A New Look at Hedging With Derivatives_Will Firms Reduce Market Risk Exposure

8/9/2019 A New Look at Hedging With Derivatives_Will Firms Reduce Market Risk Exposure

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A New Look at Hedging with Derivatives: Will Firms Reduce Market Risk

Exposure?

September 2006

Turan G. Bali, Susan R. Hume, and Terrence F. Martell♦

ABSTRACT

This paper examines derivatives use of foreign exchange, interest rate and commodities risk by non-financialfirms across multiple industries, using data from 1995 to 2001. This paper considers the interaction of afirm’s risk exposures, derivatives use, and real operations simultaneously, and considers how these factorschange over time using a consistent data base. Hedging with derivatives is only significantly related tocommodity risk exposure during most years of the study, and to a more limited degree to interest rateexposure. Further, we find a strong correlation between risk exposures for some years using a newtechnique, suggesting that univariate modeling is not always appropriate. The implications are that hedgingwith derivatives is not always important to a firm’s rate of return and is linked to other non-financial andeconomic factors.

Key words: hedging, derivatives use, risk management, risk exposure

JEL classification: G13, C13

♣ We thank Robert Webb (the editor) and anonyomous referee for their extremely helpful comments and suggestions,and Nosa Omoregie for his valuable research assistance. We also benefited from discussions with ArchishmanChakraborty, Ozgur Demirtas, Charlotte Hansen, Armen Hovakimian, Susan Ji, John Merrick, Salih Neftci, Lin Peng,Robert Schwartz, James Weston, and Liuren Wu. An earlier version of this paper was presented at Baruch College, the

Graduate School and University Center of the City University of New York, the College of New Jersey, and the 2004Financial Management Association meeting. Turan Bali gratefully acknowledges the financial support from the PSC-CUNY Research Foundation of the City University of New York. All errors remain our responsibility.♦ Turan Bali is a professor of finance at the Department of Economics and Finance, Zicklin School of Business, BaruchCollege, City University of New York, One Bernard Baruch Way, Box 10-225, New York, New York 10010. Phone:(646) 312-3506, Fax: (646) 312-3451, E-mail: [email protected]; Susan Hume is an assistant professor atthe Department of Economics, Finance and International Business, School of Business, The College of New Jersey, POBox 7718, Ewing, New Jersey, 08628. Phone: (609) 771-2305, Fax: (609) 637-5129, E-mail: [email protected]; TerrenceMartell is a professor of finance at the Department of Economics and Finance, Zicklin School of Business, BaruchCollege, City University of New York, One Bernard Baruch Way, Box 10-225, New York, New York 10010. Phone:(646) 312-2075, Fax: (646) 312-2071, E-mail: [email protected]


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A New Look at Hedging with Derivatives: Will Firms Reduce Market RiskExposure?

ABSTRACT

This paper examines derivatives use of foreign exchange, interest rate and commodities risk by non-financialfirms across multiple industries, using data from 1995 to 2001. This paper considers the interaction of afirm’s risk exposures, derivatives use, and real operations simultaneously, and considers how these factorschange over time using a consistent data base. Hedging with derivatives is only significantly related tocommodity risk exposure during most years of the study, and to a more limited degree to interest rateexposure. Further, we find a strong correlation between risk exposures for some years using a newtechnique, suggesting that univariate modeling is not always appropriate. The implications are that hedgingwith derivatives is not always important to a firm’s rate of return and is linked to other non-financial andeconomic factors.


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A New Look at Hedging with Derivatives: Will Firms Reduce Market RiskExposure?

I. Introduction

The primary objective of this research is to reconsider the question of whether or not derivatives use

by non-financial firms is of little value under the perfect markets framework (Modigliani and Miller, 1958), or

value enhancing under market imperfections violations (Froot, Scharfstein, and Stein (1993), Nance, Smith,

and Smithson (1993), Smith (1995), and Smith and Stulz (1985)). This controversy still exists as academics

discuss the theoretic rationale for hedging economic exposures and the firm practices partial hedging, or

hedges cashflows to provide constant research monies, or more generally hedges to take advantage of

perceived market anomolies.

This paper contributes to the existing literature by simultaneously considering the three most widely

used categories of derivatives risk management ─

currency (FX), interest rate (IR), and commodity (CM) ─

to

determine whether or not the practice is value enhancing for the levels undertaken. This paper is important as

there is no broad-based study of non-financial firms for all derivatives categories, using public disclosures that

are consistent over time. This study introduces a new technique to consider the effects of changes in

macroeconomic factors on market risk exposure simultaneously, based on the way that non-financial firms

generally view their exposure today (Bodnar, Hayt, and Marston (1998)).

Previous studies measure stock price changes (or variations in returns) in response to movements in

foreign exchange, interest rate and commodity exposures separately.1 While theory suggests that hedging with

derivatives is expected to improve a firm’s cost of capital, the evidence has been unconvincing in terms of

finding a positive relationship between stock prices and the most commonly studied exposure, currencies.

Jorion (1990) finds that the relationship between stock returns and exchange rates is positively related to the

foreign operations of multinationals, although this is not significant. In studies that consider foreign exchange

derivatives explicitly, the findings weakly suggest that exchange rate movements affect expected future cash

flows and consequently, firm value [Geczy, Minton and Schrand (1997), Allayannis and Ofek (2001), and

Carter, Pantzalis and Simkins (2001)]. Other studies fail to confirm this relationship strongly (Brown (2001),

Hentschel and Kothari (2001), and Guay and Kothari (2003)).

1 Studies that consider foreign currency, interest rate or commodity exposures are Allayannis and Ofek (2001), Allayannisand Weston (2001), Bodnar and Wong (2003), Carter, Pantzalis, and Simpkins (2001), Geczy, Minton, and Schrand(1997), Hentschel and Kothari (2001), Wong (2000), Barton (2001), Graham and Rogers (2002), Guay (1999), Guay andKothari (2003), Mozumdar (2001), Visvanathan (1998), Titman (1992), Blose and Shieh (1995), Haushalter (2000),Rajgopal and Pincus (2002) and Tufano (1996, 1998). The literature on individual firms and corporate surveys includeBodnar et al. (1998), Brown (2001), and Chacko, Tufano, and Verter (2001). Early studies on overall derivatives usewith non-continuous data are Dolde (1995) and Mian (1996).


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This study provides more complete estimates of a firm’s enterprise risk by extending Allayannis and

Ofek (2001) and Jorion (1990) market models for currency derivatives to also include interest rate and

commodity derivatives, using published data from 1995 to 2001. The paper investigates the use of these

categories in four selected industries: commodity processing (gold and silver mining), derived agricultural

(food processing), heavy manufacturing (primary metals processing) and high technology (pharmaceutical andlarge biotechnology firms). These industries were selected because of their likelihood of using one of the three

categories. Our model estimates the three major exposures that a firm faces in a two-stage regression. The first

stage regression provides an estimate of an individual firm’s enterprise exposure using a four-factor model:

t it mit it it iit i RCM IRFX R ,,,5,4,3,2,1, ε β β β β β +++++= (1)

where t i R , is the rate of return on the ith firm’s common stock in period t , t FX is the rate of return on a

moving trade-weighted average exchange rate index (in US $ per unit of foreign currency in period t ), t IR is

the rate of return on a short-term interest rate factor in period t , t CM is the rate of return on a commodity index

in period t , and t m R , is the rate of return on the market index in period t . In equation (1) each non-intercept

term β represents a firm’s exposure by category. The coefficient i,2 β represents exchange rate exposure,

measured by the percentage change in the rate of return on a firm’s common stock due to a 1% change in the

exchange rate. The exchange rate index is the Federal Reserve Board’s (FRB) nominal major currency index

(MCI), which measures the dollar strength relative to major trading partners in Europe, Japan, Canada, and

Australia. This index is appropriate as derivatives usage reflects hedging against nominal exposures.

Moreover, studies suggest that foreign currency exposure is robust to a variety of indices [see Brown (2001),

Allayannis and Ofek (2001), and Carter, Pantzalis and Simkins (2001)]. All factors use monthly data.

i,3 β represents the interest rate exposure measured as a percentage change in the rate of return on a

firm’s common stock due to a 1% change in interest rates. The proxy used to examine the relationship

between interest rate exposure and derivatives use is the three-month LIBOR published in the Federal

Reserve’s H.15 database. Short-term interest rates based on LIBOR are common to swaps derivatives

contracts, revolving credits and other debt financings, and debt futures contracts.

i,4 β represents commodity exposure as measured by the change in the rate of return on a firm’s

common stock due to a 1% change in the commodity price index. The CRB equal-weighted spot commodity

index was selected as a broad-based commodity measure reflecting the major groups of commodities. The

CRB index is comprised of the six categories of metals, textiles and fibers, livestock and products, fats and

oils, raw industrials, and foodstuffs, covering twenty-three markets.

i,5 β represents the rate of return on the CRSP equal-weighted market index for NYSE, AMEX and

Nasdaq firms. Equal-weighted returns provides residual exposures consistent with the actual cash flows of

firms and is appropriate for our sample of large- and small-sized firms (Bodnar and Wong (2003)).


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We test our hypothesis that there is no exposure to each price change with the second stage cross-

sectional regressions. We use the exposure estimates for each category given in equation (1) for the four-

factor model. The second stage regressions are:

(i) for exchange rate exposure:

iiiiii TAFDERTS FS ξ γ γ γ β +++= )/()/( 321

^

,2 (2)

where^

,2 i β is thethi firm’s exchange rate exposure estimated in equation (1), )/( ii TS FS is the

thi firm’s ratio

of foreign sales to total sales, and )/( ii TAFDER is thethi firm’s ratio of foreign currency derivatives to total

assets.

(ii) for interest rate exposure:

iiiiii TA DDERTA LTD υ θ θ θ β +++= )/()/( 321,3

^

(3)

where i,3

^

β is the thi firm’s interest rate exposure, )/( ii TA LTD is the thi firm’s ratio of long-term debt to

total sales, and )/( ii TA DDER is theth

i firm’s ratio of total dollar derivatives to total assets.

(iii) for commodity exposure:

iiiiii TACDERTS TI µ λ λ λ β +++= )/()/( 321,4

^

(4)

where i,4

^

β is the thi firm’s commodity exposure, )/( ii TS TI is thethi firm’s ratio of total inventory to total

sales, and )/( ii TACDER is thethi firm’s ratio of commodity derivatives to total assets.

Theory suggests that firms hold derivatives positions to offset the effects of unexpected currency,

interest rate or commodity price movements. Our empirical findings do not generally support the hypothesis

that derivatives positions offset risk. Further, the empirical results do not support a positive association

between real operations and exposures. The results are robust across several econometric tests for all of the

three derivatives risk categories. To the extent that there is no change in market risk exposure, then this

suggests: 1) firms use other forms of risk management such as operational hedging from global diversification,

or production management,2 or; 2) firms do not fully hedge the extent of the effect of exchange rate

movements, or; 3) interest rate, exchange rate and commodity risks are economically insignificant relative to

the firm’s return, or; 4) firms do not have an economic justification for derivatives hedging if they are large,

diversified, and of good credit quality, except in special cases, or; 5) they use derivatives to facilitate internal

contracting, or informational asymmetries.

2 Note that operational hedging is long-term while financial hedging is of a short-term nature.


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The paper is organized as follows. Section II describes relevant features of the data set. Section III

provides the estimation methodology and hypotheses regarding financial hedging and real operations. Section

IV presents the empirical results. Section V concludes the paper.

II. Data

A. Identification of firms in the study

Early studies examined hedging questions with binary (zero and one) variables for derivatives users

and nonusers to indicate hedging. In those studies, notional values were not consistently reported and difficult

to collect, as in Mian (1996), Dolde (1995), and Geczy, Minton, and Schrand (1997). Moreover, there is some

evidence that the use of non-continuous data does not adequately measure the extent of hedging and may lead

to biased outcomes, as in Haushalter (2000).3 Previous studies have not considered the exposures of all

categories of derivatives usage with continuous values. Studies that use continuous notional values do not

consider the effects of all types of derivatives use simultaneously, as in Allayannis and Ofek (2001),

Allayannis and Weston (2001), Guay and Kothari (2003), and Hentschel and Kothari (2001). Other

derivatives studies have been case studies, surveys, or focused on a particular firm or industry (see Haushalter

(2000), Tufano (1996, 1998)). The current study considers hedging by individual exposures and considers

large and small firms’ derivatives use over time with monthly data sets.4 There is evidence that a firm’s

hedging changes from year to year, as reflected in this study.

The sample was constructed based on a Compustat search of firms with four-digit SIC codes for

metals mining, food processing, pharmaceutical and large biotechnology, and primary metals processing. The

current study considers firms of all sizes, unrestricted to the Fortune 500 larger asset sizes. The derivatives

data are available online in a firm’s 10-K filing and annual report.

The collection of derivatives information is difficult and time-consuming, as the information is

reported in notes to financial statements and not usually directly on those statements. Published derivatives

information and reporting requirements improved under SFAS 119 [FASB (1994)], with more thorough

disclosures content.5 Better continuous derivatives data were an important motivation for the current study.

3 Continuous notional data refer to the use of actual notional amounts of derivatives use, which can start at zero and be

any positive number. Early studies captured usage as binary variables, also referred to as non-continuous data.4 At an early stage of the study, daily data were also used. The results are similar to those reported in our tables and areavailable upon request.5 Effective for large firms after June 15, 1994, SFAS 119 required disclosures about the amounts, nature and terms ofderivatives, expanded from predecessor SFAS 105. This study eliminates amounts reported as trading activity tominimize the possibility of speculation. While it is possible that a firm misclassified speculative trading into hedgingaccounts, the overall size of the hedging positions and the small trading positions reported would suggest that speculationwas not a misspecifed variable in the database. SFAS 133 [FASB (1998)] supersedes SFAS 119, with most firmsadopting the new requirements January 1, 2001. Firms are required to account for derivatives activity as either assets orliabilities and measure them at fair value. Changes in fair value are recorded in earnings, although firms under certaincondition reduce earnings impact by designating the hedging as a cash flow hedge and recorded in comprehensive


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This paper uses gross notional principal values for each firm, as this is the most consistently reported and

available hedging information, and has been standard in other studies. For commodity derivatives, some firms

reported only contract quantity and notional values were calculated by multiplying quantities by fiscal year-

end closing cash commodity prices. All Canadian firms’ data were expressed in U.S. dollar terms using

Canadian to U.S Dollar spot exchange rates.

B. Data Set

Using Edgar 10-K online filings, the data set is constructed based on a keyword search of derivatives

words. However, this did not always produce a complete profile of derivatives usage. All firms’ financial

statements, including footnotes and the Management Discussion and Analysis in the firm’s Annual Report and

10-K filing were read to confirm that no derivatives were used. Further, derivatives hedging information was

compared each year for reporting consistency.

The data set meets the following criteria:1. Publicly traded stocks: Only those firms with publicly traded stock in the United States or

Canada are included in the study. Canadian firms were included as many firms in the

mining segment are headquartered there and mining firms provide detailed derivatives data.

This study is primarily concerned with evaluating stock returns and derivatives exposure

risks for published, replicable data.

2. Four-industry SIC code classifications: The sample was restricted to four industry

classifications for gold and silver mining, food processing, pharmaceuticals and large

biotechnologies, and primary metals processing.3. Firm disclosures for published reports for 1995-2001: The data set consists of SFAS 119

and SFAS 133 derivatives data for the fiscal years between January 1, 1995 and December

31, 2001. Returns are monthly holding period returns calculated directly by the CRSP

database, including dividends. Compustat data were used for real operations variables and

to normalize derivatives data with size. Compustat geographic segment data were utilized

for foreign sales and all items were verified by manual searches of a firm’s published

annual reports. Financial statements from the firm or Edgar were used to collect derivatives

data.

income. Firm data are not listed as individual positions beginning with most 2001 annual reports. The informationcontained in 2001 is not as uniform and detailed among some firms transitioning to the new reporting requirements.


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C. Data Description

The Appendix summarizes the data collected by derivative-user categories and characteristics of the

firms in the sample. Our sample consists of 410 firms that use interest rate and currency derivatives, 392 firms

that use interest rate and commodity derivatives, and 388 firms that use currency and commodity derivatives

for the sample period. Mean firm asset size is $5,496 million for interest rate and currency user firms, $4,792million for interest rate and commodity users and $6,005 million for currency and commodity user firms for

2001.

III. Estimation Methodology

A. Hypotheses Specifications

This paper addresses several omitted variables biases in the extant literature when individual

exposures were considered. If a firm’s use of individual derivatives is just one element of its risk management

strategy, then the failure to consider all other strategies may result in a bias when using cross-sectional data as

suggested by Beatty (1999). Therefore, the study examines a broader range of risk management activities with

a cross-section of users and nonusers. Another bias that we consider is the interaction of hedging activities.

An increase in the use of derivatives of each risk class should reduce individual risk exposure, but may not

create value (Smith and Stulz, 1985). Furthermore, an increase in hedging in one category may reduce the

need to hedge in another category and this interrelationship among exposures can be considered as a basis

trade. Overall, the nature of derivatives use for the firm should take into account whether use increases,

decreases, or has no effect on risk. While the theoretical arguments suggest that hedging is beneficial in

markets with friction, it has also been shown that hedging costs can be excessive [Smith (1995) and Mozumdar

(2001)].

Previous research provides guidance in the selection of variables and the design of tests for the

hypothesis that exposure is related to derivatives use and a firm’s operations, as suggested by Allayannis and

Ofek (2001) and Jorion (1990). There are two primary determinants that influence risk exposures; these are

derivatives use from financial hedging and the firm’s real operations. Tests in this study are designed to

examine the impact of all derivatives use simultaneously on exposures of exchange rate, interest rate and

commodity risk. Further, tests are constructed to determine if exposures depend also on key factors that are

important to a firm’s real operations. A firm’s real operations determine the degree to which a firm uses

derivatives and are unique for each exposure. We construct a model that considers financial risk management

and real operations concurrently as this represents the determinants used by firms today to manage risk and

exposure volatilities.

Economic exposure to exchange-rate movement has been examined empirically as the regression

coefficient of firm value on exchange rates across states of nature as in Allayannis and Ofek (2001), Bartov

and Bodnar (1994), Bodnar and Wong (2003), Carter, Pantzalis, and Simkins (2001), and Jorion (1990).


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While these studies do not suggest that there is a casual relationship between exchange rates and stock prices

at the aggregate level since both are jointly determined and endogenous variables, there is empirical evidence

to suggest that at the individual firm level, exchange rates are exogenous to asset values. This provides

supporting evidence for the current study’s investigation of asset values, market movements and derivatives

use.The general hypotheses to be tested relate exposure levels to: 1) hedging associated with derivatives

use, and 2) real operations that make a firm more likely to need derivatives to hedge. The hypotheses are:

For Financial Hedging:

H1a. Cross-sectional variations in a firm’s risk exposures do not reflect the importance of each

category of derivatives hedging to a firm’s return.

H1b. For firms that use derivatives, there is no effect on exposure to the underlying risk factor,

regardless of magnitude of use.

For Real Operations:

H2a. Cross-sectional variations in a firm’s risk exposures do not reflect its real operations.

H2b. Firms that have greater relative real operations, have no greater specific risk exposure.

The overall set of hypotheses H1 and H2 regarding financial hedging and real operations are determined

simultaneously.

The relationship between the foreign exchange index and currency exposure is tested on cash flows

using changes in the firm’s market value as the proxy for future cash flows as in Allayannis and Ofek (2001),

Bodnar and Wong (2003), Carter, Pantzalis and Simkins (2001), Jorion (1990), and Levi (1994). The ratio of

foreign sales to total sales has been a standard measure of a firm’s real foreign operations since Jorion (1990).

We hypothesize that this ratio should be positively related to currency exposures. We measure foreign

currency derivatives use in absolute terms, using published data of gross long and short currency exposures as

in Allayannis and Ofek (2001). The use of foreign currency derivatives is expected to decrease this exposure.

The motivations for hedging interest rate exposure with derivatives are also considered. Interest rate

exposure is simultaneously determined by a firm’s real operations proxied by a long-term debt ratio and

interest rate hedging. We use long-term debt as a proxy for net nominal asset sensitivity, since many non-

financial firms do not report gap and interest rate sensitivity in a consistent format (see Flannery and James

(1984), French, Ruback and Schwert (1983)). Thus, it is expected that for higher levels of long-term debt

relative to assets, an increase in interest rate expense reduces shareholder earnings and increases interest rate

exposure. Firms with more leverage in their capital structure are expected to have a greater need to use

derivatives to manage asset sensitivity. Thus, there is a positive relationship between debt and derivatives use.

Similarly, interest rate derivatives used to hedge debt exposure should reduce interest rate exposure.

As with currencies and interest rates, commodity derivatives can be used to hedge against

unanticipated commodity price risk. This would improve the firm’s cash flow and earnings. For a given


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exposure, an increase in revenues from commodity operations as measured by inventory level should increase

exposure. The ratio of total inventory to total sales is our measure of the need to hedge commodity risk (Fama

and French (1987)). We hypothesize that the inventory operations ratio is positively related to commodity

exposure. Further, if firms use commodity derivatives to hedge these movements, then the use of derivatives

should reduce commodity exposure. The presence of a positive relationship between the values of commodityderivatives used and the values of commodity exposures, however, would suggest that the firm is using

derivatives but is not hedging.

B. Estimation Framework – Measuring Exposures

In this study each firm’s category of exposure is estimated using equation (1). The data sets use a

firm’s monthly returns for the three years prior to the hedging decision. Thus, for each firm the regressions for

1995 have monthly returns from 1993 to 1995. This methodology is more appropriate than using return data

that surround the derivatives hedging decision. In most prior exposure studies, derivatives for the year 1995

would model equation (1) using three years of monthly returns data for the period 1994 to 1996 (see for

example, Allayannis and Ofek (2001)). The benefit of the methodology in our paper is that it avoids serial

dependence in the hedging decision and returns outcomes.

Consistent with the hypothesis that derivatives management and the determinants of operational

exposure occur simultaneously with economic exposures, the study investigates the coordinated use of these

hedges to reduce exposures. Accordingly, the study models the interaction of exposures as three and four-

factor regressions for the second stage. The relationships are combinations of foreign exchange and interest

rate exposures, foreign exchange and commodity exposures, and interest rate and commodity exposures. The

four-factor model includes all exposures for the first-stage regression including commodities, with a market

return. The four-factor model uses equation (1) for the first stage and either equation (2), (3), or (4) for the

second stage cross-sectional regression. The three-factor model considers only the two exposure factors that

will be used in the second stage regression. For example, the three-factor model for interest rate and currency

exposures allows us to examine how the exclusion of commodity exposure and general commodity price level

changes impacts exposure determinants.

The regression models are tested with both univariate estimations as has been standard in other foreign

exchange studies and bivariate estimations unique to our paper to consider the interaction of exposure factors

and market returns with real operations and derivatives usage.6 The bivariate estimation framework is:

(i) for foreign currencies and interest rates:

t it mit it iit i R IRFX R ,,,4,3,2,1, ε β β β β ++++= (5)

6 While trivariate estimations framework would be ideally suited for all variables, we are unable to apply thismethodology due to lack of convergence in the maximum likelihood estimations.


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^

,2 (6)


^

(7)

where ( )

[ ]ξυ ξυ

ξυρ υ ξ ρ

ξυ υ ξ ρ σ πσ υ ξ

2)1(2

1

2

22

2

12

1

,

−+−

−

−= e f ii is a bivariate normal density function. ξ σ is the

standard deviation of i,2

^

β , υ σ is the standard deviation of i,3

^

β and ξυ ρ is the correlation between i,2

^

β and

i,3

^

β .

(ii) For foreign currencies and commodities:

t it mit it iit i RCM FX R ,,,5,4,2,1, ε β β β β ++++= (8)


^

,2 (9)


^

(10)

where ( )[ ]ξµ

ξµ

ξµρ µ ξ ρ

ξµ µ ξ ρ σ πσ µ ξ

2)1(2

1

2

22

2

12

1,

−+−

−

−

= e f ii is also a bivariate normal density function. ξ σ is the


^

β , µ σ is the standard deviation of i,4

^

β , and ξµ ρ is the correlation between i,2

^

β and

i,4

^

β .

(iii) For interest rates and commodities:

t it mit iiit i RCM IR R ,,,5,4,3,1, ε β β β β ++++= (11)


^

(12)


^

(13)

where ( ) [ ]υµ

υµ

υµρ µ υ ρ

υµ µ υ ρ σ πσ µ υ

2)1(2

1

2,

22

2

12

1−+

−−

−

= e f ii is a bivariate normal density function. υ σ is the


^

β , µ σ is the standard deviation of i,4

^

β , and υµ ρ is the correlation between i,3

^

β and

i,4

^

β .

The parameters for all bivariate regressions are estimated by maximizing the log-likelihood function

with the Berndt-Hall-Hall-Hausman (1974) algorithm. As described above, the exposures (i

^

β and j

^

β ) are


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assumed to follow a bivariate normal distribution. It is important to note that the statistical significance of

ξυ ρ , ξµ ρ , and υµ ρ implies that one should model the currency, interest rate and commodity risk exposures

jointly when testing whether derivatives use reduces the market risk exposure. The OLS regressions with

univariate distributions may bias the parameter estimates and the standard errors.

IV. Empirical Results

A. Univariate Regressions

To isolate the effects of individual components for all categories and to replicate other studies on

foreign currency, univariate exposure regressions with two factors are considered first. The univariate two-

factor regressions are:

(i) For foreign currencies:

t it mit iit i RFX R ,,,5,2,1, ε β β β +++= (14)


^

,2 (15)

(ii) For interest rates:

t it mit iit i R IR R ,,,5,3,1, ε β β β +++= (16)


^

(17)

(iii) For commodities:

t it mit iit i RCM R ,,,5,4,1, ε β β β +++= (18)

iiiiii TACDERTS TI µ λ λ λ β +++= )/()/( 321,4^

(19)

As presented in Table I, derivatives use has very low explanatory power in reducing exposures. We

can reject the null hypothesis that use reduces absolute exposure in only one year and for only one type of

exposure: interest rates in 1995. The estimated value of θ 3 in the absolute interest rate exposure equation,

)( ,3

^

iabs β , is –0.1816 with a p-value of 9.18%. Commodity derivatives use increases absolute exposure in four

years, 1996 and 1999-2001, suggesting that user firms are not hedging during that time period. Unlike prior

studies, currency derivatives use does not significantly reduce the absolute value of this exposure in any of the

study years. Currency derivatives use only reduces the actual value of currency exposure in 1995, interest rate

derivatives use reduces actual exposure in 1996 and commodity derivatives use reduces the actual value of


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commodity exposure in 1995.7 Only absolute values of exposures are important to derivatives use in the

current model since we are examining gross long and short derivatives positions. In light of the fact that most

two-factor OLS regression coefficients are insignificant, this suggests that derivatives use is not important to

the individual market risk exposures of the firms studied.

Also examined in Table I are real operational factors and exposures using univariate OLS regressionswith the two-factor model. For the currency exposure coefficient γ 3, the foreign sales ratio is negatively

associated with currency exposures in 1997; this negative relationship is not expected. For interest rate

exposure θ 2, the debt leverage ratio is significantly positive in 1998, as predicted. The estimated value of θ 2 is

3.1533 with a p-value of 2.46%. For the commodity exposure coefficient 2λ , the inventory proxy is

significant and positive for 1998 and 2000, as expected, but negative and significant for 1995 and 1996, a

relationship not expected. The estimated values of 2λ are 1.3551 and 4.2428 for 1998 and 2000, with p-

values of 0.01% and 8.83% for those years respectively. The implication is that real operational factors are

also usually not important to a firm’s exposures and returns.

We further investigate all exposure relationships for users and non-users with four-factors in Table II.

The two-stage regression model with four-factors for currency exposure is specified by equations (1) and (2).

The coefficient estimates in (1) link a firm’s currency exposure estimates with real operations and derivatives

use. Again there is little explanatory power for foreign currency derivatives use and exposure, except for one

year, 2001. There is no significant relationship between the level of exchange-rate exposure and foreign sales

during any of the period studied. In one year, 1997, there is an unexpected significantly negative coefficient.

We also examine the relation between the absolute value of currency exposure and currency derivative use.

There is little support that the use of currency derivatives reduces absolute currency exposure, except for one

year, 1997. The estimated value of γ 3 in the absolute currency exposure equation, )( ,2^

iabs β , is –1.0555 with a

p-value of 3.89% in 1997. The four-factor model shows that both real operations and currency derivatives use

do not explain exposure.

Table II also examines the coefficient estimates for interest rate exposure with four-factors using

equations (1) and (3). The coefficients link the exposure estimates from equation (1) with its determinants,

7 The use of foreign currency, interest rate, and commodity derivatives is expected to reduce )( ,2

^

iabs β , )( ,3

^

iabs β and

)( ,4

^

iabs β , respectively. We do not make predictions about the effect of derivatives use on the level of exposures, i.e.,

i,2

^

β , i,3

^

β and i,4

^

β . An increase in firms’ real operations ( ii TS FS / , ii TA LTD / , ii TS TI / ) is expected to increase

i,2

^

β , i,3

^

β and i,4

^

β , respectively. We do not make predictions regarding the effect of firms’ real operations on

)( ,2

^

iabs β , )( ,3

^

iabs β and )( ,4

^

iabs β . This is similar to the approach used in Allayannis and Ofek (2001).


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12

LTD/TA and dollar derivatives used in equation (3). There is no evidence that there is a significantly positive

relationship between interest rate exposure and the real operations ratio. We also examine the relationship

between the absolute value of interest rate exposure and dollar derivatives use. With the exception of 1995

and 2000, there is little justification for the use of interest rate derivatives. In those two years only, we find a

negative and significant association between the absolute value of the exposure and the percentage of dollarderivatives use. The coefficient θ 3 on ii TA DDER / in the interest rate exposure equation is –0.6767 with a p-

value of 2.58% for 1995 and -8.1937 with a p-value of 0.12% for 2000. The empirical evidence suggests that

interest rate derivatives use weakly explains exposure because of the two significant results in 1995 and 2000,

while real operations is not a determinant of interest rate exposure.

Table II also shows the OLS regression results for commodity derivatives using four-factor models

from equations (1) and (4). There is some evidence of a significantly positive association with commodity

exposure and the real operations ratio of total inventory to total sales for 1995, 1997 and 2000. The estimated

coefficients 2λ on TI/TS are 1.4783 with a p-value of 0.30% for 1995, a coefficient of 0.2729 with a p-value

of 4.45% for 1997, and coefficient of 3.6345 with a 0.47% p-value for 2000. We also find a significant

relationship between absolute commodity exposure and derivatives use in three years, 1999-2001. There is a

positive unexpected relationship with coefficients 3λ on ii TACDER / of 3.3210, 1.6248 and 0.4776 for 1999,

2000 and 2001 with important and significant p-values of 3.70%, 0.00% and 0.00% for those years

respectively.8 Thus, we reject the null hypothesis that commodity derivatives use is not related to commodity

exposure for the more recent years of the study. Unexpectedly, our results suggest that commodity hedging

increases commodity exposure.

B. Combinations of Exposures

We consider the relationship of derivatives users with combinations of pairs of exposures using the

three-factor model:

For currency exposure: FX, CM: t it mit it iit i RCM FX R ,,,5,4,2,1, ε β β β β ++++= (20)

FX, IR: t it mit it iit i R IRFX R ,,,5,3,2,1, ε β β β β ++++= (21)


^

,2 (22)

with equations (20) and (22) for currency and commodity derivatives users, FX and CM. The coefficientestimates in (20) link a firm’s currency exposures with real operations and derivatives use in (22). In Table

III, we do not find any significant relationship between the level of currency exposure and the ratio of foreign

sales to total sales. There is an unexpected significantly negative relationship between currency exposure and

8 We also find only one year with a significant negative relationship in the level of commodity exposure and derivatives

use. In 1995, the 3λ coefficient is -1.3478 with a p-value of 9.29%. There are three years of unexpected positive sign

relationships in 1998-2001.


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13

the real operations ratio for 1997. We also examine the relationship between the absolute value of currency

exposure and derivatives use and do not find any significantly negative relationship.

For currency exposure estimates, we also examine those firms that use currency and interest rate

derivatives (FX, IR) in Table III. Using equations (21) and (22), the coefficient estimates link currency

exposure with its determinants for those users. For the real operations ratio, the only significant coefficientsare negative in 1997 and 1999, which are not expected. As for derivatives use, there is no significantly

negative relationship that determines absolute currency exposure.

We also examine derivatives use and interest rate exposure in Table III using the following three-

factor model:

For interest rate exposure: IR, CM: t it mit it iit i RCM IR R ,,,5,4,3,1, ε β β β β ++++= (23)

IR, FX: t it mit it iit i R IRFX R ,,,5,3,2,1, ε β β β β ++++= (24)


^

(25)

The parameter estimates in equation (23) link a firm’s interest rate exposures with its determinants in equation

(25) for those firms that use interest rate and commodity derivatives (IR, CM). The exposure measured by

i,3

^

β doesn’t have explanatory power and is unexpectedly negative in 2000. Overall, the coefficient θ 2 on

LTD/TA is not significant. For derivatives use, we find little support that interest rate derivatives use reduces

absolute exposure, except in 1998 and 2000. The estimated value of the coefficient θ 3 on ii TA DDER / is

−4.4923 and -9.6892 for 1998 and 2000 respectively, with p-values of 0.74% and 0.50%.

We similarly examine interest rate exposures in Table III for those firms that use interest rate and

currency derivatives (IR, FX) using equations (24) and (25). Again, there is no significantly positive

relationship between the real operations ratio and interest rate exposure. Moreover, we do not find supporting

evidence that derivatives use reduces absolute interest rate exposure.

Further, Table III examines the relationship between commodity derivatives use and exposure

determinants using the following three-factor models:

For commodity exposure: CM, IR: t it mit it iit i RCM IR R ,,,5,4,3,1, ε β β β β ++++= (26)

CM, FX: t it mit it iit i RCM FX R ,,,5,4,2,1, ε β β β β ++++= (27)

iiiiii

TACDERTS TI µ λ λ λ β +++= )/()/(321,4

^

(28)

where equations (26) and (28) consider commodity and interest rate derivatives users and equations (27) and

(28) reflect commodity and currency users. For commodity and interest rate derivatives users (CM, IR), we

find mixed outcomes for the relationship between commodity exposure and the real operations ratio of total

inventory to total sales: commodity exposure is significant and positively related to the inventory ratio for

most years, 1998-2000, as expected. The estimated coefficient value 2λ on TI/TS is 3.5386, 3.9145 and


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14

4.2895 for 1998, 1999 and 2000, respectively with p-values of 0.53%, 2.27% and 0.27% in 1998, 1999 and

2000. However, there are two years when the exposures are significant and negatively related to real

operations (1995 and 1996), an unexpected result. Next, we examine derivatives use to determine if it reduces

absolute commodity exposure. There is no evidence that commodity derivatives use reduces the absolute level

of commodity exposure for the CM, IR group. There are unexplained increases in exposure for the three years1999-2001.

Lastly, we examine commodity exposure for commodity and currency derivatives users (CM, FX)

using equations (27) and (28). We continue to find mixed outcomes for commodity exposure and the real

operations ratio. Some years are positively related to exposure (1998, 2000, 2001), while there is an

unexpected negative relationship in one year (1995). As for the question of whether commodity derivatives

use reduces the absolute level of commodity exposure for the CM, FX group, we do not find empirical

support. We do find, however, that commodity derivatives use significantly increases exposure for almost

every year, except 1998. This suggests that commodity derivatives users may not always be hedging.

C. MLE Estimation with Bivariate Distributions

To integrate the use of derivatives in an overall approach that reflects enterprise risk, this study

considers the combinations of exposures using maximum likelihood estimation (MLE) with bivariate

distributions. This has so far not been examined in any study dealing with exposures and derivatives use. Only

user firms are examined in our MLE framework. The benefit of this methodology is that we are able to

capture the relationship of combinations of derivatives hedging and real operations to determine the

importance of hedging to a firm. Further, using the bivariate MLE procedure provides insight into theinteraction of the combinations jointly with simultaneous equations. In particular, we are interested in

determining whether bivariate combinations of exposures interact in such a way that makes the use of OLS

regressions inappropriate econometric methodologies. For example, we are interested in the interaction of the

dependent variables for interest rate exposure and currency exposure,i,2

^

β and^

,3 i β , given in equations (6)

and (7) and their standard errors. In our bivariate MLE regressions, we will reject the use of OLS type

econometric tests if the correlation coefficient ξυ ρ is statistically significant. The bivariate regressions are

constructed using equations (5) with (6) and (7) for currency and interest rate exposure, (8) with (9) and (10)

for currency and commodity exposure and (11) with (12) and (13) for interest rate and commodity exposure.

Panel A of Table IV shows that the correlation between the level of currency and commodity risk

exposure is statistically significant in 1996, 1997 and 2000, with correlation estimates of -0.6084, 0.3829 and -

0.5060 in 1996, 1997 and 2000, with p-values of 0.06%, 0.21%, and 0.37% for those years. Similarly, the

correlation between the level of interest rate and commodity risk exposures is significant in 1995, 1996, and

2000, with p-values of 3.15%, 9.29%, and 0.00% for 1995, 1996, and 2000, respectively. These results


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15

indicate that using the OLS regression based on univariate distributions is not an appropriate econometric

methodology in the analysis of a firm’s exposures and derivatives use. This also suggests that considering an

OLS framework for single exposures may be inappropriate in some cases due to the omission of the other

exposure variables.

A notable point in Panel A of Table IV is that when the level of currency exposure is modeled jointlywith the level of interest rate or commodity exposure, the firm’s real operations coefficient 2γ (FS/TS ) do not

increase the currency risk exposure. In fact, the foreign sales ratio is negatively associated with the level of

currency exposure in 1997, which is inconsistent with our expectation and some prior papers. We find a

positive and significant relation between the level of interest rate exposure and the firm’s real operations

coefficient 2θ ( LTD/TA) only in one year, 1997. This occurs when the level of interest rate exposure or

commodity exposure is modeled jointly with the level of currency exposure. When modeled jointly with the

level of commodity exposure, the interest rate exposure is not influenced by the firms’ real operations for any

of the years considered in the paper. When the level of commodity exposure is modeled jointly with the level

of interest rate or currency exposure, the firm’s real operations coefficient 2λ (TI/TS ) increases the commodity

risk exposure only in two years, 1998 and 1999. However, in 1995 and 1996, the total inventory ratio reduces

the level of commodity exposure, which is inconsistent with our expectation. The results in Panel A of Table

IV suggest that the firms’ real operations are not an important determinant of joint market risk exposures.

Panel B of Table IV provides strong evidence that derivatives use does not reduce the market risk

exposure when the absolute value of currency, interest rate and commodity exposures are modeled jointly.

Moreover we find some statistically significant correlations between the absolute value of market risk

exposures. This occurs for the absolute exposures for currencies and interest rates in 1997 and 1998, the

absolute exposures for currencies and commodities in 1996, 1997, 1999, and 2000, and the absolute exposures

for interest rates and commodities in 1996 and 2000. The correlation estimates for the absolute exposures for

currencies and interest ratesξυ ρ are 0.3834 with a p-value of 0.94% for 1997, and 0.2915 with a p-value of

7.10% for 1998. The correlation estimates for the absolute exposures for currencies and commodities ξµ ρ are

0.6457 with a p-value of 0.00% in 1996, 0.3509 with a p-value of 3.81% for 1997, -0.3033 with a p-value of

0.00% for 1999 and 0.4681 with a p-value of 0.03% for 2000. The correlation estimate for the absolute

exposures for interest rates and commodities υµ ρ is 0.4362 with a p-value of 0.00% for 1996, and 0.4512 with

a p-value of 0.03% for 2000. Overall, the maximum likelihood parameter estimates from bivariate

distributions support our earlier findings obtained from the two-, three-, and four-factor models.

When modeled jointly with the absolute value of interest rate exposure, the use of currency derivatives

does not affect the absolute value of currency exposure. In fact in 2001, derivatives use increases absolute

currency exposure against our expectations. Similarly, when it is modeled jointly with the absolute value of


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16

commodity exposure, the use of currency derivatives does not reduce the absolute value of currency risk

exposure, except for 1998 and 1999. When the absolute value of interest rate exposure is modeled jointly with

the absolute value of currency or commodity exposure, the use of interest rate derivatives does not reduce the

interest rate exposure for any of the seven years considered in the paper. When modeled jointly with the

absolute value of currency or interest rate exposure, the use of commodity derivatives does not reduce thecommodity risk exposure for any of the years in the study. In fact, in 1995 and 1999-2000, it increases the

absolute value of commodity exposure, suggesting that the user firms are increasing risk exposures and not

hedging during that time period. The positive relationship between derivatives use and commodity exposure is

a recurring empirical result.

V. Conclusions

Although multifactor market models have been used in previous studies of derivatives hedging, this is

the first use of a simultaneous approach with different econometric models to measure risk management in a

broader context. The use of MLE with bivariate distributions provides an econometric methodology that has

not been previously utilized. These tests are appropriate because they allow us to study the interaction of

exposures with derivatives use and real operations. Some of the variables have appeared in the literature

individually, but not in the context of an overall framework.

The set of variables selected for the models was consistent with previous studies for individual risk

exposures, with appropriate changes made to reflect a firm’s total exposures. The new specifications also

incorporate substitutes for derivatives hedging, by the inclusion of a firm’s real operations, extending the

works of Allayannis and Ofek (2001) and Jorion (1990). Using three and four-factor models and alternative

econometric tests, this study provides a sound statistical approach to measuring the importance of derivatives

use through exposure levels for four selected industries over time. Except for interest rates, there is little

evidence that derivatives use reduces risk exposures for the firms studied. There is some evidence that user

firms are increasing risk exposure in the use of commodity derivatives. Similar results are also obtained from

the univariate models. Moreover, for some years, a bivariate MLE econometric test is more appropriate

because of the strong correlation between risk exposures.

Further, the empirical results do not suggest a positive association between any of the variables for

real operations and related exposures. These results are robust to bivariate and univariate tests and are

consistent over time. The results imply that hedging with derivatives is not important to a firm’s rate of return,

as also found in other studies [see Brown (2001), Guay and Kothari (2003), and Hentschel and Kothari

(2001)].

The results indicate that there is little relationship between a firm’s risk exposures and the level of

derivatives use and its real operations. This seems surprising given the size of the derivatives market and the

prevalence of alternative risk management techniques used by corporations today. Another explanation is that


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17

the level of derivatives usage is just not large enough to be economically significant to a firm, which is

consistent with Brown (2001), and Guay and Kothari (2003). Some additional explanations for the

insignificant relation between derivatives use and market risk exposures can be summarized as follows.

First, other factors not measured in real operations may be more important to a firm’s management of

risk exposures. Factors such as global diversification, internal contracting, and production management have been shown in some studies to be important motivations for derivatives use as in Brown (2001), and Carter,

Pantzalis, and Simpkins (2001). Production management is also one motivation that is related to global

diversification as a possible substitute for derivatives use that has not been extensively studied, probably due

to the lack of available standardized public information on production.

Second, large, high-quality non-financial firms that are well diversified in terms of geographical

locations and investor base may not have a large economic justification for most derivatives hedging, as the

market frictions for these firms may not be sufficient to justify the transaction and operational costs. These

firms have the diversity of international production, the diversity of a large investor base and the access to

capital markets for the best possible financing alternatives to manage overall risk. The main reason for

hedging for these types of firms may be to facilitate internal contracting or informational asymmetries.

We conclude that the consistency of our results using alternative econometric methodologies is

important, despite the fact that the outcomes are sometimes contradictory to current risk management

paradigms. Our empirical findings are robust across alternative econometric methodologies, which do not

confound derivatives use with returns outcomes. Further, our database uses consistent derivatives data over a

seven-year period that considers the firm’s broad use of derivatives. Our results suggest an important direction

for future research on the interrelationship of the broad use of risk management and the value of non-financial

firms.


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18

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Appendix

Panels A, B, and C present the mean, median, and standard deviation of bivariate derivatives users and non-users firmDecember 2001. The term derivatives user means a firm that reports using either category of derivatives. TA is total athe ratio of the group’s foreign currency sales to total sales using Compustat item 12 for total sales, LTD/TA is the ratioCompustat items 9 and 6, and TI/TS is the ratio of total inventory to total sales from Compustat items 3 and 12. Foreign

reported in the geographic segment from the Compustat industrial data set or the firm’s 10-K report.

Panel A. IR and FX Derivatives Users and Non-users Firm Characteristics

IR, FX Mean Median Std. Dev. Mean Median Std. Dev. Mean Median

Users TA ($MM) FS/TS LTD/TA

2001 5,496 2,091 8,869 0.330 0.308 0.278 0.263 0.260

2000 6,272 2,416 9,323 0.300 0.273 0.250 0.222 0.179

1999 5,227 2,459 6,888 0.354 0.362 0.219 0.244 0.217

1998 4,635 1,699 6,197 0.283 0.258 0.250 0.226 0.199

1997 4,553 2,508 5,443 0.284 0.267 0.254 0.207 0.200

1996 4,426 2,032 5,324 0.303 0.268 0.274 0.195 0.179

1995 4,718 2,230 5,503 0.322 0.294 0.253 0.187 0.178

Non-users TA ($MM) FS/TS LTD/TA

2001 3,686 870 5,486 0.062 0.050 0.080 0.238 0.210

2000 2,769 728 4,467 0.077 0.017 0.106 0.204 0.180

1999 2,277 568 3,088 0.259 0.132 0.347 0.242 0.311

1998 1,003 378 1,894 0.105 0.000 0.237 0.216 0.199

1997 745 285 1,416 0.096 0.000 0.208 0.203 0.166

1996 715 264 1,522 0.092 0.000 0.198 0.204 0.203

1995 708 258 1,548 0.085 0.000 0.205 0.206 0.190


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Panel B. IR and CM Derivatives Users and Non-users Firm Characteristics

IR, CM Mean Median Std. Dev. Mean Median Std. Dev. Mean Median

Users TA ($MM) TI/TS LTD/TA

2001 4,792 1,772 6,744 0.163 0.131 0.105 0.269 0.270

2000 5,647 1,709 8,794 0.156 0.151 0.082 0.220 0.176

1999 4,982 1,687 6,823 0.144 0.140 0.074 0.260 0.240

1998 2,993 1,259 4,078 0.168 0.148 0.134 0.233 0.207

1997 3,851 1,437 5,216 0.136 0.124 0.064 0.212 0.200

1996 3,923 1,488 5,254 0.161 0.140 0.126 0.211 0.197

1995 4,566 2,503 5,482 0.140 0.113 0.093 0.198 0.181

Non-users TA ($MM) TI/TS LTD/TA

2001 6,744 2,091 12,534 0.138 0.137 0.054 0.210 0.210

2000 5,024 1,116 7,738 0.148 0.119 0.073 0.207 0.176

1999 5,033 1,400 7,116 0.145 0.148 0.051 0.162 0.147

1998 2,024 441 4,952 0.163 0.151 0.109 0.218 0.187

1997 1,004 299 2,175 0.172 0.165 0.096 0.196 0.166

1996 1,028 303 2,286 0.182 0.158 0.168 0.194 0.184

1995 839 274 1,980 0.179 0.141 0.218 0.207 0.195

Panel C. FX and CM Derivatives Users and Non-users Firm Characteristic

FX, CM Mean Median Std. Dev. Mean Median Std. Dev. Mean Median

Users TA ($MM) FS/TS TI/TS

2001 6,005 2,402 8,888 0.362 0.359 0.286 0.158 0.130

2000 6,914 3,307 9,241 0.347 0.343 0.241 0.154 0.141

1999 6,191 3,347 7,499 0.369 0.363 0.245 0.144 0.136

1998 4,190 1,699 6,006 0.274 0.241 0.275 0.153 0.143

1997 4,441 2,481 5,521 0.307 0.279 0.281 0.135 0.119

1996 4,409 2,128 5,389 0.312 0.278 0.275 0.169 0.137

1995 4,839 2,574 5,569 0.308 0.266 0.252 0.152 0.114

Non-users TA ($MM) FS/TS TI/TS 2001 1,405 856 1,724 0.099 0.019 0.152 0.152 0.155

2000 1,144 897 1,403 0.076 0.000 0.143 0.150 0.151

1999 1,206 877 1,488 0.087 0.000 0.143 0.145 0.149

1998 1,030 418 1,981 0.111 0.000 0.216 0.169 0.155

1997 818 291 1,562 0.070 0.000 0.178 0.170 0.164

1996 710 267 1,476 0.088 0.000 0.193 0.177 0.156

1995 760 273 1,664 0.100 0.000 0.216 0.175 0.140


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Table I. Relationship Between Exposures and Derivatives Use Based on Two-Factor Mod

Currency Exposure 2001 2000 1999

i,2

^

β Coeff Prob Coeff Prob Coeff Prob

2γ -2.0259 0.1451 -1.0364 0.4433 -1.5334 0.1688

3γ -3.3078 0.2190 -5.1230 0.1946 -2.3874 0.2466

)(,2

^

iabs β

2γ 0.8174 0.3681 0.2590 0.8238 0.5851 0.4724

3γ -0.5964 0.7342 4.5923 0.1784 1.0851 0.4728

Number of firms 35 38 42

Interest Rate Exposure 2001 2000 1999

i,3

^


2θ -1.4554 0.2951 -5.8866 0.1329 -2.0600 0.7272

3θ 0.7127 0.4412 2.0101 0.6990 -4.8430 0.5493

)(,3

^

iabs β

2θ -0.3585 0.6647 1.0488 0.6563 2.0913 0.5322

3θ 0.8751 0.1207 -3.2012 0.3186 -5.9434 0.1982


Commodity Exposure 2001 2000 1999

i,4

^


2λ 1.4177 0.3756 4.2428 0.0883* 2.9024 0.4418

3λ 0.4034 0.2483 2.0081 0.0014** 1.6592 0.0425**

)(,4

^

iabs β

2λ 0.0468 0.9560 2.5000 0.1594 1.7107 0.5488

3λ 0.3790 0.0523* 1.5867 0.0007*** 1.4116 0.0249**



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Table I. Relationship Between Exposures and Derivatives Use Based on Two-Factor Mod


i,2

^

β Coeff Prob Coeff Prob Coeff

2γ -1.4833 0.0090*** -0.5914 0.2685 0.4428

3γ 0.8333 0.2865 -0.7700 0.2553 -1.4293

)(,2

^

iabs β

2γ 0.7305 0.0643** 0.2269 0.5681 -0.1709

3γ -0.2766 0.6625 -0.2728 0.4516 -0.4058



i,3

^


2θ 2.3531 0.1423 0.4569 0.3864 0.3302

3θ -1.8541 0.4057 -0.5021 0.0814*

-0.0195

)(,3

^

iabs β

2θ -1.6509 0.1966 0.4086 0.2929 0.4059

3θ 2.3157 0.2353 0.2426 0.4120 -0.1816



i,4

^


2λ -0.3405 0.7935 -2.0157 0.0134** -3.3676

3λ 0.4047 0.3702 0.1353 0.7624 -1.8124

)(,4

^

iabs β

2λ 0.0166 0.9846 1.0465 0.0956* 2.5669

3λ 0.3243 0.1479 0.3377 0.0400** 0.6374



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This table provides the parameter estimates and the probability values for the two-factor model specified by the f

For Currency Exposure:t it mit iit i

RFX R,,,5,2,1,

ε β β β +++= iiii FDERTS FS γ γ γ β ++= /()/( 321

^

,2

For Interest Rate Exposure:t it mit iit i

R IR R,,,5,3,1,

ε β β β +++= iii DDERTA LTD θ θ θ β ++= ()/( 321,3

^

For Commodity Exposure:t it mit iit i

RCM R,,,5,4,1,

ε β β β +++= iiii CDERTS TI λ λ λ β ++= /()/( 321,4

^

*, **, *** denote statistical significance at the 10%, 5%, and 1%, respectively, adjusted for heteroskedasticity using


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Table II. Relationship Between Exposures and Derivatives Use Based on Four-Factor M


i,2

^


i,2γ 0.5500 0.7146 0.3613 0.7219 -1.2429 0.2448

i,3γ -16.5658 0.0213** -5.5753 0.1015 -0.9161 0.5745

)(,2

^

iabs β Coeff Prob Coeff Prob Coeff Prob

i,2γ -0.0378 0.9739 0.0066 0.9942 1.0216 0.2306

i,3γ 6.7022 0.3667 3.9505 0.1964 -0.3313 0.7953


i,3

^


i,2θ -0.4461 0.7310 -5.3341 0.0690* -3.2612 0.4839

i,3θ 0.2011 0.7850 0.3502 0.9228 -0.1465 0.9791

)(,3

^


i,2θ 0.1710 0.8458 1.3205 0.512 1.1386 0.6882

i,3θ -0.5386 0.2014 -8.1937 0.0012*** -4.3363 0.1762


i,4

^


i,2λ 0.7624 0.3424 3.6345 0.0047*** -0.0005 0.1770

i,3λ 0.5716 0.0357** 1.7395 0.0012*** 3.7565 0.0451**

)( ,4^


i,2λ 0.9586 0.1995 1.8993 0.0981* -0.0004 0.1364

i,3λ 0.4776 0.0000*** 1.6248 0.0000*** 3.3210 0.0370**


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Table II. Relationship Between Exposures and Derivatives Use Based on Four-Factor Model (A


i,2

^

β Coeff Prob Coeff Prob Coeff Pr

2γ -0.9792 0.0074*** -0.4891 0.2133 -0.0867 0.8

3γ 1.1030 0.1505 -0.0987 0.9361 -0.5289 0.6

)(,2

^

iabs β Coeff Prob Coeff Prob Coeff Pr

2γ 0.3934 0.1218 -0.0827 0.7684 -0.1623 0.6

3γ -1.0555 0.0389** -0.4252 0.6301 -0.8642 0.2


i,3

^


2θ 0.0740 0.8874 -0.0130 0.9597 -0.3383 0.4

3θ -0.7435 0.6161 0.1074 0.8635 -0.4342 0.3

)(,3

^

iabs β Coeff Prob Coeff Prob Coeff Pr

2θ 0.1773 0.6378 0.0763 0.6788 0.6024 0.1

3θ -0.0743 0.9445 -0.0603 0.8929 -0.6767 0.02


i,4

^


2λ 0.2729 0.0445** 0.8279 0.1317 1.4783 0.00

3λ 0.4167 0.3090 -0.5590 0.3377 -1.3478 0.09

)( ,4^

iabs β Coeff Prob Coeff Prob Coeff Pr2λ -0.0807 0.4229 0.2625 0.5578 1.5489 0.00

3λ 0.2512 0.2180 -0.1580 0.7247 0.5694 0.2


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This table provides the parameter estimates and the probability values for the four-factor model specified b

t it mit it it iit i RCM IRFX R

,,,5,4,3,2,1, ε β β β β β +++++=

Currency Exposure: iiiiii TAFDERTS FS ξ γ γ γ β +++= )/()/( 321

^

,2

Interest Rate Exposure: iiiiii TA DDERTA LTD υ θ θ θ β +++= )/()/( 321,3

^

Commodity Exposure: iiiiii TACDERTS TI µ λ λ λ β +++= )/()/( 321,4

^



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Table III. Relationship Between Exposures and Derivatives Use Based on Three-Factor Mod


FX,CM Coeff Prob Coeff Prob Coeff Prob

2γ -0.0361 0.9840 -0.9366 0.4885 -0.8079 0.3605

3γ -14.6306 0.0902* -5.3446 0.1072 -2.3039 0.1793

Number of Firms 30 42 45 FX,IR Coeff Prob Coeff Prob Coeff Prob

2γ 0.3656 0.8176 0.0540 0.9633 -1.2999 0.0838*

3γ -16.7424 0.0269** -6.2917 0.0957* 2.8360 0.0088***

Number of Firms 37 51 59


IR,CM Coeff Prob Coeff Prob Coeff Prob

2θ 0.2739 0.8453 -6.4643 0.0910* -3.6650 0.4793

3θ -0.0055 0.9921 0.8962 0.8577 1.3230 0.8200

Number of Firms35 44 47

IR,FX Coeff Prob Coeff Prob Coeff Prob

2θ 0.2947 0.8657 -4.0577 0.1650 3.1397 0.5353

3θ -0.6281 0.4138 -1.1695 0.7293 3.0197 0.5723



CM,IR Coeff Prob Coeff Prob Coeff Prob

2λ 1.0460 0.1675 4.2895 0.0027*** 3.9145 0.0227**

3λ 0.5244 0.0601* 1.8840 0.0013*** 1.6651 0.0057***

Number of Firms35 44 47

CM,FX Coeff Prob Coeff Prob Coeff Prob

2λ 1.7963 0.0808* 3.2357 0.0044*** 1.9246 0.2248

3λ 0.3443 0.2353 1.4775 0.0044*** 1.5466 0.0065**



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Table III. Relationship Between Exposures and Derivatives Use Based on Three-Factor Model (U


FX, CM Coeff Prob Coeff Prob Coeff Prob

2γ -1.4265 0.0005*** -0.5562 0.2035 -0.0395 0.9306

3γ 1.5403 0.0450** -0.1531 0.8405 -0.4453 0.3782


FX, IR Coeff Prob Coeff Prob Coeff Prob

2γ -1.4322 0.0028*** -0.6309 0.1328 0.1433 0.7670

3γ 0.9229 0.2359 -0.8260 0.1737 -0.8633 0.1768



IR, CM Coeff Prob Coeff Prob Coeff Prob

2θ 0.3327 0.7581 0.5137 0.2388 -0.4082 0.2448

3θ 0.6392 0.7468 0.5135 0.3783 -0.2348 0.5654


IR, FX Coeff Prob Coeff Prob Coeff Prob

2θ 1.2191 0.3470 0.1080 0.7566 0.1112 0.7104

3θ -1.1408 0.5583 -0.3838 0.2316 0.3013 0.2669



CM, IR Coeff Prob Coeff Prob Coeff Prob

2λ 0.7340 0.5775 -1.6313 0.0517* -3.6394 0.0479*

3λ 0.4324 0.3146 0.0969 0.8159 -1.1594 0.1165


CM, FX Coeff Prob Coeff Prob Coeff Prob

2λ 0.2191 0.8802 0.1224 0.9270 -3.4029 0.0293*

3λ 0.5682 0.1900 0.1546 0.7405 -1.0099 0.1625



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Table III. Relationship Between Exposures and Derivatives Use Based on Three-Factor Mod

AbsoluteCurrency Exposure

2001 2000 1999


2γ 0.0304 0.9830 0.1962 0.8741 0.0864 0.8892

3γ

6.6864 0.4146 3.5127 0.2357 0.3779 0.7458Number of firms 30 42 45


2γ -0.3145 0.7820 0.0654 0.9511 0.4515 0.5185

3γ 6.8116 0.3541 4.4850 0.1885 -0.4642 0.5623


Absolute Interest Rate Exposure

2001 2000 1999


2θ -0.6162 0.5240 2.9023 0.2766 1.8094 0.5761

3θ -0.2851 0.6019 -9.6892 0.0050*** -4.6764 0.1787



2θ 1.0368 0.4446 -0.1477 0.9432 -2.9128 0.3563

3θ -0.4273 0.5246 -2.6552 0.1796 -1.4803 0.7607


AbsoluteCommodity Exposure

2001 2000 1999


2λ 0.8015 0.2559 2.9120 0.0063*** 2.4577 0.0254**

3λ 0.5044 0.0000*** 1.7576 0.0000*** 1.4292 0.0056***



2λ 0.6977 0.2903 1.9277 0.0955* 2.3714 0.0241**

3λ 0.4485 0.0000*** 1.4836 0.0000*** 1.3652 0.0038***



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Table III. Relationship Between Exposures and Derivatives Use Based on Three-Factor Model (U

AbsoluteCurrency Exposure

1997 1996 1995


2γ 0.8109 0.0071*** 0.3299 0.2866 -0.0099 0.9745

3γ -0.8245 0.1073 -0.1459 0.6986 -0.3798 0.2559



2γ 0.6194 0.0719* 0.0318 0.9144 0.2128 0.5050

3γ -0.5978 0.2715 -0.2243 0.7593 -0.4234 0.4740


Absolute Interest Rate Exposure

1997 1996 1995


2θ 0.1710 0.8402 0.3141 0.3554 0.5032 0.0381*

3θ -0.4897 0.7611 0.4021 0.3682 -0.1738 0.5687 Number of firms 71 66 54


2θ -0.6588 0.5035 0.1555 0.5461 0.3355 0.0825*

3θ 1.1070 0.4890 0.1814 0.5242 -0.0985 0.4256


AbsoluteCommodity Exposure

1997 1996 1995


2λ 0.4661 0.5243 0.6245 0.3127 3.0371 0.0057**

3λ 0.3257 0.1395 0.1173 0.4352 0.8032 0.1563



2λ 1.1136 0.1632 -0.3339 0.7709 2.8863 0.0032**

3λ 0.3755 0.0831* 0.2673 0.0987* 1.0788 0.0606*



35/40

This table provides the parameter estimates and the probability values for the three-factor model specified b

Currency Exposure: FX, CM:t it mit it iit i

RCM FX R,,,5,4,2,1,

ε β β β β ++++=

FX, IR:t it mit it iit i

R IRFX R,,,5,3,2,1,

ε β β β β ++++=


^

,2

Interest Rate Exposure: IR, CM: t it mit it iit i RCM IR R ,,,5,4,3,1, ε β β β β ++++=

IR, FX:t it mit it iit i

R IRFX R,,,5,3,2,1,

ε β β β β ++++=


^

Commodity Exposure: CM, IR:t it mit it iit i

RCM IR R,,,5,4,3,1,

ε β β β β ++++=

CM, FX:t it mit it iit i

RCM FX R,,,5,4,2,1,

ε β β β β ++++=


^



36/40

34

Table IVPanel A. Bivariate Relationship Between Exposures and Derivatives Use

Three-Factor Model Estimated with MLE (User Firms Only)

2001 2000 1999 1998

FX, IR Coeff Prob Coeff Prob Coeff Prob Coeff Prob

1γ 0.4027 0.5137 -0.6640 0.1786 -0.3356 0.3217 0.1947 0.3451

2γ 0.4737 0.7119 0.0849 0.9424 -1.3027 0.1599 -0.9183 0.2285

3γ -17.1006 0.0066*** -6.1707 0.0866* 2.9121 0.3631 -0.1737 0.9229

1θ 0.1274 0.9311 0.8633 0.2631 -1.9568 0.1380 -0.7511 0.0363**

2θ 0.0833 0.9867 -4.2603 0.1566 2.1871 0.6642 -0.1447 0.8553

3θ -0.3441 0.9258 -1.5563 0.8382 3.0882 0.7787 2.4553 0.4820

υ σ 3.0211 0.0003*** 2.7607 0.0000*** 1.8139 0.0000*** 1.1351 0.0000***

ξ σ 3.2034 0.0010*** 9.5689 0.0000*** 24.5972 0.0001*** 1.3601 0.0000***

ξυ ρ 0.2425 0.4143 -0.0492 0.8152 0.06030 0.7703 0.1304 0.2967

FX, CM Coeff Prob Coeff Prob Coeff Prob Coeff Prob

1γ 0.6624 0.3732 -0.6780 0.2027 -0.1060 0.8455 -0.3369 0.1349

2γ -1.2370 0.5427 0.2544 0.8574 -0.8645 0.5027 -0.7398 0.1911

3γ -12.5578 0.2238 -3.2769 0.3021 0.0415 0.0003*** 1.7625 0.2995

1λ 0.0894 0.8537 0.0201 0.9642 -0.0996 0.8455 -0.3948 0.0432**

2λ 2.1611 0.4540 2.6033 0.32101 2.3303 0.3888 2.7126 0.0135**

3λ 0.1165 0.7319 0.7600 0.0738* 1.3257 0.0119** 0.7119 0.1248

µ σ 3.2085 0.0059*** 2.9009 0.0000*** 1.8611 0.0001*** 1.4070 0.0000***

ξ σ 0.5965 0.0135** 0.8599 0.0000*** 0.9153 0.0000*** 0.6343 0.0000***

ξµ ρ 0.3184 0.2092 -0.5060 0.0037*** -0.2374 0.2819 0.1405 0.2555

IR, CM Coeff Prob Coeff Prob Coeff Prob Coeff Prob

1θ -0.0335 0.9801 0.8159 0.5244 0.6449 0.7558 -1.2801 0.0008***

2θ -0.5595 0.9071 -7.7311 0.1346 -7.2564 0.2765 0.5638 0.6482

3θ �

A New Look at Hedging With Derivatives_Will Firms Reduce Market Risk Exposure

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