0.6 0.8 Hedge ratio

FIGURE 6.6 The variance ratio as a function of the hedge ratio (all data).

Hedge ratio

FIGURE 6.7 Variance reduction as a function of the hedge ratio (all data).

TABLE 6.5 Variances of the rates of return on unhedged and hedged positions.

Hedging	Base	Exposure	Hedge	Variance	Variance
technique	currency	currency	currency	(unhedged)	(hedged)
Forward	USD	GBP	GBP	23.5	0.15
Forward	USD	CAD	CAD	3.8	0.09
Forward	GBP	CAD	CAD	26.06	0.23
Cross	USD	GBP	CAD	23.5	23.06
Cross	USD	CAD	GBP	3.8	9.66
Cross	GBP	CAD	USD	26.06	5.82

It seems that it all depends on correlation. Forward hedging is more powerful than cross hedging because the percentage change in a spot rate is more highly correlated with the percentage change in the corresponding forward rate than with that of another spot rate.

(a) Base currency (USD), exposure currency (GBP)

Unhedged Hedged

(b) Base currency (USD), exposure currency (CAD) 4

-5

Dec-89 Dec-91 Dec-93 Dec-95 Dec-97 Dec-99 Dec-01

Unhedged Hedged

(c) Base currency (GBP), exposure currency (CAD)

Unhedged Hedged

FIGURE 6.8 The effectiveness of forward hedging.

(a) Base currency (USD), exposure currency (GBP), hedging currency (CAD)

Unhedged Hedged

(b) Base currency (USD), exposure currency (CAD), hedging currency (GBP)

(c) Base currency (GBP), exposure currency (CAD), hedging currency (USD)

FIGURE 6.9 The effectiveness of cross currency hedging.

Unhedged Hedged

CHAPTER 7

Speculation in the Spot and Currency Derivative Markets

7.1 DEFINITION OF SPECULATION

Speculation in the foreign exchange market is a subject that has been dealt with in the early writings on exchange rate economics. Early contributors to the post-war literature on exchange rate economics were to a large extent concerned with the role of speculation in the foreign exchange market. Nurkse (1945) warned against the dangers of "bandwagon effect" as a source of market instability. In his seminal work on the choice between fixed and flex­ible exchange rates, Friedman (1953) argued for flexible exchange rates by suggesting that speculation would be stabilising under flexible exchange rates because profit-making requires buying low and selling high, which is the action that makes speculation stabilising. A proof of this proposition will be presented later.

i

Tirole (1993) argues that the concept of speculation has always fascinated academics and practitioners alike, attributing this fascination to "inconsistent definitions, occasional misunderstanding and genuine economic importance". Speculation may be defined as the assumption of risk for the sake of making profit. Speculators act on the basis of certain beliefs or expectations, making profit if their expectations are realised (or if their forecasts turn out to be accu­rate). Another definition that can be found in the Oxford Universal Dictionary is that it is "the action or practice of buying and selling goods, stocks and shares, etc. in order to profit by the rise or fall in the market value, as distinct from regular trading or investment". Keynes (1930) and Hicks (1939) viewed speculation as a substitute for missing insurance markets, in that gains from trading are linked to differences in the trader's willingness to take risk on an initial position. This is the so-called insurance motive for speculation, whereby speculation is viewed to be used to shift price risk from more to less risk-averse traders. Apart from the insurance motive, there are the following motives for speculation:

1. The liquidity motive, whereby traders may need to sell assets in periods of financial necessity or buy to diversify.

2. The divergence of priors, whereby assets are traded because agents disagree on their future value. Working (1953b) argued that the differences in beliefs are the key to speculative behaviour.

3. Speculators may be intermediaries acting on behalf of non-participating investors, in whose case the motivation for speculation would vary, depending on how they are compensated for their services.

7.2 SPOT SPECULATION

where the term in square brackets is the percentage change in the spot exchange rate. If S_f+1 > S_f, it follows that p > 0, and vice versa.

The decision to speculate is based on the expectation that y will appreciate, which is represented by the inequality E(S_f+i) > S_f. The expectation repre­sented by the inequality pertains to the direction of the change in the exchange rate only, in the sense that it indicates that currency y will appreciate without saying by how much. Suppose now that the expectation takes the form of a formal forecast that has a quantitative dimension as well, such that E(S_f+ i ) = 0S_t where q > 1. If the forecast turns out to be accurate such that S_t+ i = dS_t , and it is acted upon, then the resulting profit will be given by

p = K(q -1) (7.2)

Speculation is the deliberate assumption of risk to obtain profit. In the case of spot speculation, the risk arises from changes in the spot exchange rate. We will initially ignore the interest rate factor by, for example, assuming that the interest rates on the two currencies that are bought and sold are equal.

The simple case

Spot speculation entails selling an amount, K, of currency x, which is expected to depreciate against currency y, which is expected to appreciate, and then reversing the operation in the future. Suppose that the present time is t such that the exchange rate is S_t. If y is expected to appreciate in the future such that E(S_t+i) > S_t, then a decision will be taken to sell an amount, K, of x to obtain KS_t of y. If the expectation turns out to be correct such that S_t+i > S_t, then the amount K/S_t of y is converted back into x at t + 1 to obtain KS_t+i/S_t. Net profit (in terms of currency x) is

Again, p > 0 because Q > 1. The difference in this case is that the forecast not only indicates that y will appreciate and that profit will be made, but also indi­cates the extent of the appreciation and hence the size of the profit.

Figure 7.1 shows this relationship diagrammatically when K =1. First, the equation S_t+1 = QS_t is represented in the S_t-S_t+1 space by a straight line falling above the 45° line S_t+1 = S_t (because Q > 1). In this part of the diagram profit is measured by the gap between the two lines S_t+1 = QS_t and S_t+1 = S_t. The second part of the diagram is a 45° line that is used to transfer St+1 from the vertical axis to the horizontal axis. The third part of the diagram is used to plot profit, p, against the exchange rate at t + 1 represented by the equation p = -1 + (1 / S t )S_t+1, which means that it is a straight line with an intercept of -1 and a positive slope of 1/St. Notice that the intercept indicates the maximum possible loss, which is realised when S_t+1 = 0. If the exchange rate does not change (Q = 1), then profit would be zero. In Figure 7.2, it is shown that when Q < 1 a loss would be made.

5

5

5

5

5_t+1= 6S_t (9 > 1) ^St+i = ⁵t

p

Profit

FIGURE 7.1 A diagrammatic representation of speculative profit (0 > 1).

^st+i - ^st

Sf+i - es_t (e <1)

Loss

FIGURE 7.2 A diagrammatic representation of speculative profit (q < 1).

St

What if the forecast is not accurate, magnitude-wise, such that S_t+1 = 1S_t , where q > 2 > 1? This means that the exchange rate has risen as the forecast indicated but not to the same extent. In this case profit will be lower, since 0 < K(2 -1) < K(q -1). Figure 7.3 provides a diagrammatic representation of this case, in which profit associated with q is larger than the profit associated with 2.

The forecast as a probability distribution

If the forecast is given in terms of a probability distribution, then the situation becomes as follows. Suppose that there are q point forecasts given by E(S_t+1,i), each materialising with a probability pi, where i = 1, 2, ..., q. Consider two fore­casts, E(S_t+1j) and E(S_t+1,k), such that E(S_t+1,j) < S_t < E(S_t+1,k). If the decision maker acts on the basis of the lower forecast, E(S_t+1,j), which materialises with a probability pj, then a decision will be taken to buy currency x and sell currency y, since the forecast indicates that the former will appreciate. Conversely, if the decision maker acts on the basis of the higher forecast,

S

5_t+1 - 6S_t

S

S

p

FIGURE 7.3 A Diagrammatic representation of speculative profit (0 > 1 > 1).

E(St+i,k), which materialises with a probability pk, then a decision will be taken to buy currency y and sell currency x, since the forecast indicates that the former will appreciate. If the decision is based on one forecast, then this natu­rally should be the forecast with the higher probability. Thus, if pj > pk a deci­sion will be taken to buy x and sell y, and vice versa.

More appropriately, the decision is made on the basis of a weighted average of

the forecasts where the weights are the probabilities. This is given by

q

E(St+1) = 1 Pi E(St+ _u ) (7.3)

i=1

The outcome will depend on the actual exchange rate at t + 1 in the same manner as before. Figure 7.4 shows four possibilities for the level of specula­tive profit with five different values for the exchange rate at t + 1.

^St+i ^St+i

Introducing the bid-offer spread

We will now introduce the bid-offer spread. Let the bid and offer exchange rates at time t be Sb,_t and S_a,_t, such that S_a,_t = (1 + m)Sb,_t, where m is the bid-offer spread expressed as a percentage of the bid rate. In the presence of the bid-offer spread, the speculator buys currency y at the higher offer rate and sells it at the lower bid rate. If the forecast bid and offer rates are E(Sb,_t+i) and E(S_a,_t+i), and assuming that there is no change in the bid-offer spread between time t and time t + 1, then

E(Sa,t₊1) = (1 + m)E(S_b ,t+1 ) (7.4)

To act on the basis of the forecast, a decision to buy y and sell x at time t will be taken if y is forecast to appreciate such that E(Sb,_t+1) > S_a,_t. If the forecast is accurate such that Sb,_t+1 > S_a,_t, then the speculator can sell currency y at time t + 1 at Sb,_t+1 to realise profit (per unit of y) that is given by

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