CURRENCY ARBITRAGE
5.4 THE BASIC PRINCIPLES OF HEDGING
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.
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 posi
tion 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 tech
niques of operational hedging will be described later in this chapter.
Financial hedging consists of five steps:
1. Exchange rate forecasting, which involves reviewing the likelihood of adverse exchange rate movements. More will be said about hedging and exchange rate forecasting later.
2. Assessing strategic plan impact. Once the future exchange rate changes are estimated, cash flows and earnings are projected and compared under alternative scenarios.
3. 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 dispro
portionate 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.
4. 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 illus
trated 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 appre
ciate, depreciate or stay unchanged against the base currency, x, between two points in time. Now, consider the case of a long exposure under the apprecia
tion of the currency of denomination. If yappreciates, 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 expo
sure, 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 condi
tions 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
Vx
(a) V x , n
V x , h
St + 1 +
(b)
St + 1
V x ,h – V x ,n _
+ (c)
V x ,n – V x , h
St + 1
_
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 deci
sion 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,
Vx
V , (a)
(b)
(c)
V , S t
S t
S t
V V , – ,
V V , – ,
n x
h x
1 +
1 +
1 + n x h x
h x n x
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 accu
racy of forecasting the level of the spot exchange rate, St+1, 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
_ _
Long exposure Short exposure
+ +
Unhedged position
St + 1
Hedging instrument _
+
Hedged position
St + 1 +
_
Hedging instrument
Unhedged position
Hedged position
St + 1
St + 1
FIGURE 5.3 Profit/loss on the unhedged position and the hedging instrument (a perfect hedge).
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
V Hx ( ) =V Sy t (5.1)
V Nx ( ) =V Sy t+ 1 (5.2)
V H Nx ( / ) =Vy [max( , ( St Et St+ 1 ))] (5.3)
+ Long exposure + Short exposure
+ _
S t
S t
_
Hedging instrument
Unhedged position
Hedged position +
_
S t
S t
_
Unhedged position
Hedging instrument
Hedged position
1 +
1 + 1
+
1 +
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+1). If forecasts are perfectly accurate, then
=
V H N( / ) V S St >S
+1
üý
þ if ü
ýþ (5.4)
y t t+1
=
V H N( / ) V Sy t St <St+1 which gives
x x
[ ,
V Sy t-max(S St t+ 1)] £ 0 (5.5)
and
,
Vy[max(S St t+ 1) -St+ 1 ] ³ 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 xvalues of the asset under the hedge/no-hedge decision and the hedge decision is positive or zero, implying the superiority of the former.
B(
Suppose that there are two forecasts, EA ( St+ 1 ) and E St + 1 ), such that the latter would turn out to be more accurate (that is, Et tA( t St+ 1) -St+ 1 >
B( ) -S 1). If E St+ 1) > EB(St+ 1) > S , then both forecasts would indicate
E St+ 1 t+ t A( t t
that the no-hedge decision should be taken, irrespective of the size of the fore
t > t A( B(
t
casting error. Likewise, if it turns out that S E St+ 1) >Et St+1 ), then the hedge decision should be taken irrespective of the forecasting error. Now,
A( B(
consider the situation when Et St+ 1) > S t 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 neces
sary for (5.6) to hold. If E S the decision to hedge will be taken. If this
t
t( t+ 1) < St
forecast is correct then St =max(S St t+ 1)and condition (5.6) will hold irrespec
tive. Similarly, if E S
,
t( t+ 1) >St , the decision not to hedge will be taken. If the forecast is correct then St+ 1 = max(S St, t+ 1 ), and again the condition is satis
fied. In short, what is important for the hedging decision is not the condition Et(St+1) = St+1, but rather the condition E St( t+ 1) =St . Hence, strict forecasting accuracy is irrelevant for the hedging decision.