CURRENCY ARBITRAGE
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 depre
ciate, 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.
Currencydiversification
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 xand long positions of Kyand Kzon currencies yand zrespectively. The base currency value of the yposition at t and t+ 1 is
y y t( /
( ) =K S x y) (5.38)
Vx t, y
( ) =K S x y (5.39)
Vx t+, 1 y t+1( / ) Thus
K S x y)
x( ) = y t+1( / ( / ) (5.40)
V y -1 =S x y
( / K Sy t x y)
Similarly, the percentage change in the xcurrency value of the zposition is
V zx ( ) =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
V yx ( ) = -V zx( ) (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 V y ( ). In this case, taking a long position on yand a short follows that
x( ) =V zx
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 ybut a contract on another foreign currency, z, is available. Cross forward hedging boils down to buying forward an amount of zthat is equivalent to the payables at the current spot rate between yand z. At this exchange rate, the zamount equivalent to K units of y is K/[S(y/z)]. The domestic currency value of this amount when it is bought forward is
t
KF t( / ) x z
VC = (5.44)
S y zt( / )
where VC is the domestic currency value of the payables under cross hedging.
At time t+ 1, the amount zbought forward, K/[St(y/z)], is converted spot to y
( / ( /
( / ( /
and the proceeds are used to meet the payables in y. The amount of yobtained is
KFt( / x z)
- ) /
VC = -( A K St+ 1(x y) (5.45)
S y zt( / )
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 yand zis stable such that St+1(y/z) = S(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 yagainst xspot at t+ 1, whereas the surplus can be converted back to xat the same rate. Hence, the base currency value of the payables under cross hedging is
t
KF t( / x z )
- ) /
VC = -( A K St+ 1(x y) (5.46)
S y zt( / )
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) demon
strated, 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 xcan hedge payables in y by buying currency z. If yappreciate against x, then zwill 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
CAD CHF DKK GBP JPY NOK NZD SEK
1.00 (1.00)
0.43 (0.82)
1.00 (1.00)
–0.13 (0.18) –0.24
(0.29) 1.00 (1.00)
0.01 (0.41) –0.17
(0.48) 0.91 (0.85)
1.00 (1.00)
0.08 (0.50)
0.05 (0.66)
0.65 (0.45)
0.71 (0.60)
1.00 (1.00)
0.04 (0.50) –0.04
(0.57) 0.46 (0.59)
0.44 (0.64)
0.26 (0.53)
1.00 (1.00)
0.06 (0.50) –0.01
(0.60) 0.84 (0.71)
0.87 (0.82)
0.83 (0.72)
0.31 (0.56)
1.00 (1.00)
0.70 (0.89)
0.16 (0.79)
0.20 (0.38)
0.26 (0.57)
0.25 (0.61)
0.32 (0.63)
0.27 (0.60)
1.00 (1.00)
0.12 – 0.07 – 0.71 – 0.73 – 0.79 – 0.19 – 0.82 – 0.20 – 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 expo
sure on the Danish kroner by going short on the Swiss franc.
Exposurenetting
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 K1 and receivables are K2 such that K1> K2, then a long forward position of K1– 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, corre
lated. 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.
Currencyofinvoicing
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.
Risk sharing means invoicing part of the shipment in base currency terms.
Sometimes, risk sharing is implemented by using a customised hedge contract embedded in the underlying trade contract. The hedge agreement typically
Px
y
x SP
P =
P y
FIGURE 5.12 Increasing the foreign currency price to counterbalance foreign currency depreciation.
takes the form of a price adjustment clause whereby a base price is adjusted to reflect certain exchange rate changes. Formally, risk sharing works as follows.
Given the ycurrency value of the contract, the xcurrency value is obtained by converting at a range of exchange rates. First, a base rate is set, say S. Then a neutral zone is set around this rate, say between S(1 -q) and S(1 +q), where 0 < <q 1. Within the neutral zone, the payables are converted at S, which means that the x currency value of the payables is KS. Formally, if
q)
S(1 - <St+1 <S(1 +q), then V x =KS and dVx/dSt+1 = 0. If the exchange rate falls below the lower limit of the neutral zone such that St+1 <S(1-q), then the payables are converted at a rate that is equal to the base rate less half the differ
ence between the lower limit and the actual exchange rate. This gives é S(1 - -q) S
Vx =K S-
2
t+1
ûú
ù (5.50)
ê ë
which can be simplified to produce + +
éS(1 q) St+1 ù
Vx =Kê ú >KSt+1 (5.51)
ë 2 û
which means that the xcurrency value of the payables is greater than what it would be if there was no hedge. The benefit of a depreciation in yis 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 =Ké q)
êS(1 + -St+1 ù
>0 (5.52)
2 ûú ë
On the other hand, if the exchange rate rises above the upper limit of the neutral zone, such that St+1 >S(1+q), 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
-S(1 +q)ù é St+1
ë 2 ûú (5.53)
Vx =KêS+
which can be simplified to produce éS(1 - +S
Vx =Kê q) t+1 ù
ú <KSt+1 (5.54)
ë 2 û
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
V x
Vx
S t
¨
¨
1 +
No hedging
Risk sharing
S K
S ( 1-q) S S (1+q)
FIGURE 5.13 A diagrammatic illustration of foreign exchange risk sharing.
under the no-hedge decision, while the payee receives less than otherwise.
The benefit accruing to the payer, as compared with the no-hedge decision is given by
S(1 - -q) S
é t+1ù
úû<0 (5.55)
-KSt+1=Kêë 2
Notice that under the no-hedge decision dVx/dSt+1 = K, but under a risk- sharing scheme, dVx/dSt+1 = K/2, which means that the base currency value of the payables changes at half the rate than under the no-hedge decision.
A foreign exchange risk sharing scheme is represented diagrammatically in Figure 5.13. The value of the payables without this arrangement is represented by an upward sloping straight line with the equation Vx = KSt+1. The value of the payables under foreign exchange risk sharing follows a staggered path. If the exchange rate falls below the lower limit of the neutral zone, it is higher than under no-hedge decision, although it rises at half the rate. If the exchange rate rises above the upper limit, it falls below that under the no- hedge decision, and rises half as fast. In between, the value is constant, as represented by a horizontal line with the equation Vx =KS.
Currency collars
We will now illustrate the use of currency collars, also called range forward, in hedging receivables. A currency collar is used to set a minimum value for the base
currency receivables at the expense of setting a maximum value. Thus, it involves a trade off between potential loss and potential gain. A currency collar contains a certain range for the exchange rate ranging between a lower limit, SL, and an upper limit, SU. If the exchange rate falls below the lower limit, the rate used to convert receivables into the base currency is the lower limit itself, and this is how the minimum value is obtained. If the exchange rate falls within the range, the conver
sion rate is the current exchange rate, which means that the base currency value of the receivables rises with the exchange rate within this range. Finally, if the exchange rate rises above the upper limit, the conversion rate is the upper limit, and this is how the maximum value is obtained. These possibilities are displayed in Table 5.10, while a diagrammatic representation can be found in Figure 5.14.
A currency collar can be created by using a cylinder consisting of a short call and a long put with the same price and exercise exchange rates of SU and SL respectively. Figure 5.15 shows how this can be made possible. The upper two parts of the diagram show the payoff on these two positions. By combining TABLE 5.10 The value of base currency receivables under
a currency collar.
Vx dVx/dSt+1
S t +1 <SL KSL 0
S L £S t+1 £SU KSt+1 K
S t +1 >SU KSU 0
Vx
S t
KS t
KS U
KS L
1 + 1
+
SL SU
FIGURE 5.14 Hedging receivables by using a currency collar.
Short call
St + 1
Long put
St + 1
Cylinder
St + 1
Unhedged position
St + 1
Hedged position
S L S U St + 1
FIGURE 5.15 Creating a currency collar by using an option cylinder.
these payoffs we obtain a cylinder, and by combining the payoff on the cylinder with the payoff on the unhedged position (the receivables), we get the payoff on the hedged position as shown in the lower part of the diagram.
This part exactly resembles the currency collar displayed in Figure 5.14.