International Short-Term Financing and Investment 251

(1 + e_y ⁾ > (1 + L ) 291

(1+f ) 300

(1+f ) 302

International Long-Term Financing, Capital Structure and the Cost of Capital 284

D = Z D, 283

E = Z 283

k = Z 289

International Long-Term Portfolio Investment 296

Rj,t = b 0,j + b 1, jR m,t + b 2,j$t + e j,t (11.40) 311

dL 319

dm ₁ -¹'—-¹'-²'"² --v-^"³ '-³ (1149) 319

+ 2ct(S 1, S ₄)w 4 +1 1 = 0 319

= 2w3 s ² (S3 ) + 2s(S 1 , S3 )w 1 + 2s(S2 , S3 )w2 320

+ 2s(S 3 , S₄ )w 4 +2 1 = 0 = 2w4 s ² (S4 ) + 2s(S 1 , S4 )w 1 + 2s(S 2 , S4 )w2 + 2s(S 3 , S4 )w 4 + 2 2 = 0 320

= w 1 + W2 + w 3 -1 = 0 320

w' = [w 1 w 2 w 3 w 4 2 1 2 2] and 331

Foreign Direct Investment 344

i 341

References 341

i 361

Index 363

The condition represented by equation (7.9) says that the operation will be profitable only if the percentage rise in the bid exchange rate is greater than the bid-offer spread. The forecast in this case must indicate not only the direc­tion but also the size of the change. The decision to buy y and sell x at time t will be taken only if

^E(Sb,t+1⁾

> 1+m (7.10)

^Sb,t

Conversely, the decision to buy x and sell y at time t will be taken if

E(Sa,t+1) < Sb,t (7.11)

If the expectation is realised such that S_at+1 < Sb,_t then the speculator can sell currency x (buy currency y) at Sb,t+1 to realise profit that is given by

P = ^Sb,t - ^Sa,t+1 (⁷.¹²)

or

p = S_b,t - (1+m)S_b ,t+1 (7.13)

For this profit to be positive, the following condition must be satisfied

(1 + m)S_b,t₊1 - S_b,t< 0 (7.14)

or

^^ < J- (7.15)

^Sb,t ¹ + ^m

which means that the operation will be profitable only if the bid exchange rate falls by a factor that is related to the bid-offer spread. Again, the forecast must

indicate the direction and the size of change. The decision to buy x and sell y will be taken only if

E( S_{b t}+₁ ) 1

^b,t+1 < — (7.16)

^Sb,t ¹ + ^m

The matter becomes more complicated if the bid-offer spread also changes between t and t + 1. So, let

Sa,t = (1+mt )S_b,t (7.17)

and

E(Sa,t+1 ) = [1 + E(mt+ 1)]E(S_b,t+1 ) (7.18)

A decision to buy x and sell y will be taken if

[1 + E(mt + i)]E(S_b,t+1 ) < S_b,t (7.19)

For this operation to be profitable, the following condition must be satisfied

E(S_{b t}+1) 1

^b,t+¹ < ¹ (7.20)

^Sb,t ¹ + ^E(mt+1⁾

which means that the change in the bid-offer spread must also be forecast.

Introducing interest rates

If interest rates are introduced, the condition for making profit by selling x and buying y will change to the following

^E(^St_± 1 ),

1 + i_x (1 + iy ) (7.21)

1 + ix ,b< _S' ¹ (1 + iy ,b ) (7.23)

a,t

S,

or

1 + ix < [1 + E(S)](1 + iy) (7.22)

which says that the rate of return on a position in x should be lower than the rate of return on a position in y. Otherwise, it will be profitable to buy y and sell x.

Without the bid-offer spreads it does not make any difference for the formula whether or not the position in x is available or that the funds have to be borrowed, because the interest rates in (7.21) and (7.22) can be taken to be the lending or the borrowing rates. If we introduce the bid-offer spreads in interest and exchange rates, the condition given by (7.21) becomes

^{E( S}b,t+1 ⁾, S

if the position in x is available. If the funds have to be borrowed, the condition changes to

1 + ix,a< ^£(S_g^{b/f+ 1 )} (1 + iy,b ) (7.24)

If we look carefully at the conditions given by (7.21)-(7.24), we find that they are equivalent to the uncovered interest arbitrage condition, which brings us back to the question of whether uncovered arbitrage is actually arbitrage or speculation. This question was discussed in Chapter 2, where we showed that under certain conditions this operation can be regarded as arbitrage. It also brings us to an issue that we will discuss later in this chapter, which is whether or not arbitrage is a risky or riskless operation.

7.3 SPOT SPECULATION BASED ON SPECIAL EVENTS

Sometimes profit can be made by speculating in the spot market based on special events. For example, George Soros made billions of dollars during the European Monetary System (EMS) crisis in September 1992, based on his fore­cast that it would be very difficult for the Bank of England to maintain the pound's fixed exchange rate within the EMS. Another example is the May 1986 devaluation of the Norwegian krone, following the collapse of oil prices in the mid-1980s. These two episodes will be described briefly here.

The EMS crisis of 1992

The UK joined the exchange rate mechanism (ERM) of the EMS in October 1991 at the central rate of 2.95 (DEM/GBP) against the German mark, a rate that many perceived to be artificially high (the pound was overvalued). Other events of the early 1990s started to unfold. First, the removal of capital controls was completed by the members of the European Economic Community in the spirit of the programme to unify financial markets within the Community. Then, there was the recession of 1992 and German reunification. The chain of events went as follows. German reunification put upward pressure on German interest rates, as the demand for funds rose with the need to finance the operation. As a result, the German mark started to appreciate against other currencies, at a time when other countries could not defend their currencies by raising interest rates, since their economies were in recession. For the UK, the situation was even more difficult, as the task of defending the overvalued pound was extremely demanding. Although the Bank of England spent almost all of its reserves to defend the pound, it was not possible to maintain the rate required by the ERM, and the pound was forced to exit in September 1992 at a lower rate. By selling the pound short in anticipation of these events, Soros made billions in profit at the expense of British taxpayers.

The Norwegian krone: May 1986

In the mid-1980s the oil market was characterised by a chronic glut resulting from a drop in demand, as industrial countries found ways to reduce oil consumption per unit of GDP. At that time, both the Norwegian krone and the pound were described as petrocurrencies because the UK and Norway had become oil exporters. The currencies were sensitive to changes in oil prices because of the dependency of the respective economies on oil revenues. Since the Norwegian economy was more dependent on oil than the British economy, it was felt that a collapse of oil prices would adversely affect both currencies, but that the Norwegian currency would be affected even more. This would also be the case because the Norwegian currency was pegged to a basket, and the defence of the rate implied by the basket required intervention in the foreign exchange market. Intervention, as we know, costs money, and if the money required for intervention is obtained from oil revenue, then a collapse of oil prices would make the Norwegian authorities less able or less willing to defend the exchange rate. At that time, the interest rates on both currencies were close at around 11%. With the Norwegian krone expected to depreciate against the pound, taking a short position on the krone and a long position on the pound would result in net profit equal to the percentage change in the exchange rate between the two currencies.

This operation can be formalised as follows. First, the cost of going short on the Norwegian krone is the interest rate on the currency, i_NOK. The return from the long position on the pound is the interest rate on the pound plus the percentage change in the exchange rate between the two currencies, iGBP + S(NOK/GBP). The net profit from this operation would be

p = (iGBP -NOK ) + S(NOK /GBP) (7.25)

If ²gbp » ²nok , it follows that

p » S(NOK /GBP ) (7.26)

Now, we have the cross exchange rate relationship

SiNOK/GBP) = ^S(NOK/USD) (7.27)

S(GBP/USD)

If the Norwegian krone falls more proportionately against the US dollar than the British pound does, such that S(NOK/USD) > S(GBP/USD), it follows that

S(NOK/GBP) = S(NOK/USD) - S(GBP/USD) > 0 (7.28)

which means that the operation would be profitable.

7.4 SPOT-FORWARD SPECULATION

Spot-forward speculation involves operations in both the spot and forward markets. Let Fj^{+ 1} be the forward rate applicable to a forward contract initiated at time t for delivery at time t + 1. If a speculator believes that the spot exchange rate prevailing at t + 1 will be higher than the forward rate then he will react by buying currency y forward at time t and selling it spot at time t + 1 when the forward contract matures. The speculator will do this if

E( St+ 1 ) > Ft (7.29)

By dividing both sides of the inequality by S_t, we obtain

E( St+ 1 ) > ft (7.30)

where f is the forward spread measured as the difference between the forward and spot rates as a percentage of the spot rate. Thus, the decision rule involves forecasting the spot exchange at time t + 1 or the percentage change in the spot exchange rate between t and t + 1. If the forecast is accurate such that E(S_t+1) = St+1, then profit (in terms of currency x) per unit of currency y is given by

p = St+ 1 - Ft (7.31)

If, on the other hand, the speculator believes that the spot rate at t + 1 will be lower than the forward rate, then he will respond by short selling currency y spot (that is, by borrowing and selling currency y) and buying it forward. Hence, the condition to indulge in spot-forward speculation is

E( St+ 1 ) < Ft (7.32)

or

E( St+ 1 ) < ft (7.33)

If the forecast is accurate such that E(S_t+1) = St+1, then profit (per unit of y) is given by

P = Ft - St+ 1 (7.34)

Spot-forward speculation in the presence of bid-offer spreads

If the bid-offer spreads in the spot and forward rates are taken into account, then the problem becomes the following. If currency y is expected to appre­ciate, a speculator will buy it forward at the offer forward rate and sell it spot at the expected bid spot rate. Hence, the condition necessary to indulge in spot-forward speculation is

E( S_b,t₊ 1 ) > Fa,t (7.35)

By definition

Fa,t = (1+m)F_b/t (7.36)

where m in this case is the bid-offer spread on the forward rate. Therefore the condition becomes

E(Sb ,t+ 1 ) > (1 + m)F_b ,t (7.37)

The expected value of the profit is

E(p) = E( S_b ,t+1 ) - (1+m)F_b,t (7.38)

which is positive when

E(S _b ) > f + m (7.39)

because F_b/t = S_b/t(1 + f). Thus, the operation will be profitable when the bid exchange rate is expected to rise by more than the sum of the forward spread and the bid-offer spread. Similar conditions can be derived for speculation by short selling y at t. Allowance can also be made for changes in the bid-offer spreads between t and t + 1.

7.5 FORWARD SPECULATION

It is possible to speculate by combining two offsetting forward transactions contracted at two different points in time but for the same delivery date; that is, by using two forward contracts with two different maturities. Consider two forward (or futures) contracts maturing at time t + 2: one is a two-period contract initiated at time t to mature at time t + 2 and the other is a one-period contract initiated at time t + 1 to mature at time t + 2. At time £, the speculator will indulge in forward speculation, by taking a long position on y, if

E(F/₊+² ) > F/+ ² (7.40)

where ² is the two-period forward rate applicable to a forward contract initiated at t to mature at t + 2 and F^² is the one-period forward rate appli­cable to a forward contract initiated at t + 1 for delivery at t + 2. Thus, E^F² ) is the one-period forward rate expected to prevail at t + 1. If this condition is satisfied, then the speculator can make profit by buying currency y on the two- period contract at t and selling the one-period contract at t + 1. At t + 2, the speculator will take delivery of currency y in accordance with the two-period contract and deliver to the counterparty in accordance with the one-period contract.

If we consider the three-period contract, then the speculator has even greater flexibility. She can speculate on the basis of the expected value of the one-period forward rate prevailing at t + 2, E( F^ ³ ), or the expected value of the two-period forward rate prevailing at t + 1, EF^³ ). Suppose that both of these rates are expected to be higher than E(Ff^{+ 3} ). The speculator can buy currency y at time t for delivery at time t + 3 and sell it at t + 1 and t + 2 for delivery at t + 3, acting on the expected values of the forward rates, E(F_tⁱ+₁³ ) and E(F_tⁱ+J⁵ ). Suppose also that she sells a fraction, w, of the amount at E(F_t^t+₁³) and the rest of the amount, 1 - w, at E(F_t^<++J^? ). The expected value of the profit is

E( p ) = w[E( F/++3 ) - F/+ ³] + (1 - w )[E(F/++|) - F/+ ³ ] (7.41)

If there are n periods, then forward speculators can speculate on a set of forward rates ranging from the one-period rate expected to prevail at t + n -1 (one period before the maturity of the n-period contract) to the (n - 1)-period rate expected to prevail at t + 1 (n - 1 periods before the maturity of the n- period contract). Again, if the speculator buys an amount at Fj + ⁿ and sells a fraction, wi, at E(F_tⁱ+ⁿ) at time t + i for i = 1 to i = t + n - 1 then the expected profit is

E( p ) = '+! w i [E(F/++") - F/+ ⁿ ] (7.42)

i=1

It is obvious that the decision rule to indulge in forward speculation requires the forecasting of the forward exchange rates prevailing between t and t + n.

7.6 SPECULATION WITH CURRENCY OPTIONS

Let us consider call and put options on currency y. The call gives the holder the right to buy currency y at the exercise exchange rate, S_t, assuming that the option is at the money, whereas the put option gives the holder the right to sell the currency at the exercise exchange rate. Let us also assume, for the time being, that we are dealing with European options, which can be exercised on the maturity of the contract only (that is on the expiry date of the option). A speculator will buy a call or sell a put if she expects currency y to appreciate and buy a put or sell a call if she expects the currency to depreciate.

Consider first the case of buying a call at time t, which expires at time t + 1. A speculator will do this if she expects the exchange rate at time t + 1 to be higher than the exercise exchange rate plus the premium, m; that is, if

E( S_t+ j) > S_t + m (7.43)

If the forecast is accurate then the speculator can make profit by exercising the option at t + 1, buying the currency at S_t and selling it spot at St+1, in which case the net profit earned per unit of y is S_t+1 - S_t - m. Based on the same forecast, the speculator may decide to sell a put. If the forecast is correct the holder of the put will not exercise and the speculator makes profit by keeping the premium paid to her (by the holder) up front.

If, on the other hand, the forecast indicates that the expected spot rate will be below the exercise exchange rate, then profit can be made by buying a put option. Thus, the condition required for buying a put option is

E(St+ 1 ) < St -m (7.44)

If the forecast is accurate, then on the expiry date, the speculator buys currency y spot at St+1 and sells it at the exercise exchange rate S_t, earning net profit of S_t - St+1 - m. Alternatively, the speculator can sell a call. If the forecast is accurate, the call will not be exercised and profit will be gained since the premium received up front can be kept. Notice that the forecast is not neces­sarily that currency y will appreciate or depreciate from the present level, but that it ends up higher or lower than the exercise exchange rate on the expiry date.

Speculation with combined option positions

We will consider two combined option positions: a short straddle and a long straddle. A short straddle involves selling a call and a put with the same exer­cise exchange rate. This position is taken when the underlying currency is not expected to move much. Suppose that at time t, a forecast indicates that E(S_t+1) = S_t. In this case, a short straddle position should be taken, because if the forecast is accurate then neither the call nor the put will be exercised and profit will be realised that is equal to the premiums received for the two options.

If, on the other hand, a forecast indicates that E(S_t+1) > (S_t + m_c + mp) or that E(S_t+1) < (S_t- m_c- mp), where m_c and mp are the premiums on the call and the put respectively, then a long straddle position should be taken. If the first forecast is accurate, the call option is exercised while the put option is left to expire, in which case the profit will be S_t+1 - (S_t + m_c + mp). If, on the other hand, the second forecast is accurate, then the put option is exercised while

the call option is left to expire, in which case net profit will be S_t - (S_t+1 + m_c + ^mp⁾.

Speculation with exotic options

We now consider an example of exotic options, the average rate option. This option gives the right to sell an amount of the underlying currency at the exer­cise exchange rate if the average spot rate over the period between t and t + n is less than the exercise exchange rate. Suppose that the average exchange rate, S, is calculated on the basis of k observations taken at times t + 1, ..., t + 2, ..., t + k, where k < n. Hence

- 1 k

^S = 1 £ ^St+ i (7.⁴5)

^k i=1

At time t, the exchange rate at t + 1, ..., t + 2, ..., t + k is not known, so S is not known. The expected value of S is

- 1 k

E( S) = 1 X E( St+ i) (7.46)

^k i=1

The option will be exercised if S < St , in which case the holder can sell the underlying currency at S_t. If the speculator buys the currency spot at the average exchange rate, S, then the profit realised is S_t -(S + m). Still better is if the speculator buys the currency spot at S_t+1, where S_t+ 1 < S. The speculator will buy an average rate option at time t if ₁ k

1 X E(St+ i) < St (7.47)

^ki=1

which obviously requires forecasting the spot exchange rate at several points in time between t and t + k.

7.7 COMBINING SPECULATION WITH ARBITRAGE AND HEDGING

The so-called "modern theory of forward exchange" has been presented as another explanation for the observed deviations from CIP by, inter alia, Spraos (1953), Tsiang (1959) and Grubel (1968). This theory is labelled "modern", although it was developed in the 1950s, because it is modern in relation to its predecessor, the CIP theory. These economists assert that operations other than arbitrage, such as hedging and speculation, also exert a determining impact on the forward exchange rate. Even earlier proponents of the CIP theory, such as Keynes (1923), Einzig (1937) and Kindleberger (1939), did not rule out the possibility of speculative pressure and offered considerations of how various speculative forces alter the relationship. According to this theory, the equilibrium forward rate is determined not only by the interest parity forward rate but also by the future spot rate expected to prevail at the maturity of the forward contract. This theory has been tested under fixed and flexible exchange rates by several economists, including Stoll (1968), Kesselman (1971), Haas (1974), McCallum (1977), Stokes and Neuburger (1979), Callier (1980, 1981), Taylor (1987a), Moosa and Bhatti (1994, 1997) and Moosa (1996a). The results of these tests have been mixed, with McCallum (1977), Callier (1981), Moosa and Bhatti (1994, 1997) and Moosa (1996a) rejecting the modern theory in favour of the traditional CIP theory.

Stoll (1968, p. 68) argues that under a flexible exchange rate system there is considerable uncertainty about the future spot rate that makes speculative demand more inelastic and, therefore, speculation less effective. This view is shared by Spraos (1953), who argues that speculative demand is highly inelastic under flexible exchange rates because speculators have no single value of the exchange rate as a reference point. While Kesselman (1971, p. 297) argues that these findings cannot be generalised for all flexible exchange markets, Moosa and Bhatti (1994) provide evidence indicating that specula­tion has no role to play in forward rate determination under the current system of flexible exchange rates. Only Taylor (1987a) found highly contrasting evidence under the flexible exchange rate period of 1973-1980.

The model

The model presented here is derived by specifying excess demand functions for forward (foreign currency) contracts. According to this model, the forward rate is determined by arbitrage, speculation and hedging. Arbitragers' excess demand for forward exchange, X^, can be defined as

X_f^a = a(F/^{+ 1} - F/+ ¹ ), a > 0 (7.48)

where Fj^{+ 1} is the actual one-period forward rate, which is determined at time t, but is applicable to delivery at time t +1, and F_t^{t+ 1} is the corresponding interest parity forward rate that is derived by adjusting the spot rate by a factor that reflects the interest rate differential. Equation (7.48) tells us that if ¹ >Fj^{+ 1} then Xj¹ > 0, implying that arbitragers will be net buyers of forward contracts. Similarly, an excess demand function can be specified for speculators which may take the form

X^s_t = b[E(S_t+ ₁ ) -F_t^{t+ 1}], b > 0 (7.49)

Thus, E(St+1) is the spot rate expected to prevail at the maturity of the forward contract (at time t + 1) conditional on the information set available at time t. If E(S_t+ 1 ) >Fj^{+ 1} then X^s > 0, implying that spot speculators will be net buyers of forward contracts.

Equilibrium cannot exist if all market participants are net buyers or net sellers of forward contracts, since it requires zero excess demand. It is achieved when there is zero excess demand, a condition that is represented by

X^a + X^s_t = 0 (7.50)

By substituting equations (7.48) and (7.49) into equation (7.50) and solving for the forward rate we obtain

:t+ 1 J ^a V t+1 ( ^b

^F> ¹ = è a+i F + Ç a+i f ^S'+* > ⁽⁷-^5I)

which tells us that the forward rate is a weighted average of the interest parity forward rate and the expected spot rate. If the coefficient on ¹ is greater than the coefficient on E(S_t+i), this means that arbitrage plays a more effective role than speculation in determining the forward rate. Moreover, if the coefficient on F^+¹ is not significantly different from unity, while the coeffi­cient on E(St+x) is not significantly different from zero, this means that CIP holds and that speculation plays no role in determining the forward rate.

It is also possible to incorporate the role of hedgers by specifying the following excess demand function

Xj¹ = g -hF_t, g ₁,h >0 (7.52)

In this case equilibrium is represented by the equation

:t+1_ ( g ^a V t+1 , ( ^h

F/+¹ = I " I +1 F/+¹ + I — |E(S_t+₁ ) (7.53)

^t I a + b + h ^J I a + b + h J ^t { a + b + h 0 ^t+¹

There are, however, two reasons why the role of hedgers may be ignored, or at least not taken into account explicitly for the purpose of specifying the model. First, Stoll (1968) argues that traders can be considered either as arbitragers or as speculators. Indeed, it is often argued that the decision whether to hedge or not is a speculative decision that depends largely on expectation. Second, McCallum (1977) concludes that if g and h are small, equation (7.53) will not be distinguishable from equation (7.51).

Figure 7.5 is a diagrammatic representation of the determination of the forward rate by arbitrage and speculation. AA is the excess demand function of arbitragers (equation 7.48) whereas SS is the excess demand function of speculators (equation 7.49). The equilibrium forward rate, F^+¹, is the one consistent with the condition of zero excess demand, which is the rate

X^s X^a

FIGURE 7.5 Determination of the forward rate by arbitrage and speculation.

satisfying the condition X^a = -X^s. It is important to notice that Fj⁺¹ is closer to Ft+ ¹ than to E(Sf+i), implying that arbitrage plays a bigger role than specula­tion in determining the forward rate (that is, a situation of arbitrage domi­nance). This is because the arbitragers' excess demand function is more elastic than the speculators' function, a situation that seems plausible under a system of flexible exchange rates.

Introducing forward speculation

Following the discussion in Section 7.5, we may specify an excess demand function for forward speculators. Considering a two-period and a one-period forward contract, this excess demand function can be written as

X f= c[E( F/+²) - F/+ ²] (7.54)

If E(Fj+ ² ) > F j^{+ 2} , then Xf > 0, implying that forward speculators will be net buyers of the two-period forward contract. In this case, the speculator can make a profit by buying the two-period contract at t and selling the one-period contract at t + 1. At t + 2 the speculator will take delivery of the foreign currency in accordance with the two-period contract and deliver to the counterparty in accordance with the one-period contract. This situation is illustrated by Figure 7.6. AA, FF and SS represent the excess demand functions

FIGURE 7.6 Determination of the forward rate by arbitrage, spot speculation and forward speculation.

of arbitragers, forward speculators and spot speculators respectively. The configuration that E(S_t+2 ) < Fj^{+ 2} < F_t^{t+ 2} < ) is only an assumption that

is used for illustrative purposes. Any other possibility can be used instead, making no difference to the description of the equilibrium position. The equi­librium two-period forward rate is determined by the point that satisfies the condition X^a + X^f = -X^s. Notice that the equilibrium forward rate, F f +², is

closer to Ft+² than to either E(Ft+² ) or E(S_t + 2 ), implying the dominance of arbitrage.

In general mathematical terms, equilibrium is achieved when there is zero excess demand, a condition that can be written as

xa

^x s

(7.55)

-^x f =⁰

in which case we obtain

b

c

F t+ 2

t

t+2

E(S+2 )+

|E(F/₊⁺i² )

F_t

a + b + c 0 ^t

(7.56)

+

a + b + c

a + b + c

where the coefficients on F ² , E(S_t+2) and E(F f+2 )signify the effectiveness of arbitrage, spot speculation and forward speculation respectively.

If we consider the three-period contract, forward speculators have even greater flexibility. They can speculate on the basis of the expected value of the one-period forward rate prevailing at t + 2, E(Ff+3 ), or the expected value of the two-period forward rate prevailing at t + 1, E(Ff+j³ ). In this case the equi­librium condition becomes

a

_Fu² +

^a 3 + ^b 3 + ^c 31 + ^c 32 0

31

b

3

3

Ft+ 3 t

^E(^St+3)

. ^a 3 + ^b 3 + ^c 31 + ^c 32 0

(7.57)

\ ^Fi+3)

32

^EK+1³)

+

^a 3 + ^b 3 + ^c 31 + ^c 32 0

. ^a 3 + ^b 3 + ^c 31 + ^c 32 0

The coefficient C31 measures the effectiveness of forward speculation in deter­mining the three-period forward rate when the one-period forward rate is used as the variable on which the (forward) speculative decision is based. Likewise, the coefficient C32 measures the effectiveness of forward speculation when speculative decisions are based on the two-period forward rate. The coefficients «3 and ^3 measure the effectiveness of arbitrage and spot specula­tion in determining the three-period forward rate.

In general, if there are n periods then forward speculators can speculate on a set of forward rates ranging from the one-period rate expected to prevail at t + n - 1 (one month before the maturity of the one-period contract) to the (n - 1)- period price expected to prevail at t + 1 (n - 1 periods before the maturity of the n-period contract). The generalisation of equation (7.57) may, therefore, be written as

b

a

rt+ n t

Ft+ n , t

n

n

^E(^St+n )

^a n + ^bn /=i^cnz 0

^an + ^bn ^cni 0

(7.58)

n-1 i=1

t+ n- i '

c

^E(^F/:n- i)

^an + ^bn ⁿ₌l^1cni 0

where the coefficient c_ni measures the effectiveness of forward speculation in determining the n-period forward rate, such that the speculative decision is based on the i-period forward rate expected to prevail at t + n - i.

Speculation as a source of deviation from CIP

(7.59)

The role of speculation as a source of deviations from CIP can be demonstrated by rewriting equation (7.51) as

F/+¹ = b o + b iF/⁺¹ + b 2 E(St+1 )

which can be rewritten as

Ft+1 t

^E(^St+1 )

(7.60)

b

b 1 0

1

:t+1 ^b0

t

1 0

Since CIP holds precisely for ¹, the modified CIP condition prevailing at time t becomes

(7.61)

^b

^St

₁ . [F/⁺¹ -b0 — b2 E(St+1 )] œ¹ + K ö 1 + l_x = —^t—

1 0

or

Ft+ ¹ œ 1+L ö

œ 1+iy ö b

(7.62)

¹ + ⁱx = -

^b

^St

1 0

1 0

( b 0 + b 2 E(St+1 )

By manipulating equation (7.62), we obtain

:t+1

t

( b 0 + b 2 E(St+1 ))

¹ + ïx = ■

S

(7.63)

œ¹+iy ö

-⁽¹ + ⁱy ^{) —}

^b

1 0

^St

v

œ Ft+1 ö

(1 + iy )(b 1 —1) b 1

V

Equation (7.63) implies the presence of a neutral band of ±D, where

œ _Ft+1 ö t

(7.64)

D =

^St

1 0

y

V

(i+i_y V

^y

b 0 + b 2 E(St+1) — ( b 1 — 1)

^b

Therefore, the effect of speculation is to distort the CIP relationship, such that the covered margin must exceed D in order to trigger arbitrage. Otherwise, equilibrium will be maintained with the presence of what may appear to be deviation from CIP.

7.8 HEDGING AS A SPECULATIVE ACTIVITY

Hedging and speculation are normally defined to imply that they are diamet­rically opposite to each other, and the same applies to hedgers and specula­tors. Hedging is the covering of risk, whereas speculation is the deliberate assumption of risk in anticipation of profit. Hedgers hate risk and therefore they cover it, whereas speculators love risk and strive to bear it. Hedgers and speculators are, therefore, two different species with diametrically opposite tastes for risk. However, it can be argued that this is not the case and that hedging can be viewed as a speculative activity. It will also be demonstrated that, at least in some cases, hedgers and speculators may behave in similar manners and react to changes in the same parameters.

The definition of hedging and the description of hedgers stated earlier are based on the assumption that the agent's objective is to minimise risk rather than to maximise expected utility, the latter being dependent on risk as well as expected return. It is arguable that risk minimisation without any regard to the effect on expected return cannot be optimal (see, for example, Cecchetti et al., 1988). This is because risky assets are priced to earn expected premium over the riskless rate. Hence, hedging away the risk must also hedge away the expected return to bearing that risk, which may not be desir­able. It is indeed the case that only a totally risk averse agent can make an optimal hedging decision without taking the impact on both risk and return into account. In practice, hedgers are aware of the trade-off between risk and return, and this is why they may hedge partially or selectively. This is also why they may remain exposed to market risk on part of their position or part of the time. Therefore, hedgers do not hedge automatically but take a deci­sion whether or not to hedge on the basis of expectation with respect to the decision variable.

There is some body of theoretical and empirical literature indicating that the decision to hedge is not as automatic as the decision to pray for a religious person. For example, Dolde (1993) argues that firms with exposure to foreign exchange risk may not hedge, partially hedge or stay unhedged depending on their perception abut the behaviour of exchange rates. This is essentially spec­ulative behaviour, and it is obvious that there is significant overlapping between hedging and speculation in this case. Joseph (2000) and Marshall (2000) provide some survey evidence on this issue. Furthermore, Culp and Miller (1995) argue that "most value-maximising firms do not hedge". Finally, Stulz (1995) argues that a firm with little debt or with highly-rated debt has no need to hedge, as the risk of it getting into financial trouble is tiny. Therefore, hedging is invariably a speculative activity.

It is also possible to show that speculators and hedgers use the same decision variables. For this purpose we refer the model of pricing futures contracts proposed by Moosa and Al-Loughani (1995) and its extension in Moosa (2000b), a version of which was presented in the previous section. In this model specula­tors have an excess demand function for crude oil futures contracts that can be written as Xf = b[E( S_t+ 1 ) - Fj+ ¹], where b > 0. Speculators have an incentive to enter the market whenever there is a difference between E(St+1) and F* + ¹. If E(S_t+ 1 ) > Fj+ ¹ there will be excess demand by speculators who will buy the commodity futures at t and sell it spot at t + 1, making profit of S_t+ 1 - F* + ¹ if their expectations are realised. Otherwise, they will buy futures and sell spot.

It can be demonstrated that the behaviour of hedgers is identical to the behav­iour of speculators. Consider first long hedgers who buy futures contracts. For these hedgers, the expected cost of hedging is the difference between the futures price and the expected spot price, Fj+ ¹ - E(S_t+ 1 ), which is the expected cost they are willing to accept to avoid uncertainty. Naturally, the smaller the expected cost, the greater will be the demand for futures contracts, implying that excess demand by long hedgers is a positive function of E(S_t+ 1) - Fj+ ¹. Conversely, the expected cost of hedging for short hedgers is E(S_t+ 1) - Fj + ¹. Since short hedgers are suppliers of futures contracts, supply will decrease (excess demand will increase) as the expected cost of hedging increases. Again, excess demand is a positive function of E(S_t+ 1) - F_t^{i+ 1}. It is obvious that the expected cost of long hedgers, Ft+ ¹ - E(S_t+ 1 ), is equivalent to the profit made by speculators who buy spot and sell futures, whereas the expected cost of short hedgers, E(S_t+ 1) - F_t^{i+ 1}, is equivalent to the profit made by speculators who buy futures and short sell spot. Hedgers and speculators act upon the same variables, and this is why this model does not distinguish between them.

There may be only one difference between hedgers and speculators in this particular case. Hedgers are more likely to be market participants who actually require the physical commodity (for example, industrial companies). Specula­tors, on the other hand, are the participants who are not interested in the physical commodity per se but rather in generating speculative profit from holding ownership titles in that commodity (for example, financial institu­tions). This is an institutional difference. As far as behaviour is concerned, hedgers and speculators belong to the same species.

7.9 STABILISING AND DESTABILISING SPECULATION

Speculators participate in the foreign exchange market, buying and selling currencies on the basis of certain expectations about the future movements of exchange rates. By their actions, speculators affect the supply of and demand for currencies and, therefore, exchange rates.

Speculation can be stabilising and destabilising. Figure 7.7 shows the effect of destabilising and stabilising speculation on exchange rate volatility. Desta­bilising speculation, which leads to an increase in exchange rate volatility, occurs when speculators buy a currency when it is high and sell it when it is low. This kind of behaviour arises, for example, when speculators believe that there are "bubbles" in the market. Thus, when a currency appreciates, they think that it will keep on appreciating, so they will buy it until the bubble bursts for one reason or another. Conversely, when a currency depreciates they believe that it will keep on depreciating, so they will keep on selling it, inducing a run on the currency. Krugman (1989) identifies two episodes of destabilising speculation on the US dollar: the 1984-1985 appreciation and the surge of April-June 1989.

Stabilising speculation works the other way round. When the demand for a currency increases, it appreciates, and as it appreciates further speculators start thinking that it is overvalued so they sell it, causing it to depreciate. Conversely, when a currency depreciates, because of an increase in its supply, speculators will start thinking that it is undervalued and hence it is a bargain. Therefore they will buy it, reversing the trend in the foreign exchange market. Stabilising speculation, therefore, reduces exchange rate volatility.

Is profitable speculation stabilising?

St

FIGURE 7.7 The effect of stabilising and destabilising speculation on exchange rate volatility.

Following Farrell (1966), it can be shown that profitable speculation is stabi­lising. Let S_t and St+1 be the exchange rates in two successive periods in the

absence of speculation. Speculation takes the form of buying Q units of the foreign currency at t and selling it at t + 1. Speculative purchases and sales produce the exchange rates S_t and S_t+ 1, which are given by

~_t = S_t + aQ (7.65)

~t + 1 = St+ 1 - aQ (7.66)

where a > 0. The mean value of the exchange rate in the absence of speculation is given by

S =^(St + ^St+ 1⁾ = ⁽~ + 1 ⁾ (7.67)

22

which means that speculation (in this case) does not change the mean value of the exchange rate. Speculative profit is given by

p = Q(% 1 -~t ) (7.68)

By substituting equations (7.65) and (7.66) into (7.68) we obtain

p = Q(St+1 - St ) - 2aQ² (7.69)

Exchange rate volatility is measured by the variance of the exchange rate. Without speculation, the variance is given by

s ² = JL[(St -S)² + (St+ 1 -S)² ] = 4(St -St+ 1 )² (7.70)

On the other hand, the variance of the exchange rate with speculation is given by

s - S)²+ (~t + 1 - S)² ] (7.71) By substitution and manipulation we obtain

s 2 = 4 (St - St+ 1 )² + (St - St+ 1 )aQ + a² Q ² (7.72)

or

s 2= s n- ap - a² Q ² (7.73)

Equation (7.73) shows that if p > 0, then s ² < s j2 . Hence, profitable specula­tion is stabilising.

7.10 SPECULATIVE BUBBLES

A bubble is a self-reinforcing movement in prices (including exchange rates) away from their equilibrium level that is determined by fundamentals. This happens, for example, when everyone thinks that the price is too high (low),

but no-one expects it to fall (rise). Sometimes, bubbles are explained in terms of trader irrationality, market psychology, mass hysteria and so on. However, bubbles can be reconciled with rational behaviour, hence the term "rational bubbles".

Once a bubble starts, it becomes a reality that traders have to live with. The equilibrium value or fair value, as envisaged by an economist, becomes irrele­vant. Traders take the attitude whereby they will buy as long as the market believes that prices will keep on rising. The perceived continuation of the price rise provides compensation for risk bearing. This is why traders kept on buying the US dollar in the 1980s although it was overvalued by all measures. In hindsight, we know that the 1980-85 appreciation of the dollar was a spec­tacular bubble (Figure 7.8).

If the foreign exchange market is not experiencing a bubble, the exchange rate is determined by fundamentals, the expected values of the fundamentals to be precise. Thus

St = /[X t , E(Xt+ 1), E(Xt+ 2 ),•.., E(Xt+ _k)] (7.74)

In the presence of a bubble, equation (7.74) becomes

St = /[X t , E(Xt+ 1), E(Xt+ 2 ),•.., E(Xt+ k)] + Bt (7.75)

where the bubble term represents the extent of the deviation from the funda­mental equilibrium rate. The bubble, B_t, has the property

EEBt+ 1 ) = b^-1Bt (7.76)

where b < 1. Existing theory has nothing to say about how and why a bubble develops. However, two propositions stand out. The first is that it is sufficient for traders to perceive the bubble factor to be important for it to become

FIGURE 7.8 The US dollar's effective exchange rate.

important. Second, a bubble can be viewed as a variable that is unobservable to economists but observable to traders.

At any point in time, there must be some perceived probability that the bubble will burst in the next period. If this happens, the term Bt will disappear from equation (7.75), which means that the exchange rate will revert back to its fundamental equilibrium level. By introducing this probability, the behaviour of the bubble can be represented as follows:

^E(Bt+ 1⁾ = ^{b -1B}t 1 ₍₇₇₇₎ E(Bt+ 1) = 0 j ⁽.⁾

with probabilities p and 1 - p respectively. In this case, as long as the bubble persists the exchange rate will rise sufficiently in order to compensate traders for the possibility of loss when the bubble bursts. The greater the exchange rate's deviation from fundamentals, the further it has to fall and hence the greater the prospective capital gains needed to sustain the process.

Bubbles may be triggered by fundamental changes, actual or perceived, but they may be spontaneous. Empirical research reveals, for example, that the behaviour of the dollar until the mid-1980 was a rational bubble. The presence of bubbles is often suggested as a reason for the failure of fundamental models of exchange rates, such as the monetary model (for example, Lane 1991).

CHAPTER 8

Speculation: Generating Buy and

Sell Signals

8.1 SPECULATION ON THE BASIS OF EXPECTATION FORMATION

Foreign exchange market participants may act on the basis of expectations on the future change in the exchange rate, such that the expectation is formed in a mechanical manner following one or more expectation formation mecha­nisms. These mechanisms will be specified in terms of the percentage change in the exchange rate, S, which may be approximated by the first log difference of the exchange rate. Again, it will be assumed that t is the present time, when the expectation is formed, whereas t + 1 is future point in time at which the actual value of the expected variable materialises and which coincides with the outcome of the decision taken at time t. For the purpose of the following analysis, the words "forecasting" and "prediction" may be used interchange­ably with the word "expectation". Strictly speaking, however, forecasting may be defined as a formal way of forming expectations. Another point that is worthy of mentioning here is that the expectation formation mechanisms may be written in terms of the level rather than the percentage change in the exchange rate.

Extrapolative expectations

There are four versions of extrapolative expectations, which are represented by the equations

palgrave 1

palgrave 2

i 19

i 23

CHAPTER 3 44

Other Kinds of Arbitrage and Some Extensions 46

3.1 COMMODITY ARBITRAGE 46

^Py ,t+ 1^/Py ,t 55

3.2 ARBITRAGE UNDER THE GOLD STANDARD 61

3.3 ARBITRAGE BETWEEN EUROCURRENCY AND DOMESTIC INTEREST RATES 63

3.4 EUROCURRENCY-EUROBOND ARBITRAGE 74

3.5 ARBITRAGE BETWEEN CURRENCY FUTURES AND FORWARD CONTRACTS 52

3.6 REAL INTEREST ARBITRAGE 54

3.7 UNCOVERED ARBITRAGE WHEN THE CROSS RATES ARE STABLE 55

3.8 UNCOVERED INTEREST ARBITRAGE WHEN THE BASE CURRENCY IS PEGGED TO A BASKET 57

^ ^ 1=1 »j ^ j=1 and 57

E1= S ₀ - S j (3.40) 57

3.9 MISCONCEPTIONS ABOUT ARBITRAGE 83

CHAPTER 4 65

Hedging Exposure to Foreign Exchange Risk: The Basic Concepts 65

4.1 DEFINITION AND MEASUREMENT OF FOREIGN EXCHANGE RISK 65

4.2 VALUE AT RISK 69

4.3 DEFINITION AND MEASUREMENT OF EXPOSURE TO FOREIGN EXCHANGE RISK 74

4.4 TRANSACTION EXPOSURE 82

4.5 ECONOMIC AND OPERATING EXPOSURE 84

4.6 A FORMAL TREATMENT OF OPERATING EXPOSURE 95

dQ_py_ dPy Q 102

4.7 TRANSLATION EXPOSURE 123

Financial and Operational Hedging of Exposure to Foreign Exchange Risk 105

^Fb,t - ^Sb,t 123

^{p - K(F}a,t ^{- S}b,t+ 1 ⁾ 133

Measuring the Hedge Ratio 158

, ^s(DPu,t, ^DPA,t I^f t-1) ,_{t t} . 164

^h = ^ ^ r" = ^P(X 1,t , ^X 2 ,t ⁾ 164

^{s 2(D}P A,t^|f t-1 ⁾ 164

^DP u,t = t-1 + Z ^ai ^DP U,t-i +Z ^bi ^dPa ,t-i +^x 1,t ⁽⁶.³³⁾ 186

^DP A,t =^-bft-1 + Z ^ci ^DP U,t-i +Z ^d i ^DP A,t - i +^X 2 ,t ⁽⁶.³⁴⁾ 186

^s(DPU,t^{, D}PA,t I^f t-1^{, D}PU,t-i^{, D}PA,t-i⁾ 186

^s2 (^APA,t I^f t-1' ^APU,t-i ' ^APA,t-i ⁾ _{(6 35}) 186

I,t ' X 2,t ) / s(X i,t ) ^ 186

= P^(X 1't ' ^X 2 ,t ⁾ 186

_ P^(X 1,t ^{, X} 2 ,t^)s(X 1,t^)s(X 2 ,t^{) -2 (f} t-1^{1 A}P U,t-i^{, A}PA,t-i⁾ 187

^s2 (^X2 ,t ) + ^{b2 s 2} (f t-1^{1 A}PU,t-i^{, A}PA,t-i ) 187

Speculation in the Spot and Currency Derivative Markets 184

^Sb,t 198

^Sb,t ¹ + ^m 198

^Sb,t ¹ + ^E(mt+1⁾ 199

^{E( S}b,t+1 ⁾, S 200

if the position in x is available. If the funds have to be borrowed, the condition changes to 201

Speculation: Generating Buy and 209

Sell Signals 209

St = f (Xt) 257

where the vector of variables varies according to the underlying fundamental model. The current level of the exchange rate may deviate from the equilib­rium level because of the effect of random shocks that tend to have a tempo­rary effect. Hence the current level of the exchange rate may be represented by 258