I At the outset, a question should be answered concerning the motivation for hedging. It is often assumed that the motivation to hedge is risk reduction or
finding an optimal balance between risk and return. Hoffman (1932, p. 382) argued that "hedging is shifting risk". Smith (1922, p. 81) suggested that "hedging enables hedgers to insure against the risk of price fluctuations". Marshall (1919, p. 260) confirmed this view by stating that "the hedger does not speculate: he insures". Keynes (1930), Hicks (1939) and Kaldor (1939) discussed hedging in terms of risk avoidance. According to this view, any loss made by the hedger on the hedged transaction represents an insurance premium paid on the risk-assuming speculator. Blau (1944) defines hedging as the shifting of risk arising from unknown future changes in prices, which cannot be covered by means of ordinary insurance.
Working (1953a) challenged the idea of risk insurance by arguing that hedging is motivated by the desire to make profit by expecting the prospective movement of the prices of the assets to be hedged and those of the spot and hedging instruments. According to this view, hedging is some sort of arbitrage to be engaged in only when the hedger perceives a promising opportunity for profit. On the other hand, the portfolio theory stresses the risk-return trade-off. Stein (1961) and Johnson (1960) used the foundations of the portfolio theory as put forward by Markowitz (1959) to explain hedging. The hedger is viewed as maximising the expected utility derived from a portfolio of the asset and the hedging instrument. Williams (1986) challenged the portfolio theory by arguing that it is risk in operations that motivates hedging. Kamara (1982, p. 263) argues that hedging is motivated in part by the desire to stabilise income and in part by the desire to increase expected profits.
5.2 TO HEDGE OR NOT TO HEDGE?
In general, existing work suggests that firms hedge to reduce (i) the agency problem (Bessembrinder, 1991); (ii) effective corporate taxes (Smith and Stulz, 1985); (iii) risk aversion among managers and other contracting parties (Stulz, 1984); (iv) the probability of financial distress (Smith and Stulz, 1985); and (v) the adverse information content of earnings (De Marzo and Duffie, 1995). The theoretical explanations identified by these incentives for hedging are likely to benefit the contracting parties. However, hedging might not benefit all parties equally and, therefore, the hedging strategies of firms vary.
As documented by Rawls and Smithson (1990), hedging is considered by financial managers to be one of their primary objectives. However, there hardly exists a consensus view on whether a firm should or should not hedge. This debate involves two issues: (i) whether or not hedging is necessary, and (ii) whether hedging should be undertaken by the firm or by individual shareholders. We start with the first issue of whether or not hedging is indeed worthwhile.
First of all, there is the idea stipulating an inverse relationship between risk and shareholder value (for example, Bishop, 1996), implying that hedging can boost the value of the firm. However, this proposition is not universally accepted. In the 1950s Modigliani and Miller (1958) demonstrated, by coming up with the Modigliani-Miller Theorem, that the mode of financing does not determine the value of the firm. This conclusion implies that managing risk does not add to the value of the firm, and could even lower this value because the use of hedging instruments and techniques is not free of charge. A similar argument is that what matters for the valuation of the firm is systematic risk, whereas hedging may only reduce total risk. It follows once more that hedging may not add to the value of a firm. But some economists do not agree with this proposition. Froot et al. (1994) argue that firms should hedge to ensure that they always have cash flows to fund their planned investment programmes. Otherwise, some potentially profitable investments may be missed because of inefficiencies in the bond and equity markets, which are the alternative means of raising funds (as opposed to internal financing). Lewent and Kearney (1993) explained the strategy of Merck (an American pharmaceutical firm), using derivatives to ensure that R&D plans can always be financed. They argue that cash flows and earnings uncertainty caused by exchange rate volatility lead to a reduction in research spending. However, it is arguable that factors causing cash flows to fall below expectations may also cut the number of profitable investment opportunities, which reduces the need to hedge anyway.
Stulz (1995) argues that there are two reasons why a firm should hedge: the desire to cut its tax bill and because it is unable to get cash when it is needed. Thus, a firm with little or highly rated debt has no need to hedge, as the probability of getting into financial trouble is low. However, it can be argued that even firms with little debt can reduce their riskiness by hedging, and this enables them to borrow more and rely less on equity, which is more expensive.
An elaboration on Stulz's argument about tax is warranted. Under a progressive corporate tax system, stable before-tax earnings lead to lower taxes than volatile earnings with the same average value. This is because under a progressive tax system the firm pays more in high earning periods than it saves in low earning periods, which can be explained as follows. Suppose that the corporate income tax rate is t^ for earnings up to a certain level, y\, and t2 for anything higher than y\. Consider two firms, A and B. A does not hedge, and because of exchange rate fluctuations its expected income ranges between y\ and y2 (y2 > yt) with equal probabilities, such that y1 falls within the first tax bracket and y2 falls within the second bracket. Thus, A's expected tax payment is (t^y 1 + t2 y2 )/2. On the other hand, B always hedges its exposure and so its income is more certain at y3, which is equal to the expected value of A's income (y3 = (y\ + y2)/2) and falls within the first bracket. This means that the tax payment of B is t 1 y3 or t 1_(y 1 + y2 )/2. Thus, the firm's average tax bill can be reduced through hedging so that profits are reduced in good years and increased in bad years.
Another argument as to why hedging is unnecessary is that the effects of exchange rate fluctuations on a firm average out over the long run. Moosa (2002c) used historical data on three exchange rates (yen, mark and pound against the dollar) to demonstrate that if the exposure is recurrent, then over a long period of time hedging the exposure by using a forward contract will not produce results that are superior to those obtained by leaving the exposure unhedged. The explanation put forward for this result is that the unbiased efficiency hypothesis holds over a long period of time. Thus, although the forward rate may overestimate or underestimate the future spot rate in the short run, it gets it right on average in the long run. As we will find out later, forward hedging of the exposure means that foreign currency payables and receivables are converted at the forward rate, whereas leaving it unhedged means that payables and receivables are converted at the spot rate prevailing on the date when they become due. If, as the unbiased efficiency hypothesis stipulates, the current forward rate and the future spot rate are equal over a long period of time, it follows that the results will be similar with and without hedging. Indeed, given that the bid-offer spread in the forward market is wider than the spread in the spot market, leaving the exposure uncovered may be more profitable. However, Moosa warns of the hazard of interpreting this result to mean that exposure to foreign exchange risk should never be hedged. This result, it is stressed, holds only over a long period of time or on average. The story may be completely different in the short run or when the operation is not repeated frequently, thus not allowing the "on average" qualification to materialise. If, for example, a large exposure arises at a particular point in time, a significantly adverse exchange rate movement could wipe out the whole business, and there would no long run to count on.
This brings us to the general argument that if international parity conditions hold, there is no need to hedge exposure to foreign exchange risk. We have already considered the unbiased efficiency hypothesis, so we turn to uncovered interest parity (UIP) and ex ante purchasing power parity (PPP). If UIP holds then the (uncovered) foreign currency return will be equal to the base currency return (or the cost of borrowing), and hence the former is known with certainty. Any change in the exchange rate will be counterbalanced by a change in the interest rate differential in such a way as to keep returns at the same level. But the available empirical evidence indicates that deviations from UIP are significant, and hence the base currency value of the foreign return will not be known with certainty. Consequently, risk would arise.
If ex ante PPP holds, then real currency depreciations and appreciations will not occur. This is because changes in the nominal exchange rate will be counterbalanced by equivalent changes in prices. Again, the empirical evidence shows that deviations from PPP in the short run are large and persistent. But even if that was the case, it is unusual for the firm's individual costs and revenues to move proportionately with inflation. Hence economic exposure would arise.
In general, international parity conditions hold, at best, in the long run if at all, and the long run can be very long indeed, as in the case of PPP. In the short run, deviations from the conditions are significant and persistent. The empirical failure of international parity conditions is that foreign exchange risk is alive and kicking.
The other argument why hedging may not be necessary is that if it is possible to forecast exchange rates then there is no need to hedge exposure to foreign exchange risk. However, it has for a long time been established (by both academics and practitioners) that forecasting exchange rates is a rather difficult task (see, for example, Moosa, 2000a). Some views even point to the near impossibility of forecasting exchange rates because they are driven by "news", which is unpredictable by definition. The empirical failure of unbiased efficiency and UIP implies that foreign exchange risk cannot be controlled by using the forward rate or the interest differential as forecasters of the future spot rate. Similarly, we cannot control foreign exchange risk by using any other forecaster, since the accuracy of the forecasts is questionable, to say the least.
An argument why hedging is important is that it results in a more stable income stream (as we have seen before), which has several benefits. It may be conducive to sales in the case of consumer durables and capital goods. This is because a stable income may give the impression that the firm will last for long enough to provide after-sale services. On the other hand, volatile earnings may cause a high degree of employee turnover or demands for higher wages if they are interpreted to imply lack of job security.
Now we turn to the second issue involving the argument that hedging at the firm level is redundant because shareholders are naturally hedged through diversification. Some of the arguments for hedging that we have discussed so far are relevant to this issue, but the following are more relevant. These include: (i) information asymmetry, (ii) differential transaction costs and (iii) default costs. Hedging should be carried out at the firm level based on arguments pertaining to (i), (ii) and (iii). First, the management knows better about the firm's exposure position than shareholders. Second, the firm is in a position to acquire low-cost hedges, whereas individual shareholders can hedge only at a substantial cost, and some investors may not be willing or able to hold diversified portfolios. Third, if default costs are significant, corporate hedging would be justifiable, because it would reduce the probability of default.
Having gone through the arguments for and against hedging, it is time to find out whether or not firms hedge in practice. Culp and Miller (1995) argue that most value-maximising firms do not hedge. But surveys of big US non- financial firms conducted by the Wharton School and Chase Manhattan Bank found that 75% of the firms that use derivatives do so to hedge their commitments. Forty per cent of the respondents said they sometimes took a view on the direction of markets, but only 8% admitted that they did that frequently. Dolde (1993) found that some firms may not hedge simply because they have no exposure, whereas others may not hedge or partially hedge depending on their perception about the exchange rate behaviour. Joseph (2000) shows in a survey of 109 British firms that all of them hedge foreign exchange risk.
THE DESIGN OF A HEDGING STRATEGY
Evans and Folks (1979) identify the following elements in an effective hedging strategy:
Determining the types of exposure to be monitored: transaction, economic and accounting.
Formulating corporate objectives, including guidance in resolving potential conflicts in objectives: hedging may be in conflict with other corporate objectives.
Ensuring that the objectives are consistent with maximising shareholder value and that they are implementable.
Assigning responsibilities for each exposure, and determining the criteria whereby each manager is to be judged.
Making explicit any constraints on the use of hedging techniques, such as limitations on entering into forward contracts and other derivatives.
Identifying the channels through which exchange rate considerations are incorporated into operating decisions that affect exposure to foreign exchange risk.
Developing a system for monitoring and evaluating hedging operations.
A hedging strategy should have an objective, and this objective should be compatible with the overall corporate objectives. Table 5.1 presents a set of possible objectives (Zenoff, 1978).
One question that arises here is whether hedging should be centralised or decentralised. Centralisation is favoured for the following reasons: (i) the fear that local managers want to optimise their exposure positions irrespective of the overall corporate objective; (ii) the ability to take advantage through exposure netting of the portfolio effects, which is not possible under decentralised hedging; (iii) it enables the choice of the cheapest means of hedging worldwide; and (iv) international tax considerations. Arguments against centralisation include the loss of local knowledge and the lack of incentive for local managers to take advantage of particular situations with which they are familiar.
THE BASIC PRINCIPLES OF HEDGING
Hedging is of two kinds: operational and financial. As the name implies, operational hedging involves some operational measures that aim at reducing
TABLE
5.1
Objectives
of hedging strategies.
Objective
Requirement
Minimising
translation
Protecting
foreign currency denominated assets and
exposure
liabilities
from exchange rate fluctuations
Minimising
fluctuations in
Considering
both transaction and translation
earnings
exposure
Minimising
transaction
Managing
a subset of the firm's cash flow exposure
exposure
Minimising
economic
Ignoring
accounting earnings while concentrating
exposure
on
reducing cash flow fluctuations resulting from
changes
in exchange rates
Minimising
hedging costs
Balancing
the costs and benefits of hedging
Avoiding
surprises
Preventing
large foreign exchange losses
exposure to foreign exchange risk, and this is why it is sometimes described as involving the use of "internal" hedging techniques (for example, Joseph, 2000). It is mainly, but not exclusively, used to hedge economic exposure. Financial hedging of a currency exposure involves entering an offsetting position so that whatever is lost or gained on the original exposure is offset by a corresponding foreign exchange gain or loss on the hedge. It typically involves the use of a financial hedging instrument (such as forwards and options), and this is why it is sometimes described as involving "external" hedging techniques (for example, Joseph, 2000). Regardless of what happens to the future exchange rate, hedging locks in the base currency value of the exposure. In this section, we concentrate on financial hedging, but the techniques of operational hedging will be described later in this chapter. Financial hedging consists of five steps:
Exchange rate forecasting, which involves reviewing the likelihood of adverse exchange rate movements. More will be said about hedging and exchange rate forecasting later.
Assessing strategic plan impact. Once the future exchange rate changes are estimated, cash flows and earnings are projected and compared under alternative scenarios.
Deciding whether or not to hedge. A company will decide to hedge if, for example, it has a large portion of earnings generated abroad, while a disproportionate share is denominated in the base currency. The decision to hedge or not to hedge may be affected by a host of other factors, such as those discussed earlier, and the outlook for changes in exchange rates, as we will find out later.
Selecting the hedging instrument, which is the most cost-effective hedging tool that accommodates the firm's risk preferences. We will show later how
the choice of the instrument can be determined by the base currency value of the payables and receivables. 5. Constructing a hedging programme, including the time horizon and the hedge ratio. The estimation of the hedge ratio will be dealt with in Chapter 6.
Illustrating financial hedging
In the remainder of this section the principles of financial hedging are illustrated by assuming that the y value of an asset (long exposure) or a liability (short exposure) is known. Consider the following possibilities, which are shown in Table 5.2. First, two decisions are involved: the hedge decision and the no-hedge decision. Second, the currency of denomination, y, may appreciate, depreciate or stay unchanged against the base currency, x, between two points in time. Now, consider the case of a long exposure under the appreciation of the currency of denomination. If y appreciates, the base currency value of the asset rises, which makes the no-hedge decision the right decision, in the sense that profit would materialise as compared with what would be obtained under the hedge decision. This (relative) profit is equal to the difference between the base currency value of the asset under the no-hedge and hedge decisions. In Table 5.2, this is indicated by a plus sign. If there is a short exposure, then under the same conditions the no-hedge decision would be the wrong decision, as a loss would be incurred compared with the outcome under the hedge decision. Remember that the appreciation of the currency of denomination is favourable if the exposure is long, and unfavourable if the exposure is short.
There are two equivalent ways of looking at the hedging operation, both of which involve a hedging instrument or a hedge. The first is to look at it as an operation whereby the base currency value of assets, liabilities and cash flows is locked in, in the sense that this value would be independent of movements in the exchange rate. This is applicable to cash flows. The second is to view the operation as taking an opposite position on a hedging instrument so that any deterioration in the base currency value of the asset is offset by gains on the
TABLE
5.2
Outcomes
under the hedge and no-hedge decisions.
Decision/currency
change
Long
exposure
Short
exposure
No-hedge
decision
Appreciation
of y
+
-
Depreciation
of y
-
+
Hedge
decision
Appreciation
of y
-
+
Depreciation
of y
+
-
hedging instrument. In this case, the base currency value of the combined position (the asset and the hedging instrument) is unaffected.
Consider Figure 5.1, which shows the outcome of hedging a long exposure by locking in the base currency value of an asset. Panel (a) shows the base currency value of the asset under the no-hedge and the hedge decisions (Vx,n and Vx,h respectively). As we can see, the value of the asset under the hedge decision is unaffected by changes in the exchange rate, but the value of the asset under the no-hedge decision varies, increasing with the exchange rate. They are equal at one level of the exchange rate only. Panel (b) shows the profile of the profit/loss realised from the hedge decision relative to the no-hedge decision (Vx,h - Vx,n). At low exchange rates, profit would be made, but at high exchange rates loss would be incurred. The opposite is true if we measure profit/loss under the no- hedge decision relative to the outcome under the hedge decision, as shown in panel (c). Figure 5.2 shows exactly the same thing when exposure is short (and this is why the value is shown to be negative). As we can see, the profiles under long and short exposures are reversed.
Now, examine Figure 5.3, which is derived from Figures 5.1 and 5.2. Under a long exposure, the upper part of the diagram shows the payoff on the asset (the unhedged position) relative to the hedging instrument, as well as the payoff on the hedging instrument relative to the hedged position. These payoffs are exactly equivalent to the profiles shown in Panels (c) and (b) of Figure 5.1. As we can see, the two payoffs offset each other exactly, so that the combined position (shown in the bottom part of the diagram) has a zero payoff. This is because Vx,n - Vx,h + Vx,h - Vx,n = 0. In this case any loss incurred on the asset (the unhedged position) will be offset by profit on the hedging instrument, and vice versa. The same applies to the hedging of a short exposure, which is shown in the left part of Figure 5.3 as derived from Figure 5.2.
If the profit/loss on the asset (the unhedged position) can be offset exactly by equivalent loss/profit on the hedging instrument, then we have what is called a "perfect hedge". A perfect hedge may not always be obtained because it requires certain conditions to be satisfied: (i) the unhedged position and the hedging instrument must have the same maturity or liquidation date; (ii) the total value of the unhedged position must be hedged (that is, the hedge ratio should be one), which means that the y currency value must be known precisely; and (iii) the values or prices of the unhedged position and the hedging instrument must be perfectly correlated. Only under these conditions will the relative payoff of the combined position be zero, as in Figure 5.3. If one or more of these conditions are not satisfied, then we have a less than perfect hedge, as we can see in Figure 5.4.
Hedging and exchange rate forecasting
The decision to hedge or not to hedge an uncovered or open foreign currency position is basically a speculative decision. It all depends on the expected spot
FIGURE
5.1
Hedging
a
long exposure.
rate or the movement of the exchange rate between the point in time when the decision is taken and when its effect materialises. Remember that if the decision to hedge is taken, then some costs may be incurred up front, such as the premium paid to acquire an option. If the decision to hedge the position is taken, and the exchange rate moves in a favourable direction (for example the currency denominating receivables appreciates against the base currency) then some potential gain would be lost. Some gain would be made by leaving the position unhedged. On the other hand, if the decision not to hedge is taken and the exchange rate moves in an unfavourable direction (for example,
FIGURE
5.2
Hedging a short exposure.
the currency denominating payables appreciates against the base currency) then some losses would be incurred. These losses can be avoided by taking a decision to hedge. This is why exchange rate forecasting is Step 1 in financial hedging.
We will now put forward the proposition that what matters for the hedge/ no-hedge decision is not the absolute forecasting accuracy but rather the accuracy of forecasting the level of the spot exchange rate, St+i, relative to the guaranteed exchange rate implied by the hedge, St . As we shall find out later, St is equivalent to the actual forward rate in forward hedging and the interest
parity forward rate in money market hedging. The base currency value of a y- denominated asset depends on which of the following three policies are adopted by the hedger: (i) always hedge; (ii) never hedge; and (iii) hedge or no-hedge, depending on exchange rate forecasting (the hedge/no-hedge strategy). Under the three strategies, the base currency value of a y-denomi- nated asset is given by
Vx (H ) = Vy St Vx (N ) = Vy St+ 1
Long
exposure
Short
exposure
FIGURE
5.3
Profit/loss on
the
unhedged position
and
the hedging instrument
(a perfect
hedge).
+
+
Short
exposure
Hedging
instrument
Unhedged
+
position
Hedged
position
Long
exposure
Unhedged
position
Hedging
instrument
+
+
s
s
+
s
FIGURE 5.4 A less than perfect hedge.
Equation (5.1) tells us that under the hedge decision (H), conversion is made at the exchange rate implicit in the hedging instrument, whereas equation (5.2) says that under the no-hedge decision conversion takes place at the actual exchange rate prevailing in the future. Equation (5.3) says that if the hedging decision is based on forecasting, conversion takes place at the higher of the exchange rate implicit in the hedging instrument and the forecast exchange rate, Et(St+i). If forecasts are perfectly accurate, then
Vx
(
H
/
N ) =
VySt
Vx
(
H
/
N ) =
VySt+
!
if
S
>
St+
1
St
<
St+1
(5.4)
which gives
Vy [St - max(St, Si+ 1)] < 0 (5.5)
and
Vy [max( St, St+1) - St+1 ] > 0 (5.6)
Equation (5.5) tells us that the difference between the x values of the asset under the hedge decision and the hedge/no-hedge decision (based on the forecast) is negative or zero, implying that the hedge/no-hedge strategy is better. Equation (5.6) says that the difference between the x values of the asset under the hedge/no-hedge decision and the hedge decision is positive or zero, implying the superiority of the former.
Suppose that there are two forecasts, EA (St+ 1 ) and EtB(St+ 1 ), such that the latter would turn out to be more accurate (that is, EA (St+ 1 ) - St+ 1 > EtB( St+ 1 ) - St+ 1). If Ef(St+ 1) > EtB(St+ 1) > St , then both forecasts would indicate that the no-hedge decision should be taken, irrespective of the size of the forecasting error. Likewise, if it turns out that St > EA(St+ 1) > EtB(St+ 1 ), then the hedge decision should be taken irrespective of the forecasting error. Now, consider the situation when EA(St+ 1) > St and E^(St+ 1 ) < St. In this case, the first forecast tells us that the no-hedge decision is better, whereas the second tells us that the hedge decision is better. If it turns out that St+ 1 > St, then the less accurate forecast leads us to take the right decision and vice versa.
Moreover, the condition Et(St+1) = St+1 (accurate forecasting) is not necessary for (5.6) to hold. If Et(St+ 1 ) < St the decision to hedge will be taken. If this forecast is correct then St = max( St, St+ 1)and condition (5.6) will hold irrespective. Similarly, if Et (St+ 1 ) > St , the decision not to hedge will be taken. If the forecast is correct then St+ 1 = max( St, St + 1 ), and again the condition is satisfied. In short, what is important for the hedging decision is not the condition Et(St+1) = St+1, but rather the condition Et (St+ 1 ) = St .Hence, strictforecasting accuracy is irrelevant for the hedging decision.
5.5 MONEY MARKET HEDGING OF SHORT-TERM TRANSACTION EXPOSURE
In this section we explain how to hedge foreign currency payables (outflows) and receivables (inflows) in the money market. We will make the assumption that the hedge ratio is one (that is, the full exposure is hedged). We will also assume that the decision to hedge is not always taken, but it is rather considered in view of exchange rate expectations. For the purpose of illustration, we will consider a two-period model in which t is the present time (when the decision to hedge or not to hedge is taken) and t + 1 is the point in time when the payables or receivables are due.
A money market hedge involves taking a money market position to cover expected payables or receivables. Taking these positions means borrowing
and lending the base currency (x) and the currency of denomination (y). We start by illustrating how to hedge payables.
Money market hedging of payables
Assume the amount due at t + 1 is K units of y. Obviously, a decision not to hedge at time t means waiting until the amount becomes due at t +1 and converting an amount of the base currency at the spot exchange rate prevailing then to obtain K units of y. A money market hedge of payables involves borrowing and lending such that the final product is K units of currency y. A money market hedge consists of the following steps:
At time t an amount equal to KSt/(1 + iy) of the base currency is borrowed, where K is the y currency value of the payables.
This amount is converted into currency y at the prevailing exchange rate, St, to obtain K/(1 + iy) units of y. This amount is the present value of the payables.
This amount is invested at the interest rate on y (iy) to obtain K units of currency y when the payables are due at time t + 1. This amount is then paid out.
At time t + 1, the base currency loan becomes due, so the amount of the principal and interest should be repaid. This amount is equal to KSt(1 + ix)/ (1 + iy).
1
+
ix
1
+
y
0
ft ■ ^ 1 + ix
< KSt+1 (5.7)
è 1 + ly 0 or if
œ 1 + i ^
< St+1 (5.8)
KSt
The left-hand side of the inequality given by (5.8) is the interest parity forward rate, Ft , which is the forward rate consistent with covered interest parity (the spot rate adjusted for a factor reflecting the interest rate differential). Hence, decision to hedge payables will be taken if
(5.9)
which represents a violation of uncovered interest parity (Ft = St+ 1). Notice that Ft is an implicit forward rate resulting from the hedging process. It can be calculated directly from the base currency amount required to meet the payables and the foreign currency value of the payables. Thus
1 + ix
=
S
(5.10)
1
+
i
y
0
Ft =
K
Let us now examine the conditions under which a decision to hedge or not to hedge is taken. If the condition represented by (5.7) holds, then a hedge decision should be taken. This is because the base currency amount required to meet the payables is smaller under the hedge decision than under the no- hedge decision. The hedge decision would, therefore, involve some sort of gain relative to the alternative course of action, which is the difference between the two amounts. This gain is given by
1
+
ix
(5.11)
1
+
i
y
0
(5.12)
or
p = K(St+ 1 - Ft )
The size of this gain depends on the value of St+1 (since K and Ft are known at time t). The higher St+1, the greater is the gain made. If, on the other hand, a no-hedge decision is taken, then a loss equivalent to p would be incurred, in the sense that more money is paid to meet the payables than under the hedge decision.
Money market hedging of receivables
Hedging receivables works the other way round. This time, a y amount is
expected to be received, but how much this amount is worth in terms of x
when it is received is unknown. The following steps are involved:
At time t an amount of y equal to K/(1 + iy), which is the present value of the receivables, is borrowed.
This amount is then converted into currency x at the prevailing exchange rate, St, to obtain KSt/(1 + iy) units.
This amount is invested at the base currency interest rate to obtain KSt(1 + ix)/(1 + iy) units of x when the receivables are due at time t +1.
At time t + 1, the foreign currency loan becomes due, and the amount of the principal and interest should be repaid. This amount is equal to K, which is covered by the receivables.
TABLE
5.3
The
hedge/no-hedge decision (money market).
Payables
Receivables
Ft
<
St+1
Hedge
No
hedge
Ft
>
St+1
No
hedge
Hedge
Ft
=
St+1
Indifference
Indifference
Again, this operation does not involve the exchange rate prevailing at time t + 1. The x amount received is KSt(1 + ix)/(1 + iy), which is known at time t. The decision to hedge receivables will be taken if
f.
■
\
1+x
1 +
KSt
or if
Ft > St+ i (5.14)
If this is the case then a hedge decision will produce a gain that is given by
p = K(Ft - St+ 1) (5.15)
whereas the no-hedge decision produces an equivalent loss. Table 5.3 lists all of the possibilities. Notice that if Ft = St+ 1, then the gain as given by equations (5.12) and (5.15) will be zero. In this case, the hedge and no-hedge decisions produce similar results.
Introducing the bid-offer spread
Now, we examine money market hedging by allowing for the bid-offer spreads in interest and exchange rates. The process of hedging payables in the money market changes to the following:
f
1
• 1
+ ,a
.
+ Vb
KSa,t
(5.17)
(5.18)
y,b
Fa,t < Sa,t+ 1
where
ft- ^ 1 + »x,a
Fa,t ~ Sa,t
1 + i
Notice that Fa t can also be calculated directly from the base currency amount required to meet the payables and the foreign currency value of the payables, that is
ft-
\ 1
+
lx,a
=
S
(5.19)
a,t
1
+
i
y,b
Fa,t =
K
The hedge decision would, in this case, produce some gain relative to the no- hedge decision, which is given by
(5.20)
y,b
(5.21)
p = KS a,t+ 1 - KS a,t
1 + i
or
p = K(Sa,t+ 1 - Fa,t )
Now we consider hedging receivables. The following steps are involved in
the process:
At time t an amount of y equal to K/(1 + iy a), which is the present value of the receivables, is borrowed.
This amount is converted into x at the prevailing bid exchange rate, Sb,t, to obtain KSb,t/(1 + iy,a) units of x.
This amount is invested at the interest rate on x to obtain KSb,t(1 + ix ,b)/(1 + iy a) units of x when the receivables are due at time t + 1.
At t + 1, the foreign currency loan becomes due, and the amount of the principal and interest should be repaid. This amount is equal to K units of y, which is covered by the receivables.
The decision to hedge receivables will be taken if
(5.23)
or if
Fb,t
>
Sb,t+
1
KS
>
KS
(5.22)
b,t
b,t+
1
1
+
i
x
,b
(5.24)
1 +
y,a
0
Fb,t - Sb,t
Notice that Fb t can also be calculated directly from the domestic currency amount received and the foreign currency value of the receivables, that is
1
+
i 1
+
x
,b
-
S
(5.25)
b,t
1
+
i
y,a
Fb,t-
K
The hedge decision would, in this case, produce a gain relative to the no- hedge decision, which is given by
p
- KSb,t
-
KS
(5.26)
b,t+
1
or
p - K(Fa,t - Sb,t+ 1 )
Table 5.4 lists all of the possibilities in the presence of a bid-offer spread.
(5.27)
1
+
i
x,a
KS
(5.28)
a,t+
1
1
+
i
y,b
y
0
> KSt
1 + i
Consider now the amount received under the hedge decision. Since Sb < S, ix,b < ix and iy,a > iy, it follows that
TABLE 5.4 The hedge/no-hedge decision |
in the presence of bid-offer spreads. |
|
|
Payables |
Receivables |
Fa,t < Sa,t+1 |
Hedge |
|
Fa,t > Sa,t+1 |
No hedge |
|
Fa,t - Sa,t+1 |
Indifference |
|
b,t > Sb,t+1 |
|
Hedge |
b,t < Sb,t+1 |
|
No hedge |
lb,t - Sb,t+1 |
|
Indifference |
TABLE 5.5 The effect of bid-offer spreads on the hedging process.
With bid-offer Without bid-offer
spread spread
Payables
Amount paid under hedge KSat (1 + ix ,a)/(1 + iy ,b)
Amount paid under no hedge KSat+1
Receivables
KSt
(1
+
ix
)/(1 +
iy
)
KSt
+1
KSt
(1
+ ix
)/(1 + iy
,b)
KSt
+1
^1+
1 ^
1
+ lx,b
f-1
■
^
1
+
ix
KS
<
KS,
(5.29)
b,t+
1
1
+
i
1
+
i
y,a
0
y
0
Table 5.5 shows the amounts paid and received under the hedge and no- hedge decisions with and without the bid-offer spreads.
5.6 FORWARD AND FUTURES HEDGING OF SHORT-TERM TRANSACTION EXPOSURE
Forward hedging of foreign currency payables and receivables entails locking in the rate at which the payables and receivables are converted from a foreign currency, y, into the base currency, x. This is achieved by buying y forward in the case of payables and selling it forward in the case of receivables.
Forward hedging of payables
Forward hedging of payables denominated in currency y amounts to buying the currency forward. Thus, the amount of payables, K units of y, is bought forward at time t at a cost of KFt units of x. Since this amount is known with certainty at time t, the exposure is covered. The decision to hedge payables is taken if
KFt < KSt+1 (5.30)
If this is the case, some gain will be made out of the hedge decision. This gain is given by
p = K(St+ 1 - Ft ) (5.31)
If a decision to hedge is not taken, then a loss of a similar amount would be incurred. Notice that if covered interest parity holds then Ft = Ft, so the gain will be equal to that made under a money market hedge. In fact, if
covered interest parity holds, then money market hedging and forward hedging will produce identical results in terms of the base currency value of the payables. Otherwise, forward hedging would be preferred to money market hedging if
KFt < KFt (5.32)
The two conditions that trigger the hedge decision and the one under which forward hedging is preferred can be combined to produce the following. Forward hedging of payables would be preferred to money market hedging and to the no-hedge alternative if
KFt < KFt < KSt+ 1 (5.33)
If the bid-offer spreads are allowed for, then the conditions change as follows. If the decision to hedge is taken, then the foreign currency is bought forward at the offer forward rate. Thus the decision to hedge is taken if
KFa,t < KSa,t + 1 (5.34)
and the gain resulting from the hedge decision is
p = K( Sa,t+ 1 - Fa,t ) (5.35)
Forward hedging is preferred to money market hedging if
KFa,t< KF a,t (5.36)
The general condition for preferring forward hedging to money market hedging and the no-hedge alternative is
KFa,t < KFa,t < KSa,t+ 1 (5.37)
Hedging receivables works the other way round. In this case currency y is sold forward at the bid forward rate. Table 5.6 summarises all of the possibilities.
Let us examine the diagrammatic representation of forward hedging as shown in Figure 5.5. Consider the hedging of payables first. If the position is hedged, then the base currency value of the payables will be unchanged at KFt. If, on the other hand, the position is not hedged, then the base currency value of the payables rises as the spot exchange rate rises. The top part of the diagram shows the profit/loss on the unhedged position relative to the alternative of hedging, which is K(Ft - St+i). As St+i rises losses will be incurred on the unhedged position. In the second part of the diagram, we plot the profit/ loss on the hedging instrument (long forward) relative to the alternative of no- hedging, which is K(St+i - Ft). As St+i rises, profit will be made on the long forward position. When the two positions are combined we get the payoff on the hedged position, which is zero, as shown in the lower part of the diagram. The right-hand panel shows the hedging of receivables, which works in exactly the opposite way to that of the payables.
TABLE
5.6
General
conditions and
the hedge/no-hedge decision.
Condition
Payables
Receivables
Without
bid-offer spreads
Ft
< Ft
< St+1
Hedge
(forward)
No
hedge
Ft<
Ft<
St+i
Hedge
(money market)
No
hedge
Ft>
Ft>
St+i
No
hedge
Hedge
(forward)
Ft>
Ft>
St+i
No
hedge
Hedge
(money market)
Ft
=
Ft
=
St+1
Indifference
Indifference
With
bid-offer spreads
Fa,t
< Fa,t
<
Sa,t+1
Hedge
(forward)
Fa,t
< Fa,t
<
Sa,t+1
Hedge
(money market)
Fa,t
> Fa,t
>
Sa,t+1
No
hedge
Fa,t
> Fa,t
>
Sa,t+1
No
hedge
Fa,t
= Fa,t
=
Sa,t+1
Indifference
tb,t
< lb,t
<
Sb,t+1
No
hedge
tb,t
<
Fb
,t <
Sb,t+1
No
hedge
Fb
,t >
Fb
,t >
Sb,t+1
Hedge
(forward)
Fb
,t >
Fb
,t >
Sb,t+1
Hedge
(money market)
Fb
,t =
Fb
,t =
Sb,t+1
Indifference
Futures hedging
The consequences of using futures contracts to hedge transaction exposure are the same as those of using forward contracts. However, because of the standardisation of the futures contracts and because they involve marking-to- market, some quantitative rather than qualitative differences may arise. First, it may not be possible to hedge the amount of payables or receivables exactly because futures contracts are standardised with respect to size. For example, if the amount of the payables is K units of y and the size of the futures contract on y is 2K/5 then buying two contracts leaves the amount K/5 uncovered, in which case it has to be bought in the spot market at St+i. The x currency value of the payables will thus be (4KFt/5) + (KSm/5) or (K/5)(4Ft + Sm), where Ft in this case is the futures rate. Alternatively, if three contracts are bought then the excess amount of y (K/5 units) has to be sold spot, in which case the x value of the payables will be (6KFt/5) - (KSt+i/5) or (K/5)(6Ft - St+i). Second, it is more likely the case that the date on which the receivables are due does not coincide with a settlement date because futures contracts are standardised with respect to the settlement date. Even if the size and the settlement dates are the same as what is required, marking-to-market risk will introduce some variation vis-à-vis the forward market. Third, some variation results from changes in the margin account associated with any futures position.
Payables
Unhedged
position
K
(F
t
- st+1)
St+i 0
Receivables
Unhedged position
K
(St+i- Ft
)
0
+
+
+
Long
forward
K
(St+i-
Ft)
+
S
FIGURE 5.5 Forward hedging of payables and receivables.
The standardisation of futures contracts makes forward hedging more appealing than futures hedging. However, there are compelling reasons why futures contracts are used for the purpose of hedging. Telser (1981) argued that organised futures markets exist because they are superior to informal forward markets. An organised futures market has elaborate written rules, standing committees for adjudicating disputes, and a limited membership. In contrast to futures contracts, forward contracts rely on the good faith of individual parties. Because forward contracts are tailor-made they cannot be
offset by identical contracts, and there is no scope for the advantages of clearing houses and settlement by the payment of the difference. Through their rules and standardisation, futures provide liquidity and eliminate counterparty risk. Penings and Leuthold (2000) argue that futures contracts can provide jointly preferred contracting arrangement, enhancing relationships between firms. What motivates the use of futures contracts is then contract preference, level of power and conflicts in contractual relationships of firms.
CIP and the relative effectiveness of forward and money market hedging
We have seen that money market hedging entails the conversion of payables and receivables at the interest parity forward rate, whereas forward hedging amounts to conversion at the actual forward rate. Under covered interest parity these rates are equal, which means that money market hedging and forward hedging will produce similar results. Al-Loughani and Moosa (2000) use this idea to devise an indirect test of CIP. The idea is that if money market hedging and forward hedging produce similar results then CIP must be valid. They tested this hypothesis using five exchange rates and found that CIP actually holds.
5.7 OPTIONS HEDGING OF SHORT-TERM TRANSACTION EXPOSURE
Unlike the case of money market hedging, forward hedging and futures hedging, the outcome of options hedging is not known with certainty because it depends on whether or not the option is exercised. This in turn depends on whether the actual exchange rate when the payables or receivables are due, St+i, is higher or lower than the exercise exchange rate. However, options can be used to ensure that the domestic currency value of payables does not rise above a certain value, and that the domestic currency value of receivables does not fall below a certain value. It is also possible, by using over the counter non- standardised options, to hedge the exact amount of payables and receivables.
Hedging payables with a call option
A call option gives the hedger the right to buy K units of a currency at the exercise exchange rate. For simplicity let us assume that the option is a European option with an expiry date that coincides with the date when the payables are due, t + 1. Let us also assume that the exercise exchange rate is equal to the current exchange rate, St (the option is at the money). The exchange rate prevailing on the expiry date, St+i, will assume any value, and depending on this value we have the following possibilities:
If it assumes the value St+i,i, such that St+i,i < St, then the option will not be exercised, and the foreign currency will be bought on the spot market. The total cost of covering the payables is the base currency value, KSt+i,i and the option premium lost, which is equal to Km, where m is the premium per unit of the underlying currency. The total cost will thus be K(St+i,i + m).
If it assumes the value St+i,2, such that St+i,2 > St, then the option will be exercised, and the foreign currency will be bought at the exercise exchange rate, St. The total cost of covering the payables is the base currency value, KSt, and the option premium paid up front, which is equal to Km. The total cost will thus be K(St + m).
Hedging receivables with a put option
We now consider the case of hedging receivables worth K units of currency y via a put option. In this case the put option used as a hedging instrument gives the hedger the right to sell K units of currency y at the exercise exchange rate. Making the same assumptions as before, we have the following possibilities:
If Sf+1,1 < St, then the option will be exercised, and the underlying amount of currency y will be sold to the option writer. The value obtained will be equal to the domestic currency value, KSt, minus the option premium paid up front, which is equal to Km. Thus, the net amount is equal to K(St - m).
If St+12 > St, then the option will not be exercised, and the foreign currency will be sold on the spot market at St+12. The net amount received is therefore K(Sf+1,2 - m).
A summary of the decision rules
If the exchange rates St+1,1 and St+1,2 are expected with probabilities of p1 and P2 respectively, then the decision to hedge payables and receivables will depend on the expected domestic currency values under the hedge and no- hedge decisions. Table 5.7 lists all of the possibilities.
TABLE 5.7 The options hedge/no-hedge decision.
Condition
Payables
(St+11 + m)Pi + (Sc + m)P2 < (Sc+11P1 + St+12P2)
(St+11 + m)Pi + (St + m)P2 > (St + 11P1 + St + i2P2) (St+11 + m) Pi + (St + m)P2 = (St + 11P1 + St + 12P2)
Hedge
No hedge Indifference
No
hedge
Hedge
Indifference
Payables
Unhedged
position
Vi
o
Receivables
Unhedged
position
+
+
s
Long
put
0
Hedged
position
s
+
FIGURE 5.6 Options hedging of payables and receivables.
Figure 5.6 illustrates options hedging of payables and receivables assuming an exercise exchange rate of St, which implies that the option is at the money. Consider the hedging of payables, which is shown in the left-hand panel of Figure 5.6. The top part of the diagram shows the payoff on the unhedged position measured as the difference between the value of the payables at St and St+i. The middle part of the diagram shows the payoff on a long call position at an exercise exchange rate of St. The bottom part of the diagram shows the payoff on the combined position. Unlike the unhedged position, the combined position shows an upper limit on the possible loss arising from
adverse exchange rate movements. To hedge receivables, a long put position is taken as the hedging instrument. The hedged position shows that while there is a lower limit on the loss arising from adverse exchange rate movements, there is no limit on the potential gain arising from favourable exchange rate movements.
Hedging a contingent exposure
A contingent exposure means that the exposure arises only if a certain outcome materialises (for example, when a contract is awarded to the underlying firm). In this case, an option hedge is preferable to a forward hedge because the latter can cover all possible eventualities. Let us assume that a firm bids for a contract valued at K units of currency y. Exposure to currency y would arise only if the contract is awarded to the firm, in which case the firm would have receivables worth the value of the contract. If, in the mean time, currency y depreciates against the base currency, the firm would incur some losses.
Let us see what happens when the firm uses forward contracts and options to hedge this contingent exposure. To use a forward contract, the firm takes a short forward position on currency y by selling K units of the currency forward. In any case (that is, whether or not the contract is awarded) the firm is committed to come up with K units of currency y on the maturity of the contract. There are then two outcomes:
The contract is awarded, in which case the amount of the receivables covers the forward contract. Hence there is no problem, as the hedge works in the sense that the firm manages to lock in the base currency value of the receivables.
The contract is not awarded, in which case the amount of y has to be provided at the pre-specified forward rate. If the spot rate at that time happens to be higher than the forward rate, the firm would incur unlimited loss, proportional to the difference between the spot and forward rates.
Now, let us consider what happens if a put option is used to hedge this contingent exposure. In this case there are four possible outcomes, because the option may or may not be exercised. The following outcomes are possible:
The contract is awarded and the actual exchange rate turns out to be less than the exercise exchange rate (Sf+i < St). The firm exercises the option, converting the proceeds of the contract to the base currency at the exercise exchange rate, obtaining KSt units of x.
The contract is awarded but the exchange rate turns out to be greater than the exercise exchange rate (St+i > St). The firm does not exercise, losing the premium on the option but the proceeds from the contract are converted at the higher rate (KSt+i).
(a) Forward contract
Contract
not awarded
Firm receives KFt units of x for K units of y
Firm receives K5t+i units of x for K units of y
(b) Put option 5t+1 < 5t ^ Firm exercises Put to obtain
^^ K5t units of x
Contract awarded
r r Firm does not exercise put, 5t+1 > 5t^ .
Contract
not awarded
5t+1
<
St
^
Firm exercises put for profit
Firm does not exercise put, 5t+i > 5t ^ losing premium
FIGURE 5.7 Hedging a contingent exposure with forward contracts and options.
The contract is not awarded and the actual exchange rate turns out to be less than the exercise exchange rate (Sf+i < St). The firm exercises the option, making profit of K(St - St+i).
The contract is awarded but the exchange rate turns out to be greater than the exercise exchange rate (St+i > St). The firm does not exercise, losing the premium on the option.
All of these outcomes are illustrated in Figure 5.7. It is obvious that if a forward contract is used to hedge a contingent exposure, then the loss will be unlimited if the exchange rate rises and the contract is not awarded. If, on the other hand, a put option is used to hedge this exposure, then the maximum loss would be the premium on the option, whether or not the contract is awarded.
+
Writing an option in itself creates a contingent exposure that can be hedged by taking an opposite option position. Figure 5.8 shows the payoff on a short call, which arises when a firm writes a call, giving the holder the right to buy the currency at an exercise exchange rate of St. As long as the actual exchange rate does not turn out to be higher than the exercise exchange rate (St+i < St), the option will not be exercised and the firm writing the option will make profit equal to the option premium paid by the holder (m). But if the actual exchange rate turns out to be higher than the exercise exchange rate (St+i > St), the option will be exercised and the loss will be unlimited, increasing with the level of Sf+i. Suppose now that the firm decided to hedge this exposure
with a forward contract, assuming for simplicity that the forward rate is equal to the exercise exchange rate. The payoff on the forward contract is shown by the middle part of the diagram. Profit will be made on this position as long as the actual exchange rate turns out to be higher than the exercise exchange rate and the forward rate. The bottom part of the diagram shows the payoff on the combined (hedged) position. If the actual exchange rate turns out to be higher than the exercise exchange rate, profit on the forward contract will offset the loss on the option, and the firm will gain the premium on the put option. If, on
the other hand, the actual exchange rate turns out to be lower than the exercise exchange rate, losses on the forward contract will be unlimited.
+
Short
call (exposure)
m
S
+
m'
FIGURE
5.9
Hedging a contingent exposure with an option (same exercise
exchange rate).
S
m
-
m
S
position will be offset by the gains on the hedge (the long call). Net profit remains at m - m'.
+
exchange
rate).
Hedging against exchange rate volatility
A trading firm engaged in exporting and importing may find it desirable to work with stable exchange rates. This firm can hedge the risk arising from exchange rate volatility by taking an option position that compensates it if the underlying exchange rate rises above or falls below a certain level. This position is called a long straddle, which consists of a long call and a long put at the same exercise exchange rate.
Long
call
FIGURE
5.11
Hedging against exchange rate volatility by using a long straddle.
m
c
+
whose payoff is shown in the bottom part of the diagram, is mc + mp. If the exchange rate at time t + 1 goes above or below the exercise exchange rate, St, by more than mc + mp, the firm will be compensated for the difference by exercising the call (above) or the put (below).
5.8 FINANCIAL HEDGING OF LONG-TERM TRANSACTION EXPOSURE
Long-term transaction exposure involves payables and receivables materialising over a long time in the future (say five years). If it is possible to estimate this exposure, it can be hedged using three alternative techniques. These techniques are discussed in turn.
Long-term forward contracts
Commercial banks do provide forward contracts in major currencies with long maturities (for example, five or ten years). However, because of the risk involved, banks only offer these contracts to the most creditworthy customers.
Currency swaps
Swaps are suitable for hedging a recurrent exposure that consists of a series of payables or receivables. A currency swap resembles a portfolio of forward contracts, whereby two parties agree to exchange two cash flows denominated in two different currencies at a predetermined exchange rate on a sequence of future dates.
Suppose that a firm whose base currency is x anticipates a series of receivables (K units of y) arising at points in time 1, 2, 3, ..., n. To hedge this exposure, the firm arranges a swap with a counterparty whereby the firm receives payments in terms of x equal to K converted at the contract rate, St, while the counterparty receives K units of y. Table 5.8 shows the payments received by the firm and the counterparty at each payment period in both currencies.
TABLE
5.8
Payments
involved in a currency swap.
Payment
date
The
firm receives
The
counterparty receives
Units
of
x
Units
of
y
Units
of
x
Units
of
y
1
KSt
K
KSt+1
K
2
KSt
K
KSt+2
K
3
KSt
K
KSt
+3
K
n
KSt
K
KSt
+n
K
Parallel loans
Parallel loans (or back-to-back loans) can be used to hedge long-term payables and receivables in exactly the same way as swaps. In this case, however, the exchanged payments are based on the forward rates.
5.9 OTHER FINANCIAL AND OPERATIONAL TECHNIQUES OF HEDGING TRANSACTION EXPOSURE
It may not be possible to implement the hedging techniques discussed so far. This may be due, for example, to the inability to forecast the sales resulting from an advertised reduction in prices over the following six months. Another reason is that the hedging costs may be prohibitively high. A third reason is the unavailability of forward, futures or options contracts for the underlying currency. When this is the case the following techniques may be considered.
Leading and lagging
Leading and lagging represent an operational hedging technique that involves an adjustment in the timing of the realisation of foreign currency payables or receivables. If the foreign currency is expected to appreciate it would be a good idea to pay the foreign currency dues sooner than later. This is called leading. If, on the other hand, the base currency is expected to depreciate, it would be a good idea to meet the payables later than sooner. This is lagging.
There are some problems with the implementation of leading and lagging. Suppose that a firm requires a prepayment because there are concerns about a depreciating currency. This firm would face the following problems: (i) the payer may not agree to pay unless there is some incentive such as discounts; (ii) pressing for prepayments may hamper future sales efforts; and (iii) to the extent that the original invoice price incorporates the expected depreciation of the foreign currency, the receiving firm is already partially protected. The technique of leading and lagging is more appropriate for intra-firm trade.
Currency diversification
Currency diversification is again an operational hedging technique. The depreciation and appreciation of foreign currencies against the base currency will not be as harmful if a large number of currencies are involved, provided that the exchange rates of these currencies against the base currency are not highly correlated. The base currency value of foreign currency payables rises when the foreign currencies appreciate against the base currency. If the exchange rates are not highly and positively correlated, then the adverse effect will be smaller, because some of these currencies will appreciate only slightly, while others may even depreciate.
Consider a firm with a base currency x and long positions of Ky and Kz on currencies y and z respectively. The base currency value of the y position at t and t + 1 is
Vx,t (y) = KySt ( x/y) (5.38)
Vx,t+ 1(y) = KySt+1 ( x/y) (5.39)
Thus
KySt+ 1( x/y)
yx(y)
=
y
,
-1
=
S(x/y) (5.40)
KySt ( x/y)
Similarly, the percentage change in the x currency value of the z position is
Vx ( z) = S( x/z) (5.41) If S(x/y) and S(x/z) are perfectly negatively correlated, it follows that
S( x/z) = -S( x/y) (5.42) which gives
Vx ( y) = -Vx ( z) (5.43)
implying that the profit/loss on one position is completely offset by the loss/ profit on the other. If S (x/y) and S(x/z) are perfectly positively correlated, it follows that Vx (y) = Vx (z). In this case, taking a long position on y and a short position on z, or vice versa, produces the same result.
Cross hedging
Cross hedging is used when it is not possible to hedge exposure to a foreign currency because of the unavailability of hedging instruments, such as forward contracts and options, on this currency. In this case we look for another foreign currency that is highly correlated with the currency to be hedged, and then take a forward, futures or an options position on this currency.
Let us now assume that a forward contract is not available on currency y but a contract on another foreign currency, z, is available. Cross forward hedging boils down to buying forward an amount of z that is equivalent to the payables at the current spot rate between y and z. At this exchange rate, the z amount equivalent to K units of y is K/[St(y/z)]. The domestic currency value of this amount when it is bought forward is
Vc = (5.44)
St( y/z)
where Vc is the domestic currency value of the payables under cross hedging. At time t + 1, the amount z bought forward, K/[St(y/z)], is converted spot to y and the proceeds are used to meet the payables in y. The amount of y obtained is
yC = ^TT^TV-(A - K )St+ i(x/y) (5.45)
St(y/z)
Notice, however, that this amount may or may not be equal to the amount of the payables, K. The two amounts are equal (that is, A = K) only if the spot exchange rate between y and z is stable such that St+i(y/z) = St(y/z). This will be the case if S(x/y) and S(x/z) are perfectly correlated. If this is not the case then the deficit is met by buying currency y against x spot at t + 1, whereas the surplus can be converted back to x at the same rate. Hence, the base currency value of the payables under cross hedging is
KF (x/z)
VC = Syz-(A - K)St+ i(x/y (546)
Notice that if A - K = 0, then equation (5.46) will be identical to equation (5.44). By following this approach to cross currency hedging, Moosa (2001b) demonstrated, by using historical data on four currencies, that cross and direct hedging of recurrent exposure produced similar results.
Another approach to cross currency hedging does not involve the forward market. In this case a long (short) position on one currency can be hedged by taking a short (long) spot position on another currency. If S(x/y) and S(x/z) are highly correlated, then a firm with a base currency x can hedge payables in y by buying currency z. If y appreciate against x, then z will also appreciate, in which case the loss incurred on the short position in y will be offset by the profit on the long position in z. Formally, if S(x/y) and S(x/z) are related by the equation
S(x/z) = a + bS(x/y) (5.47)
then
S( x/z) = bS( x/y) (5.48)
and thus perfect correlation implies a perfect hedge because
S( x/z) - bS( x/y) = 0 (5.49)
which means that any loss on one position will be completely offset by gains on the other and vice versa. Brooks and Chong (2001) found that cross currency hedging reduces volatility by about 15%. Siegel (1997) used a similar approach to hedging currency risk.
Table 5.9 shows the correlation coefficients of the percentage changes in the exchange rates of a number of currencies when the exchange rates are measured against the US dollar and when they are measured against the Swedish krona (in parentheses). It can be seen that there are some really high
TABLE
5.9
Correlations of percentage changes in exchange rates against the USD
and SEK.
AUD
CAD
CHF
DKK
GBP
JPY
NOK
NZD
SEK
AUD
1.00
0.43
-0.13
0.01
0.08
0.04
0.06
0.70
0.12
(1.00)
(0.82)
(0.18)
(0.41)
(0.50)
(0.50)
(0.50)
(0.89)
-
CAD
1.00
-0.24
-0.17
0.05
-0.04
-0.01
0.16
0.07
(1.00)
(0.29)
(0.48)
(0.66)
(0.57)
(0.60)
(0.79)
-
CHF
1.00
0.91
0.65
0.46
0.84
0.20
0.71
(1.00)
(0.85)
(0.45)
(0.59)
(0.71)
(0.38)
-
DKK
1.00
(1.00)
0.71
(0.60)
0.44
(0.64)
0.87
(0.82)
0.26
(0.57)
0.73
GBP
1.00
(1.00)
0.26
(0.53)
0.83
(0.72)
0.25
(0.61)
0.79
JPY
1.00
(1.00)
0.31
(0.56)
0.32
(0.63)
0.19
NOK
1.00
(1.00)
0.27
(0.60)
0.82
NZD
1.00
(1.00)
0.20
SEK 1.00
correlations that would make spot cross currency hedging successful. For example, a firm whose base currency is the Swedish krona can hedge a short exposure on the Canadian dollar by going long on the New Zealand dollar or the Canadian dollar. Likewise, a US dollar based firm can hedge a long exposure on the Danish kroner by going short on the Swiss franc.
Exposure netting
A natural hedge would arise when a firm has both payables and receivables in the same currency. In this case only the net exposure should be covered. Jorion (2001, p. 475) argued that, until recently, hedging systems typically consisted of focusing on and hedging each source of risk separately, which is an inefficient approach.
Exposure netting may involve the same currency or currencies with highly correlated exchange rates. Consider the case of the same currency first by assuming that a firm has both payables and receivables in currency y. If the positions are of equal sizes, then the net position will be zero, and there is no need to do anything about it because a natural perfect hedge is in place. If the positions are of different sizes then only the difference should be hedged. For example, if payables are Ki and receivables are K2 such that Ki > K2, then a long forward position of Ki - K2 should be taken on currency y.
Consider now a position of payables in currency y and receivables in currency z, such that S(x/y) and S(x/z) are highly, but not perfectly, correlated. A gain on one position will be partially offset by a loss on the other. In this case only the residual risk that cannot be eliminated by combining the two positions should be hedged via a forward or a futures contract.
Currency of invoicing
A firm can shift, share or diversify exposure by choosing an appropriate currency of invoicing. Price shifting is implemented by setting the price completely in base currency terms. In this case, the base currency price will be fixed but the foreign currency price will change with the exchange rate, rising as the exchange rate falls, as shown in Figure 5.12. From the perspective of the exporting firm this method eliminates foreign currency exposure, but it may not be possible to implement if, for example, foreign prices are fixed by contract. Another way to reduce foreign exchange exposure by shifting is to invoice receivables in the same currency used to invoice payables, be it the base or a foreign currency. Diversifying means using currency baskets or composite currencies, such as the SDR, as the currency of invoicing. On several occasions it has been mentioned that OPEC may invoice oil in SDR rather than in US dollar.
Px
Px
=
SPy
FIGURE
5.12
Increasing the foreign currency price to counterbalance foreign
currency depreciation.
P
y
(5.50)
_ S(1 - 0) - S,+1
Vx= K
2
which can be simplified to produce
(5.51)
>
KS
t+1
Vx= K
2
which means that the x currency value of the payables is greater than what it would be if there was no hedge. The benefit of a depreciation in y is shared between the payer and the payee in the sense that the payer does not enjoy the full extent of the depreciation of y, whereas the payee does not suffer to the full extent. The benefit accruing to the payee, compared with the no-hedge decision, is given by
Vx
- KSt+1 = K
(5.52)
>0
On the other hand, if the exchange rate rises above the upper limit of the neutral zone, such that St+1 > S(1 + 0), then the payables are converted at a rate that is equal to the base rate and half the difference between the actual exchange rate and the upper limit of the neutral zone. This gives
(5.53)
Vx=
K
2
which can be simplified to produce
(5.54)
<
KS
Vx=
K
t+1
which means that the x currency value of the payables is lower than what it would be if there was no hedge. The result of an appreciation of y is shared between the payer and the payee in the sense that the payer pays less than