CURRENCY ARBITRAGE
5.6 FORWARD AND FUTURES HEDGING OF SHORT-TERM TRANSACTION EXPOSURE
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 KSa,t (1+ ix ,a)/ (1+ iy ,b) KSt (1+ i x )/ (1+ iy ) Amount paid under no hedge KSa,t+1 KSt +1
Receivables
Amount received under hedge KSb ,t (1+ ix ,b)/(1+ iy ,a) KSt (1+ i x )/ (1+ iy ,b) Amount received under no hedge KSb ,t+1 KSt +1
æ1 +ix,b ö ç (5.29)
KSb ,t+ 1 çç
1 +iy,a ÷
÷< KSt æ1 +ix ö÷
ç1 +iy ÷
è ø è ø
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
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
( ) (5.35)
p=K Sa,t+ 1 -Fa,t
Forward hedging is preferred to money market hedging if
(5.36) KFa,t < KFa,t
The general condition for preferring forward hedging to money market hedging and the no-hedge alternative is
(5.37) KFa,t < KFa,t < KSa,t+ 1
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 alter
native of hedging, which is K(Ft – St+1). As St+1 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+1 – Ft). As St+1 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
F t <F t <St+1 Hedge (forward) No hedge F t <F t <St+1 Hedge (money market) No hedge F t >F t >St+1 No hedge Hedge (forward) F t >F t >St+1 No hedge Hedge (money market) F t =F t =St +1 Indifference Indifference
With bid–offer spreads
F a , t <Fa,t <S a,t+1 Hedge (forward) F a , t <Fa,t <S a,t+1 Hedge (money market) F a , t >Fa,t >S a,t+1 No hedge
F a , t >Fa,t >S a,t+1 No hedge F a , t =Fa, t =S a, t+1 Indifference
F b , t <F b , t <Sb,t+1 No hedge F b , t <F b , t <Sb,t+1 No hedge F b , t >F b , t >Sb,t+1 Hedge (forward) F b , t >F b , t >Sb,t+1 Hedge (money market) F b , t =F b , 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 Kunits of yand 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+1. The x currency value of the payables will thus be (4KFt/5) + (KSt+1/5) or (K/5)(4Ft + St+1), 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+1/5) or (K/5)(6Ft – St+1). 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 Receivables
+ +
Unhedged position K (S Unhedged position
t +1– Ft )
St+ 1 0 St + 1
K (F t – St + 1)
_ _
+ +
Long forward Short forward
K (S t +1– Ft )
0 St + 1
St+ 1
K (F t – St + 1)
+ +
Hedged position Hedged position
St + 1 St + 1
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 indi
vidual 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 relation
ships 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 actu
ally holds.