Covered Interest Rate Arbitrage in the Interwar Period and the Keynes-Einzig Conjecture

Covered Interest Rate Arbitrage in the Interwar Period and the Keynes-Einzig ConjectureAuthor(s): David A. Peel and Mark P. TaylorSource: Journal of Money, Credit and Banking, Vol. 34, No. 1 (Feb., 2002), pp. 51-75Published by: Blackwell PublishingStable URL: http://www.jstor.org/stable/3270675Accessed: 28/07/2009 22:43

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DAVID A. PEEL

MARK P. TAYLOR

Covered Interest Rate Arbitrage in the Interwar

Period and the Keynes-Einzig Conjecture

In the Tract on Monetary Reform, Keynes (1923) conjectured that deviations from covered interest rate parity would not be arbitraged unless a profit of at least a half of one percent on an annualized basis was available, and that larger deviations would still be mod- erately persistent because of less than perfect elasticity of supply of arbitrage funds. This two-part conjecture was given further empha- sis by other writers on this period, notably Einzig (1937). We apply nonlinear econometric techniques to a previously unexploited weekly data base for the 1920s London and New York markets and find strong support for the conjecture.

It may be said, therefore, that discrepancies between Interest Parities and forward rates do not cause deliberate transfers through interest arbitrage on a large scale unless and until the profit on the operation is at least 1/2 percent per annum. This has been recog- nised by Mr. Keynes and by other writers, but is often overlooked by those who are not in contact with the market. (Einzig 1937, pp. 172-73)

THE COVERED INTEREST PARITY (CIP) condition entails that the interest rate differential between similar financial assets of the same maturity denominated in different currencies should be equal to the cost of covering the re-

sulting currency risk in the forward market. In symbols, if St is the spot exchange rate

(domestic price of foreign currency) at time t, i and i represent the domestic and

foreign interest rates on the assets concerned, and Ft is the forward exchange rate

(the rate at which a future exchange of currencies is agreed at time t) of same term to

maturity as the assets, then the CIP condition may be expressed as

pF -S i . (1) p t =-it'(l

St

The authors are grateful to two anonymous referees as well as to Nelson Mark, William Branson, Richard Clarida, Jacob Frenkel, Clive Granger, Peter Kenen, Richard Levich, and Lawrence Officer for helpful and constructive comments on a previous version of this paper.

DAVID A. PEEL is professor of economics at Cardiff Business School, Cardiff University. MARK P. TAYLOR is professor of economics at the University of Warwick, and a fellow of the Centrefor Economic Policy Research. E-Mail: mark.taylor@warwick.ac.uk

Journal of Money, Credit, and Banking, Vol. 34, No. 1 (February 2002) Copyright 2002 by The Ohio State University

I

52 : MONEY, CREDIT, AND BANKING

where P is a period adjustment term (in the case where the interest rates are ex- pressed on an annualized basis and the forward rate is of three months maturity, for example, P = 400).

The interest of international economists in CIP stems from at least three sources (Taylor 1992). First, deviations from CIP may indicate unexploited, riskless, prof- itable arbitrage opportunities, so that empirical investigations of CIP form part of an ongoing research program into the efficiency of the foreign exchange and interna- tional capital markets.1 Second, CIP is often used much as an identity in testing other international parity conditions. For example, given CIP, then the uncovered interest parity condition (that is, the condition that the domestic-foreign interest differential be equal to the expected rate of depreciation of the domestic currency in terms of the foreign currency) implies that the forward rate should act as a spot rate predictor (Taylor 1995). Third, a general motivation for examining international parity condi- tions such as CIP arises from their explicit or implicit use in the construction of the- oretical and empirical models of exchange rate determination. Empirically, moder exchange rate models have not performed well (Taylor 1995; Frankel and Rose 1995), so that examination of their underlying assumptions is therefore warranted.

In this paper, we present a study of covered interest parity and covered interest arbitrage in the interwar foreign exchange market of the 1920s. In particular, em- ploying hitherto unexploited weekly data on spot and forward rates and interest rates, and recently developed techniques in the econometrics of nonlinear processes, we provide evidence on a conjecture primarily due to Keynes (1922, 1923) and given further emphasis by Einzig (1937, 1961, 1962).

What may be termed the Keynes-Einzig conjecture has two components: first, that covered arbitrage between the major financial centers in the interwar period was only triggered once the deviation from CIP exceeded about 1/2 percent (that is, fifty basis points) on an annualized basis, and, second, that even when arbitrage was triggered, deviations were arbitraged away only slowly because of the less than perfect elastic- ity of supply of arbitrage funds. In this paper we examine both of these components of the conjecture.

The remainder of the paper is structured as follows. In the next section we provide a discussion of covered arbitrage and the Keynes-Einzig conjecture. In section 2 we briefly review the literature on CIP in both the postwar and interwar periods. In sec- tion 3 we describe our data while in section 4 we discuss our econometric methods. Section 5 contains our empirical results and a final section concludes.

1. COVERED INTEREST ARBITRAGE, COVERED INTEREST PARITY AND THE KEYNES-EINZIG CONJECTURE

Anecdotal evidence suggests that covered interest rate arbitrage was certainly common in the late nineteenth century, both in Europe (Lotz 1889; Raffalovich

1. See, for example, Taylor (1995).

DAVID A. PEEL AND MARK P. TAYLOR : 53

1895; Schulze-Gaeveritz 1899)2 and in the United States (Haupt 1892; Margraff 1904), although activity in forward exchange operations in general became much more intense in the interwar floating rate period (Keynes 1923; Einzig 1937, 1962). Published accounts of international interest arbitrage are, however, remarkably rare before the Second World War. Perhaps the earliest discussion of the relationship be- tween spot and forward rates and interest rates-although stopping short of explic- itly setting out the CIP condition-was published in German in the late nineteenth century (Lotz 1889), and gives a colorful account of movements in the forward mar- ket for German marks in Vienna occasioned by movements in the interest rate differ- ential between bourse loans in Berlin and Vienna.

Characteristically, however, in an article first published in a British newspaper (The Manchester Guardian) in 1922 and subsequently published in revised form in the Tract on Monetary Reform a year later, it is Keynes (1923) who gives the first clear written statement of the CIP condition by a professional economist:

... forward quotations for the purchase of the currency of the dearer money market tend to be cheaper than spot quotations by a percentage per month equal to the excess of the interest which can be earned in a month in the dearer market over what can be earned in the cheaper. (Keynes 1923, p. 103)

Keynes was also instrumental in the publication of data on forward premia, both in his 1922 Manchester Guardian article and the Tract on Monetary Reform, and in his encouragement of Einzig to produce his work on forward exchange (Einzig 1937, p. xi) together with its valuable data appendix.3 Nevertheless, there seems to have been a considerable degree of confusion surrounding the idea of international inter- est arbitrage during this period among economists, government officials, the general public and even professional bankers.4 Even after Keynes' contributions, moreover, scholarly work on international financial markets during the interwar period appears to have been very scarce and often confused. Duncan (1934), for example, studies the implications of arbitrage involving ratios of domestic to foreign net interest rates, rather than the interest differential. Nor was the confusion confined to acade- mic economists. For the practitioners, in an article in a publication of the Royal So- ciety of Bankers (The Banker) as late as 1936, a professional banker argues that "when in a purely non-speculative forward market supply and demand are equal...

2. Einzig (1937) conjectures that the Vienna forward market began in the mid-nineteenth century when the wars of 1848-9 had led to exchange fluctuations. Forward exchange transactions, however, ap- pear to have a much longer history. Possibly the earliest recorded instance of such a transaction occurred in the early fourteenth century, when Pope John XXII concluded a deal with the Florentine banking houses of Bardi and Peruzzi providing for the transfer to Avignon of the proceeds of papal collections in England and other European countries, with the relevant exchange rates fixed in advance for twelve months (Renouard 1941, p. 502).

3. The paucity of published data in this period is indicated by Keynes' remarks in his 1922 Manches- ter Guardian article: "I should be grateful if readers who are in possession of tables showing the rates which have been charged in European centres for forward dealings during the recent past would be good enough to send them to me" (Keynes 1922). Largely as a result of Keynes' influence, the Manchester Guardian did later begin to publish spot and forward rates in the 1920s, but not the relevant interest rates.

4. Thus Keynes again: "The nature of forward dealings in exchange is not generally understood. The rates are seldom quoted in the newspapers. There are few financial topics of equal importance which have received so little discussion or publicity" (Keynes 1923, pp. 100-101).

54 : MONEY, CREDIT, AND BANKING

the forward rates will be at par with the spot rates" (Huizinga 1936, p. 120). For the officials, the British Macmillan Committee, referring to Keynes' proposal for central bank forward exchange intervention,5 flatly conceded that an analysis of forward ex- change operations was beyond its competence (Macmillan Committee 1931, p. 154). Furthermore, this ignorance appears to have been compounded by a widespread pop- ular belief in the interwar period that arbitrage activity might lead to the destabiliza- tion of the currency (see, for example, Casamajor 1925). Thus Einzig:

Indeed, ignorant politicians, Government officials and journalists denounced these transactions as speculative, even though they represented pure arbitrage, and in spite of the obvious fact that they tended to correct the excesses of speculation. (Einzig 1937, p. 68.)

Striking evidence of this attitude is given by the case of the arrest of five foreign ex- change dealers by the authorities in Antwerp in December 1922 on the charge of bear speculation against the Belgian franc. In fact, the dealers had been carrying out covered arbitrage operations.6

Of course, it would not be logically inconsistent for there to have been few prof- itable arbitrage opportunities that were not quickly arbitraged away while the nature of covered arbitrage was at the same time widely misunderstood, since only a few well-informed agents are all that may be required to police arbitrage opportunities in any financial market. If anecdotal evidence is anything to go by, however, this does not appear to have been the case.7

The major element of the Keynes-Einzig conjecture, namely, that deviations from CIP in the interwar period did not tend to be arbitraged at all until they were of the order of fifty basis points, makes its first appearance in Keynes (1922, 1923):

To fix our minds, let us suppose that money-market conditions exist in which a sale of forward dollars against the purchase of spot dollars, at a discount of 11/2 percent per annum for the former, yields neither profit nor loss. Now if in these conditions the pur- chasers of forward dollars, other than arbitragers, exceed sellers of forward dollars, then this excess of demand for forward dollars can be met by arbitragers, who have cash resources in London, at a discount which falls short of 11/2 percent per annum by such amount (say 1/2 percent) as will yield the arbitragers sufficient profit for their trou- ble. If, however, sellers of forward dollars exceed the purchasers, then a sufficient dis- count has to be accepted by the former to induce arbitrage the other way round-that is to say, by arbitragers who have cash resources in New York-namely, a discount which exceeds 11/2 percent per annum by, say, 1/2 percent. Thus, the discount on forward dol-

5. Keynes (1923); see footnote 9. 6. For contemporary accounts of this case, see the London newspaper The limes, December 16, 1922,

and the Antwerp Le Neptune, December 17, 1922. 7. See, for example, Einzig (1937):

The main reason for these abnormal margins-which persisted in some currencies for quite a long time-was the widespread feeling of optimism that set in after the war regarding the future of the de- preciated currencies. It was generally taken for granted that not only sterling, but the franc and the lira, even the German mark, would eventually return to their Purchasing Power Parities, and even to their pre-war Mint parities. Speculative anticipation of the rise of these currencies resulted in a per- sistent premium on forward sterling against dollars, and in a premium on the forward lira, mark, etc., against both sterling and the dollar. Ample opportunities were thus affordedfor highly profitable in- terest arbitrage with the exchange risk covered. (Einzig 1937, pp. 67-68, emphasis added)

DAVID A. PEEL AND MARK P. TAYLOR : 55

lars will fluctuate between 1 and 2 percent per annum according as buyers or sellers predominate. (Keynes 1923, p. 106)

It is given further emphasis by Einzig (1937, 1962): Keynes was the first to present the Interest Parity theory in a systematic form. Accord- ing to his theory, forward margins, expressed in percentage per annum, tend to be equal to the difference between interest rates in the two centres ... Keynes laid down the rule that whenever they departed from their interest parities to an extent of at least half per- cent per annum, interest arbitrage set into motion transactions which tended to readjust them. Deviations of a lasting nature were liable to arise, however, among other reasons, because the liquid capital available for arbitrage was not unlimited and at times it was not large enough to bring about readjustment. (Einzig 1962, p. 275)

As the last sentence of the preceding quotation illustrates, both Keynes and Einzig suggest that the persistence of deviations from CIP outside of the (? 1/2 percent neu- tral band may be due to the inelasticity of arbitrage funds arising from prudential limits on banks' outstanding liabilities, or to market inefficiencies of one kind or an- other:

It must be remembered that the floating capital normally available, and ready to move from centre to centre for the purpose of taking advantage of moderate arbitrage profits between spot and forward exchange, is by no means unlimited in amount, and is not al- ways adequate to the market's requirements ... [An] abnormal discount can only dis- appear when the high profit of arbitrage between spot and forward has drawn fresh capital into the arbitrage business. So few persons understand even the elements of the theory of the forward exchanges that there was an occasion in 1920, even between Lon- don and New York, when a seller of spot dollars could earn at the rate of 6 percent per annum above the London rate for short money. (Keynes 1923, pp. 107-108)

Later work on the determinants of deviations from CIP stressed the interaction of arbitrageurs, speculators and commercial hedgers in the forward market (for exam- ple, Spraos 1959; Tsiang 1959; Sohmen 1961).8 Kenen (1965) provides a unified theoretical view of CIP deviations when the same economic unit is engaged in arbi- trage, speculation, and hedging.9

Overall, the Keynes-Einzig conjecture-that deviations from CIP were only arbi- traged when they were of the order of fifty basis points on an annualized basis and that the supply of arbitrage funds even at this point would be less than perfectly elas- tic-is implicit in much of the work on foreign exchange markets in the interwar pe-

8. See also Spraos (1953), Grubel (1963, 1968), Stoll (1966), Jasay (1958), and Reading (1960). For more recent treatments of the moder theory of forward exchange, see, for example, McCallum (1977) and Taylor (1987b).

9. Kenen (1965) argues that the impetus for much of the work on spot and forward market analysis was derived in large measure from British policy dilemmas of the 1920s and 1950s:

If Great Britain had been paradise for the last two hundred years, economic analysis might still be quite primitive . . . The interest parity doctrine, constructed by Keynes and christened by Einzig, replied to the dilemma that Britain confronted in the early 1920s-domestic stagnation combined with a payments deficit. Keynes showed that changes in forward exchange rates have the same effect on capital flows as changes in the difference between national interest rates. He urged intervention to support forward sterling in lieu of raising Bank rate higher, thereby to strengthen Britain's reserves without doing damage to the British economy. When Britain faced the same dilemma in the late 1950s, another generation of economists revived Keynes's suggestion, inspiring additional advances in analysis. (Kenen 1965, p. 143)

56 : MONEY, CREDIT, AND BANKING

riod (see for example, Aliber 1962a; Officer 1993, 1996).10 It is interesting, however, that to the best of the present authors' knowledge, the present paper represents the first attempt to test the Keynes-Einzig conjecture empirically.

2. COVERED INTEREST PARITY: A BRIEF REVIEW OF THE LITERATURE

Much of the published empirical work on CIP has concentrated on the postwar pe- riod and it is important to review this work as a point of comparison for our interwar study. To date, essentially two types of empirical test of CIP have been conducted. The first relies on computing the actual deviations from interest parity to see if they differ "significantly" from zero. The significance is often defined with respect to a neutral band, which is determined by transactions costs such as the bid-ask spread and brokerage fees (Demsetz 1968). For example, the classic study of Frenkel and Levich (1975) demonstrates that, for arbitrage between sterling, U.S. dollar, and Canadian dollar securities, 80 to 90 percent of apparent profit opportunities in weekly data over the period January 1962 through November 1967 lie within a neu- tral band when ninety-day treasury bills are used and almost 100 percent when Euro- deposit rates are considered." Furthermore, in Frenkel and Levich (1977) it is demonstrated that in periods of turbulence a much smaller percentage of deviations from CIP may be explained by transactions costs; this is interpreted as reflecting higher financial uncertainty in such periods. Clinton (1988) demonstrates that devia- tions from covered interest parity should be no greater than the minimum transaction costs in one of three markets: the two underlying deposit markets (for example, Euro-marks and Euro-dollars) and the foreign exchange swap market (that is, the market in which a currency can be simultaneously bought and sold forward against another currency). On the basis of analysis of data for five major currencies against the U.S. dollar "taken from mid morning quotes on the Reuter Money Rates Service from November 1985 to May 1986," Clinton finds that the neutral band should be within ?0.06 percent per annum from parity and that although the hypothesis of zero profitable deviations from parity can be rejected, "empirically, profitable trad- ing opportunities are neither large enough nor long-lived enough to yield a flow of excess returns over time to any factor."

Taylor (1987a, 1989) uses high-quality, high-frequency contemporaneously sam- pled data for spot and forward dollar-sterling and dollar-mark exchange rates and corresponding Euro-deposit interest rates for a number of maturities and makes al- lowance for bid-ask spreads and brokerage costs in his calculations for the 1980s and selected postwar periods. He finds, inter alia, that there are few profitable violations

10. In particular, both Aliber and Officer assume a neutral band of no arbitrage of plus or minus fifty basis points around the covered interest parity: "All adjustments of forward discount and forward pre- mium include an adjustment for money market interest differential... The adjusted forward premium or discount is termed significant if it exceeds one half of one percent. (Aliber 1962, p. 191, emphasis added)

11. Arbitrage with Canadian dollar securities is not included in the Frenkel-Levich analysis of Euro- deposits due to a lack of data.

DAVID A. PEEL AND MARK P. TAYLOR : 57

of CIP, even during periods of market uncertainty and turbulence. One interesting feature of Taylor's work is the finding that where profitable violations of CIP do occur, their frequency, size, and persistence appear to be an increasing function of the length of the period to maturity of the underlying financial instruments. A ratio- nale is offered for this in terms of banks' prudential credit limits: since banks impose prudential limits on the amount of outstanding deposits they have with other parties, arbitraging at the shorter maturities will result in limits being filled for shorter peri- ods, leaving dealers on average freer to take advantage of other profit opportunities as they arise.

A second method for testing the validity of CIP has been the use of econometric regression analysis. Thus, if CIP holds, and in the absence of transaction costs, esti- mation of the following equation:

P = + 1(it -t ) + ut, (2) St

(where ut is the regression error) should result in estimates of a and , differing in- significantly from zero and unity respectively. Equation (2) has been tested by a number of researchers for a variety of currencies and time periods (for example, Grubel 1966; Branson 1969; Marston 1976; Cosandier and Lang 1981; Fratianni and Wakeman 1982), with the general conclusion that, with important exceptions due to factors such as political risk (see, for example, Aliber 1973; Frankel and MacArthur 1988) CIP is not rejected.12

Similar studies of the CIP relationship for earlier historical periods are compara- tively rare. Both Aliber (1962a) and Officer (1993, 1996) examine interest arbitrage in the interwar market. Aliber (1962a) considers a number of European exchange rates against the dollar in the floating rate period following the end of the First World War up to 1925 or 1926. Both authors, however, use monthly sampled and averaged interest rate data rather than point-in-time data, since their primary concerns are somewhat different from those of the present authors. Aliber's concern, for example, is not with deviations from covered arbitrage per se, but more with assessing the role of speculation in driving the spot exchange rate and the influence of forward transac- tions on spot rate movements, building on and anticipating much of the literature on the "moder theory" of forward exchange (Spraos 1959; Tsiang 1959; Sohmen 1961).13 In effect, Aliber's starting point is both elements of the Keynes-Einzig con- jecture. On the relative inelasticity of arbitrage funds, for example, he notes:

To use the forward market as a source of inferences about speculative behavior, it is im- portant to show that in some cases the forward market is dominated by individuals who seek speculative profits from carrying exchange risk... Forward market facilities pro- vide the opportunity to secure extremely high leverage since the margin requirements

12. Officer and Willett (1979) survey much of the earlier postwar literature. See also Taylor (1992, 1995) and McCallum (1996, chapter 9).

13. See also Aliber (1962b, 1963).

58 : MONEY, CREDIT, AND BANKING

for forward transactions have been low ... The forward transactions of those who seek leverage alter the spread between the price of foreign exchange in the spot market and the forward market... As long as the supply schedule of arbitrage funds is not perfectly elastic and as long as the schedule remains fairly stable, changes in the forward differ- ential are likely to reflect changes in the demand for leverage. (Aliber 1962a, pp. 179-80, emphasis added)

Officer's (1993, 1996) main concern is in assessing the efficiency of interwar dollar- sterling gold standard from May 1925. He also uses averaged data and assumes a neutral band width of plus or minus fifty basis points which, as we have noted, ap- pears to be a standard assumption in discussions of the interwar period (see, for example, Bloomfield 1950).

In fact, an interesting feature of the literature on covered interest arbitrage in the post-Second World War period is the relatively small size of the neutral bands within which arbitrage is not deemed to take place during normal periods, compared to the ? 1/2 percent conjectured by Keynes and Einzig for the interwar period. Frenkel and Levich (1975), for example, estimate that the width of this band is of the order of plus or minus fifteen basis points during the 1960s, while Clinton (1988) estimates a neutral band of plus or minus six basis points during the 1980s. Einzig, writing in the early 1960s, gives an estimate closer to that of Clinton, noting that this is a great deal smaller than before the war:

In The Theory of Forward Exchange14 I said that discrepancies between forward rates and their Interest Parities must reach 1/2 percent per annum before they would induce banks to take advantage of them for the purpose of interest arbitrage... Though this had been in accordance with conditions existing in 1922 when Keynes first stated it and in 1937 when I reaffirmed it, in conditions prevailing in the 'fifties it ceased to apply. At the time of writing 1/16 percent, and even 1/32 percent, is deemed to be sufficient profit to induce them to engage in arbitrage operations in normal conditions ... By and large it is correct to say that interest arbitrage is apt to take place nowadays at a profit that represents a bare fraction of what was considered to be the minimum before the war. (Einzig 1961, pp. 166-67)

From an examination of covered arbitrage involving treasury bills over the period 1959-1964 for U.S. dollar-sterling arbitrage and 1962-1964 for U.S.-Canadian dol- lar arbitrage, Branson (1969) concludes:

[The] minimum profit was independently estimated to be 0.18 percent per annum for both U.S.-U.K. treasury bill arbitrage and the U.S.-Canada treasury bill arbitrage. The 0.18 estimate falls between the 0.50 percent offhandedly suggested by Keynes (1923), and the more recent figure of 0.06 suggested by Einzig (1961). (Branson 1969, p. 1034)

What is clear from a reading of this literature is a consensus that the size of the "minimum covered interest differential needed for international arbitrage activity" (Branson 1969) declined markedly after the Second World War. What is remarkable, however, is that the assertion that the minimum differential before the war was about one half of one percent appears to be supported only by anecdotal evidence and what appears to be, to use Branson's term, a rather offhand suggestion by Keynes (1923).

14. Einzig (1937).

DAVID A. PEEL AND MARK P. TAYLOR : 59

It is one purpose of this paper to provide a more rigorous examination of this propo- sition than has hitherto been offered in the literature.

3. DATA SOURCES AND EMPIRICAL PRELIMINARIES

Empirical tests of covered interest parity should ideally ensure that the assets in- volved are "identical" in every relevant aspect except currency of denomination (Levich 1985), and that the components of (1) are measured at the same point in time (Taylor 1989). An immediate problem for analysis of the interwar period is that, in the absence of a well-developed Euro-deposit market, it is not possible to obtain in- terest rates on U.K. and U.S. assets satisfying the first criterion. Nevertheless, we en- deavored to find returns on money market instruments quoted on the London and New York markets for similar assets of the same maturity and quoted at the same point in time. Einzig (1937) provides weekly quotations for spot and three-month dollar-sterling forward exchange rates for each Saturday in the interwar period, orig- inally gathered from the weekly circular of the Anglo-Portuguese Colonial and Overseas Bank. We also were able to find a British interest rate with a ninety-day maturity with a Saturday quotation. These are ninety-day treasury bill rates reported in the London newspaper The Economist during the period. For the United States we discovered Saturday quotations on the discount on ninety-day prime bankers' accep- tances in New York City, published in Banking and Monetary Statistics, 1914-1941 (Board of Governors of the Federal Reserve System 1943). An examination of arbi- trage between the London and New York markets seems appropriate since, as today, these were the two preeminent financial centers in the interwar period (Einzig 1962; Officer 1993, 1996). As noted by Officer (1993, 1996) and others, moreover, New York prime bankers' acceptances and London treasury bills were dominant instru- ments in their respective money markets for three-month international investment. Our data spans the period of January 7 1922 through March 21 1925,15 a total of 168 weekly observations.

The annualized percentage deviation from CIP at time t, 6t, is defined:

8t 400 St +(3) S,

where it represents the interest rate on ninety-day prime bankers' acceptances in New York and i* represents the ninety-day U.K. treasury bill rate. As we can observe from Figure 1, which is a plot of the time series for 8t, there are a number of devia-

15. Sterling returned to the gold standard in May 1925, which raises a number of extra issues con- cerning market efficiency, such as evaluation of the gold export and import points (Officer, 1986, 1989, 1993, 1996a, 1996b). Because of possible market distortions due to the imminent return of sterling to the gold standard in May 1925 (Aliber 1962; Taylor and McMahon 1988), data for April 1925 are excluded from our analysis.

60 : MONEY, CREDIT, AND BANKING

2.0

1.5 -

C 1.0-

'0.5

-1.5 -

-2.0 1 1 I 1 [ I I 1 I 1922 1923 1924

year

FIG. 1. Deviations from Covered Interest Parity

tions in excess of 1 percent per annum on an annualized basis, the range being -1.22 to 1.33 percent per annum.

4. ECONOMETRIC METHODS

Single-Equation Estimation and Testing The purpose of this paper is to test the Keynes-Einzig conjecture concerning cov-

ered interest rate arbitrage in the interwar, pre-gold standard foreign exchange mar- ket. As discussed above, the essence of this conjecture is, first, that arbitrage only became significant once the deviations from covered interest parity were of the order of fifty basis points on an annualized basis and, second, that deviations from CIP even outside of this range may be arbitraged away only slowly either because of banks' prudential limits on foreign balances or because of market inefficiencies. This would suggest that CIP deviations would be largely indeterminate in a neighborhood of approximately plus or minus fifty basis points or so around the parity, while devia- tions from CIP outside of this range would not be immediately returned into the neu- tral band but would instead show a statistical tendency to revert towards the band. Overall, the Keynes-Einzig conjecture implies that deviations from CIP may behave in a highly nonlinear fashion.16

16. Michael, Nobay, and Peel (1997) apply nonlinear modeling techniques to the Lothian-Taylor (1996) long span of real exchange rate data. Other recent applications of nonlinear modeling in interna- tional finance include Obstfeld and A.M. Taylor (1997), Prakash and A.M. Taylor (1997), and Taylor, Peel, and Sarno (2001).

DAVID A. PEEL AND MARK P. TAYLOR 61

A parametric model that may capture this nonlinear behavior-and that nests both instantaneous and slower mean reversion toward the band-is the threshold autore- gressive (TAR) model (Tong 1990; Granger and Terasvirta 1993). A simple TAR model may be written thus:

,t = aoct- + -t if I|8_l1 < K, (4a)

,t = K(l1-P) + p6t-i + ?t if 6t_- K , (4b)

at = -K(1 - p) + p5t-_ + ?t if t,_-1 -K , (4c)

?t N(0,a2). (4d)

This is a band-TAR model (Balke and Fomby 1997). It implies that, within the band, deviations from CIP essentially follow an autoregressive process with slope coeffi- cient ct. Once at or beyond the threshold, however, 1|t-I1 - K, the deviations switch to a different autoregressive process and tend to revert toward the edge of the band rather than its center.17 If o = 1, then deviations from CIP within the band follow a random walk.

For known bandwidth K, standard asymptotic theory shows that the slope parame- ters in the band-TAR model may be consistently estimated by ordinary least squares applied separately to the two regimes within and without the band, with the asymp- totic distribution of these estimators given by the usual formulae. This can be seen most easily by rewriting (4) using the indicator variables l(|6t-_l < K), l(t-_1 > K), and 1 (6t_ 1 -K), each of which takes the value unity when the inequality indicated in parentheses is satisfied, and zero otherwise:

8t =

1(8t,_1 K)K(l-p)-l(t,_1 < -K)K(l-p)

+ [1-1(|6,_11 < K)]p8,_1+ l(|,t-_ < K)a6,t-_+ E,. (5)

For known K, (5) is linear in the parameters and is, in fact, a simple dummy variables regression posing no special estimation problems. Estimation of K can, however, be undertaken jointly with estimation of a and p by a grid search over K in order to min- imize the overall sum of squared residuals. In the present context, an appropriate range for the grid search for K is K = [0, maxl|6t]. If a2(k) is 1/T times the sum of squared residuals resulting from estimation of (5) with an assumed bandwidth para-

17. That the process mean reverts toward the edge of the band when it is outside of the band may be seen most easily by noting that equation (4b) could be reparameterized to a first-order autoregression with zero intercept in the 'mean-adjusted' variable (8t-K) and (4c) could be similarly reparameterized in terms of the variable [6t-(-K)]. A variant of this model would allow the error variance, that is, 62, to vary ac- cording to whether the deviation from CIP was inside or outside the band. A priori, however, there seems no obvious economic reason to expect this to be the case and, in fact, estimation allowing for this extra de- gree of freedom (not reported) yielded almost identical results for the estimated variances inside and out- side the band. Accordingly, we report here only the results with a constant innovation variance across regimes.

62 : MONEY, CREDIT, AND BANKING

meter of k (where T is the number of observations), then the nonlinear least squares estimator of K may be expressed:

K = arg minkE/ 2(k). (6)

Given the assumption that et is Gaussian, this is equivalent to maximum likelihood estimation (Obstfeld and A.M. Taylor 1997; Prakash and A.M. Taylor 1997).18 Since the nonlinear least squares estimator of K is consistent for K at fast rate (Hansen 1997), it is legitimate to treat the estimated bandwidth parameter as fixed when cal- culating the other parameter estimates and their distributions, especially where-as we shall see below-the estimated 95 percent confidence interval for K is small.

Having obtained estimates of the parameters, we then need to design procedures for testing a number of hypotheses of interest, beginning with a test for random walk behavior within the band:

H'o a = 1. (7)

If, as we expect, Ho is not rejected, our strategy is to impose this restriction before testing further hypotheses, in order to improve test power. Assuming this hypothesis is not rejected at the 5 percent level, therefore, we test the following hypotheses con- ditional on random walk behavior of deviations from CIP within the band:

H : K > maxl|t ; (8)

HC :K = 0; (9)

Ho : K= 0.5 . (10)

Given HA, H is effectively the null hypothesis that deviations from CIP are in fact a uniform random walk process. Hc is the converse null hypothesis that the band width is effectively zero so that (given |p|<l) a6 is uniformly mean reverting. Ho may be viewed as a formalization of one element of the Keynes-Einzig conjecture, namely, that the neutral bandwidth is plus or minus fifty basis points. As noted by Davies (1977, 1987), Obstfeld and A.M. Taylor (1997), Hansen (1997), and others, statistical inference in the context of a TAR model is complicated by the fact that some of the TAR model parameters may be unidentified under the null hypothesis in question. Hence, we cannot assume the usual 2 or F distributions for test statistics relating to various hypotheses. Moreover, the presence of a unit root under one of the null hypotheses that we wish to test, uniform random walk behavior Ho : K > maxtl6tl,

18. In a previous version of this paper we wrote down the likelihood function explicitly. We prefer to set out the univariate estimation problem as a nonlinear least squares estimation problem because this gives a more straightforward guide to readers of the estimation issues and also because much of the work on inference in TAR models takes the nonlinear least squares approach (see, for example, Hansen 1997).

DAVID A. PEEL AND MARK P. TAYLOR : 63

introduces further complications.19 Accordingly, the appropriate empirical marginal significance levels of test statistics must be calculated by Monte Carlo methods. Fol- lowing Davies (1977, 1987), Andrews and Ploberger (1994), and Hansen (1997), we used the likelihood ratio statistic

=T _2 - (11)

where T is the sample size and d2 and 62 are the unrestricted and restricted maxi- mum likelihood estimates of the residual variance, that is, 62 is 1/T times the sum of squared residuals resulting from unconstrained nonlinear least squares estimation of (5) and 62 is 1/T times the sum of squared residuals resulting from estimation of (5) with the restrictions to be tested imposed. Marginal significance levels for X were then constructed by the following parametric bootstrap procedure:20 (i) estimate the model under the relevant null hypothesis; (ii) generate 268 artificial observations from a data-generating process calibrated using the restricted estimates and with 60 = 0; (iii) discard the first 100 artificial data points and use the remaining 168 data points to estimate the restricted and unrestricted models and construct a value of the likeli- hood ratio statistic; (iv) repeat steps (ii) and (iii) five thousand times.21 This yields five thousand simulated values of the likelihood ratio statistic. The percentage of oc- casions on which the simulated likelihood ratio statistic exceeds the actual likelihood ratio statistic is then the empirical marginal significance level of the actual statistic.

Following Hansen (1997), the parametric bootstrap may also be used to construct a confidence interval for the estimated threshold parameter K as follows: (i) from the parametric bootstrap procedure outlined in the previous paragraph, construct the em- pirical distribution of the likelihood ratio statistic for the null hypothesis of no threshold behavior (that is, K = 0) and take the ninety-fifth percentile of this set as the empirical 5 percent critical value, c(5 percent); (ii) estimate the model using the actual data for a set of values of K in the range K = [0, max|6t8] and in each case cal- culate the likelihood ratio statistic X(K) for that value of K against the value of the likelihood obtained by unrestricted maximum likelihood; (iii) form the set of values of K in such a way that the likelihood ratio statistic is less than the empirical 5 per-

19. The hypothesis of a random walk within the band is not as problematic as a uniform unit root, be- cause the behavior of the deviations from CIP is still bounded so long as there is mean reversion outside the band. Nevertheless, we also computed the empirical marginal significance level of the test statistic for this hypothesis by Monte Carlo methods.

20. By "parametric bootstrap" is meant a Monte Carlo procedure where the artificial data generating process is calibrated using parameters estimated on the actual data under investigation.

21. Note that, for a given threshold, the model becomes linear in the parameters and the least squares estimation algorithm converges in one iteration; flatness of the objective function did not appear a prob- lem across the grid search in either estimation or simulation. In the multivariate estimation methods dis- cussed below, the estimated model also becomes linear in the parameters for given bandwidth; there is some iteration at each grid point in the multivariate case, but this is to allow for a nondiagonal error co- variance matrix rather than nonlinearity in the parameters, and we again encountered no convergence problems in either estimation or simulation.

64 : MONEY, CREDIT, AND BANKING

cent critical value, that is, A = {K : (Kc) < c(5 percent)}, and take the 95 percent confidence interval for the maximum likelihood estimate of K as the lower and upper bounds of the convexified A, that is, [KL, Ku] where KL = mincA and KL = maxKA.

Graphically, this can be thought of as plotting the likelihood ratio statistic X(K) (which will be zero at the maximum likelihood estimate of K), and drawing a hori- zontal flat line at c(5 percent) on the vertical axis. Taking the lower and upper bounds of the convexified region of A is a conservative procedure to allow for possible dis- jointness in A [(that is, the graph of (Kc) may not be smooth; see Hansen (1997)].

Estimation and Testing with a Nonlinear Error Correction Model A closely related way of modeling the time series properties of the data, which

may be more informative about the adjustment process, is in terms of a threshold error correction model (Balke and Fomby 1997). Define the vector Xt = (it,it*,t)', where dt = 400(S, = Ft)/S,. Given the definition of (,, the deviation from CIP may be viewed as an error correction term relating the three elements of X,, since 6, =

-i,+i,*+,t. Hence, a simple first-order threshold vector error correction model (TVECM) may be written:

AXt = Et if 1|t-,_ < K, (12a)

AXt = 0 + rF,_ + Et if 8t-6 K, (12b)

AXt = -0 + + _ + Et if 6t-< I -K , (12c)

Et - N(O,) (12d)

where Et is a 3 X1 disturbance vector, and F and 0 are 3X 1 parameter vectors. Within the band, the error correction term has no effect on any of the variables and there is no tendency to adjust toward CIP. Once outside of the band, however, we ex- pect at least one of the elements of F to be non-zero, so that one or more of Ot, it, and it adjust toward CIP so that 8t also adjusts. The statistical significance and relative size of the estimated elements of F, the error-correction parameters, should give an indication of which of the components-U.S. or U.K interest rates or the forward premium-is adjusting most rapidly in response to large deviations from covered in- terest parity.

Note that, because the hypothesis of a unit root within the band is never rejected at the 5 percent level in univariate analysis, we impose random walk behavior inside the band [equation (12a)]. The TVECM may be written as a set of dummy variable regressions using the indicator variables defined above:

AXt= l(6t-_ > K)O - l(,i-1 < -K)O + [1-1(Ibt-ll < K)]rFt,_+ Et,(13)

and estimation may be carried out by nonlinear least squares through a grid search over K, analogously to the univariate case. A complication arises here, however, be-

DAVID A. PEEL AND MARK P. TAYLOR 65

cause of the need to form an overall objective function from three sets of residuals, and it is easier in the multivariate case to think directly in terms of maximum likeli- hood estimation. The concentrated log-likelihood function for this system, for known K, is

L(, F, |K) = ~-r(3{1 + ln(2r)} + ln l|) (14)

where Z = (1/T)XTEtEt is the maximum likelihood estimator of the covariance ma- trix (see, for example, Davidson and MacKinnon 1993, p. 316). This was maximized through a grid search over K, with (13) estimated using a full information maximum likelihood (FIML) estimator at each point in the grid. If L(k) is the maximized log- likelihood conditional on a bandwidth parameter k, the resulting estimator of K may be expressed:

K = arg maxkEKL(k), (15)

where, as before, K = [0, max|ltl] is the range of the grid search. Hypotheses concerning the parameters were then tested using a likelihood ratio

statistic, defined as 3' = 2(L - L) where L denotes the value of the maximized log- likelihood and L denotes the maximized log-likelihood with the relevant restrictions imposed. From (14), X' can be written

' = T(ln|I - ln | |) (16)

where Z and Z are the unrestricted and restricted maximum likelihood estimates of the covariance matrix of the system residuals. Comparing (16) and (11), it is clear that 3' is a multivariate analogue of k.

As in the univariate case, empirical marginal significance levels for this statistic were calculated using the parametric bootstrap, and this method was also used to construct a 95 percent confidence interval for the estimated value of K, again follow- ing Hansen (1997).

5. ECONOMETRIC RESULTS

Univariate Threshold Autoregression Results We initially estimated the band-TAR model with an unrestricted value of a, the

slope coefficient of the autoregression inside the band. This yielded a point estimate of a of 0.976. Estimating the model with a constrained to unity allowed us to con- struct a likelihood ratio statistic for the null hypothesis that deviations from CIP fol- low a random walk within the band, Ho, and a value of 0.136 was obtained. The empirical marginal significance of this statistic, constructed as discussed above, was 92 percent, and so we were unable to reject the hypothesis that 6t follows a random

66 : MONEY, CREDIT, AND BANKING

walk inside the band at the 5 percent level. Hence, we imposed this restriction and proceed to report only the restricted results with a set equal to unity, and with further hypothesis tests conditioned on this restriction.

Table 1 gives details of the univariate threshold autoregressive model fitted to the deviations from CIP. The maximum likelihood estimation procedure yields a band- width of +0.422 percent-very close to the +0.5 percent conjectured by Keynes and Einzig, and the 95 percent confidence interval for K is (0.409, 0.513). Hence, within the band, deviations from CIP follow a random walk, while outside of the band they switch to a first-order autoregressive process that is significantly mean reverting, with a first-order autoregressive coefficient outside of the band of 0.775. The coeffi- cient of determination indicates a high degree of explanatory power of the model- over 80 percent of the variation in 5t is explained-and the Ljung-Box statistics indicate the absence of significant residual serial correlation. Table 1 also gives the results of three hypothesis tests. Testing the hypothesis that 8t everywhere follows a random walk, X3{K > max|It| }, we easily reject at standard significance levels. Simi- larly, we easily reject, at the 1 percent level, the hypothesis of uniform mean re- version, X(K = 0), although-perhaps most importantly-we cannot reject at the

TABLE 1 RESULTS FOR THE UNIVARIATE THRESHOLD AUTOREGRESSIVE MODEL, K ESTIMATED

A. The Estimated Model ,t

= _t- + t if |st-,1 < K,

8, = K(1-p)+pS_t- + et if 6_ t- Kc,

8t = -K(l-p)+p _t- + Et if 6t_1 K,

?t ~ N(0,a2)

B. The Parameter Estimates = 0.422 {0.409,0.513}

= 0.775 (0.0715)

62 = 0.232

C. Goodness of Fit R2 = 0.82

D. Test results Ljung-Box statistics for white noise residuals: Q(4) =2.51; Q(13)= 16.47

[0.64] [0.22]

Test for uniform random walk; -,(K > max|6St)=7.624 [0.006]

Test for uniform mean reversion: X(K=0)=8.589 [0.005]

Test for bandwidth equals + 1/2 percent: X(K=0.5)=3.635 [0.061]

NOTES: Estimation results were obtained using nonlinear least squares estimation as described in the text. Figures in parentheses denote esti- mated standard errors. The figures in curly brackets in Panel B indicate the 95 percent confidence interval. R2 denotes the coefficient of de- termination for each equation for the variable in levels. With the exception of the Ljung-Box statistic, the test statistics reported are likelihood ratio statistics for the null hypothesis indicated, with empirical marginal significance levels, generated by Monte Carlo methods as described in the text, given in square brackets. Q(j) denotes the Ljung-Box statistic applied to the estimated residuals forj correlations, with marginal significance levels given in square brackets.

DAVID A. PEEL AND MARK P. TAYLOR : 67

5 percent significance level the Keynes-Einzig conjecture of a bandwidth of ?0.5, X(Kc = 0.5).

We therefore estimated the univariate threshold autoregressive model with the bandwidth constrained to ?0.5 percent, the results of which are shown in Table 2. The main feature of the restricted estimation results compared to the previous results is a reduction in the point estimate of the autoregressive coefficient outside of the band to 0.729.

Overall, therefore, the univariate econometric results are supportive of the Keynes-Einzig conjecture. We find that the data are well characterized by a band- TAR model with a bandwidth of plus or minus fifty basis points around covered in- terest rate parity and, while mean reversion of CIP deviations outside of the neutral band is statistically significant, the deviations are moderately persistent, as also con- jectured by Keynes and Einzig.

Multivariate Threshold Vector Error Correction Model Results Table 3 gives details of the multivariate threshold vector error correction model

fitted to the data. We again can not reject, at standard significance levels, the restric- tion that the bandwidth is in fact equal to ?0.5 percent on the basis of a likelihood ratio test, X'(K = 0.5) (Table 3 Panel D), and so we report only the restricted esti- mates (that is, with the restriction K = 0.5) in order to conserve space. The unre- stricted estimate of K was, however, 0.483, with a 95 percent confidence interval of (0.451, 0.518). In addition, the intercept term for the U.S. interest rate equation was found to be insignificantly different from zero at the 5 percent level, and so this pa- rameter restriction was also imposed.

TABLE 2 RESULTS FOR THE UNIVARIATE THRESHOLD AUTOREGRESSIVE MODEL, K SET AT 0.5

A. The Estimated Model t = 8_t-1 + ?t if |ISt-l < 0.5,

6t = 0.5(1-p)+P6t-, + ?t if 8t- 0.5,

8t = -0.5(1-p)+p6,_1 + Et if t,_1 -0.5,

E, - N(0,o2)

B. The Parameter Estimates p = 0.729 (0.0791)

o2 = 0.243

C. Goodness of Fit R2 = 0.82

D. Test results Ljung-Box statistics for white noise residuals: Q(4)=2.68; Q(13) 16.92

[0.61] [0.20]

NOTES: Estimation results were obtained using nonlinear least squares estimation as described in the text. Figures in parentheses denote esti- mated standard errors. R2 denotes the coefficient of determination. With the exception of the Ljung-Box statistic, the test statistics reported are likelihood ratio statistics for the null hypothesis indicated, with empirical marginal significance levels, generated by Monte Carlo meth- ods as described in the text, given in square brackets. Q(j) denotes the Ljung-Box statistic applied to the estimated residuals forj correlations, with marginal significance levels given in square brackets.

TABLE 3 RESULTS FOR THE THRESHOLD VECTOR ERROR CORRECTION MODEL, K = 0.5

A. The Estimated Model

AX, = E, if Is,_11 < K,

AX, =- +r 8 +E, if t_- 2 K,

AX, = -O + rF,_l + E, if 6,_ -K ,

E, - N(O, )

Xt=(i,,it ,, )', , = 400(S, -F,)/ S,, , ,=-it + i + , .

B. The Parameter Estimates

0.0

e= 0.038 (0.017) 0.075 (0.019)

0.034 (0.011) r= -0.057 (0.026)

-0.128 (0.032)

0.040

I= 0.005 0.008

-0.006 -0.001 0.031

C. Goodness of Fit i: R2 = 0.98

i : R2 = 0.92

t: R2 = 0.96

D. Test Results Ljung-Box statistics for white noise residuals: it: Q(4) = 6.19; Q(13) = 15.55

[0.19] [0.127]

it Q(4) = 5.13; Q(13) = 9.81 [0.27] [0.71]

t: Q(4) = 5.12; Q(13) = 15.66 [0.27] [0.27]

Test for bandwidth equals + 1/2 percent: '(K= 0.5) =2.761 [0.12]

NoTEs: Estimation results were obtained using maximum likelihood estimation as described in the text. R2 denotes the coefficient of deter- mination. Figures in parentheses denote estimated standard errors. With the exception of the Ljung-Box statistics, the test statistics reported are likelihood ratio statistics for the null hypothesis indicated, with empirical marginal significance levels, generated by Monte Carlo meth- ods as described in the text, given in square brackets. Q(j) denotes the Ljung-Box statistic applied to the estimated residuals for each variable forj correlations, with marginal significance levels given in square brackets.

DAVID A. PEEL AND MARK P. TAYLOR : 69

The coefficients of determination reported in Table 3 indicate a high degree of ex- planatory power and the Ljung-Box statistics indicate absence of serial correlation in the estimated residuals.

Within the ?0.5 percent band, both U.S. and U.K. interest rates and the forward premium follow a random walk. For larger deviations from CIP, however, both the discount on New York prime bankers' acceptances and the U.K. treasury bill rate as well as the forward exchange discount show significant adjustment to the error cor- rection term, that is, the lagged deviation from CIP, in the sense that the estimated slope coefficient attaching to the error correction term is in each case strongly signif- icantly different from zero at normal significance levels and is also of the correct sign to ensure stability, given the definition of 8t in (3). The relative magnitudes of the error correction coefficients, however, indicate that the strongest adjustment was in the forward premium, which has an error correction coefficient more than twice as large as that for the discount on U.K. treasury bills in absolute magnitude, and nearly four times that for the discount on prime bankers' acceptances in New York. Thus, al- though all three of the variables display a tendency to adjust so that large deviations from CIP tend to return toward the band, it seems that U.S. interest rates show the least tendency to do so.22

Since 8t = -it+it*+t, the multivariate estimation results outside the band re- ported in Table 3 imply (ignoring the error terms) A8t = +0.113 - 0.219 t-_1 above the band and A8t = -0.113 - 0.219 8t_1 below the band, or 8t = +0.516(1-0.781) + 0.781 8,_1 above the band and 8t = -0.516(1-0.781) + 0.781 8,_1 below the band, which is strikingly close to the univariate estimation results reported in Tables 1 and 2, providing further corroborating evidence for a univariate band-TAR model for deviations from CIP.

6. CONCLUSION

In this paper we have applied recently developed but intuitively straightforward nonlinear econometric methods to previously unexploited data on deviations from covered interest parity between the London and New York money markets in the 1920s. Our results are broadly consistent with the conjecture of Keynes (1922, 1923) and Einzig (1937) that arbitrage activity during this period was triggered only once a "significant" deviation from CIP occurred. Keynes and Einzig conjectured that this "significant" deviation was of the order of fifty basis points on an annualized basis, and our empirical analysis strongly supports this conjecture. Moreover, even when this threshold is crossed, our analysis suggests that the supply of arbitrage funds was not generally elastic enough to ensure instantaneous reversion to the neutral band. Instead, deviations from CIP become significantly mean reverting outside of the neu-

22. The implication that U.S. monetary policy was set in a relatively autonomous fashion over the sample period, with U.K. interest rates behaving in a largely accommodating fashion, is also evident in econometric studies of the postwar Bretton Woods period and the first decade of the recent float (for ex- ample, Branson 1968, 1984).

70 : MONEY, CREDIT, AND BANKING

tral band, but are still moderately persistent. The relatively sluggish arbitrage even of larger deviations from CIP which this implies is also a feature of the interwar market emphasized by Keynes and Einzig. Estimation of a threshold vector error correction model for interest rates and the forward premium implies that, although all three of the variables display a tendency to adjust so that large deviations from CIP tend to return towards the band, it seems that U.S. interest rates show the least tendency to do so during this period.

The research reported in this paper is, to the best of the authors' knowledge, the first empirical analysis of the Keynes-Einzig conjecture, although this conjecture appears to be an implicit assumption in a large amount of theoretical and empirical analysis of the interwar period. Our research supports both elements of the Keynes-Einzig con- jecture, both that the neutral band appears to be about +0.5 percent on an annualized basis and that the deviations are moderately persistent even outside of the band.

These results, of course, raise further issues, in particular the issue of why the min- imum covered interest rate differential needed for international arbitrage activity should have been so high in the interwar period. The discussion in, for example, Keynes (1923) and Einzig (1937) tends to treat a neutral bandwidth of +0.5 percent as relatively small, "of a magnitude as will yield the arbitragers sufficient profit for their trouble" (Keynes 1923, p. 106). From a moder-day perspective, however, the differential seems huge. Since we are dealing with onshore securities, one possibility is that the band is due to political risk. Although one would not a priori expect this to be so large for arbitrage between the United Kingdom and the United States in this period, further work might usefully explore this avenue.

Another possibility is simply that the markets were to this extent inefficient, which indeed seems to be a moder interpretation of Keynes and Einzig's explanation, as we discussed in section 2, and this again might warrant further analysis.

An alternative but related view, also developed by Einzig (1937) as well as Hawtrey (1932), would be that banks were unwilling to place large deposits in pur- suance of covered interest arbitrage unless the resulting profit were large enough in percentage terms because of the effect this would have had on their overall liquidity:

If the banks possessed unlimited amounts of funds for the purpose of interest arbitrage ... then there could be no lasting discrepancy between Interest Parities and the forward rate. No matter how persistent the overvaluation or undervaluation of the forward rate as a result of commercial demands or speculative operations, it would be offset by arbi- trage transactions as soon as it reached the limit at which banks considered it worth their while to operate. In reality, there can be lasting discrepancies between forward rates and their Interest Parities, even in normal conditions, because the volume of funds available for interest arbitrage is limited. The volume of susceptible funds-to use the term employed by Mr. Hawtrey [1932]-may be large, but it has its limits. Even if the banks have no reason whatsoever to distrust the foreign centre, they are not prepared to transfer there more than a small percentage of their liquid resources.' (Einzig 1937 pp. 171-72)

This argument is in fact similar to that employed by Taylor (1987a, 1989) to explain the "maturity effect" of small and persistent deviations from covered interest rate parity appearing at the longer end of the maturity structure for Euro-deposits, albeit

DAVID A. PEEL AND MARK P. TAYLOR : 71

of a magnitude very much smaller than fifty basis points. This, however, only raises a further question, namely, why should banks care about liquidity in this fashion, over and above any issues of political risk? Taylor (1987a, 1989) suggests that banks may wish to retain liquidity in order to be ready to exploit other arbitrage opportuni- ties which may arise (although a fifty basis points deviation would still seem large). It is also possible that banks may have wished to retain liquidity because of the fear of a run on the bank, and that this effect may have declined in the postwar period be- cause of the growth in the asset base of large investment banks and the general deep- ening of the forward exchange markets (Einzig 1962). Further work might explore these possibilities, perhaps through formal modeling.

Yet another possibility may be related to the assumed risklessness of covered in- terest arbitrage. Covered arbitrage is only riskless if all of the transactions-the tak- ing of a deposit, the placing of a deposit, a spot foreign exchange transaction and a forward foreign exchange transaction-are effected simultaneously. In a modem for- eign exchange dealing room, equipped with highly sophisticated communication equipment and served by a sophisticated system of foreign exchange and money market brokers, prices can be obtained and orders carried out literally within seconds (and may even be automated and synchronized), so that covered arbitrage will in- deed be virtually riskless. Although poorly documented, the dealing room environ- ment of the 1920s must have been quite different, with communication between London and New York banks taking place by cable and "long-distance trunk calls" (Einzig 1937, p. 57) and therefore being much slower.23 In this environment, it may have been prudent to wait for a sizeable deviation from CIP to arise before arbitrag- ing in order to be sure of effecting the necessary transactions before prices moved against the arbitrageur.

Still another explanation might be that the transactions costs of covered arbitrage have fallen substantially since the 1920s because of improved efficiency and produc- tivity in the banking sector [see, for example, Clark (1996) and Berger and Mester (1997), for recent studies of banking efficiency]. Indeed, this seems almost certain to be the case to some extent, although a formal examination and quantification of this conjecture would be a useful research exercise.

Overall, what is clear is that the results reported in this paper raise important issues for further research into the interwar financial markets.

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