchange rate movements are associated with industry returns after controlling for movements

in the market premium, then this foreign currency risk would have direct implication for hedging

strategies if the currency risk is a priced factor in international financial markets. This is the case

because any source of risk that is not compensated in terms of returns should be hedged. (Santis

and Gerard, 1998).1

The second issue is which industries become more sensitive to the market premium and to

exchange rate movements, during a financial crisis and after a financial crisis. Typically

―defensive‖ stocks, i.e. those with low betas, are expected to fare better than other stocks during

a financial crisis as investors flee from riskier alternatives. Another relevant point when focusing

on US data is that international financial crises tend to put downward pressure on returns and

can put upward pressure on the dollar as investors consider it a safe-haven—even if the US is at

the center of the financial crisis.

A third issue is whether findings relevant for the first issues vary by the time horizon over which

returns and exchange rate movements are measured. One may expect that at short time horizons

stock price movements are highly influenced by technical factors, with speculators reacting solely

to stock price movements throughout the market due the lack of information (or cost of

collection that information) as to what is the fundamental reason behind the movements. This

arguably creates higher market betas at shorter time horizons than at longer time horizons, at

which point fundamentals become more relevant in stock valuation. On the other hand, Gensay,

Whitcher, and Selcuk (2005) claim that since macroeconomic variables are harder to predict over

longer time horizons, beta estimates should be higher at those longer time horizons. They

investigate this claim with results from wavelet analysis, which dissects time series into different

layers without losing original information. They reported that beta indeed becomes stronger as

the wavelet scale increases and that predictions of the CAPM are more relevant at medium- to

long-run horizons as compared to short time horizons.

Similar arguments arise when considering the relationship of returns to exchange rate

movements. At short time horizons investors may overestimate the impact of exchange rate

movements and can consider such movements as part of a longer trend which may not occur.

1 Empirical studies on exchange rate exposure point out that the effect of exchange rate shock is made very complex

because firms often hedge some of their foreign exchange exposures. Those empirical studies, therefore, had only

limited success in finding statistically significant exposures for most firms, which was called ‗exposure puzzle.‘ Two-

types of hedging activities of firms were presented to explain the puzzle: 1) financial hedging activities which reduce

exposure by using foreign currency derivatives or other type of financial instruments; 2) operational hedging which

is geared toward reducing long-run exchange rate exposure by pricing practices or marketing decisions in response

to exchange rate movements (Bartram and Bodnar, 2007).

3

Due to this we may find stronger relationships between returns and exchange rates at shorter

time horizons rather than at longer ones. However, Bartov and Bodnar (1994) note that

prediction of the firms value from the changes in exchange rate would be reflected in stock

returns only when information about the effects of exchange rate changes on future cash flows is

revealed over time. Using long-horizon exchange rates and stock returns, therefore, may be more

informative compared to utilizing short-horizon exchange rates. Building on this insight, we

suggest also that at short time horizons the impact of exchange rate changes on investment

decisions will not be strong, but the effect of investment decisions across various international

asset markets will affect the exchange rate rather strongly at short time horizons. Thus we expect

at short time horizons a rise in expected US returns to positively affect the value of the US dollar,

but as the time horizon expands, a lower positive or even negative relationship between the US

dollar and US returns may arise. This relationship at the longer time horizon may come about as

the profitability in many US industries decline with a loss in international competitiveness of US

products due to US dollar appreciation.

To investigate these various issues, this paper presents time-varying coefficient estimates from an

industry-level international CAPM model, which includes exchange rate changes as an additional

explanatory variable in a CAPM-type model. A Kalman filter is used in the estimation of these

coefficients, and the estimates are performed at different time horizons for the data: daily, weekly,

monthly, quarterly, and yearly.

The paper is organized as follows. In the next section a background discussion is provided, and

in the section following that data used in this study is described along with methodology adopted

in this paper. In section 4 the empirical findings are presented, then in section 5 the conclusions

drawn are summarized.

2. Background

Estimating a beta of a stock to the overall market can be done in the single factor capital asset

pricing model (CAPM) developed by Sharpe (1964), Lintner (1965) and Black (1972). Beta

measures the systematic risk, i.e. the sensitivity of a stock to the market index, which determines

the required rate of return on equity (i.e. the cost of equity for the firm). The CAPM set a corner

stone of modern finance with beta representing one of the most widely used concepts in finance

and there is controversy about how serious the evidence against it really is (Campbell, Lo and

Mackinlay (1997). The CAPM has been questioned by several empirical studies, which are

presented in table 1. While the early literature on CAPM is included in the cell (1) where one

factor―the rate of return on the market portfolio―is linearly related to the security rates of

return, empirical studies in the categories of the cells (2)-(4) found that the one constant beta

does not explain much of the cross-section variations of average returns.

Table 1. Categories of literatures in asset pricing models

Constant Time-varying

One-β (1) (3)

Multiple- β (2) (4)

4

One line of empirical studies of the CAPM was done for its theoretical extensions.2 One of such

an extension is international CAPM which considers an additional source of risk, exposure to

exchange rate risks, in the asset pricing models (Solnik, 1974; Stulz, 1981; and Adler and Dumas,

1983).3 Dumas and Solnik (1995) was supportive of the existence of a foreign exchange risk by

using a conditional approach that allows for time variation in the returns for exchange rate risk in

international asset markets. Consistent with the results of Dumas and Solnik (1995), Santis and

Gerard (1998) and Santis et al. (2003) also support a model which includes both the market and

exchange risks in a conditional version of the international CAPM. 4 As regards multifactor

models, Fama and French (1992), in particular, has received a lot of attention and led

propagation of multifactor models including Fama-French type factors, which belongs to the cell

(2).

The other line of empirical studies, which belong to the cell (3), questioned the validity of beta

stability assumption (Fabozzi and Francis, 1978; Sunder, 1980; Bos and Newbold, 1984; Collins

et al., 1987). This area of empirical study is known as conditional-CAPM testing which updates

expected returns or volatility conditioned on the most recent past information. Researchers in

this area of study have used different methodologies including GARCH, GARCH-in-means,

Kalman filter for studying time-varying systematic risks(Fernandez, 2006). Allowing for betas to

vary over time not only removes the assumption on linearity in asset price modeling but also

accounts for possible effect of omitted variables (Gonzalez-Rivera, 1997).

Given the results of the previous studies in the subject area, the Kalman filter (KF) is employed

in this paper as an empirical methodology to consider time-varying beta (sensitivities) in studying

sectoral returns. In so doing, this paper lends itself to an understanding of the time-varying

relationship with the two given variables―a market portfolio return and a rate of change in

exchange rate. This paper, thus, can be categorized in the cell (4) of table 1 in asset pricing

models. Additionally, tests results are compared by using different frequency of data observation

to see whether the results hinge on using certain frequency of the data.

The Kalman filter(KF) is a recursive algorithm for numerical estimation of state space models

where the observed dependent variables are parameterized as function of unobserved state

2 The theoretical extensions of the CAPM include 1) after-tax CAPM in which investors must be compensated with

higher pre-tax returns due to higher taxes imposed on high dividend-yield stocks; 2) the inter-temporal CAPM in

which investors are concerned not only with their end-of-period payoff, but also their wealth at time t ,which might

vary depending on labor income, the prices of consumption goods, and expectations about them; 3) the

consumption CAPM (C-CAPM) in which the risk in future consumption is the only one risk. 3 If purchasing power parity (PPP) does not hold continuously in an international context, any investment in a

foreign asset entails the performance of the domestic currency relative to the foreign currency along with the

performance in an investment of the foreign asset and. Investing in foreign markets, thus, is combined with

exposure to exchange rate risks (Dumas, 1983). Stulz (1995) includes a survey of empirical studies which are limited

to unconditional version of the international CAPM model. The results are inconclusive. 4 The existing literature on the relationship between stock prices and exchange rates, however, provides inconclusive

results or only weak evidence of systematic exchange rate exposure. Overall, evidences of the empirical studies on

exchange rate risk suggest that it is marginally larger in open, exports-oriented economies (Bartram and Bodnar,

2007).

5

variables. The unobserved state variables in this paper are sensitivities to market excess returns

and exchange rate movements, both of which are modeled as following a random walk process.

This framework was chosen given the latest finding by Mergner and Bulla (2008) where different

modeling techniques were compared to analyze the time-varying behavior of the systematic risk.

By comparing ex-ante forecast performances (the mean absolute error (MAE) and the mean

squared error (MSE)) of the six models―a bivariate t-GARCH (1.1) model, two Kalman filter

(KF)-based approaches, a bivariate stochastic volatility model estimated via the efficient Monte

Carlo likelihood techniques and two Markov switching models―the Kalman filter approach with

the random walk process is preferred to other models to describe and forecast the time-varying

behavior of the beta.5

Time-varying sensitivities in this paper are focused on the US industry portfolio. The

macroeconomic and industry analysis are two of major aspects in the process of security analysis.

It is necessary to examine sensitivities of industry groups since the investment advice of portfolio

managers are tied to the macroeconomic forecasts, however, not all industries are equally

sensitive to the macroeconomic conditions (Yao and Gao, 2004). Industries are also related with

the world economy with varying degrees of returns in response to the exchange rate fluctuations

(Bodnar and Gentry, 1993; Griffin and Stulz, 2001; Doidge et al., 2003). Therefore, by

comparing exchange risk sensitivities of different industries, this paper explores whether they

display varying sensitivities to the exchange risk

Additionally, time-varying sensitivities of each sector are compared at different frequencies of

data observation to examine the impact of time horizons on the beta estimates. Studies on the

return interval of beta estimate provided evidence that time scale is an important issue in beta

estimation. One study on this issue, that by Gensay, Whitcher, and Selcuk (2005), was already

discussed in the introduction. Another study, by Brailsford and Faff (1997), documented that

greater support for CAPM with a GARCH-M specification was found using weekly return than

using monthly interval returns, while the daily return interval in that study did not support the

CAPM.

3. Empirical methodology and data description 3.1. Data description

The nominal exchange rate variable used in this paper is the foreign currency value of a U.S.

dollar (nominal effective exchange rate, NEER),6 i.e. an increase in the exchange rate implies an

5 Brooks, Faff, and Mckenzie (1998) compared three different techniques for the estimation of conditional time-

varying betas, where the Kalman filter approach was more supportive than the others based on in-sample forecast

errors. Different papers which used each of the modeling techniques are well summarized in Mergner and Bulla

(2008). 6 Many studies on foreign exchange exposure use nominal effective exchange rate for a relevant exchange rate.

However, using trade-weighted exchange rate bears a shortcoming of lacking power if a firm or an industry is

exposed only to a small number of currencies. Creating a firm- or industry-specific exchange rate could mitigate this

problem, yet this approach lacks of basis on which these bilateral exchange rates should be chosen (Williamson,

2001). Other than the nominal effective exchange rates used and reported in the following empirical section, USD

against major currencies, USD against G10 economies were also used in empirical test.

6

appreciation of the U.S. dollar and a depreciation of the foreign currency. The foreign currency is

the multilateral trade-weighted currencies of a large group of major U.S. trading partners, which

is computed with the following weights: Japan (30.29%), Canada (25.09%), Germany (11.50%),

United Kingdom (8.91%), and France (5.84%). The EU accounts for 41.19% and euro area

countries for 29.80%. The nominal effective exchange rate is used instead of real effective

exchange rate for the following two reasons (Bodnar and Gentry, 1993). One is that the real

exchange rate is based on the assumption that financial markets instantaneously observe inflation.

The other is that nominal and real effective exchange rates are highly correlated during the

sample period. The correlation between them is 0.876.

For the market returns, the total return (i.e. dividends are reinvested) series of the MSCI ACWI

(All Country World Index) Index are used.7 The MSCI ACWI is a free float-adjusted market

capitalization weighted index that is constructed by gathering equity market performance of

developed and emerging markets.8

7 Other than MSCI ACWI, MSCI Asia (standard, large), MSCI Europe (standard, large), FTSE World index, and

Dow Jones US total market index were also used for the market portfolio. Mckenzie et al. (2000) reported that the

domestic index generates considerably higher risk estimates than using world index for market risk of the Australian

industry portfolio. For US industry portfolio, US domestic index generates lower risk estimates compared to the

world index. Results are available upon requests. 8 As of May 27, 2010 the MSCI ACWI consisted of 45 country indices comprising 24 developed and 21 emerging

market country indices. The developed market country indices included are: Australia, Austria, Belgium, Canada,

Denmark, Finland, France, Germany, Greece, Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand,

Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the United Kingdom and the United States. The emerging

market country indices included are: Brazil, Chile, China, Colombia, Czech Republic, Egypt, Hungary, India,

Indonesia, Korea, Malaysia, Mexico, Morocco, Peru, Philippines, Poland, Russia, South Africa, Taiwan, Thailand,

and Turkey. Data of the market capitalization with different sizes (such as large cap, mid cap, standard cap

(large+mid cap), and small cap) are available, among which large cap series are used in this paper.

7

Figure 1. Monthly MSCI ACWI, Dow Jones US and the nominal effective exchange rate (NEER)

For the easiness of presenting the MSCI ACWI and the nominal effective exchange rate of the

U.S. dollar during the sample period, time plots of the monthly level series were drawn in figure

1. The MSCI ACWI was on an increasing trend since the early 1995 to the early 2000. With the

dot-com bubble bust, the index takes a downturn during the year 2000, which lasts until the

beginning of the year 2003. Stock markets in the world continued to rally until the subprime

mortgage crisis hit the financial market with the failure of Lehman brothers and other major

institutions during the year 2008. As of October, 2010, the index recovered its level of before the

crisis. The U.S. dollar, in general, shows an opposite movement to the MSCI ACWI. The

nominal effective exchange rate has been decreasing (i.e. dollar depreciation) between the year

2002 and early 2008, while the exchange rate rose sharply (i.e. dollar appreciation) during the year

2008-9.

The data used for sectoral return series in this paper are Dow Jones U.S. industry indexes of

total return indices for 19 American industry portfolios covering the period from January 3, 1995

to November 4, 2010. Dow Jones Sector Index is classified into Industry Classification

Benchmark (IBC) which contains four classification levels: Industries (10), Supersectors (19),

Sectors (41), and Subsectors (114).9 Among those classification levels, supersectors were adopted

for this paper as is listed in table 1. Supersectors and sector fall on different categories within

ICB classification, however, the term ‗sectors‘ would be used in place of ‗supersectors‘ hereafter

in this paper due to the former‘s familiarity as a general term than the latter. In order to use

excess returns from the total return indices, the riskless rate is approximated by the return

9 Numbers in parenthesis of each classification level stand for how many are included in each level.

0

20

40

60

80

100

120

140

0

200

400

600

800

1000

1200MSCI ACWI

Dow Jones US

NEER

8

(interest rate) on 3-month treasury bills. All the return series are observed at the daily, weekly,

monthly, quarterly and annual intervals. All the indices are expressed in U.S. dollars and are

obtained from Thomson Financial Datatream. All returns are expressed in percentage.

Table 2. Dow Jones U.S. industry index at supersectoral level (Abbreviations)

Industry Supersectors*

Oil & Gas Oil & Gas (Oil)

Basic Materials Basic Resources (Basic)

Chemicals (Chemicals)

Industrials Construction and Materials (Construction)

Industrial Goods & Services (Industrial)

Consumer Goods

Automobiles & Parts (Auto)

Food and Beverages (Food)

Personal and Household Goods (Households)

Health Care Health care (Health)

Consumer Services

Retail (Retail)

Media (Media)

Travel & Leisure (Travel)

Telecommunications Telecommunications (Telecom)

Utilities Utilities (Utilities)

Financials

Banks (Banks)

Insurance (Insurance)

Financial services (Financials)

Technology Technology (Tech.) * Abbreviations are in parenthesis.

The descriptive statistics of the daily, weekly, monthly and quarterly excess returns of each sector

are provided in table 3. In most cases the index of kurtosis and the Bera–Jarque test statistic

reject the hypothesis of normally distributed returns. The two statistics are particularly large for

daily and weekly interval series.

Table 3. Descriptive statistics of sectoral excess returns

Sectors Freq. Mean S.D. Skew. Kurt. J-B

Auto Daily ,021386 1,8606469 ,007 4,725 3687.376

Weekly ,097479 4,1715156 -,055 5,146 929.1259

Monthly ,439826 8,5938580 ,074 4,717 164.9446

Quarterly ,866326 14,9957517 -,172 1,617 5.423960

Yearly 5,327851 39,3190583 ,809 2,088 2.043485

Banks Daily ,036483 2,2351684 ,860 19,057 60493.57

Weekly ,157202 4,6834040 1,282 20,268 14543.96

Monthly ,520055 7,3726742 -,482 2,944 70.89168

Quarterly 1,371427 13,0487204 -,617 1,997 11.82884

Yearly 6,714960 39,3190583 ,809 2,088 0.300256

Basic Daily ,035315 2,0573889 -,277 9,456 14721,55

Weekly .152939 4,2926115 -,084 5,309 936.8892

Monthly ,622797 8,0258151 -,710 3,670 115.0932

Quarterly 1,632124 14,5909365 -,991 1,628 15.02707

9

Yearly 8,413478 33,6814069 ,181 1,815 0.559854

Chemicals Daily ,035198 1,5898460 -,112 5,412 4845.144

Weekly ,160675 3,3460465 -,123 3,117 285.6166

Monthly ,675491 6,3112341 ,214 2,758 57.22735

Quarterly 1,696295 11,2361662 -,562 1,404 6.941371

Yearly 7,340541 24,6457170 -,117 1,690 0.429305

Construction Daily ,027424 1,6127530 -,212 6,807 7683.455

Weekly ,129469 3,6305112 ,403 7,475 1916.049

Monthly ,520286 6,5172710 -,630 3,182 86.87423

Quarterly 1,213704 11,2442696 -,474 ,119 2.248044

Yearly 6,098594 22,3235169 -,951 1,242 1.969733

Financials Daily ,043141 1,9624610 ,484 15,512 39910.94

Weekly ,182605 3,8399159 ,475 7,019 1793.399

Monthly ,708728 6,3967114 -,395 1,643 24.36309

Quarterly 1,885236 11,7500868 -,870 1,699 13.27965

Yearly 12,081843 31,3600523 -,856 1,249 1.625658

Food Daily ,028003 1,0702670 ,091 5,436 4885.745

Weekly ,132029 2,2818371 -,514 4,661 799.2701

Monthly .581009 4,3820049 -,361 1,560 21.58576

Quarterly 1,432205 7,9296440 -,806 ,983 8.232744

Yearly 6,889809 16,8333484 -,573 -,302 0.874527

Health Daily ,034484 1,2362945 -,076 6,248 6451.813

Weekly ,159998 2,5683519 -,460 4,702 864.1315

Monthly ,671579 4,3524742 -,297 ,600 5.171561

Quarterly 1,709998 7,5795903 -,404 ,981 3.356479

Yearly 9,684959 22,6472212 -,039 -,613 0.404636

Households Daily ,031042 1,0864892 -,295 7,251 8741.461

Weekly ,144797 2,3230435 -,736 4,993 1592.968

Monthly ,628182 4,2864407 -,571 1,389 24.00181

Quarterly 1,597263 8,2521312 -,519 ,522 3.085632

Yearly 6,941767 16,1126016 -,722 ,324 1.045023

Industrial Daily ,028130 1,3875476 -,186 5,353 4755.255

Weekly ,128272 2,9539756 -,311 3,889 474.9801

Monthly ,541615 5,4422081 -,628 1,405 26.44462

Quarterly 1,352190 10,2209125 -,480 ,347 2.434452

Yearly 6,513566 22,2700778 -1,035 ,756 2.169904

Insurance Daily ,028446 1,6901163 ,358 14,289 33817.96

Weekly ,121482 3,4133397 -,225 8,708 2734.399

Monthly ,487041 6,1161958 -,408 4,069 127.5209

Quarterly 1,095754 10,1202024 -,380 ,929 2.975087

Yearly 6,122713 24,0619066 -1,042 1,684 2.583865

Media Daily ,025279 1,5419636 ,012 7,597 9533.826

Weekly ,112495 3,1763139 -,338 5,584 1069.442

Monthly ,478423 6,0295132 -,767 2,082 49.86374

Quarterly 1,118258 11,3852314 -,216 1,380 4.119966

Yearly 7,282198 32,7961161 -,160 -1,168 0.934235

Retail Daily ,032420 1,4112105 ,026 4,558 3431.126

Weekly -,037 3,036 -,126 2,936 260.7884

Monthly ,621736 5,4054400 -,202 ,528 3.117013

Quarterly 1,576929 10,1112659 ,590 1,437 7.469588

Yearly 8,541496 26,5715368 ,126 ,254 0.056677

Oil Daily ,049883 1,7062396 -,001 10,808 19298.69

Weekly ,221088 2,3230435 -,807 6,449 914.2290

Monthly ,925925 6,1129610 -,225 1,602 20.08544

Quarterly 2,263968 9,0428151 -1,118 2,034 20.83804

Yearly 11,970384 21,8166491 -1,394 1,453 4.165648

Technology Daily ,044971 2,0405885 ,298 4,271 3071.223

Weekly ,201687 4,2161373 -,308 2,504 65.40886

10

Monthly ,897492 8,7629716 -,185 ,268 1.478472

Quarterly 2,474971 16,0241481 -,451 ,536 2.454630

Yearly 13,840117 42,2096179 ,043 -1,089 0.807098

Telecom Daily ,014685 1,5389709 ,305 7,291 8842.458

Weekly ,057084 4,2161373 -,088 4,290 634.3648

Monthly ,267545 6,3531483 -,161 1,358 14.00879

Quarterly ,524785 11,6782233 ,186 ,446 0.612541

Yearly 3,897197 28,4623434 -,368 -,662 0.710200

Travel Daily ,037230 1,4059328 -,042 3,826 2418.281

Weekly ,133937 2,9202825 -,181 1,735 109.8778

Monthly ,671681 5,8021607 -,427 1,154 15.13145

Quarterly 1,621095 10,6540234 -,265 -,157 0.575271

Yearly 6,571538 22,5330050 -,265 -,004 0.230961

Utilities Daily ,024976 1,1829485 ,181 11,068 20260.15

Weekly ,115302 2,4663454 -1,042 7,621 2089.972

Monthly ,511844 4,8715467 -,734 2,104 49.00493

Quarterly 1,230856 8,7872784 ,040 1,897 7.216619

Yearly 7,238245 23,8734188 -,435 -,331 0.609167

MSCI World Daily ,017655 1,0491412 ,017 11,884 22347,51

Weekly ,083639 2,4323846 -,774 7,843 2205.217

Monthly ,526924 4,7542560 -,758 1,652 37.58005

Quarterly 1,275129 8,7799404 -,710 1,195 7.711073

Yearly 5,373939 23,0003383 -,878 ,305 1.568316

3.2 Empirical model and methodology

The market and exchange rate risk are included in the two-factor model specification with time

varying betas in the following form10

(1)

where is the return on industry i, is the risk-free rate, is the return on the market

portfolio, and is a rate of change in the nominal effective exchange rate of the U.S. dollar.11

Eq. (1) is referred to as signal or observation equation. The state equations are:

The observation error and the state equation errors, and , are assumed to be Gaussian and are taken to be serially uncorrelated. The Kalman filter is an algorithm employed to estimate equation (1) is an optimum recursive estimation method for the signal. Throughout this recursive

10 An intercept term is not included in the specification eq. (1) due to the fact that a singular variance-covariance

matrix is generated with a time-varying constant term in eq. (1). Including a none-time-varying constant term turned

out not to be significantly different from zero. 11 The theoretical formation of both CAPM and APT model is based on expectations or ex ante form. To empirically

tests the models, expectations are transformed into a form that uses observed data by assuming that the rate of

return on any asset is a fair game ― i.e. realized return on any asset is equal to the expected rate of return (Copeland

et al., 2003).

11

estimation algorithm, a new estimate is obtained by adding a correction term to the previous estimate, where the new information has a weight on 1/T. This process consists of two steps, prediction and updates, which calculates the parameters of the distributions.

A problem in estimating eq. (1) arose from diagnostic checking which shows that the market

return and exchange movements were correlated.12 Following the approach of Elton and Gruber

(1991), a side regression of the rate of changes in exchange rate on the market return were run to

orthogonalize the exchange risk factor, i.e. residuals of the side regression were used as an

orthogonalized exchange risk factor. Instead of including a size factor, a two-factor model is

used in this paper because the market returns from MSCI covers large capitalization only.

Including a size factor along with an index of large capitalization would not allow a meaningful

size effect to be captured (Banz, 1981; Heston, Rouwenhorst and Wessels, 1995; Fama and

French, 1998).

Tests for unit root were performed for all the series using Augmented Dickey Fuller test,

indicating all the series are stationary process. The coefficients estimates of the ordinary least

squares of the eq.(1) were given as initial values of the state equations. CUSUM tests were

performed for the recursive residuals in the observation equation of all sectors at all the

frequencies of data observation. Daily and weekly series indicate instability of betas, while the

recursive residuals of the monthly, quarterly and yearly series tend to fail to exceed the 5%

bound of significance, indicating beta stability.

and are called beta, factor loading or sensitivity within a factor-model framework.

measures sensitivity of the sector i to the market. This market beta is the covariance between

returns on a risky asset divided by the variance of the market portfolio―an asset covaries with

the economy―which quantifies risk of the asset. is interpreted as exchange rate exposure. 13

It reflects the change in returns, which can be explained by exchange rates movements after

conditioning on the market return. Exchange rate exposure in this context is marginal since each

sector‘s exposure is measure relative to the market average (Dominguez and Tesar, 2006). The

betas for the market and foreign exchange rate risks presented in figures and tables in the

following section is based on Kalman smoothing. The Kalman smoother calculates recursively

the state posterior distributions for the linear filtering model, eq. (1). The posterior distribution

calculated by Kalman filter is different from that of the Kalman smoother in the sense that the

former are conditional only to the measurements obtained before and at the time step, k, while

the latter are conditioned to all the measurement data.

12 The pearson correlation coefficients between the market factor and the exchange risk factor during the sample

period are -0,198, -0,246, -0,420 -0,341 ,and -0,503 for daily, weekly, monthly, quarterly and yearly frequencies of the

data observation, respectively. All are statistically significant at 0.05 level. Estimations were done with both with and

without orthogonalization. The results were similar. 13 Exchange rate exposure is defined following the literature defining exchange rate exposure as a statistically

significant (ex post) relationship between excess returns at the firm-or industry- level and foreign exchange returns

(Dominguez and Tesar, 2006).

12

4. Empirical findings 4.1. Time-varying risks with industry comparisons 4.1.1 Market sensitivity

Market systematic (sensitivity) risk measures how each industry covaries with the economy, the higher the sensitivity to the market, the more sensitive the industry is to the market. Figure 2 presents plots of the time-varying market risk series by using daily return series during the sample period. Due to limitation of space, the time plots of the figures are presented at the industry level which includes relevant sectors. Bank and technology are the two sectors with wider ranges of the market sensitivities over the sample period compared to those of other sectors. The market sensitivities of all the three sectors within financial industry (banks, financials services, and insurance) soared during the house bubble and credit crisis when the market sensitivities top 4.52 (bank), 2.56 (financial services), and 1.96 (insurance), respectively. The market sensitivity of technology sector also increased during this crisis period, however, drastic changes of market sensitivity of technology sector are observed during dot-com bubble bust when it rose up to 3.67. A quite similar pattern of a change in market sensitivity is also detected in telecom industry during the dot-com bubble bust.

At the onset of the credit crisis, market sensitivities of the basic resources (2,25), construction

and material (1.79) and auto (2.02) sectors surged, whereas the movements of the market

sensitivities for all the other sectors, which are not mentioned so far, are not noticeable under

the times of crisis. Among the three crisis periods, market sensitivities of the US sectoral returns

were not as responsive in the Asian financial crisis as the other two crisis periods.

The inspection of the time-varying sensitivities of the sectoral returns the market shows that the

time-varying beta of sectors generally rise due to the financial crisis. Such time-varying market

sensitivities may be affected by both microeconomic and macroeconomic factors (Bos and

Newbold, 1984). During those three crisis periods―financial crisis, dot-com bubble bust, and

housing bubble and credit crisis―increases in volatility of the financial markets and capital flows

around the world were observed (Chen and So, 2002; Ofek and Richarson, 2003; Gotham, 2009).

A rise in the stock market volatility, therefore, make investors perceive it as an increase in risk of

equity investment (Choudhry, 2005). However, the effects of the crisis on the market sensitivities

of industries are different, i.e. the larger the market risk of an industry, the more it greater the

exposure to the source of risk, which is what is exactly observable in figure 2.

4.1.2 Exchange rate exposure

Since the trade-weighted nominal effective exchange rate is constructed as foreign currencies per

dollar, a negative exchange risk sensitivity implies that an unexpected appreciation of the U.S.

dollar makes the U.S. industries worse off relative to the market. The point estimates of the

foreign exchange risk using daily return series, however, are staying positive for almost all the

sectors during the whole sample period as shown in figure 3. This means that for most of the US

industries, US dollar appreciation improves daily returns. One thing also to note from figure 3 is

the movement of the exchange risk beta during the period of US dollar depreciation (from the

year 2002 to the end of the year 2007). During this time period, the exchange risks are on the

13

rise, which is clearly noticeable for the oil, consumer goods (auto, food, household goods),

consumer services (retail, media, travel), telecom, and financial (banks, insurance, financial

services) industries. Exchange risks of these industries took a downturn at the start of the US

dollar appreciation from the year 2008.

Taken as a whole, the exchange risks are larger for the sectors such as construction, auto, travel,

telecom, bank and technology sectors which involve more international activity compared to the

other sectors. The determinants of the varying exchange rate exposure, however, is not clear to

identify because the co-movements of exchange rates and excess returns incorporate the effects

of any hedging activities taken by firms (Dominguez and Tesar, 2006). The finding from the

figure 3 would suggest that the firms belong to each industries or sectors dynamically adjust their

behavior to exchange rate risks over time.

4.2 Econometric Issues The fact that betas are estimated with a Kalman filter raises three methodological issues,

which are not present in standard time-series empirical tests of the asset price models. One

concern is that the prediction residuals in the Equation (1) were found to have autocorrelation

and conditional heteroskedasticity. This is not unexpected since market returns tend to go

through periods of volatility leading to heteroscedasticity, and randomness in the explanatory

variables in combination with randomness in their coefficients can lead to autocorrelation in the

residuals even if the assumptions of the model are true [needs further verification]. A second

concern is that estimation of equation (1) with an additional time-varying constant results in a

singular variance-covariance matrix. In order to check whether the time-varying beta over the

sample period is a statistical artifact generated by the specification of the model, ordinary least

squares estimator for four different subperiods―Asian financial crisis (Jul.1997-Dec.1999), dot-

com bubble bust (Jan.2000-Dec.2001), inter-crisis period (Jan. 2003-Dec.2006), and housing

bubble and credit crisis (Jul. 2007-Jun.2009)―were used.. The point estimates from these

additional regressions indicate patterns broadly similar to the ones presented above using the

Kalman Filter, albeit in a blunt step-function manner with four steps. A third issue is that

confidence intervals for point estimates, which are valid in case of OLS estimates, cannot be

applied.[ Extend this section]

14

Figure 2. The time-varying market risk for industries (using daily interval returns).

15

Figure 3. The time-varying foreign exchange risk for industries (using daily interval returns)

16

4.3. Time horizons and sensitivities

Market risks (sensitivities) using Kalman filter with different return intervals are presented in

table 4. There is a general tendency of a market risk decline, judging from the medians of all the

time-varying risks, as the return intervals gets larger. There are some exceptions to the general

tendency (for example, the market risk of the media sector for the yearly interval series is larger

than that for the daily). As a whole, however, it is observable that the market risks shrink over

longer time-horizons.

Table 4. Market risk (sensitivities) using Kalman filter with different return intervals

Sectors Daily median

(High/Low) Weekly median

(High/Low) Monthly median

(High/Low) Quarterly median

(High/Low) Yearly median (High/Low)

Oil 0,941877 (1,701538/-0,07924)

0,879271 (1,461538/0,128835)

0,772712 (0,927033/0,580222)

0.640030 (0.832501/0.373368)

0.709022 (0.794777/ 0.648436)

Chemicals 1,095583 (1,546959/0,282551)

0,979974 (1,25026/0,68581)

0,824203 (1,232064/0,519125 )

0.830427 (1.115398/ 0.747824)

0.659328 ( 1.341539/0.399531)

Basic 1,126876 (2,252905/0,099949)

1,121088 (1,732528/0,66244)

1,212561 (1,677944/0,382758 )

1.097863 ( 1.340188/0.876047)

0.975993 (1.927711/0.323441)

Construction 1,06392 (1,796565/0,206542)

0,990323 (1,608159/0,417845)

0,989904 ( 1,37242/0,345977)

1.023057 ( 1.423526/0.361682)

1.049196 (2.109813/-0.725244)

Industrial 1,112129 (1,720969/0,384358 )

1,106897 (1,373876/0,63736)

0,983205 (1,000455/0,973045)

1.041460a 0.980697 (2.422790/0.216774)

Auto 1,137936 (2,02954/0,299071 )

1,185925 (1,894686/0,487387)

1,003554 (1,712592/0,651976 )

1.240272 (1.795683/ 0.820447)

1.053556 (2.038295/0.794094)

Food 0,583771 (1,455414/-0,25517 )

0,529264 (1,307315/-0,29061)

0,523121 ( 0,92225/-0,45088)

0.538528 ( 0.706083/0.280216)

0.451469 (3.199617/-1.037888)

Households 0,737398 (1,245407/0,232621)

0,68603 (0,903825/0,368147)

0,695798 (0,894051/0,076743)

0.660452a 0.595870 (2.837570/-0.580889)

Health 0,841336 (1,65096/0,074355 )

0,705951 (1,334419/-0,03624)

0,614205 (0,696156/0,233771)

0.505123 (0.534356/ 0.487373)

0.375884 (0.526186/0.375884)

Retail 0,97933 (1,015893/0,270598 )

0,904728 (1,320605/0,675794)

0,794209

0.822655 ( 1.304934/ 0.602688)

0.970380 (1.281005/0.731490)

Media 1,068827 (1,558115/0,289924 )

0,917319 (1,381074/0,313267)

0,987042 (1,121026/0,641382 )

1.074015a 1.255822 (1.319284/1.186723)

Travel 0,961985 (1,587345/0,326064)

0,942366 (1,268553/0,361962)

0,867056 ( 1,006543/0,491919)

0.858547

0.934302 ( 1.777917/-0.056074)

Telecom 0,921731 (1,716674/0,399317)

0,837209 (1,323844/0,443838)

0,768064 (1,586352/0,239985 )

0.847520 (0.903721/0.658189)

1.034644 (1.414146/ 0.684696)

Utilities 0,6087 (1,323949/-0,12821)

0,630293 (0,832292/-0,02845)

0,553094 (1,146329/-0,30285)

0.613965 (0.964144/-0.113835)

0.948809 (1.596269/-1.744177)

Banks 1,088966 (4,524682/0,176108)

0,9823 (3,646238/0,381098)

0,780874 (1,918307/-0,1321 )

0.653843 (1.122145/0.457596)

0.598857 (2.960831/-0.424662)

Insurance 1,007155 (1,908474/0,460005 )

0,991047 (1,624234/-0,00339)

0,883563 ( 1,423523/-0,24117)

0.788055

0.562416 (2.945138/-1.390253)

Financials 1,263331 (2,561842/0,549397)

1,18116 (1,836656/0,889041)

1,050091 (1,23045/0,78799 )

1.015944 (1.335889/0.621709)

Tech. 1,419746 (3,670405/0,438647 )

1,267035 (1,993415/0,860204)

1,335441 (1,834191/1,020775 )

1.333361 (1.844434/1.092687)

aOLS estimates based on the specification of the eq.(1), but without state-space modeling.

Exchange rate risks show similar patterns to those of the market risks over different time

horizons. Two things are noticeable in table 5. First, the exchange rate risks at daily intervals are

all positive across sectors. It means that a US dollar appreciation is associated with an increase in

returns, which is counter to the general notion of losing competitiveness for exports caused by a

strong domestic currency, which would negatively affect returns. However the findings are

consistent with the notion that high US returns will induce a greater capital inflow into the US

17

stock market and thereby cause an appreciation of the US dollar. Second the exchange rate risks

appear to be declining with longer time horizons, in some cases resulting ultimately in a negative

relationship between the US dollar and the industry returns. This is consistent with the idea that

the effect of a US dollar appreciation on competitiveness of US exports becomes stronger with

the larger time horizons.

Our finding in the empirical section in general stand in contrast to the results of the previous

studies which examined the size of the beta at different time horizons. The market and foreign

exchange risks tend to decrease at longer time-horizons.

Table 5. Exchange risk (sensitivities) using Kalman filter with different return intervals

Sectors Daily median.

(High/Low) Weekly median.

(High/Low) Monthly median.

(High/Low) Quarterly median

(High/Low) yearly median (High/Low)

Oil 0,191006 (0,529834/-0,00028 )

-0,10928

-0,06757

0.208675 0.434271

Chemicals 0,405647 (0,729224/0,093259)

0,250109

0,045821

-0.129417 -0.299066

Basic 0,105488 (0,717302/-0,31422 )

-0,14071

-0,39912

-0.329838 -0.325546

Construction 0,377523

(0,851141/0,269514) 0,358929

(1,035824/0,044063)

0,088842 (0,828277/-

0,40256)

-0.196349 -0.225854

Industrial 0,484523 (1,089218/0,325583 )

0,491009 (0,58254/0,473923)

0,261427

0.194570a -0.051033

Auto 0,500831 (1,144882/0,330579)

0,662274

0,588254

0.655536 -0.296557

Food 0,281376

(0,737532/-0,15302) 0,306047

(1,441769/-1,01306 )

-0,14538 (0,633996/-

0,73964)

-0.092111 0.162290

Households 0,449817 (0,903593/0,055023)

0,422827 (0,849092/0,15468)

0,088621

-0.011217a 0.014412

Health 0,457656 (0,818755/-0,10098)

0,369703 (1,193302/-0,37529 )

0,26461

0.276072 0.162290

Retail 0,510489 (1,015893/0,409744)

0,629242 (0,921122/0,515055 )

0,512928

0.627618 0.557557

Media 0,413571 (1,222223/0,199701)

0,386356 (1,108885/0,068936)

0,383287

0.592566a 0.999701

Travel 0,499242 (1,333853/0,243698 )

0,511204 (1,046427/0,238567)

0,239398

0.089999 -0.111578

Telecom 0,407672 (0,920785/-0,00246

0,388399 (0,573157/0,238893 )

0,407081

0.046713 0.275630

Utilities 0,206825 (1,08254/-0,82761 )

0,182687 (0,303675/0,001633)

-0,01965

-0.027937 0.277119

Banks 0,48536

(3,112313/-0,03748) 0,631582

(1,512973/0,18665 )

0,083652 (0,565539/-

0,24471)

0.350113 0.843399

Insurance 0,501781 (1,704297/0,14476)

0,588202

0,264304

0.397000 1.122979

Financials 0,675933 (2,343678/0,037962 )

0,87672 (1,338372/0,206309)

0,475833

0.742483

Tech. 0,683265

(1,525932/0,163008) 0,49531

0,741378

0.705538 (0.927482/-

.062683)

OLS estimates based on the specification of the eq.(1), but without state-space modeling.

18

Figure 4. The time-varying market risk for industries (Monthly)

19

Figure 5. The time-varying foreign exchange risk for industries (Monthly)

20

5. Conclusion

In this paper, an approach to estimate the time varying risks, or sensitivities (beta), of US industry portfolio was adopted. The method is based on an recursive algorithm known as Kalman filter in state space models.

As a whole, however, it is observable that the market risks shrink over longer time-horizons. However the findings are consistent with the notion that high US returns will induce a

greater capital inflow into the US stock market and thereby cause an appreciation of the US

dollar. Second the exchange rate risks appear to be declining with longer time horizons, in some

cases resulting ultimately in a negative relationship between the US dollar and the industry

returns. This is consistent with the idea that the effect of a US dollar appreciation on

competitiveness of US exports becomes stronger with the larger time horizons.

Our finding in the empirical section in general stand in contrast to the results of the previous

studies which examined the size of the beta at different time horizons. The market and foreign

exchange risks tend to decrease at longer time-horizons.

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