(c)
Adaptive expectations (constant exchange rate)
0.08
0.06
0.04
0.02 0.00 -0.02
(d)
Regressive expectations (fluctuating exchange rate)
0.02
0.00
-0.02
0
Actual Expected
•
Error
FIGURE
8.2
(continued)
0.08
0.06 0.04
1 23456789 10 Actual Expected • Error
There is also the problem of picking the "correct" exchange rate determination model, given that most fundamental models have been shown to be inadequate (Moosa, 2000a). Pilbeam (1995a), for example, uses the forward rate to proxy rational expectations, an option that we do not find that appealing. Takagi (1991) argues against using the forward rate to represent expectations because this procedure presupposes that there is no risk premium, which is a testable hypothesis. Another problem with the rational expectations hypothesis is that it rules out the existence of differences between the predictions of various participants, since the "true stochastic process" should be unique. However, MacDonald (2000) presents survey evidence on unbiasedness, orthogonality and expectation formation that reveals differences between forecasters. The absence of heterogeneity in expectation formation is
inconsistent with the market microstructure literature that stresses the presence of heterogeneity and its implications for volatility (see, for example, Lyons, 2001).
One way to use rational expectations to generate buy and sell signals is to follow Pilbeam (1995a), who assumes that all of the market information is reflected in the forward spread, such that if a currency is selling at a premium, then it should be expected to appreciate and vice versa. This in fact is a prediction of the version of the flexible price monetary model that incorporates covered interest parity (see, for example, Moosa (2000b, Chapter 4)). Hence, rational expectations may have the representation
E(St+ 1 ) > 0 E(S t+ 1) < 0
Thus a buy signal is indicated when there is a forward premium and a sell signal is indicated when there is a forward discount.
The learning mechanism
Marcet and Nicolini (1998) suggested an expectation formation mechanism of the form
1
Et (S t+1 ) = Et-1 (S t ) + — [S t-1 - Et- 1(S t)] (8.17)
at
which says that the expected change in the exchange rate is updated by a term that depends on the last error weighted by 1/at. The behaviour of at is represented by
a t= a t-1 + 1 (8.18)
where a0 is set exogenously to be equal to zero. In this case at = t, and it follows that
1 t
E(S t+1 ) =1 I S ; (8.19)
t i=1
which means that the expected change in the exchange rate is equal to the sample mean of past changes. Equivalently, it is the result of regressing Si on a constant.
Mixed and contrarian expectations
Ft - St > 0 Ft - St < 0
if
(8.16)
expected change in the exchange rate to be the average of the expected changes obtained from other mechanisms, or by following the majority signal. Contrarian expectations are formed by market participants who hold a diametrically opposite view to the market as a whole. They can be proxied by the negative of what is obtained under mixed expectations.
Evidence on expectation formation in the foreign exchange market
Studies on expectation formation in the foreign exchange market follow two approaches. The first approach is based on survey data, whereas the second approach is based on estimating demand for money functions that incorporate various expectation formation mechanisms.
Broadly speaking, two sets of results are reported in studies based on survey data: one set deals with testing for rational expectations, whereas the other deals with the expectation formation mechanisms. Testing for rational expectations boils down to testing for (expectation) unbiasedness (that the expected exchange rate is an unbiased predictor of the spot rate that will prevail in the future) and orthogonality (that expectations incorporate all available information). Takagi (1991) surveyed the studies conducted by Dominguez (1986), Frankel and Froot (1987a,b), Bank of Japan (1989), Wakita (1989), Froot and Frankel (1990) and Ito (1990). He concludes, on the basis of his survey, that the evidence overwhelmingly rejects rational expectations. For example, Dominguez (1986) almost unanimously rejected rational expectations, concluding that forecasters missed the direction of exchange rate movements, and that forecasters overpredicted the size of future dollar depreciation. Takagi (1991) obtained what he calls the crucial result that whereas short-run expectations tend to move away from some long-run "normal value", longrun expectations tend to move back towards it. He calls this reversal in the direction of expectation a "twist". The evidence in general supports extrapolative and regressive expectations, but not static expectations.
MacDonald (2000) surveyed some of the same studies covered by Takagi (1991) as well as more recent studies. These studies include Dominguez (1986), MacDonald and Torrance (1988), Frankel and Froot (1987a, 1989), Cavaglia et al. (1993), Chinn and Frankel (1994), Prat and Uctum (1996) and Kim (1997). His results strongly rejected both unbiasedness and orthogonality. He also found evidence for the "twist" in expectation formation, concluding that forecasting at horizons longer than three months exhibit clear evidence for stabilising expectation.
Most of the studies following the second approach (of estimating demand for money functions incorporating expectation formation mechanisms) impose rather than test for the mechanisms. One exception is the study of Moosa (1999) in which he tests for expectation formation under the German hyperinflation of the 1920s using static, extrapolative, adaptive, regressive and rational expectations. The results of this analysis reject rational expectations, lending most support to extrapolative and adaptive expectations. It is also revealed that expectation is destabilising under conditions of hyperinflation.
Moosa and Shamsuddin (2002) used historical data to conduct a study in which they related the dominance, or otherwise, of an expectation formation mechanism to the profitability of a trading rule based on it. By calculating the accumulated profit generated over a long period of time by trading on the basis of buy and sell signals generated by various mechanisms, they reached the following conclusions. First, the dominant mechanism is extrapolative expectations, indicating that most market participants believe that a rise in the exchange rate will be followed by a rise and vice versa. Second, the superiority of mixed expectations over contrarian expectations, indicating that market participants follow some sort of a herd behaviour and that they pay attention to the expectations of other participants.
8.2 SPECULATION ON THE BASIS OF TECHNICAL ANALYSIS
Definitions and principles
Technical analysis can be defined as the study of exchange rates (and other financial prices) based on supply and demand. Technical analysts (also called technicians or chartists) record, normally in chart form, historical exchange rates and try to deduce from the pictured history the probable future trend, generating buy and sell signals in the process. They may also use quantitative technical indicators. The basic idea is that exchange rates as observed in the foreign exchange market are determined by supply and demand, and this is all that is needed to be known.
Traditionally, economists have rejected the propositions put forward by technical analysts, since they believe that economic fundamentals are the only determinants of exchange rates. Given the notion of market efficiency, old information (particularly publicly available information) must be useless because it is already incorporated in the current exchange rate. Malkiel (1996) puts forward the cynical view that "technical strategies are usually amusing, often comforting, but of no real value". A question that seeks an answer is that if this is the case, why is it that technical analysts are still in demand by financial institutions? Malkiel has a ready answer: they are hired by brokers largely in order to generate trades and hence commissions. Allen and Taylor (1993) put forward the counter argument that even if this is the case, "the results of this policy manifest themselves as self-fulfilling chartist strategies". The fact remains, however, that the failure of fundamental models has forced economists to take technical analysis more seriously.
Lo et al. (2000) evaluated the status quo of technical analysis in terms of the separation between technical analysts and their academic critics, which they describe as "one of the greatest gulfs between academic finance and industry practice". To emphasise this point, they cite anti-technical analysis slogans, such as the following:
The difference between technical analysis and fundamental analysis is not unlike the difference between astrology and astronomy.
Technical analysis is "voodoo finance".
Under scientific scrutiny, chart-reading must share a pedestal with alchemy (Malkiel, 1996).
Indeed, some economists have gone as far as saying that one reason for the popularity of technical analysis is that it uses rather "erotic terms", such as "penetration points". But, Lo et al. (2000) defend technical analysis, arguing that it may be an effective means for extracting useful information from market prices. They base this argument on the findings of a large number of studies revealing that financial markets are not fully efficient and rejecting the random walk hypothesis. These findings provide some support for using technical analysis. Furthermore, they argue that technical analysis and fundamental analysis share the premise that past prices contain information for predicting future prices, except that they put that differently. Campbell et al. (1997, pp. 43-44) provide two statements to demonstrate the difference between technical analysis and academic finance. While technical analysts talk about "support and resistance levels", "retrenchment parameter", and so on, finance academics talk about "the first twelve autocorrelations" and the "statistical significance of the Box-Pierce Q-statistic".
Technical analysis is based on the postulation that exchange rates do not move randomly but rather in repeated and identifiable patterns. The exchange rate series that is recorded over time reflects all available information on which supply and demand decisions are based. This information pertains to economic fundamentals as well as to other non-quantifiable factors such as expectations, sentiment and psychology. It is these factors that lead to the emergence of the patterns observed by technical analysts. This postulation does not go without a challenge, however. For example, Cootner (1964) and Malkeil (1996) argue that the apparent cycles in stock prices (and financial prices in general) are no more regular than the run of chance, and that they can be replicated by the toss of a coin.
Technical analysis is based on the following principles:
All of the factors affecting exchange rates are discounted: they are reflected in the actual behaviour of exchange rates as shown on a chart.
The movements of exchange rates simply reflect changes in the forces of supply and demand.
Exchange rates move in trends that persist. The supply and demand balance sets a trend in motion, and this trend remains intact until it ends.
Market behaviour is repetitive. This is so because human nature means that people react to similar situations in a consistent manner. Since the foreign exchange market is a reflection of the actions of people (the traders), technical analysts study these actions to determine how people react under
certain conditions and thus how exchange rates move.
The empirical evidence on technical analysis
Studies on the extent of the use of technical analysis have produced results showing extensive use of this technique, particularly for short-term trading. Allen and Taylor (1989, 1990) and Taylor and Allen (1992) present evidence on the use of technical analysis based on a survey of some 240 foreign exchange dealers in London. The survey revealed a broad consensus view on the weights given to technical analysis at different time horizons. At short horizons (ranging from intra-day to weekly) 90% of the participants reported using technical analysis. Some 60% of the participants said that they regarded technical analysis at least as important as fundamental analysis. The results also revealed that the weight given to technical analysis is greater at short horizons. There was a very small minority (2%) who claimed never to have used fundamental analysis. The overall conclusion that can be derived from the survey is that technical analysis and fundamental analysis are complimentary.
Menkhoff (1997) surveyed the practices of foreign exchange traders in Germany, reaching the conclusion that technical analysis is used extensively. In contrast with Taylor and Allen, Menkhoff found that technical analysis was not primarily associated with short-term trading. Whether forecasting horizons were limited to an intraday perspective or to 2-6 month view, respondents gave technical analysis a similar weight between 33.9% and 40.4%. Menkhoff argued that the findings of Taylor and Allen that reliance on technical analysis decreases at longer time horizons is due to the exclusion of information on flows (what traders are doing and what orders exist). However, Menkhoff also agrees with the finding that the use of fundamentals is associated with long-term trading.
Lui and Mole (1998) conducted a similar survey involving 153 foreign exchange dealers in the Hong Kong market. This survey revealed that a very high proportion of the respondents placed some weight on both technical and fundamental analysis at all time horizons. At shorter horizons, however, there exists a skew towards reliance on technical analysis. Moreover, a view was revealed that technical analysis is only slightly more useful than fundamental analysis in predicting trends, but significantly more useful in predicting turning points.
Oberlechner (2001) presented findings of a survey of the perceived importance of technical versus fundamental analysis among foreign exchange traders and financial journalists in European financial centres. The results confirm the proposition that most traders use both forecasting approaches and that the shorter the forecasting horizon the more important technical analysis becomes. Results also indicate that the importance of technical analysis has increased since the 1990s. Financial journalists seem to put more emphasis on fundamental analysis than do foreign exchange traders.
Cheung and Chinn (1999) report the findings of a survey of US foreign exchange traders. The results show that technical trading best characterises about 30% of traders, with the proportion rising steadily, and that the importance of fundamental analysis increases at longer horizons.
As to the effectiveness and usefulness of technical analysis, Lo et al. (2000) found that several technical indicators provide incremental information, which means that they should have value. They reached this conclusion by comparing the unconditional empirical distribution of daily stock returns with the conditional distributions conditioned on specific technical indicators, such as head and shoulders and double bottoms. This is probably why economists have started to assign some role to the activity of technical analysts in the process of exchange rate determination. This is legitimate, particularly over short periods and in the absence of major changes in the fundamentals. Under these conditions, acting on technical analysis becomes a self-fulfilling prophecy. When a trader is convinced, by a certain chart pattern, that the exchange rate is going to rise after a long decline (that is a trend reversal upwards is expected) he will buy the currency, with the resulting increase in demand causing the exchange rate to rise as indicated by the chart. The opposite is also true.
The behaviour of traders who act on the basis of fundamental analysis and those who act on the basis of technical analysis may differ drastically. Fundamental analysts watch deviations from an equilibrium level of the exchange rate as implied by a fundamental model (for example, the PPP model and the monetary model). If the exchange rate is above the equilibrium level the currency is sold, which should lead to currency depreciation. This is not necessarily the case, however. If technical analysts believe that there is no indication of a trend reversal they will keep on buying it, lending support to the currency. What happens to the exchange rate depends on the net effect of the forces of supply and demand by fundamental analysts and technical analysts. The same argument is valid if the exchange rate falls below the equilibrium value.
Several economists have formalised the idea put forward in the preceding paragraph. Goodhart (1988) suggests that exchange rate misalignment is determined by the balance of the predictions of technical analysts and fundamental analysts. Likewise, Frankel and Froot (1990b) specify a model based on the same idea to explain the sharp rise in the demand for the dollar in the first half of the 1980s. The explanation provided on the basis of this model is that the increase in the demand for the dollar is the overwhelming role of technical analysts during that period. Kirman (1991) presents an extension of the Frankel-Froot model.
Moosa and Korczak (2000) carried out similar work. A model relating changes in the exchange rate to the activities of fundamentalists and technicians is specified and estimated using some exchange rates involving major currencies. The results show that both types of traders play a role in exchange rate determination and that fundamentalists play a bigger role. The results of model selection tests reveal that models based on the activities of fundamentalists only or technicians only are misspecified. Moosa and Al-Loughani (2002) applied a modified version of the model (that takes into account the effect of the exchange rate arrangement) to the exchange rate of a currency that is pegged to a basket (the Kuwaiti dinar) against the Japanese yen. The results show that market forces, as represented by the activities of traders, play a role in the determination of the exchange rate although this role is secondary to the effect of the exchange rate arrangement as represented by changes in the exchange rate of the Kuwaiti dinar against the US dollar. Non-nested model selection tests reveal that models that are based on market forces only or the exchange rate arrangement only are misspecified. They also found some evidence indicating that the activity of technicians is more important for this process than the activity of fundamentalists.
Generating buy and sell signals from chart formations
While chartists observe a wide range of chart formations or patterns, we will concentrate on the so-called reversal patterns, which can be used to generate buy and sell signals because they (allegedly) identify directional changes in exchange rates. Currency traders using charts can use reversal patterns to sell a currency before considerable depreciation and cover short positions prior to considerable appreciation. Trends change direction because of the interaction of the forces of supply of and demand for the underlying currency. The forming of a top and the subsequent reversal occur as a result of supply overcoming demand, or excess supply. The opposite occurs when demand overcomes supply.
Figures 8.3 and 8.4 show respectively how buy and sell signals are generated by chart formations (reversal patterns) known as head and shoulders, triangles, rectangles, double tops and bottoms, triple tops and bottoms and wedges (for a detailed treatment, see Moosa (2000a, Chapter 7)).
Generating buy and sell signals from quantitative technical indicators
Quantitative technical indicators have numerical values that can be calculated from certain equations. Two quantitative technical indicators are described in turn: oscillators and the relative strength index.
Oscillators are typically constructed with lower and upper boundaries, such as -1 to +1 or 0 to 100. A momentum oscillator is designed to measure the speed or the rate of change in the exchange rate. Hence, a momentum oscillator measures the acceleration or deceleration in the exchange rate. The value of a k-period momentum oscillator at a particular point in time is calculated as
Ok= St - St-k (8.20)
St St
where k may also be called the order of the momentum oscillator. When the momentum oscillator goes up in the current time period it means that the exchange rate rose by more or declined by less than what happened k periods ago. Similar interpretations are assigned to flat and downward movements in momentum oscillators. One of the benefits of momentum oscillators is that they lead exchange rate movements at market turning points. A momentum oscillator flattens out while the current exchange rate trend is still in effect.
On the other hand, a rate of change oscillator of order k is calculated as
St
Double
top
Sell
t
S
Sell
t
S
Triple top
Descending
triangle
Sell
t
Rising
wedge
Sell
Sell
t
FIGURE 8.4 Sell signals (technical analysis).
Ok =
(8.21)
(8.22)
The relative strength index (RSI) is calculated as follows 100
(RSI)t = 100 -
1 + ( RS) t
where
1 \n n 6 t=
(RS) t =
1 vn
1DS+
(8.23)
I
DS- |
1
where n is the number of periods over which the RSI is calculated, AS+ is a positive change and | AS- | is the absolute value of a negative change. Notice that, for the purpose of this calculation, when ASt > 0, then | AS- | = 0, and when ASt < 0, then AS+ = 0.
Oscillators and the RSI can be used to generate buy and sell signals as follows (Figure 8.5). A buy signal is generated when the oscillator cuts the midway line from below and when the RSI goes below 30. Sell signals are
Ot
Oscillator |
||||
|
Sell \/ |
Sell |
|
Sell |
Buy |
|
Buy |
Buy |
|
100
50
RSI
t
The
RSI
FIGURE
8.5
Generating buy/sell signals from oscillators and the RSI.
t
8.3 SPECULATION ON THE BASIS OF TRADING RULES
In technical trading rules, a buy signal is indicated if it is established that an upward trend will continue and a sell signal is indicated if a downward trend is perceived to continue for some time in the future. We will consider filter rules and moving average rules.
Filter rules
Filter rules were initially developed by Alexander (1961) who applied them to the stock market. A similar attempt was made by Fama and Blume (1966). Subsequently, filter rules were applied to other financial markets, including the foreign exchange market. Later attempts have been made by several economists including Dooley and Shafer (1976, 1983) and Sweeney (1986, 1988).
The working of the filter rule depends on the recognition of peaks and troughs (ex post) in the exchange rate series. Assume that the exchange rate is observed at points in time t - k, t-k + 1, ..., t - 1, t, t + 1. The value of the exchange rate at time t, St defines a trough if
St+1 - St > 0 (8.24)
and
St-i -St-i-1 <0 for i = 0,1, ..., k-1 (8.25)
Equations (8.24) and (8.25) imply that for St to define a trough, the necessary condition is that ASt+1 > 0, whereas the sufficient condition is that ASt-i < 0 for i = 0, 1, ..., k - 1. On the other hand, St defines a peak if
St+1 -St < 0 (8.26)
and
St-i -St-i-1 >0 for i = 0,1, ..., k-1 (8.27)
Equations (8.26) and (8.27) imply that for St to define a peak, the necessary condition is that ASt+1 < 0, whereas the sufficient condition is that ASt-; > 0 for i = 0, 1, ..., k -1.
A g per cent filter rule can be used to generate buy and sell signals as follows. If there is a trough at St, then a buy signal emerges at St+i if
St+ i ^(1 + g)St (8.28)
On the other hand, if there is a peak at St, then a sell signal emerges at St+i if St+ i £(1 -g)St (8.29)
The representation of the g-h filter rule (such that g > h or g < h) is similar. A buy signal emerges when the exchange rate rises by g per cent from the trough as represented by equation (8.28). A sell signal, on the other hand, emerges when the exchange rate falls by h per cent from its most recent peak. This is represented by equation (8.29) with h replacing g. The buy and sell signals generated from a g per cent rule and a g-h per cent rule are shown in Figure 8.6. If the peak occurs at St (1 + 0), then the profit realised from the g and g-h filter rules is
p(g) = St [(1 + 0)(1 - g) - (1 + g)] (8.30)
p(g-h) = St [(1 + 0)(1 -h) -(1 + g)] (8.31)
which means that if h >g, as in Figure 8.6, then p(g) >p(g-h).
If we allow for the bid-offer spread in exchange rates, then currency y must be bought at the offer rate and sold at the bid rate. Hence profit will be
P(g) = Sb,t (1 + 0)(1 -g) - Sa,t (1 + g) (8.32)
p(g - h) = Sb/t (1 + 0)(1 - h) - Sa,t (1 + g) (8.33)
We can modify these rules by allowing for interest rates, and hence the possibility of borrowing x to finance the purchase of currency y. Assume that a buy signal arises at t + j and that there are j time periods between buying and selling in the g filter rule and k time periods in the g-h filter rule. For each unit of x borrowed, profit realised from the trading rule is
(1 + 0)(1 - g)(1 + iy ) j
p( g) = 7i (1 + ix)j (8.34)
t
FIGURE
8.6
Generating buy/sell signals from filter rules.
St
Peak
(1+q)(1 -h)(1+iy )k
p(g - h) = 7i—r^ (1 + ix)k (8.35)
(1 + g)
And, of course, the matter becomes more complicated if we allow for bid-offer spreads in both interest and exchange rates. In this case
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(Fa,t - Sb,t+ 1 ) 133
Measuring the Hedge Ratio 158
, s(DPu,t, DPA,t If t-1) ,t t . 164
h = ^ ^ r" = P(X 1,t , X 2 ,t ) 164
s 2(DP 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, DPA,t If t-1, DPU,t-i, DPA,t-i) 186
s2 (APA,t If 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-11 AP U,t-i, APA,t-i) 187
s2 (X2 ,t ) + b2 s 2 (f t-11 APU,t-i, APA,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( Sb,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