Figure 2.4 shows the behaviour of the covered margin (in percentage points) resulting from covered arbitrage involving the US, British and Canadian currencies. It is obvious that the covered margin can deviate from zero, partic
ularly when arbitrage involves the pound against either the Canadian dollar or the US dollar. These deviations imply the availability of profitable arbitrage operations, which begs the question as to why they are not exploited to the extent that reduces the margins to zero. One answer to this question is that these observed deviations may be due to measurement errors. The data used to calculate the covered margins shown in Figure 2.4 are published data, not the data on which transactions could have been conducted. Moreover, they are taken from various sources, which means that they are probably measured or observed at different points in time (for example, mid-day rather than closing).
Economists have repeatedly tested CIP to find out if there are profitable arbitrage opportunities. Two important studies of the empirical validity of CIP were conducted in the 1980s by Taylor (1987b, 1989). What was different about these studies was that they were not based on published data, which have some measurement errors. There are certain requirements for proper testing of CIP, including the following: (i) observations on exchange and interest rates must be recorded at the same point in time; (ii) they must include the bid–offer spreads and transaction costs; and (iii) they must represent the data on which arbitragers take decisions. Obviously, these three requirements are not satis
fied by published data, which had been used to test CIP. Taylor (1987b) over
came all of these problems by collecting the data himself from dealers operating in the London foreign exchange market. He found no deviations from CIP (that is, the absence of profitable covered arbitrage opportunities) or zero covered margins. In his subsequent paper, however, he concluded that small but potentially exploitable opportunities of profitable arbitrage emerged occasionally during periods of turbulence in the foreign exchange
(a) USD/GBP 4
3 2 1 0 –1 –2
–3
Mar-78 Mar-82 Mar-86 Mar-90 Mar-94 Mar-98 Mar-02
(b) USD/CAD
–0.6 –0.4 –0.2 0.0 0.2 0.4 0.6
Mar-78 Mar-82 Mar-86 Mar-90 Mar-94 Mar-98 Mar-02
(c) GBP/CAD
–4 –3 –2 –1 0
1 2 3
Mar-78 Mar-82 Mar-86 Mar-90 Mar-94 Mar-98 Mar-02
FIGURE 2.4 The covered margin (percentage points).
market, but not during periods of tranquillity. He also found that the degree of reduction in the size and persistence of arbitrage increased with the passage of time. Furthermore, he established the notion of the term structure of arbitrage opportunities, indicating that profitable arbitrage opportunities are positively related to the length of the forward contract (the shorter the maturity, the smaller the profitable arbitrage opportunity). One explanation that Taylor presented for observed deviations from covered interest parity is the size and extent of credit limits. If banks impose restrictions on the amounts, maturities and the counterparties they deal with, this will operate as a liquidity constraint on covered arbitrage, in which case profitable opportunities would arise. In another study, Committeri etal.(1993) cast doubt on Taylor’s results on the following grounds. First, his analysis was based on data collected in a specific segment of the Eurocurrency market. Second, the data used in his first study did not cover a long period of time. Third, the data did not represent those that the dealers were actually prepared to deal on. By doing their own analysis, they found no profitable arbitrage opportunities.
Apart from measurement errors, some other factors lead to the distortion of the simple no-arbitrage condition given by (2.8), leading to the belief that there may be a profitable arbitrage operation. The fact of the matter is that there are certain factors that affect the simple no-arbitrage condition just like the case with two-currency arbitrage. These factors will be considered in turn.
Transactioncosts
Deviations from CIP have been attributed to transaction costs, which are repre
sented by the bid–offer spread of exchange rates (the cost of transacting in the foreign exchange market), the bid–offer spread of interest rates (the cost of trans
acting in the money market) and brokerage fees. Keynes (1923) asserted that the covered margin must exceed some minimum amount before arbitrage becomes profitable, estimating it to be half a percentage point. Branson (1969) put forward two reasons why such a minimum should exist: (i) each transaction in financial markets requires a payment of brokerage fees, and (ii) banks may require their foreign exchange departments to earn a higher yield than that of their domestic departments.
The effect of transaction costs is to create a band around the CIP no-arbi- trage line within which arbitrage is not profitable, as shown in Figure 2.5.
Points falling off the CIP line but within the band indicate that although arbi
trage is possible it is not profitable, since the covered margin is not sufficiently large to offset transaction costs. Points falling outside the band indicate profit
able arbitrage opportunities, because the covered margin is large enough to cover transaction costs and leave out some profit.
To be more precise, recall that the equation of the no-arbitrage line in Figure 2.5 is ix – iy = f. Without transaction costs, arbitrage from x to y is profitable if ix – iy < f, whereas arbitrage from yto xis profitable if ix – iy > f. Let transac
tion costs (measured in percentage points) be t. The equations of the lines
ix -iy
ix -iy = f + ix -iy = f
ix -iy = f -t y Æ x
y Æ x
x Æ y Æ
¨ t
f
y Æ x
x Æ y x Æ y
FIGURE 2.5 Covered arbitrage in the presence of transaction costs.
representing the lower and upper limits of the band are ix – iy = f+ tand ix – iy
= f – t respectively. Arbitrage from x to y is not profitable within the lower part of the band because ix – iy ³f – t. Similarly, arbitrage from y to x is not profitable within the upper part of the band if ix – iy £f+ t. Arbitrage from xto yis profit
able if ix – iy < f– t, in which case the covered margin is ix – iy + f– t. Arbitrage from y to x is profitable if ix – iy > f + t, in which case the covered margin is ix – iy – f – t. Table 2.1 summarises these possibilities.
Political risk
Another explanation for deviations from CIP is political risk, which involves the uncertainty that while the funds are invested abroad they may be frozen, become inconvertible or be confiscated. In a less extreme case they may face new or higher taxes. Aliber (1973) argues that the comparability criterion, which is critical for choosing the money market assets used to test CIP, requires assets to be identical in terms of political risk. Accordingly, he argues that while Eurocurrency assets satisfy the comparability criterion, domestic assets do not because they are issued under different political jurisdictions.
In diagrammatic terms, political risk creates a band, as described by Figure 2.6, because arbitragers require a risk premium and hence some minimum
- -
- - TABLE 2.1 The effect of transaction costs.
x ®y y ®x
Without transaction costs
No arbitrage i x - =i y f i x - =i y f Profitable arbitrage i x - <i y f i x - >i y f Covered margin i y - +i x f i x i y f
With transaction costs
No arbitrage i x - ³ -i y f t i x - £ +i y f t Profitable arbitrage i x - < -i y f t i x - > +i y f t Covered margin i y - + -i x f t i x i y f -t
covered margin. This band, however, does not have to be of equal width on either side of the CIP line. For example, if investors from country y view country x as being politically more risky than investors from country x view country y, then there will be a larger political risk premium on x-denominated securities, and the band will be wider to the left of the no-arbitrage line. Moosa (1996a) attributes deviations from CIP between Australia and New Zealand in the period immediately following the abolition of capital controls in the mid-1980s to political risk, in the sense that investors on both sides of the Tasman Sea could have been worried about the possibility of either government reimposing capital controls.
Let us examine Figure 2.6 with some scrutiny. Suppose that y-based inves
tors require a risk premium of rx to invest in x-denominated assets, whereas x- based investors require a risk premium of ry to invest in y-denominated assets such that rx >ry . The equations of the lines defining the lower and upper limits of the band created by political risk are i x -iy =f -ry and ix -iy =f +rx . Arbitrage from xto yis not initiated within the lower part of the band because ix -iy ³f-ry . Similarly, arbitrage from yto xis not initiated within the upper part of the band because i x -iy £f +rx . Arbitrage from x to y is initiated when ix -iy <f -ry . Notice that the covered margins are equal in both cases because the risk premium is not an actual cost or a source of revenue. Therefore, it only determines the no-arbitrage zone. Table 2.2 summarises the situation.
Tax differentials
Levi (1977) explains deviations from the no-arbitrage condition in terms of differences in tax rates. If tax rates on interest income (tn ) and foreign exchange or capital gains (tg ) are different (tn ¹tg ), the no-arbitrage line will no longer be a 45° line. Rather, it will have the equation ix -iy =qf, where
1 -tg
q= (2.22)
1 -tn
- -
- - ix -iy
f i i x -y=
y Æ x
y Æ x y Æ x
x Æ y x Æ y
x Æ y
f
x y
x i f
i - = +r
y y
x i f
i - = -r
FIGURE 2.6 Covered arbitrage in the presence of political risk.
If the capital gains tax rate is higher than the income tax rate, the line will be flatter than the 45° line, as shown in Figure 2.7(a). Otherwise, it will be steeper as shown in Figure 2.7(b). Hence, points falling on the line i x -iy =qf (and hence off the line ix – iy = f) represent deviations from the no-arbitrage condi
tion in the absence, but not in the presence, of taxes. Table 2.3 shows all of the possibilities.
TABLE 2.2 The effect of political risk.
x ®y y ®x
Without political risk
No arbitrage i x - =i y f i x - =i y f Arbitrage initiated i x - <i y f i x - >i y f Covered margin i y - +i x f i x i y f
With political risk
No arbitrage i x - ³ -i y f ry i x - £ +i y f rx Arbitrage initiated i x - < -i y f ry i x - > +i y f rx Covered margin i y - +i x f i x i y f
- -
- - TABLE 2.3 The effect of tax differentials.
x ®y y ®x
Without tax differentials (q=1)
No arbitrage i x - =i y f i x - =i y f Profitable arbitrage i x - <i y f i x - >i y f Covered margin i y - +i x f i x i y f
With tax differentials (q¹1)
No arbitrage i x - =i y qf i x - =i y qf Profitable arbitrage i x - <i y qf i x - >i y qf Covered margin i y - +i x qf i x i y qf
TABLE 2.4 The combined effect of transaction costs, political risk and tax differen- tials (q>1).
x ®y y ®x
Without the effect
No arbitrage ix -iy =f ix -iy =f Profitable arbitrage ix -iy <f ix -iy >f
ix - -f
Covered margin iy - +f ix iy With the effect
qf qf
No arbitrage ix -iy ³ -t -ry ix -iy £ +t +rx
qf qf
Profitable arbitrage ix -iy < -t -ry ix -iy > +t +rx
ix qf iy qf
Covered margin iy - + -t ix - - -t
Combiningthethreefactors
It is possible to combine the three factors mentioned so far: transaction costs, political risk and tax differentials. The effect of this combination of factors is represented by Figure 2.8 when q>1. In this case, the no-arbitrage line is steeper than the 45° line with an equation i x -iy =qf. The effect of transaction costs and political risk is to create a band around this line. The unequal band width is due to differences in the risk premia, as we are assuming that invest
ment in country x is more risky as viewed by investors from country y. The no- arbitrage line in the absence of these factors is the 45° line with the equation ix – iy = f. Table 2.4 illustrates all of the possibilities.
Liquidity differences
Liquidity differences may also cause deviations from the no-arbitrage condi
tion. The liquidity of an asset can be judged by how quickly and cheaply it can be converted into cash. The more uncertainty there is concerning future needs
(a) q < 1 ix -iy
f i i x -y=q
y Æ x
y Æ x y Æ x
x Æ y
x Æ y
x Æ y
f f i i x -y=
x Æ y
y Æ x
(b) q >1 ix -iy
f i i x -y=q
y Æ x y Æ x
y Æ x
x Æ y
x Æ y
x Æ y
f f i i x -y= x Æ y
y Æ x
FIGURE 2.7 Covered arbitrage in the presence of tax differentials.
and alternative sources of short-term financing, the higher will be the premium that should be received before choosing to invest in the non- base currency, y. This again implies the existence of a band around the no- arbitrage line, and this band may have different widths on the two sides of the line.
Other factors
Some other factors have been suggested to explain deviations from the CIP no-arbitrage condition because they hinder the movement of arbitrage
ix -iy
ix -iy =qf y Æ x
ix -iy = f
y Æ x y Æ x
x Æ y x Æ y
x Æ y x Æ y
f
ix -iy =qf +t +rx
ix -iy =qf -t -ry
FIGURE 2.8 Covered arbitrage in the presence of transaction costs, political risk and tax differentials.
funds when the possibility for arbitrage arises. One of these factors is the exis
tence of inelastic (or less than perfectly elastic) supply and demand for arbitrage funds (Pippenger, 1978), which amounts to a violation of one of the basic assumptions of CIP. A related factor is capital market imperfections (Prachowny, 1970), which is not important at the present time given the increasing degree of market perfection. Another factor is capital controls, a factor that has lost importance because of the worldwide tendency to abolish these controls and implement financial deregulation.
These factors prevent the forces of supply and demand from moving to the extent required to restore the equilibrium condition. We have seen from Figure 2.2 that equilibrium is restored when arbitrage causes some changes that take interest and exchange rates to the levels required to achieve the no- arbitrage condition. Let us denote the initial levels of the variables ix,0, iy,0, S0 and F0. Consider now the situation illustrated by Figure 2.9 assuming that the levels of the variables required to restore equilibrium are ix,2 (>ix,1), iy,2 (<iy,1), S2 (>S1) and F2 (<F1). If these factors prevent the forces of supply and demand
ix iy
Supply Demand
Supply Demand
i x
i x
i x
,0
i y
i y
i y 2
, 1 ,
0 ,
1 ,
2 ,
Money market ( x) Money market ( y )
Supply
Demand Supply
S
Demand
F
S 2
S 1
S 0
F 0
F 1
F 2
Spot market Forward market
FIGURE 2.9 The effect of covered arbitrage in the presence of inelastic supply and demand and similar factors.
from achieving the levels of the variables consistent with the no-arbitrage condition, then deviations from this condition will persist. Figure 2.9 shows that changes in supply and demand can only achieve the levels ix,1, iy,1, S1 and F1. In terms of the CIP diagram represented by Figure 2.10, changes in the forces of supply and demand lead to a fall in the forward spread from f0 to f1 and to a rise in the interest differential from (ix – iy)0 to (ix – iy)1, which is inade
quate to restore the no-arbitrage condition. In other words, arbitrage causes a move towards the no-arbitrage line from A to B. To achieve equilibrium, however, a further move from B to C is required, as indicated by the dotted arrow. Because of these factors, changes in supply and demand reduce, but do not eliminate, deviations from the no-arbitrage condition.
ix -iy
f i i x -y=
f
2 y x i )
(i - C
B A
1 y x i ) (i -
0 y x i ) (i -
f 2 f 1 f 0
FIGURE 2.10 The effect of covered arbitrage in the presence of inelastic supply and demand and similar factors (the CIP diagram).