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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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1
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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iiiiii TAFDERTS FS ξ γ γ γ β +++= )/()/( 321
^
,2 (6)
iiiiii TA DDERTA LTD υ θ θ θ β +++= )/()/( 321,3
^
(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)
iiiiii TAFDERTS FS ξ γ γ γ β +++= )/()/( 321
^
,2 (9)
iiiiii TACDERTS TI µ λ λ λ β +++= )/()/( 321,4
^
(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
standard deviation of i,2
^
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)
iiiiii TA DDERTA LTD υ θ θ θ β +++= )/()/( 321,3
^
(12)
iiiiii TACDERTS TI µ λ λ λ β +++= )/()/( 321,4
^
(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
standard deviation of i,3
^
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)
iiiiii TAFDERTS FS ξ γ γ γ β +++= )/()/( 321
^
,2 (15)
(ii) For interest rates:
t it mit iit i R IR R ,,,5,3,1, ε β β β +++= (16)
iiiiii TA DDERTA LTD υ θ θ θ β +++= )/()/( 321,3
^
(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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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)
iiiiii TAFDERTS FS ξ γ γ γ β +++= )/()/( 321
^
,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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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)
iiiiii TA DDERTA LTD υ θ θ θ β +++= )/()/( 321,3
^
(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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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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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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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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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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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
^
β Coeff Prob Coeff Prob Coeff Prob
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
Number of firms 32 32 39
Commodity Exposure 2001 2000 1999
i,4
^
β Coeff Prob Coeff Prob Coeff Prob
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**
Number of firms 19 21 20
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Table I. Relationship Between Exposures and Derivatives Use Based on Two-Factor Mod
Currency Exposure 1997 1996 199
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
Number of firms 43 48 40
Interest Rate Exposure 1997 1996 199
i,3
^
β Coeff Prob Coeff Prob Coeff
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
Number of firms 46 43 38
Commodity Exposure 1997 1996 199
i,4
^
β Coeff Prob Coeff Prob Coeff
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
Number of firms 42 34 28
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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
Currency Exposure 2001 2000 1999
i,2
^
β Coeff Prob Coeff Prob Coeff Prob
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
Interest Rate Exposure 2001 2000 1999
i,3
^
β Coeff Prob Coeff Prob Coeff Prob
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
^
iabs β Coeff Prob Coeff Prob Coeff Prob
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
Commodity Exposure 2001 2000 1999
i,4
^
β Coeff Prob Coeff Prob Coeff Prob
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^
iabs β Coeff Prob Coeff Prob Coeff Prob
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
Currency Exposure 1997 1996 1995
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
Interest Rate Exposure 1997 1996 1995
i,3
^
β Coeff Prob Coeff Prob Coeff Pr
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
Commodity Exposure 1997 1996 1995
i,4
^
β Coeff Prob Coeff Prob Coeff Pr
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
^
*, **, *** denote statistical significance at the 10%, 5%, and 1%, respectively, adjusted for heteroskedasticity using
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Table III. Relationship Between Exposures and Derivatives Use Based on Three-Factor Mod
Currency Exposure 2001 2000 1999
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
Interest Rate Exposure 2001 2000 1999
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
Number of Firms 37 51 59
Commodity Exposure 2001 2000 1999
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**
Number of Firms 30 42 45
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Table III. Relationship Between Exposures and Derivatives Use Based on Three-Factor Model (U
Currency Exposure 1997 1996 1995
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
Number of firms 66 66 55
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
Number of firms 67 67 56
Interest Rate Exposure 1997 1996 1995
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
Number of firms 71 66 54
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
Number of firms 67 68 57
Commodity Exposure 1997 1996 1995
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
Number of firms 71 66 54
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
Number of firms 66 66 55
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Table III. Relationship Between Exposures and Derivatives Use Based on Three-Factor Mod
AbsoluteCurrency Exposure
2001 2000 1999
FX, CM Coeff Prob Coeff Prob Coeff Prob
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
FX, IR Coeff Prob Coeff Prob Coeff Prob
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
Number of firms 37 51 59
Absolute Interest Rate Exposure
2001 2000 1999
IR, CM Coeff Prob Coeff Prob Coeff Prob
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
Number of firms 35 44 47
IR, FX Coeff Prob Coeff Prob Coeff Prob
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
Number of firms 37 51 59
AbsoluteCommodity Exposure
2001 2000 1999
CM, IR Coeff Prob Coeff Prob Coeff Prob
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***
Number of firms 35 44 47
CM, FX Coeff Prob Coeff Prob Coeff Prob
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***
Number of firms 30 42 45
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Table III. Relationship Between Exposures and Derivatives Use Based on Three-Factor Model (U
AbsoluteCurrency Exposure
1997 1996 1995
FX, CM Coeff Prob Coeff Prob Coeff Prob
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
Number of firms 66 66 55
FX, IR Coeff Prob Coeff Prob Coeff Prob
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
Number of firms 67 67 56
Absolute Interest Rate Exposure
1997 1996 1995
IR, CM Coeff Prob Coeff Prob Coeff Prob
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
IR, FX Coeff Prob Coeff Prob Coeff Prob
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
Number of firms 67 68 57
AbsoluteCommodity Exposure
1997 1996 1995
CM, IR Coeff Prob Coeff Prob Coeff Prob
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
Number of firms 71 66 54
CM, FX Coeff Prob Coeff Prob Coeff Prob
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*
Number of firms 66 66 55
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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 ++++=
iiiiii TAFDERTS FS ξ γ γ γ β +++= )/()/( 321
^
,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 ++++=
iiiiii TA DDERTA LTD υ θ θ θ β +++= )/()/( 321,3
^
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 ++++=
iiiiii TACDERTS TI µ λ λ λ β +++= )/()/( 321,4
^
*, **, *** denote statistical significance at the 10%, 5%, and 1%, respectively, adjusted for heteroskedasticity using
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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 �