Description
Under what conditions will a multinational corporation alter its operations to manage its risk exposure? We show that multinational firms will engage in operational hedging only when both exchange rate uncertainty and demand uncertainty are present. Operational hedging is less important for managing short-term exposures, since demand uncertainty is lower in the short term.
European Finance Review 2: 229–246, 1999.
© 1999 Kluwer Academic Publishers. Printed in the Netherlands.
229
Corporate Risk Management for Multinational
Corporations: Financial and Operational Hedging
Policies
BHAGWAN CHOWDHRY
1
and JONATHAN T. B. HOWE
2,
1
The Anderson School at UCLA, 110 Westwood Plaza, Los Angeles, CA 90095-1481, USA; Phone:
(310)-825-5883; Fax: (310)-206-5455; E-mail: [email protected];
2
Hotchkis and
Wiley, Division of Merrill Lynch Capital Management Group, Los Angeles; Phone: (213)-362-8949;
E-mail: jonathan [email protected].
Abstract. Under what conditions will a multinational corporation alter its operations to manage its
risk exposure? We show that multinational ?rms will engage in operational hedging only when both
exchange rate uncertainty and demand uncertainty are present. Operational hedging is less important
for managing short-term exposures, since demand uncertainty is lower in the short term. Opera-
tional hedging is also less important for commodity-based ?rms, which face price but not quantity
uncertainty. When the ?xed costs of establishing a plant are low or the variability of the exchange
rate is high, a ?rm may bene?t from establishing plants in both the domestic and foreign location.
Capacity allocated to the foreign location relative to the domestic location will increase when the
variability of foreign demand increases relative to the variability of domestic demand or when the
expected pro?t margin is larger. For ?rms with plants in both a domestic and foreign location, the
foreign currency cash ?ow generally will not be independent of the exchange rate and consequently
the optimal ?nancial hedging policy cannot be implemented with forward contracts alone. We show
that the optimal ?nancial hedging policy can be implemented using foreign currency call and put
options and forward contracts.
1. Introduction
Multinational corporations often sell products in various countries with prices de-
nominated in corresponding local currencies. It is widely recognized that as the
volatility in exchange rates has increased dramatically after the breakdown of the
Bretton Woods system of ?xed exchange rates (see Smith, Smithson and Wilford
(1990)), multinational corporations may have become increasingly vulnerable to
We thank participants at the March 1996 conference on corporate Risk Management in honor
of Fischer Black at the Anderson School at UCLA, the June 1996 meetings of the Western Finance
Association at Sunriver, Oregon, and the 1997 meetings of the European Finance Association in
Vienna, Austria for helpful comments on earlier drafts. We are especially grateful for the suggestions
of John Parsons, Sugato Bhattacharya and an anonymous referee.
The views expressed in this article are the personal views of the authors and do not represent
the of?cial views of Hotchkis and Wiley or Merrill Lynch.
230 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
exchange risk since the short term movements in exchange rates are often not
accompanied by offsetting changes in prices in the corresponding countries (see
Shapiro (1992), for example).
Of course, in perfect capital markets, corporations need not hedge exchange
risk at all since investors can do it on their own (see Aliber (1978)). Market im-
perfections, such as taxes, agency problems, asymmetric information, dead-weight
costs associated with ?nancial distress, however, may provide incentives for cor-
porations to hedge the exchange risk (see Dufey and Srinivasulu (1983), Stulz
(1984), Shapiro and Titman (1985), Smith and Stulz (1985), Froot, Scharfstein and
Stein (1992) and DeMarzo and Duf?e (1995)). A number of ?nance scholars and
practitioners have discussed how ?rms could use ?nancial instruments to hedge
?nancial price risk (see, among others, Giddy (1983), Lewent and Kearney (1990),
Smith, Smithson and Wilford (1990), Froot, Scharfstein and Stein (1994) and two
popular textbooks Shapiro (1992) and Eiteman, Stonehill and Moffett (1995)).
In addition to using ?nancial contracts, a ?rm could manage its risk exposure
through operational hedging. An example of an operational hedging policy would
be to locate production in a country where signi?cant sales revenues in the local
(i.e., foreign) currency are expected. The effect of unexpected changes in exchange
rates and foreign demand conditions on domestic currency value of sales revenues
is hedged by similar changes in the the domestic currency value of local production
costs. Operational hedging motives thus may provide a reason for direct foreign
investment by ?rms and may further explain the existence of multinational ?rms
with production facilities at several foreign locations.
When should a multinational corporation adopt ?nancial hedging policies to
manage risk? Under what conditions should it resort to operational hedging? When
should it use both simultaneously and what should be the extent of each type of
policy? A systematic analysis of these questions, to our knowledge, does not exist
in the literature. This paper attempts to ?ll this gap.
The costs of implementing a ?nancial hedge are likely to be an order of magni-
tude smaller than those of implementing an operational hedge. After all, in order to
implement an operational hedge, a ?rm may be required to open a production plant
in another country whereas to implement a ?nancial hedge may simply require a
phone call to the ?rm’s bank. What could, then, be the advantages of operational
hedging policies?
If the quantity of foreign currency revenues the ?rm is expected to generate is
certain, it is easy to hedge the exchange risk exposure associated with it by using a
forward contract for that certain quantity. This eliminates the associated transaction
exposure completely with a relatively simple ?nancial hedge. However, ?uctuating
foreign currency cash ?ow represents an additional source of uncertainty for many
multinationals. For certain products, demand conditions can swing dramatically
from year to year, inducing large changes in foreign currency revenues. If the
quantity of foreign currency revenues is uncertain (and not perfectly correlated
with the exchange rate), no ?nancial contract (that must be agreed upon ex ante)
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 231
that is contingent only on ex post observable and non-manipulable variables such
as the exchange rate, can completely eliminate the exchange risk.
1
We argue that
one of the advantages of an operational hedge is that it allows the ?rm to align
domestic currency production costs and revenues more closely. It is as if the ?rm
had a forward contract whose quantity is contingent upon sales in the foreign
country. Clearly, this dominates a ?xed quantity forward contract. An operational
hedge, by aligning local costs with local revenues amounts to self-insurance by the
?rm against demand uncertainty; market insurance for demand uncertainty is not
feasible because of the severe moral hazard problem since sales can be manipulated
by the ?rm.
Unlike ?nancial hedging contracts, a ?rm’s operational policies are likely to
affect expected pro?ts. For example, having plants in several countries allows
the ?rm to shift some production to the location where costs, after observing the
exchange rate movements, are the smallest in domestic currency terms. Creating
this production ?exibility may have a positive expected payoff. This bene?t has
been discussed in the literature (see Dasu and Li (1994) and the textbooks Shapiro
(1992) and Eiteman, Stonehill and Moffett (1995)). Production ?exibility may also
affect the variance of pro?ts, an effect that has been neglected in the literature. We
contend that ?rms concerned with managing risk will want to take this hedging
effect into account, and are likely to adopt operational policies that differ from
those that maximize expected pro?ts.
Mello, Parsons, and Triantis (1995) consider the design of an optimal ?nancial
hedging policy for a multinational with production ?exibility. Financial hedging
helps alleviate the agency problem associated with the ?rm’s outstanding debt and
moves equity owners to closer to the ?rst best operating policy. Mello, Parsons, and
Triantis analyze a model in which exchange rate movements are the only source of
risk. In such a setting, production ?exibility raises ?rm value but does not confer a
hedging bene?t. We examine a setting in which there is also uncertainty regarding
the quantity of foreign currency cash?ow It is this additional source of risk that
creates a risk management rationale for production ?exibility.
We develop a formal model in the following section to analyze the issues dis-
cussed above. For concreteness, Section 3 then presents a numerical example of
the model. Implications of the model are discussed in Section 4, which is followed
by some concluding remarks.
2. The model
Consider a ?rm based in the U.S. that produces a single good for sale at a fu-
ture date (time 1) in a foreign market. Demand for the good at time 1, denoted
1
Chowdhry (1995) and Kerkvliet and Moffett (1991) analyze optimal ?nancial hedging policies
for multinational ?rms facing uncertain future foreign currency cash ?ow. However, they focus on ?-
nancial hedging policies and do not consider the possibility of operational hedging. Earlier treatments
of hedging under price and quantity uncertainty include Anderson and Danthine (1978).
232 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
x ? [0, x
max
] in the U.S. and x
?
? [0, x
?
max
] in the foreign market, is uncertain
at time 0. There is no demand for the good after time 1. The time 0 exchange
rate between the two currencies is normalized to 1. Let s denote the time 1 price
of one unit of foreign currency in terms of domestic currency units. For simplic-
ity, we normalize E = 1. Assume further that s, x and x
?
are stochastically
independent. Let p and p
?
denote the sale prices of the good in the U.S. and in
the foreign market respectively. The assumption of stochastic quantities sold at
exogenously ?xed prices can be rationalized as a result of a ?rm facing (downward
sloping) demand curves whose locations are uncertain at the time of setting prices.
Similarly let c and c
?
denote per unit costs of production in the U.S. and the foreign
location respectively. For simplicity and analytical tractability, we assume that per
unit sale prices and costs at time 1 are known with certainty at time 0. We further
normalize p = p
?
> c = c
?
so that there are no expected differences ex ante in
sale prices and marginal costs at the two locations.
At time 0, the ?rm decides to build plants with capacities k and k
?
respectively
at the U.S. and the foreign location. We assume that the total capacity is enough
to meet the maximum demand at the two locations, i.e., k + k
?
= x
max
+ x
?
max
. At
time 1, the ?rm can produce up to its capacity at each location. Let q and q
?
denote
the quantities of the good produced at each location at time 1 to satisfy the total
demand.
2
Thus,
q + q
?
= x + x
?
. (1)
Let y and y
?
denote the cash ?ows in US$ and the foreign currency respectively.
Then,
y = px ? cq, (2)
y
?
= px
?
? cq
?
. (3)
The ?rm’s pro?ts (excluding any ?xed costs of establishing plants), without any
?nancial hedging contract, at time 1, thus can be written as:
? = y + sy
?
. (4)
There are some features of our setup that may appear restrictive at ?rst glance.
First, it would be more natural to assume downward sloping demand curves where
?rms can set prices after observing the demand conditions at each location. Second,
?rms may be able to adjust the prices charged at each location after observing
the exchange rate s.
3
Third, one could specify more general cost functions in
2
It will be optimal to satisfy total demand if p/c ? s ? c/p. If this condition does not always
hold, then under certain circumstances meeting demand fully in one of the markets is not optimal.
Consideration of this additional “abandonment” option would complicate the analysis somewhat and
not affect the basic results.
3
These were brought up by the referee commenting on an earlier draft.
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 233
which costs are increasing and convex in quantities produced and decreasing in
the installed capacities at each location.
An important feature that we are trying to capture in our model is uncertainty
about the quantity of foreign currency cash ?ow y
?
. Our setup allows us to capture
this uncertainty in a particularly tractable manner since revenues at each location
(in local currencies), px and px
?
, are independent of the exchange rate s. This
makes domestic currency value of revenues at the foreign location, spx
?
, sensitive
to foreign exchange rate ?uctuations which is another feature that we are trying
to capture in our model. Generalizing the model in which prices are set after
observing the demand states at each location as well as the exchange rate will
preserve the features that cash ?ow in foreign currency y
?
will be uncertain and the
domestic currency value of revenues at the foreign location, sp
?
x
?
will be sensitive
to the exchange rate ?uctuations (except in some very special and restrictive cases
4
but the local currency revenues at each location, px and p
?
x
?
will no longer be
independent of the exchange rate. This complicates the model and makes it some-
what cumbersome. But, as we shall later explain, the central results of the paper
are likely to go through in a much richer framework that accomodates some of the
generalizations.
5
At time 0 the ?rm may enter into forward and option contracts on the time 1
exchange rate. The use of both forwards and options allows the ?rm to construct
a ?nancial hedging instrument whose payoff is any arbitrary (possibly nonlinear)
function of the time 1 exchange rate. Let h(s) denote the time 1 payoff on this
contract. Assume that the ?rm has a competitive risk-neutral counterparty and that
the contract has no credit risk so that Eh(s) = 0. The ?rm’s pro?ts at time 1 with
the ?nancial hedging contract can be written as:
?
h
= ? + h(s).
We assume that the ?rm is a mean variance optimizer so that its objective
function takes the form
E[?
h
] ?
?
2
Var[?
h
].
Since the expected payoff on any ?nancial hedge contract is zero, the optimal
?nancial hedge contract solves
Min
h(s)
Var[? + h(s)] s.t. Eh(s) = 0.
4
For instance, if the ?rm faces demand curves with constant elasticities and is able to pass on
the exchange rate changes completely in its pricing decisions, the domestic currency value of its
revenues in the foreign market may be completely insensitive to exchange rate changes. In this paper,
our focus is on situations when ?rms face signi?cant exchange rate exposure in revenues generated
at the foreign location.
5
We will he more precise later about the exact nature of these generalizations.
234 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
Writing the Lagrangian, we get
L = EE[?
2
+ 2?h(s) + h(s)
2
|s] ? (E?)
2
? ?Eh(s),
where ? denotes the Lagrangian multiplier. Rearranging, we get
L = EE[?
2
+ 2?h(s) + h(s)
2
? ?h(s)|s] ? (E?)
2
.
The ?rst order condition for the minimum gives
h(s) =
?
2
? E[?|s].
Imposing the constraint that Eh(s) = 0, we get ?/2 = E[?]. The optimal ?nancial
hedging contract thus is given by:
h(s) = E[?] ? E[?|s]. (5)
The expression for ? in (4) can be rewritten as:
? = (y + y
?
) ? (1 ? s)y
?
. (6)
From (1)–(3),
y + y
?
= p(x + x
?
) ? c(q + q
?
) = (p ? c)(x + x
?
). (7)
Notice that y +y
?
is independent of s. Substituting from (6) into (5) and simplify-
ing, the optimal ?nancial hedging contract can be rewritten as
h(s) = (1 ? s)E[y
?
|s] + Cov(s, y
?
). (8)
Notice that if the foreign currency cash ?ow y
?
is independent of the exchange
rate realization s, the optimal ?nancial hedging contract is a forward contract in
which the ?rm sells a quantity of foreign currency equal to Ey
?
in the forward
exchange market. But, if y
?
is not independent of s, then in general, the optimal
?nancial hedging contract will not be a forward contract but some claim that is
non-linearly contingent on s.
The ?rm’s pro?ts at time 1 with the ?nancial hedging contract can now be
rewritten as:
?
h
= (y + y
?
) ? (1 ? s){y
?
? E[y
?
|s} + Cov(s, y
?
). (9)
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 235
2.1. CASE 1: LARGE FIXED COSTS
Suppose that there are large ?xed costs associated with establishing a plant so that
the ?rm will choose to establish a plant at only one location. Then there are two
possibilities:
1. The ?rm establishes the plant domestically. In this case:
q = x + x
?
, q
?
= 0.
2. The ?rm establishes the plant at the foreign location. In this case:
q = 0, q
?
= x + x
?
.
In either case, since q
?
is independent of the realization of s, the foreign cur-
rency cash ?ow y
?
will also be independent of s. The optimal hedge contract in (8)
then simpli?es to
h(s) = (1 ? s)Ey
?
.
If Ey
?
> 0, this is a contract to sell forward Ey
?
units of foreign currency at a
price of 1 unit of domestic currency per unit of foreign currency. If Ey
?
< 0 then
the contract would involve purchasing forward Ey
?
foreign currency units at the
same price.
The ?rm’s pro?ts after ?nancial hedging, speci?ed in (9), simplify to
?
h
= (y + y
?
) ? (1 ? s)[y
?
? Ey
?
]. (10)
Notice that the expected hedged pro?ts (from (7))
E?
h
= E(y + y
?
) = (p ? c)E(x + x
?
)
are the same whether the ?rm locates its plant domestically or at the foreign loca-
tion. The decision of where to locate the plant, therefore, is determined solely by
which location leads to a smaller variance of hedged pro?ts. From (10),
Var[?
h
] = Var(y + y
?
) + Var s Var y
?
. (11)
First, from (7), we notice that Var(y + y
?
) is independent of the plant location
decision. Second, the location decision – which is the operational hedging decision
– matters only if both Var s as well as Var y
?
are not equal to zero. This indicates
that operational hedging decisions matter only when there is both exchange rate
uncertainty and quantity uncertainty. Given Var s, the plant location decision is
determined by which location leads to a smaller Var y
?
.
1. If the ?rm establishes the plant domestically,
y
?
= px
?
, Var y
?
= p
2
Var x
?
. (12)
236 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
2. If the ?rm establishes the plant at the foreign location,
y
?
= px
?
? c(x + x
?
),
Var y
?
= p
2
Var x
?
+ c
2
Var(x + x
?
) ? 2pc Cov(x
?
, x + x
?
). (13)
The ?rm will choose to produce at the foreign location if and only if the expres-
sion in (12) exceeds the one in (13) or equivalently if:
p
2
Var x
?
> p
2
Var x
?
+ c
2
Var x + c(c ? 2p) Var x
?
.
The above condition simpli?es to:
1 + 2
p ? c
c
Var x
?
Var x
> 1. (14)
The ?rst term on the left hand side of the above condition is positively and
linearly related to expected pro?tability and the second term represents relative
total variability of foreign demand to total variability of domestic demand.
2.2. CASE 2: SMALL FIXED COSTS
Now suppose that the ?xed costs of establishing a plant with a given capacity are
small enough so that the ?rm is indifferent between dividing the total capacity
between plants at two locations based only on the costs of establishing the plants.
Suppose that at time 0, the ?rm decides to build plants with capacities k and k
?
respectively at the U.S. and the foreign location. At time 1, the ?rm can produce
up to its capacity at each location.
Based on the realization of the exchange rate, the ?rm, in order to satisfy de-
mand, will produce as much as possible at the location where it is cheaper to do so.
If the exchange rate s > 1, it is cheaper to produce domestically. If the total demand
is less than the domestic capacity, the ?rm will produce everything domestically.
If the total demand exceeds the domestic capacity, the ?rm will produce up to its
capacity domestically and produce the rest at the foreign location. Similarly, if
s < 1 it is cheaper to produce at the foreign location and analogous production
decisions will be made by the ?rm. The quantities produced at each location are
thus:
(q, q
?
) =
?
?
?
?
?
?
?
(k, x + x
?
? k) if x + x
?
> k, s > 1
(x + x
?
, 0) x + x
?
< k, s > 1.
(x + x
?
? k
?
, k
?
) x + x
?
> k
?
, s < 1
(0, x + x
?
) x + x
?
< k
?
, s < 1
(15)
Suppose the ?rm chooses the capacities at time 0 to maximize expected pro?ts,
i.e., suppose it chooses k to maximize E?
h
which is equivalent to maximizing E?.
The ?rst order condition is:
d
dk
E? = E
d?
dk
= E
dy
dk
+ s
dy
?
dk
= 0. (16)
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 237
Now, from (2) and (3),
dy
dk
= ?c
dq
dk
,
dy
?
dk
= ?c
dq
?
dk
,
Thus, from (15),
dy
dk
,
dy
?
dk
= ?c
?
?
?
?
?
?
?
(1, ?1) if x + x
?
> k, s > 1
(0, 0) x + x
?
< k, s > 1.
(1, ?1) x + x
?
> k
?
, s < 1
(0, 0) x + x
?
< k
?
, s < 1
Therefore,
d?
dk
= ?c
?
?
?
?
?
?
?
1 ? s if x + x
?
> k, s > 1
0 x + x
?
< k, s > 1.
1 ? s x + x
?
> k
?
, s < 1
0 x + x
?
< k
?
, s < 1
It is clear that the ?rst order condition in (16) is satis?ed if k = k
?
. In other words,
if the ?rm were concerned only with maximizing expected pro?ts it would divide
the capacity equally between the two plants.
6
We will call this solution the benchmark solution that does not take into con-
sideration any hedging considerations. But what if the ?rm were also concerned
about the variance of its pro?ts? We will now see that hedging considerations will,
in general, move the ?rm away from choosing equal capacity. This deviation from
the benchmark capacity solution is tantamount to operational hedging.
Whether the ?rm chooses a larger domestic or foreign capacity compared to
the bench-mark solution of equal capacity depends on the sign of the following
expression:
d
dk
Var ?
h
= 2E
?
h
d?
h
dk
. (17)
6
The ?rst order condition is suf?cient for a maximum because expected pro?ts are globally
concave in k, provided the distribution of s is symmetric. If s is distributed symmetrically then
E
d
2
?
dk
2
=
c
2
E[s ? 1|s > 1]
?
dF(k)
dk
+
dF(k
?
)
dk
< 0,
where F is the joint probability distribution function for x and x
?
(assumed to be differentiable).
238 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
The right hand side of the above equation obtains since d/dk E?
h
= 0.
7
The
expression in (17), after simplifying, equals:
2E
(1 ? s)
2
d
dk
Var(y
?
|s)
. (18)
The ?rm will choose a larger foreign capacity if the sign of the above expression
is positive. As in the case in the previous subsection, the above expression will
equal zero if either there is no exchange rate uncertainty or if there is no quantity
uncertainty. Thus operational hedging decisions matter only when there is both
exchange rate uncertainty and quantity uncertainty.
8
7
The above condition obtains in general, not just in the setup we have developed in our model.
8
This result obtains even in a more general framework that we now describe more precisely.
Notice that the hedged pro?ts can in general be written as follows:
?
h
= y + sy
?
+ E(y + sy
?
) ? E(y + sy
?
|s).
The condition in (17) can be expanded as:
E
?
h
d?
h
dk
= E
{y ? E(y|s)}
d
dk
{y ? E(y|s)}
+E
s
2
{y
?
? E(y
?
|s)}
d
dk
{y
?
? E(y
?
|s)}
+E
s{y ? E(y|s)}
d
dk
{y
?
? E(y
?
|s)}
+E
s{y
?
? E(y
?
|s)}
d
dk
{y ? E(y|s)}
Notice that in any general framework in which the parameters in the two countries are symmetric,
and the distribution of the exchange rate s is symmetric around its mean of 1, the last two terms will
cancel each other and the ?rst term:
E
{y ? E(y|s)}
d
dk
{y ? E(y|s)}
= ?E
{y
?
? E(y
?
|s)}
d
dk
{y
?
? E(y
?
|s)}
.
Making these substitutions and simplifying, we obtain:
E
?
h
d?
h
dk
= E
(s
2
? 1){y
?
? E(y
?
|s)}
d
dk
{y
?
? E(y
?
|s)}
= E(s
2
? 1)E
d
dk
Var(y
?
|s)
+ Cov
(s
2
? 1),
d
dk
Var(y
?
|s)
= Var(s)E
d
dk
Var(y
?
|s)
+ Cov
(s
2
? 1),
d
dk
Var(y
?
|s)
.
Notice that if there is no exchange rate uncertainty the above expression equals zero. We know that
d/dk Var(y
?
|s) is positive because increasing domestic capacity implies that the ?rmproduces less at
its foreign location which increases the variability of pro?ts in the foreign currency. Therefore, when
Var(s) > 0, the ?rst term in the expression above is positive. The second covariance term will be
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 239
The above expression can be further rewritten as:
2E
(1 ? s)
2
d
dk
{p
2
Var x
?
+ c
2
Var[q
?
|s] ? 2pc Cov[x
?
, q
?
|s]}
.
If Prob[s > 1] = Prob[s < 1] and E[(1 ? s)
2
|s > 1] = E[(1 ? s)
2
|s < 1] – a
suf?cient condition for these is that the distribution of s be symmetric around its
mean of 1 – then the sign of the above expression is positive if and only if:
1 + 2
p ? c
c
E[x
?
|x + x
?
> k] ? Ex
?
E[x|x + x
?
> k] ? Ex
> 1. (19)
Notice the similarity between the above condition to the condition in (14).
The ?rst term on the left hand side of the above condition – which is identical
to the corresponding term in (14) – is positively and linearly related to expected
pro?tability. The second term in (19) is analogous to the corresponding term in
(14) and represents relative variability of foreign demand to variability of domestic
demand.
In addition to operational hedging, the ?rmwill also engage in ?nancial hedging
through the contract speci?ed in (8). This contract can be constructed using forward
and option contracts. Option contracts must be used because E[y
?
|s] in (8) depends
on s. Speci?cally the conditional expectation can take two values: E[y
?
|s ? 1] and
E[y
?
|s < 1], with E[y
?
|s ? 1] > E[y
?
|s < 1]. The optimal ?nancial hedging
contract is therefore
h(s) = (1 ? s)E[y
?
|s ? 1] + Cov(s, y
?
) s ? 1,
h(s) = (1 ? s)E[y
?
|s < 1] + Cov(s, y
?
) s < 1.
This expression can be rewritten
h(s) = (1 ? s)E[y
?
|s < 1] ? max(s ? 1, 0)
× (E[y
?
|s ? 1] ? E[y
?
|s < 1]) + Cov(s, y
?
).
From the above expression it is evident that a simple method of constructing h(s)
is for the ?rm to: (1) “sell” forward E[y
?
|s < 1] units of the foreign currency at
a price of 1 unit of domestic currency for each unit of foreign currency;
9
(2) write
European call options exercisable at date 1 with a strike price of 1 unit of domestic
currency for each unit of foreign currency on E[y
?
|s ? 1] ? E[y
?
|s < 1] units of
positive if d/dk Var(y
?
|s) is not decreasing in s which is likely under fairly general circumstances.
The intuitive interpretation is as follows. The increase in variability of foreign currency pro?ts as the
?rm increases its domestic capacity is more pronounced when the exchange rate is high because the
?rm shifts its production to the domestic location even more.
9
If E[y
?
|s < 1] < 0, then the transaction is a forward purchase.
240 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
foreign currency; (3) invest the call premiums at the risk-free rate.
10
The role of the
call option in h(s) is to increase the amount of foreign currency sold forward when
the exchange rate is high (s > 1). When the exchange rate is high expected foreign
production and foreign currency production costs are smaller. Net foreign currency
cash?ow is thus expected to be higher and forward sale of a larger quantity of
foreign currency is optimal.
3. Numerical example
For concreteness, this section presents a numerical example of the model for the
case of small ?xed costs. We assume that demands in the two markets x and x
?
are each distributed uniformly on the interval [0, 1], while the exchange rate s is
distributed uniformly on the interval [0, 2]. The unit sales price of the product p (=
p
?
) is 1 domestic currency unit and the unit production cost c (= c
?
) is
1
2
domestic
currency unit. We also assume that the ?rm has 2 units of total capacity that it can
distribute between the two markets and that ? = 1.
The variance of hedged pro?ts under the optimal ?nancial hedging policy for
each possible distribution of capacity is depicted in Figure 1. As demonstrated
in the previous section, the ?rm’s expected pro?t is maximized at the point of
equal capacity in each country. But notice that at that same point, the variance
of ?nancially hedged pro?ts is declining as foreign capacity is increased. We can
therefore conclude that the ?rm’s optimal choice of capacity is greater than 1, since
a local increase in foreign capacity beyond the equality point reduces the variance
of ?nancially hedged pro?ts while not affecting expected pro?ts (a local change in
a choice variable will not affect the value of a function at an interior maximum).
We also know that the optimal amount of foreign capacity is smaller than the
amount that minimizes the variance of ?nancially hedged pro?ts. We know this
because, as demonstrated earlier, expected pro?ts always decline as we move away
from the equal capacity point. And of course the variance of pro?ts increases
beyond the variance minimizing point. So the ?rm could not possibly gain from
choosing foreign capacity greater than the variance minimizing amount. For the
numerical values assumed in this example, the optimal amount of foreign capacity
turns out to be 1.06 units, 0.06 units greater than the expected pro?t maximizing
amount.
What form does the optimal ?nancial hedging policy take for this numerical
example? Figure 2 depicts the payoff on the optimal ?nancial hedge for the ?rm’s
optimal foreign capacity choice of 1.06 units. The hedge can be implemented by
selling 0.07 foreign currency units forward at a price of 1 unit of foreign currency
per unit of domestic currency, writing a call option contract on 0.33 units of foreign
currency at a price of 1 unit of foreign currency per unit of domestic currency, and
investing the call premium at the risk free rate.
10
Since Eh(s) = 0 and there is no credit risk, it, is clear that the present value of E max(s ?
1, 0)(E[y
?
|s ? 1] ? E[y
?
|s < 1]) equals the present value of Cov(s, y
?
).
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 241
Figure 1. Variance of pro?ts under optimal ?nancial hedging policy.
4. Implications
The model generates several implications that we now discuss.
Implication 1. The optimal ?nancial hedging contract is a forward contract to
sell the expected foreign currency cash ?ow if and, in general, only if the foreign
currency cash ?ow is independent of the exchange rate.
This implication follows directly from the optimal ?nancial hedging contract spec-
i?ed in (8). The intuition for this result is straightforward. The payoff on a forward
242 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
Figure 2. Payoff on optimal ?nancial contract.
contract on foreign currency is linear in the exchange rate. A forward contract will
optimally hedge the underlying exposure if the underlying exposure is also linear
in the exchange rate. When the foreign currency cash itself is contingent on the
exchange rate then the dollar value of it will, in general, be a non-linear function
of the exchange rate. Clearly, a ?nancial instrument that is also non-linear In the
exchange rate is needed to hedge the exposure.
Implication 2. The ?rm will engage in operational hedging only when both ex-
change rate uncertainty and demand uncertainty are present.
This is the key insight in the paper. It follows from expressions (11) and (18) in the
model. The intuition is clear. If there is no exchange rate uncertainty, the realized
prices and costs are identical in the two countries. The only residual uncertainty is
demand uncertainty which can be hedged only if we can create an instrument that
is correlated with demand; it cannot be hedged by operational production decisions
of the type considered in the paper. Now, consider the case when there is exchange
rate uncertainty but there is no demand uncertainty. In this case, the exchange rate
can be hedged entirely by using ?nancial contracts – i.e., forward contracts – which
obviates the need for relatively expensive operational hedging.
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 243
Implication 3. The ?rm is more likely to establish plants in both the domestic as
well as the foreign location if the ?xed costs of establishing a plant are lower or if
the variability in the exchange rate is higher.
Clearly, creating production ?exibility may be relatively expensive, as establishing
plants at two locations rather than one may involve additional ?xed costs. The
bene?ts of having multiple plants at different locations derive from two distinct
mechanisms. In the presence of demand uncertainty, the ?rm will often ?nd it
prudent to build aggregate capacity that can handle demand larger than the smallest
possible demand realization. As a result, there will often be situations in which the
?rm has excess capacity because demand is low. In these situations, the ?rm has the
option to switch production to the location where costs are lowest. Variability in ex-
change rates is precisely the mechanism that creates differences in costs over time
that the ?rm can take advantage of. In effect, the ?rm has a real option when there
is excess capacity. The value of this real option is increasing in the volatility of the
exchange rate. This is the expected cost effect. The second mechanism derives from
hedging considerations. It is precisely when the variability of the exchange rate is
higher that the variance of pro?ts will be higher and consequently the bene?ts of
hedging will be higher for a ?rm that is concerned about the variability of pro?ts
(for reasons discussed by the ?nance scholars mentioned in the introduction).
Implication 4. If the ?rm establishes plants in both the domestic as well as the
foreign location, the foreign currency cash ?ow will, in general; will not be inde-
pendent of the exchange rate and therefore the optimal ?nancial hedging contract
will not be a forward contract.
As we discussed above, creating plants at multiple locations creates production
?exibility in some instances when there is demand uncertainty. This production
?exibility can be exploited when cost differences arise. Movements in exchange
rates often create these cost differences. In these instances, the ?rm may switch
production to a low cost location, which in turn lowers foreign currency cash
?ow. Clearly then, foreign currency cash ?ow will not be independent of the ex-
change rate. As we discussed above, this results in an underlying exposure that is
non-linear in the exchange rate, making forward contracts unsuitable for optimal
hedging.
In the case of our model, the use of written option contracts in addition to
forward contracts allows implementation of the optimal hedging policy. Written
call options allow the ?rm to reduce the amount of foreign currency sold forward
when the the real value of the domestic currency appreciates. The reduction is
desirable because domestic currency appreciation induces the ?rm to shift more
production abroad, increasing expected foreign currency costs and thus lowering
expected net foreign currency cash?ow.
244 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
Implication 5. The ?rm is more likely to establish larger capacity in the foreign
location if the variability of foreign demand relative to the variability of domestic
demand is larger or if the expected pro?t margin is larger. If the variability of
foreign demand is equal to the variability of domestic demand, the ?rm will still
establish larger capacity in the foreign location as long as expected pro?t margin is
positive.
This is a key result in the paper that follows from the conditions (14) and (19) in
the model. Notice ?rst that it is not the relative size of the two markets – measured
by the ratio of expected demands in the two markets – that matters in determining
relative capacity at the two locations. The intuition, of course, is that even if say
the size of the foreign market is large but is certain, a ?nancial contract such
as a forward contract can adequately hedge the exposure, obviating the need for
building extra capacity for operational hedge. The size of the market would matter,
however, if there was variability in demand. So, in some sense, both the percent
variability and the size of the market jointly matter since it is the product of these
that determines the total variability in demand. Second, notice that when the two
markets are identical in terms of total variability in demand, the optimal solution
for capacity however is not symmetric. In this situation, the optimal solution will
yield either larger capacity at the foreign location (for the small ?xed costs case)
or the entire capacity at the foreign location (for the large ?xed costs case) as long
as expected pro?t margin is positive (i.e., p > c). The intuition for this asymmetry
is as follows. Since the price per unit of the good exceeds the per unit cost at
the foreign location (and at the domestic location as well), sales revenues cannot
be hedged perfectly by one-to-one matching of the quantity sold and the quantity
produced; the pro?t margin results in a residual foreign currency cash ?ow. The
?rm will need to produce a quantity larger than the quantity sold at the foreign
location in order to align total costs with total revenues in the foreign currency.
The larger the difference between the sale price and the unit cost, the larger will be
this asymmetry.
5. Conclusion
The key insight that we develop in the paper is that corporations will engage in
operational hedging only when both exchange rate uncertainty and demand uncer-
tainty are present. Firms whose main products are commodities – e.g., oil, copper,
grains – are exposed only to price uncertainty not quantity uncertainty. Further-
more, the relevant prices, such as the spot prices of the commodities as well as
the exchange rates, cannot be manipulated by any single ?rm. It follows from our
analysis that we would expect such ?rms to hedge their exposure using mainly
?nancial instruments; operational hedging by such ?rms would be rare. Some
survey evidence in Bodnar, Hayt, Marston and Smithson (1995) indicates that the
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 245
percentage of ?rms that use ?nancial derivatives for hedging is the highest for ?rms
that are classi?ed as Commodity Based than for ?rms in any other classi?cation.
Our insight is also consistent with the empirical observation that ?rms often
seem to use ?nancial instruments to hedge short-term exposure but not long-term
exposure. It seems plausible that demand uncertainty will be smaller for shorter
horizons than for longer horizons as ?rms will be able to forecast their sales more
accurately in the short term. Our analysis thus predicts that ?rms are likely to use
?nancial instruments to a greater extent to hedge short term exposure and rely on
operational hedging more heavily to hedge long term exposure.
Our model provides several other testable implications. We leave it to future
research to generalize our results and to empirical test its predictions. We believe
that the analysis in our paper has demonstrated that a framework in which ?nancial
as well as operational hedging decisions of ?rms are analyzed in a uni?ed frame-
work is likely to produce a rich set of positive as well as normative implications
for hedging policies of multinational corporations.
References
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Backwardation and the Coordination of Plans, Working Paper No. 71A, Columbia University
Graduate School of Business.
Bodnar, Gordon M., Hayt, Gregory S., Marston, Richard C., and Smithson (1995) Wharton survey
of derivatives usage by U.S. Non-Financial Firms, Financial Management 24, 104–114.
Chowdhry, Bhagwan (1995) Corporate hedging of exchange risk when foreign currency cash ?ow is
uncertain, Management Science 41, 1083–1090.
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Variability, Working Paper, AGSM-UCLA.
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accounting, Review of Financial Studies 8, 743–771.
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risk, Financial Management 54–62.
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Finance, Seventh Edition, Addison Wesley Publishing Company.
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corporate investment and ?nancing policies, Journal of Finance 48, 1629–1658.
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management, Harvard Business Review, November–December 1994, 91–102.
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246 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
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doc_286438281.pdf
Under what conditions will a multinational corporation alter its operations to manage its risk exposure? We show that multinational firms will engage in operational hedging only when both exchange rate uncertainty and demand uncertainty are present. Operational hedging is less important for managing short-term exposures, since demand uncertainty is lower in the short term.
European Finance Review 2: 229–246, 1999.
© 1999 Kluwer Academic Publishers. Printed in the Netherlands.
229
Corporate Risk Management for Multinational
Corporations: Financial and Operational Hedging
Policies
BHAGWAN CHOWDHRY
1
and JONATHAN T. B. HOWE
2,
1
The Anderson School at UCLA, 110 Westwood Plaza, Los Angeles, CA 90095-1481, USA; Phone:
(310)-825-5883; Fax: (310)-206-5455; E-mail: [email protected];
2
Hotchkis and
Wiley, Division of Merrill Lynch Capital Management Group, Los Angeles; Phone: (213)-362-8949;
E-mail: jonathan [email protected].
Abstract. Under what conditions will a multinational corporation alter its operations to manage its
risk exposure? We show that multinational ?rms will engage in operational hedging only when both
exchange rate uncertainty and demand uncertainty are present. Operational hedging is less important
for managing short-term exposures, since demand uncertainty is lower in the short term. Opera-
tional hedging is also less important for commodity-based ?rms, which face price but not quantity
uncertainty. When the ?xed costs of establishing a plant are low or the variability of the exchange
rate is high, a ?rm may bene?t from establishing plants in both the domestic and foreign location.
Capacity allocated to the foreign location relative to the domestic location will increase when the
variability of foreign demand increases relative to the variability of domestic demand or when the
expected pro?t margin is larger. For ?rms with plants in both a domestic and foreign location, the
foreign currency cash ?ow generally will not be independent of the exchange rate and consequently
the optimal ?nancial hedging policy cannot be implemented with forward contracts alone. We show
that the optimal ?nancial hedging policy can be implemented using foreign currency call and put
options and forward contracts.
1. Introduction
Multinational corporations often sell products in various countries with prices de-
nominated in corresponding local currencies. It is widely recognized that as the
volatility in exchange rates has increased dramatically after the breakdown of the
Bretton Woods system of ?xed exchange rates (see Smith, Smithson and Wilford
(1990)), multinational corporations may have become increasingly vulnerable to
We thank participants at the March 1996 conference on corporate Risk Management in honor
of Fischer Black at the Anderson School at UCLA, the June 1996 meetings of the Western Finance
Association at Sunriver, Oregon, and the 1997 meetings of the European Finance Association in
Vienna, Austria for helpful comments on earlier drafts. We are especially grateful for the suggestions
of John Parsons, Sugato Bhattacharya and an anonymous referee.
The views expressed in this article are the personal views of the authors and do not represent
the of?cial views of Hotchkis and Wiley or Merrill Lynch.
230 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
exchange risk since the short term movements in exchange rates are often not
accompanied by offsetting changes in prices in the corresponding countries (see
Shapiro (1992), for example).
Of course, in perfect capital markets, corporations need not hedge exchange
risk at all since investors can do it on their own (see Aliber (1978)). Market im-
perfections, such as taxes, agency problems, asymmetric information, dead-weight
costs associated with ?nancial distress, however, may provide incentives for cor-
porations to hedge the exchange risk (see Dufey and Srinivasulu (1983), Stulz
(1984), Shapiro and Titman (1985), Smith and Stulz (1985), Froot, Scharfstein and
Stein (1992) and DeMarzo and Duf?e (1995)). A number of ?nance scholars and
practitioners have discussed how ?rms could use ?nancial instruments to hedge
?nancial price risk (see, among others, Giddy (1983), Lewent and Kearney (1990),
Smith, Smithson and Wilford (1990), Froot, Scharfstein and Stein (1994) and two
popular textbooks Shapiro (1992) and Eiteman, Stonehill and Moffett (1995)).
In addition to using ?nancial contracts, a ?rm could manage its risk exposure
through operational hedging. An example of an operational hedging policy would
be to locate production in a country where signi?cant sales revenues in the local
(i.e., foreign) currency are expected. The effect of unexpected changes in exchange
rates and foreign demand conditions on domestic currency value of sales revenues
is hedged by similar changes in the the domestic currency value of local production
costs. Operational hedging motives thus may provide a reason for direct foreign
investment by ?rms and may further explain the existence of multinational ?rms
with production facilities at several foreign locations.
When should a multinational corporation adopt ?nancial hedging policies to
manage risk? Under what conditions should it resort to operational hedging? When
should it use both simultaneously and what should be the extent of each type of
policy? A systematic analysis of these questions, to our knowledge, does not exist
in the literature. This paper attempts to ?ll this gap.
The costs of implementing a ?nancial hedge are likely to be an order of magni-
tude smaller than those of implementing an operational hedge. After all, in order to
implement an operational hedge, a ?rm may be required to open a production plant
in another country whereas to implement a ?nancial hedge may simply require a
phone call to the ?rm’s bank. What could, then, be the advantages of operational
hedging policies?
If the quantity of foreign currency revenues the ?rm is expected to generate is
certain, it is easy to hedge the exchange risk exposure associated with it by using a
forward contract for that certain quantity. This eliminates the associated transaction
exposure completely with a relatively simple ?nancial hedge. However, ?uctuating
foreign currency cash ?ow represents an additional source of uncertainty for many
multinationals. For certain products, demand conditions can swing dramatically
from year to year, inducing large changes in foreign currency revenues. If the
quantity of foreign currency revenues is uncertain (and not perfectly correlated
with the exchange rate), no ?nancial contract (that must be agreed upon ex ante)
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 231
that is contingent only on ex post observable and non-manipulable variables such
as the exchange rate, can completely eliminate the exchange risk.
1
We argue that
one of the advantages of an operational hedge is that it allows the ?rm to align
domestic currency production costs and revenues more closely. It is as if the ?rm
had a forward contract whose quantity is contingent upon sales in the foreign
country. Clearly, this dominates a ?xed quantity forward contract. An operational
hedge, by aligning local costs with local revenues amounts to self-insurance by the
?rm against demand uncertainty; market insurance for demand uncertainty is not
feasible because of the severe moral hazard problem since sales can be manipulated
by the ?rm.
Unlike ?nancial hedging contracts, a ?rm’s operational policies are likely to
affect expected pro?ts. For example, having plants in several countries allows
the ?rm to shift some production to the location where costs, after observing the
exchange rate movements, are the smallest in domestic currency terms. Creating
this production ?exibility may have a positive expected payoff. This bene?t has
been discussed in the literature (see Dasu and Li (1994) and the textbooks Shapiro
(1992) and Eiteman, Stonehill and Moffett (1995)). Production ?exibility may also
affect the variance of pro?ts, an effect that has been neglected in the literature. We
contend that ?rms concerned with managing risk will want to take this hedging
effect into account, and are likely to adopt operational policies that differ from
those that maximize expected pro?ts.
Mello, Parsons, and Triantis (1995) consider the design of an optimal ?nancial
hedging policy for a multinational with production ?exibility. Financial hedging
helps alleviate the agency problem associated with the ?rm’s outstanding debt and
moves equity owners to closer to the ?rst best operating policy. Mello, Parsons, and
Triantis analyze a model in which exchange rate movements are the only source of
risk. In such a setting, production ?exibility raises ?rm value but does not confer a
hedging bene?t. We examine a setting in which there is also uncertainty regarding
the quantity of foreign currency cash?ow It is this additional source of risk that
creates a risk management rationale for production ?exibility.
We develop a formal model in the following section to analyze the issues dis-
cussed above. For concreteness, Section 3 then presents a numerical example of
the model. Implications of the model are discussed in Section 4, which is followed
by some concluding remarks.
2. The model
Consider a ?rm based in the U.S. that produces a single good for sale at a fu-
ture date (time 1) in a foreign market. Demand for the good at time 1, denoted
1
Chowdhry (1995) and Kerkvliet and Moffett (1991) analyze optimal ?nancial hedging policies
for multinational ?rms facing uncertain future foreign currency cash ?ow. However, they focus on ?-
nancial hedging policies and do not consider the possibility of operational hedging. Earlier treatments
of hedging under price and quantity uncertainty include Anderson and Danthine (1978).
232 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
x ? [0, x
max
] in the U.S. and x
?
? [0, x
?
max
] in the foreign market, is uncertain
at time 0. There is no demand for the good after time 1. The time 0 exchange
rate between the two currencies is normalized to 1. Let s denote the time 1 price
of one unit of foreign currency in terms of domestic currency units. For simplic-
ity, we normalize E
?
are stochastically
independent. Let p and p
?
denote the sale prices of the good in the U.S. and in
the foreign market respectively. The assumption of stochastic quantities sold at
exogenously ?xed prices can be rationalized as a result of a ?rm facing (downward
sloping) demand curves whose locations are uncertain at the time of setting prices.
Similarly let c and c
?
denote per unit costs of production in the U.S. and the foreign
location respectively. For simplicity and analytical tractability, we assume that per
unit sale prices and costs at time 1 are known with certainty at time 0. We further
normalize p = p
?
> c = c
?
so that there are no expected differences ex ante in
sale prices and marginal costs at the two locations.
At time 0, the ?rm decides to build plants with capacities k and k
?
respectively
at the U.S. and the foreign location. We assume that the total capacity is enough
to meet the maximum demand at the two locations, i.e., k + k
?
= x
max
+ x
?
max
. At
time 1, the ?rm can produce up to its capacity at each location. Let q and q
?
denote
the quantities of the good produced at each location at time 1 to satisfy the total
demand.
2
Thus,
q + q
?
= x + x
?
. (1)
Let y and y
?
denote the cash ?ows in US$ and the foreign currency respectively.
Then,
y = px ? cq, (2)
y
?
= px
?
? cq
?
. (3)
The ?rm’s pro?ts (excluding any ?xed costs of establishing plants), without any
?nancial hedging contract, at time 1, thus can be written as:
? = y + sy
?
. (4)
There are some features of our setup that may appear restrictive at ?rst glance.
First, it would be more natural to assume downward sloping demand curves where
?rms can set prices after observing the demand conditions at each location. Second,
?rms may be able to adjust the prices charged at each location after observing
the exchange rate s.
3
Third, one could specify more general cost functions in
2
It will be optimal to satisfy total demand if p/c ? s ? c/p. If this condition does not always
hold, then under certain circumstances meeting demand fully in one of the markets is not optimal.
Consideration of this additional “abandonment” option would complicate the analysis somewhat and
not affect the basic results.
3
These were brought up by the referee commenting on an earlier draft.
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 233
which costs are increasing and convex in quantities produced and decreasing in
the installed capacities at each location.
An important feature that we are trying to capture in our model is uncertainty
about the quantity of foreign currency cash ?ow y
?
. Our setup allows us to capture
this uncertainty in a particularly tractable manner since revenues at each location
(in local currencies), px and px
?
, are independent of the exchange rate s. This
makes domestic currency value of revenues at the foreign location, spx
?
, sensitive
to foreign exchange rate ?uctuations which is another feature that we are trying
to capture in our model. Generalizing the model in which prices are set after
observing the demand states at each location as well as the exchange rate will
preserve the features that cash ?ow in foreign currency y
?
will be uncertain and the
domestic currency value of revenues at the foreign location, sp
?
x
?
will be sensitive
to the exchange rate ?uctuations (except in some very special and restrictive cases
4
but the local currency revenues at each location, px and p
?
x
?
will no longer be
independent of the exchange rate. This complicates the model and makes it some-
what cumbersome. But, as we shall later explain, the central results of the paper
are likely to go through in a much richer framework that accomodates some of the
generalizations.
5
At time 0 the ?rm may enter into forward and option contracts on the time 1
exchange rate. The use of both forwards and options allows the ?rm to construct
a ?nancial hedging instrument whose payoff is any arbitrary (possibly nonlinear)
function of the time 1 exchange rate. Let h(s) denote the time 1 payoff on this
contract. Assume that the ?rm has a competitive risk-neutral counterparty and that
the contract has no credit risk so that Eh(s) = 0. The ?rm’s pro?ts at time 1 with
the ?nancial hedging contract can be written as:
?
h
= ? + h(s).
We assume that the ?rm is a mean variance optimizer so that its objective
function takes the form
E[?
h
] ?
?
2
Var[?
h
].
Since the expected payoff on any ?nancial hedge contract is zero, the optimal
?nancial hedge contract solves
Min
h(s)
Var[? + h(s)] s.t. Eh(s) = 0.
4
For instance, if the ?rm faces demand curves with constant elasticities and is able to pass on
the exchange rate changes completely in its pricing decisions, the domestic currency value of its
revenues in the foreign market may be completely insensitive to exchange rate changes. In this paper,
our focus is on situations when ?rms face signi?cant exchange rate exposure in revenues generated
at the foreign location.
5
We will he more precise later about the exact nature of these generalizations.
234 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
Writing the Lagrangian, we get
L = EE[?
2
+ 2?h(s) + h(s)
2
|s] ? (E?)
2
? ?Eh(s),
where ? denotes the Lagrangian multiplier. Rearranging, we get
L = EE[?
2
+ 2?h(s) + h(s)
2
? ?h(s)|s] ? (E?)
2
.
The ?rst order condition for the minimum gives
h(s) =
?
2
? E[?|s].
Imposing the constraint that Eh(s) = 0, we get ?/2 = E[?]. The optimal ?nancial
hedging contract thus is given by:
h(s) = E[?] ? E[?|s]. (5)
The expression for ? in (4) can be rewritten as:
? = (y + y
?
) ? (1 ? s)y
?
. (6)
From (1)–(3),
y + y
?
= p(x + x
?
) ? c(q + q
?
) = (p ? c)(x + x
?
). (7)
Notice that y +y
?
is independent of s. Substituting from (6) into (5) and simplify-
ing, the optimal ?nancial hedging contract can be rewritten as
h(s) = (1 ? s)E[y
?
|s] + Cov(s, y
?
). (8)
Notice that if the foreign currency cash ?ow y
?
is independent of the exchange
rate realization s, the optimal ?nancial hedging contract is a forward contract in
which the ?rm sells a quantity of foreign currency equal to Ey
?
in the forward
exchange market. But, if y
?
is not independent of s, then in general, the optimal
?nancial hedging contract will not be a forward contract but some claim that is
non-linearly contingent on s.
The ?rm’s pro?ts at time 1 with the ?nancial hedging contract can now be
rewritten as:
?
h
= (y + y
?
) ? (1 ? s){y
?
? E[y
?
|s} + Cov(s, y
?
). (9)
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 235
2.1. CASE 1: LARGE FIXED COSTS
Suppose that there are large ?xed costs associated with establishing a plant so that
the ?rm will choose to establish a plant at only one location. Then there are two
possibilities:
1. The ?rm establishes the plant domestically. In this case:
q = x + x
?
, q
?
= 0.
2. The ?rm establishes the plant at the foreign location. In this case:
q = 0, q
?
= x + x
?
.
In either case, since q
?
is independent of the realization of s, the foreign cur-
rency cash ?ow y
?
will also be independent of s. The optimal hedge contract in (8)
then simpli?es to
h(s) = (1 ? s)Ey
?
.
If Ey
?
> 0, this is a contract to sell forward Ey
?
units of foreign currency at a
price of 1 unit of domestic currency per unit of foreign currency. If Ey
?
< 0 then
the contract would involve purchasing forward Ey
?
foreign currency units at the
same price.
The ?rm’s pro?ts after ?nancial hedging, speci?ed in (9), simplify to
?
h
= (y + y
?
) ? (1 ? s)[y
?
? Ey
?
]. (10)
Notice that the expected hedged pro?ts (from (7))
E?
h
= E(y + y
?
) = (p ? c)E(x + x
?
)
are the same whether the ?rm locates its plant domestically or at the foreign loca-
tion. The decision of where to locate the plant, therefore, is determined solely by
which location leads to a smaller variance of hedged pro?ts. From (10),
Var[?
h
] = Var(y + y
?
) + Var s Var y
?
. (11)
First, from (7), we notice that Var(y + y
?
) is independent of the plant location
decision. Second, the location decision – which is the operational hedging decision
– matters only if both Var s as well as Var y
?
are not equal to zero. This indicates
that operational hedging decisions matter only when there is both exchange rate
uncertainty and quantity uncertainty. Given Var s, the plant location decision is
determined by which location leads to a smaller Var y
?
.
1. If the ?rm establishes the plant domestically,
y
?
= px
?
, Var y
?
= p
2
Var x
?
. (12)
236 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
2. If the ?rm establishes the plant at the foreign location,
y
?
= px
?
? c(x + x
?
),
Var y
?
= p
2
Var x
?
+ c
2
Var(x + x
?
) ? 2pc Cov(x
?
, x + x
?
). (13)
The ?rm will choose to produce at the foreign location if and only if the expres-
sion in (12) exceeds the one in (13) or equivalently if:
p
2
Var x
?
> p
2
Var x
?
+ c
2
Var x + c(c ? 2p) Var x
?
.
The above condition simpli?es to:
1 + 2
p ? c
c
Var x
?
Var x
> 1. (14)
The ?rst term on the left hand side of the above condition is positively and
linearly related to expected pro?tability and the second term represents relative
total variability of foreign demand to total variability of domestic demand.
2.2. CASE 2: SMALL FIXED COSTS
Now suppose that the ?xed costs of establishing a plant with a given capacity are
small enough so that the ?rm is indifferent between dividing the total capacity
between plants at two locations based only on the costs of establishing the plants.
Suppose that at time 0, the ?rm decides to build plants with capacities k and k
?
respectively at the U.S. and the foreign location. At time 1, the ?rm can produce
up to its capacity at each location.
Based on the realization of the exchange rate, the ?rm, in order to satisfy de-
mand, will produce as much as possible at the location where it is cheaper to do so.
If the exchange rate s > 1, it is cheaper to produce domestically. If the total demand
is less than the domestic capacity, the ?rm will produce everything domestically.
If the total demand exceeds the domestic capacity, the ?rm will produce up to its
capacity domestically and produce the rest at the foreign location. Similarly, if
s < 1 it is cheaper to produce at the foreign location and analogous production
decisions will be made by the ?rm. The quantities produced at each location are
thus:
(q, q
?
) =
?
?
?
?
?
?
?
(k, x + x
?
? k) if x + x
?
> k, s > 1
(x + x
?
, 0) x + x
?
< k, s > 1.
(x + x
?
? k
?
, k
?
) x + x
?
> k
?
, s < 1
(0, x + x
?
) x + x
?
< k
?
, s < 1
(15)
Suppose the ?rm chooses the capacities at time 0 to maximize expected pro?ts,
i.e., suppose it chooses k to maximize E?
h
which is equivalent to maximizing E?.
The ?rst order condition is:
d
dk
E? = E
d?
dk
= E
dy
dk
+ s
dy
?
dk
= 0. (16)
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 237
Now, from (2) and (3),
dy
dk
= ?c
dq
dk
,
dy
?
dk
= ?c
dq
?
dk
,
Thus, from (15),
dy
dk
,
dy
?
dk
= ?c
?
?
?
?
?
?
?
(1, ?1) if x + x
?
> k, s > 1
(0, 0) x + x
?
< k, s > 1.
(1, ?1) x + x
?
> k
?
, s < 1
(0, 0) x + x
?
< k
?
, s < 1
Therefore,
d?
dk
= ?c
?
?
?
?
?
?
?
1 ? s if x + x
?
> k, s > 1
0 x + x
?
< k, s > 1.
1 ? s x + x
?
> k
?
, s < 1
0 x + x
?
< k
?
, s < 1
It is clear that the ?rst order condition in (16) is satis?ed if k = k
?
. In other words,
if the ?rm were concerned only with maximizing expected pro?ts it would divide
the capacity equally between the two plants.
6
We will call this solution the benchmark solution that does not take into con-
sideration any hedging considerations. But what if the ?rm were also concerned
about the variance of its pro?ts? We will now see that hedging considerations will,
in general, move the ?rm away from choosing equal capacity. This deviation from
the benchmark capacity solution is tantamount to operational hedging.
Whether the ?rm chooses a larger domestic or foreign capacity compared to
the bench-mark solution of equal capacity depends on the sign of the following
expression:
d
dk
Var ?
h
= 2E
?
h
d?
h
dk
. (17)
6
The ?rst order condition is suf?cient for a maximum because expected pro?ts are globally
concave in k, provided the distribution of s is symmetric. If s is distributed symmetrically then
E
d
2
?
dk
2
=
c
2
E[s ? 1|s > 1]
?
dF(k)
dk
+
dF(k
?
)
dk
< 0,
where F is the joint probability distribution function for x and x
?
(assumed to be differentiable).
238 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
The right hand side of the above equation obtains since d/dk E?
h
= 0.
7
The
expression in (17), after simplifying, equals:
2E
(1 ? s)
2
d
dk
Var(y
?
|s)
. (18)
The ?rm will choose a larger foreign capacity if the sign of the above expression
is positive. As in the case in the previous subsection, the above expression will
equal zero if either there is no exchange rate uncertainty or if there is no quantity
uncertainty. Thus operational hedging decisions matter only when there is both
exchange rate uncertainty and quantity uncertainty.
8
7
The above condition obtains in general, not just in the setup we have developed in our model.
8
This result obtains even in a more general framework that we now describe more precisely.
Notice that the hedged pro?ts can in general be written as follows:
?
h
= y + sy
?
+ E(y + sy
?
) ? E(y + sy
?
|s).
The condition in (17) can be expanded as:
E
?
h
d?
h
dk
= E
{y ? E(y|s)}
d
dk
{y ? E(y|s)}
+E
s
2
{y
?
? E(y
?
|s)}
d
dk
{y
?
? E(y
?
|s)}
+E
s{y ? E(y|s)}
d
dk
{y
?
? E(y
?
|s)}
+E
s{y
?
? E(y
?
|s)}
d
dk
{y ? E(y|s)}
Notice that in any general framework in which the parameters in the two countries are symmetric,
and the distribution of the exchange rate s is symmetric around its mean of 1, the last two terms will
cancel each other and the ?rst term:
E
{y ? E(y|s)}
d
dk
{y ? E(y|s)}
= ?E
{y
?
? E(y
?
|s)}
d
dk
{y
?
? E(y
?
|s)}
.
Making these substitutions and simplifying, we obtain:
E
?
h
d?
h
dk
= E
(s
2
? 1){y
?
? E(y
?
|s)}
d
dk
{y
?
? E(y
?
|s)}
= E(s
2
? 1)E
d
dk
Var(y
?
|s)
+ Cov
(s
2
? 1),
d
dk
Var(y
?
|s)
= Var(s)E
d
dk
Var(y
?
|s)
+ Cov
(s
2
? 1),
d
dk
Var(y
?
|s)
.
Notice that if there is no exchange rate uncertainty the above expression equals zero. We know that
d/dk Var(y
?
|s) is positive because increasing domestic capacity implies that the ?rmproduces less at
its foreign location which increases the variability of pro?ts in the foreign currency. Therefore, when
Var(s) > 0, the ?rst term in the expression above is positive. The second covariance term will be
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 239
The above expression can be further rewritten as:
2E
(1 ? s)
2
d
dk
{p
2
Var x
?
+ c
2
Var[q
?
|s] ? 2pc Cov[x
?
, q
?
|s]}
.
If Prob[s > 1] = Prob[s < 1] and E[(1 ? s)
2
|s > 1] = E[(1 ? s)
2
|s < 1] – a
suf?cient condition for these is that the distribution of s be symmetric around its
mean of 1 – then the sign of the above expression is positive if and only if:
1 + 2
p ? c
c
E[x
?
|x + x
?
> k] ? Ex
?
E[x|x + x
?
> k] ? Ex
> 1. (19)
Notice the similarity between the above condition to the condition in (14).
The ?rst term on the left hand side of the above condition – which is identical
to the corresponding term in (14) – is positively and linearly related to expected
pro?tability. The second term in (19) is analogous to the corresponding term in
(14) and represents relative variability of foreign demand to variability of domestic
demand.
In addition to operational hedging, the ?rmwill also engage in ?nancial hedging
through the contract speci?ed in (8). This contract can be constructed using forward
and option contracts. Option contracts must be used because E[y
?
|s] in (8) depends
on s. Speci?cally the conditional expectation can take two values: E[y
?
|s ? 1] and
E[y
?
|s < 1], with E[y
?
|s ? 1] > E[y
?
|s < 1]. The optimal ?nancial hedging
contract is therefore
h(s) = (1 ? s)E[y
?
|s ? 1] + Cov(s, y
?
) s ? 1,
h(s) = (1 ? s)E[y
?
|s < 1] + Cov(s, y
?
) s < 1.
This expression can be rewritten
h(s) = (1 ? s)E[y
?
|s < 1] ? max(s ? 1, 0)
× (E[y
?
|s ? 1] ? E[y
?
|s < 1]) + Cov(s, y
?
).
From the above expression it is evident that a simple method of constructing h(s)
is for the ?rm to: (1) “sell” forward E[y
?
|s < 1] units of the foreign currency at
a price of 1 unit of domestic currency for each unit of foreign currency;
9
(2) write
European call options exercisable at date 1 with a strike price of 1 unit of domestic
currency for each unit of foreign currency on E[y
?
|s ? 1] ? E[y
?
|s < 1] units of
positive if d/dk Var(y
?
|s) is not decreasing in s which is likely under fairly general circumstances.
The intuitive interpretation is as follows. The increase in variability of foreign currency pro?ts as the
?rm increases its domestic capacity is more pronounced when the exchange rate is high because the
?rm shifts its production to the domestic location even more.
9
If E[y
?
|s < 1] < 0, then the transaction is a forward purchase.
240 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
foreign currency; (3) invest the call premiums at the risk-free rate.
10
The role of the
call option in h(s) is to increase the amount of foreign currency sold forward when
the exchange rate is high (s > 1). When the exchange rate is high expected foreign
production and foreign currency production costs are smaller. Net foreign currency
cash?ow is thus expected to be higher and forward sale of a larger quantity of
foreign currency is optimal.
3. Numerical example
For concreteness, this section presents a numerical example of the model for the
case of small ?xed costs. We assume that demands in the two markets x and x
?
are each distributed uniformly on the interval [0, 1], while the exchange rate s is
distributed uniformly on the interval [0, 2]. The unit sales price of the product p (=
p
?
) is 1 domestic currency unit and the unit production cost c (= c
?
) is
1
2
domestic
currency unit. We also assume that the ?rm has 2 units of total capacity that it can
distribute between the two markets and that ? = 1.
The variance of hedged pro?ts under the optimal ?nancial hedging policy for
each possible distribution of capacity is depicted in Figure 1. As demonstrated
in the previous section, the ?rm’s expected pro?t is maximized at the point of
equal capacity in each country. But notice that at that same point, the variance
of ?nancially hedged pro?ts is declining as foreign capacity is increased. We can
therefore conclude that the ?rm’s optimal choice of capacity is greater than 1, since
a local increase in foreign capacity beyond the equality point reduces the variance
of ?nancially hedged pro?ts while not affecting expected pro?ts (a local change in
a choice variable will not affect the value of a function at an interior maximum).
We also know that the optimal amount of foreign capacity is smaller than the
amount that minimizes the variance of ?nancially hedged pro?ts. We know this
because, as demonstrated earlier, expected pro?ts always decline as we move away
from the equal capacity point. And of course the variance of pro?ts increases
beyond the variance minimizing point. So the ?rm could not possibly gain from
choosing foreign capacity greater than the variance minimizing amount. For the
numerical values assumed in this example, the optimal amount of foreign capacity
turns out to be 1.06 units, 0.06 units greater than the expected pro?t maximizing
amount.
What form does the optimal ?nancial hedging policy take for this numerical
example? Figure 2 depicts the payoff on the optimal ?nancial hedge for the ?rm’s
optimal foreign capacity choice of 1.06 units. The hedge can be implemented by
selling 0.07 foreign currency units forward at a price of 1 unit of foreign currency
per unit of domestic currency, writing a call option contract on 0.33 units of foreign
currency at a price of 1 unit of foreign currency per unit of domestic currency, and
investing the call premium at the risk free rate.
10
Since Eh(s) = 0 and there is no credit risk, it, is clear that the present value of E max(s ?
1, 0)(E[y
?
|s ? 1] ? E[y
?
|s < 1]) equals the present value of Cov(s, y
?
).
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 241
Figure 1. Variance of pro?ts under optimal ?nancial hedging policy.
4. Implications
The model generates several implications that we now discuss.
Implication 1. The optimal ?nancial hedging contract is a forward contract to
sell the expected foreign currency cash ?ow if and, in general, only if the foreign
currency cash ?ow is independent of the exchange rate.
This implication follows directly from the optimal ?nancial hedging contract spec-
i?ed in (8). The intuition for this result is straightforward. The payoff on a forward
242 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
Figure 2. Payoff on optimal ?nancial contract.
contract on foreign currency is linear in the exchange rate. A forward contract will
optimally hedge the underlying exposure if the underlying exposure is also linear
in the exchange rate. When the foreign currency cash itself is contingent on the
exchange rate then the dollar value of it will, in general, be a non-linear function
of the exchange rate. Clearly, a ?nancial instrument that is also non-linear In the
exchange rate is needed to hedge the exposure.
Implication 2. The ?rm will engage in operational hedging only when both ex-
change rate uncertainty and demand uncertainty are present.
This is the key insight in the paper. It follows from expressions (11) and (18) in the
model. The intuition is clear. If there is no exchange rate uncertainty, the realized
prices and costs are identical in the two countries. The only residual uncertainty is
demand uncertainty which can be hedged only if we can create an instrument that
is correlated with demand; it cannot be hedged by operational production decisions
of the type considered in the paper. Now, consider the case when there is exchange
rate uncertainty but there is no demand uncertainty. In this case, the exchange rate
can be hedged entirely by using ?nancial contracts – i.e., forward contracts – which
obviates the need for relatively expensive operational hedging.
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 243
Implication 3. The ?rm is more likely to establish plants in both the domestic as
well as the foreign location if the ?xed costs of establishing a plant are lower or if
the variability in the exchange rate is higher.
Clearly, creating production ?exibility may be relatively expensive, as establishing
plants at two locations rather than one may involve additional ?xed costs. The
bene?ts of having multiple plants at different locations derive from two distinct
mechanisms. In the presence of demand uncertainty, the ?rm will often ?nd it
prudent to build aggregate capacity that can handle demand larger than the smallest
possible demand realization. As a result, there will often be situations in which the
?rm has excess capacity because demand is low. In these situations, the ?rm has the
option to switch production to the location where costs are lowest. Variability in ex-
change rates is precisely the mechanism that creates differences in costs over time
that the ?rm can take advantage of. In effect, the ?rm has a real option when there
is excess capacity. The value of this real option is increasing in the volatility of the
exchange rate. This is the expected cost effect. The second mechanism derives from
hedging considerations. It is precisely when the variability of the exchange rate is
higher that the variance of pro?ts will be higher and consequently the bene?ts of
hedging will be higher for a ?rm that is concerned about the variability of pro?ts
(for reasons discussed by the ?nance scholars mentioned in the introduction).
Implication 4. If the ?rm establishes plants in both the domestic as well as the
foreign location, the foreign currency cash ?ow will, in general; will not be inde-
pendent of the exchange rate and therefore the optimal ?nancial hedging contract
will not be a forward contract.
As we discussed above, creating plants at multiple locations creates production
?exibility in some instances when there is demand uncertainty. This production
?exibility can be exploited when cost differences arise. Movements in exchange
rates often create these cost differences. In these instances, the ?rm may switch
production to a low cost location, which in turn lowers foreign currency cash
?ow. Clearly then, foreign currency cash ?ow will not be independent of the ex-
change rate. As we discussed above, this results in an underlying exposure that is
non-linear in the exchange rate, making forward contracts unsuitable for optimal
hedging.
In the case of our model, the use of written option contracts in addition to
forward contracts allows implementation of the optimal hedging policy. Written
call options allow the ?rm to reduce the amount of foreign currency sold forward
when the the real value of the domestic currency appreciates. The reduction is
desirable because domestic currency appreciation induces the ?rm to shift more
production abroad, increasing expected foreign currency costs and thus lowering
expected net foreign currency cash?ow.
244 BHAGWAN CHOWDHRY AND JONATHAN T. B. HOWE
Implication 5. The ?rm is more likely to establish larger capacity in the foreign
location if the variability of foreign demand relative to the variability of domestic
demand is larger or if the expected pro?t margin is larger. If the variability of
foreign demand is equal to the variability of domestic demand, the ?rm will still
establish larger capacity in the foreign location as long as expected pro?t margin is
positive.
This is a key result in the paper that follows from the conditions (14) and (19) in
the model. Notice ?rst that it is not the relative size of the two markets – measured
by the ratio of expected demands in the two markets – that matters in determining
relative capacity at the two locations. The intuition, of course, is that even if say
the size of the foreign market is large but is certain, a ?nancial contract such
as a forward contract can adequately hedge the exposure, obviating the need for
building extra capacity for operational hedge. The size of the market would matter,
however, if there was variability in demand. So, in some sense, both the percent
variability and the size of the market jointly matter since it is the product of these
that determines the total variability in demand. Second, notice that when the two
markets are identical in terms of total variability in demand, the optimal solution
for capacity however is not symmetric. In this situation, the optimal solution will
yield either larger capacity at the foreign location (for the small ?xed costs case)
or the entire capacity at the foreign location (for the large ?xed costs case) as long
as expected pro?t margin is positive (i.e., p > c). The intuition for this asymmetry
is as follows. Since the price per unit of the good exceeds the per unit cost at
the foreign location (and at the domestic location as well), sales revenues cannot
be hedged perfectly by one-to-one matching of the quantity sold and the quantity
produced; the pro?t margin results in a residual foreign currency cash ?ow. The
?rm will need to produce a quantity larger than the quantity sold at the foreign
location in order to align total costs with total revenues in the foreign currency.
The larger the difference between the sale price and the unit cost, the larger will be
this asymmetry.
5. Conclusion
The key insight that we develop in the paper is that corporations will engage in
operational hedging only when both exchange rate uncertainty and demand uncer-
tainty are present. Firms whose main products are commodities – e.g., oil, copper,
grains – are exposed only to price uncertainty not quantity uncertainty. Further-
more, the relevant prices, such as the spot prices of the commodities as well as
the exchange rates, cannot be manipulated by any single ?rm. It follows from our
analysis that we would expect such ?rms to hedge their exposure using mainly
?nancial instruments; operational hedging by such ?rms would be rare. Some
survey evidence in Bodnar, Hayt, Marston and Smithson (1995) indicates that the
CORPORATE RISK MANAGEMENT FOR MULTINATIONAL CORPORATIONS 245
percentage of ?rms that use ?nancial derivatives for hedging is the highest for ?rms
that are classi?ed as Commodity Based than for ?rms in any other classi?cation.
Our insight is also consistent with the empirical observation that ?rms often
seem to use ?nancial instruments to hedge short-term exposure but not long-term
exposure. It seems plausible that demand uncertainty will be smaller for shorter
horizons than for longer horizons as ?rms will be able to forecast their sales more
accurately in the short term. Our analysis thus predicts that ?rms are likely to use
?nancial instruments to a greater extent to hedge short term exposure and rely on
operational hedging more heavily to hedge long term exposure.
Our model provides several other testable implications. We leave it to future
research to generalize our results and to empirical test its predictions. We believe
that the analysis in our paper has demonstrated that a framework in which ?nancial
as well as operational hedging decisions of ?rms are analyzed in a uni?ed frame-
work is likely to produce a rich set of positive as well as normative implications
for hedging policies of multinational corporations.
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