The impact of macrofinancial variables on Covered
Interest Parity violations after the 2008 global financial
crisis
Mémoire
Khodeu Thuo Zhagnin Kossa
Maîtrise en économique - avec mémoire
Maître ès arts (M.A.)
The impact of macrofinancial variables on Covered
Interest Parity violations after the 2008 global
financial crisis
Mémoire
Thuo KOSSA
Sous la direction de:
Résumé
Ce mémoire analyse les déterminants des déviations à la parité des taux d’intérêts couverts (PTIC) après la crise financière de 2008. Notre modèle analyse la relation de long terme entre certaines variables macroéconomiques et les déviations mesurées à la PTIC. Nous utilisons les données sur les instruments du marché financier, l’offre de monnaie ainsi que le PIB réel entre 2009 et 2019, pour le Canada et les États-Unis, comme déterminants de ces déviations. Notre approche méthodologique utilise des techniques d’économétrie des séries temporelles. Les paramètres du modèle sont estimés à l’aide des méthodes Fully-Modified OLS (FM-OLS), Dynamic OLS (DOLS) et Integrated modified OLS (IM-OLS). Pour les données couvrant l’horizon de 5 ans, nous trouvons des résultats contradictoires pour l’offre de monnaie, mais établissent une relation négative entre le PIB réel et les déviations observées à la PTIC. Sur un horizon plus long (10 et 20 ans), l’offre de monnaie et le PIB réel ont tous deux un effet négatif sur les déviations de la PTIC mais celui du PIB réel est plus important. En outre, l’inclusion dans le modèle de l’indice de volatilité du marché américain s’est montré significatif dans la plupart des cas.
Abstract
We analyze the macroeconomic determinants to the deviations from Covered Interest Rate Parity (CIP) after the 2008 financial crisis. Our model analyzes the long-term relationship between some macroeconomic variables and measured CIP deviations. We use data on financial market instruments, on relative money supply and relative real GDP between 2009 and 2019 for Canada and the United States. Our theoretical approach uses time series econometrics tools adapted to non-stationary series and the model parameters are estimated using fully modified OLS (FM-OLS), dynamic OLS (DOLS) and integrated modified OLS (IM-OLS) regressions. On the 5 year horizon, the estimated effect of relative money supply on the deviations is mixed. On the other hand, there is a negative relationship between real GDP and the deviations observed. For longer-term horizons (10 and 20 years), both money supply and real output have a negative effect on the deviations. Yet, that of real GDP is stronger. In addition, the inclusion of the VIX volatility index in the model was significant in most cases.
Contents
Résumé iii
Abstract iv
Contents v
List of Tables vi
List of Figures vii
Remerciements x
Introduction 1
1 Literature Review 2
1.1 Foreign Exchange Market . . . 2
1.2 Unbiased Expectations Hypothesis (UEH) . . . 4
1.3 Deviations from CIP . . . 5
2 Theoretical Framework 8 2.1 CIP Model . . . 8
2.2 Cross-Currency Basis. . . 9
2.3 Measure of the deviations . . . 10
2.4 Monetary Model of Exchange Rate . . . 14
3 Data 19 4 Empirical Strategy and Results 23 4.1 Econometric methodology . . . 23
4.2 Regressions results . . . 25
Conclusion 32
A Data sources 33
B Tables & Graphs 34
List of Tables
1.1 OTC foreign exchange turnover by instrument. . . 3
1.2 OTC foreign exchange turnover US and Canada. . . 3
1.3 OTC foreign exchange turnover by currency pair . . . 4
2.1 Mean and standard deviations of cross-currency basis swap - 5-years horizon . . 15
4.1 Unit Root Tests. . . 24
4.2 Johansen Cointegration test - 5 years cross-currency basis swaps . . . 25
4.3 Regression results. . . 26
4.4 Johansen Cointegration test - by variable . . . 28
4.5 Regression results - alternative specification . . . 30
A.1 Data source . . . 33
List of Figures
2.1 Cash flow diagram for CAD/USD 3 months cross-currency basis swap . . . 10
2.2 Short run USD/CAD cross-currency basis swaps . . . 11
2.3 Long run USD/CAD cross-currency basis swaps . . . 12
2.4 Short run cross-currency basis swaps: 3-months (other G10 countries) . . . 13
2.5 Short run cross-currency basis swap: 6-months (other G10 countries) . . . 13
2.6 Long run cross-currency basis swaps: 5-years (other G10 countries) . . . 14
3.1 Forward points USD/CAD. . . 20
3.2 Spot exchange rate USD/CAD . . . 20
3.3 Relative money supply between the United and States and Canada . . . 21
3.4 Relative GDP between the United States and Canada . . . 22
À toi mon défunt Papa, Dr. Anatole KOSSA
« Le travail et après le travail l’indépendance mon enfant, n’être à la charge de personne telle doit être la devise de votre génération. Et il faut toujours fuir l’homme qui n’aime pas le travail. »
Remerciements
J’écris ces lignes en pleine crise du Coronavirus (COVID-19), les économies des différents pays sont sur pause. Le ”Great Lockdown” a mis un arrêt brutal et sans précédent à la production, le prix du pétrole est passé au négatif. Les gouvernements et Banques Centrales prennent toutes sortes de mesures pour stimuler, soutenir l’économie. ”Quantitative Easing” ou ”Money Printing”? Bref! J’aurais pris plaisir à écrire mon mémoire en abordant le contexte actuel. Ce mémoire, bien qu’étant le fruit d’un travail hautement solitaire a été rendu possible par le soutien de nombreuses âmes. Je rends grâce à DIEU d’avoir mis ces personnes sur mon chemin. Trouvez dans ces quelques lignes l’expression de mon incommensurable reconnaissance. J’aimerais tout d’abord remercier mon directeur de recherche pour son aide, sa disponibilité et ses orientations dans la rédaction de ce mémoire. MERCI Kevin pour ta sagacité. J’aimerais remercier également tout le corps professoral du département d’Économique de l’Université Laval pour le jeune Économiste qu’ils ont formé depuis 2013.
J’aurais aimé présenter ce travail à Feu Dr. Anatole KOSSA. Merci Papa d’avoir investi dans notre éducation. J’ai en tête tous tes conseils, MERCI. À toi Maman, qui nous a inculqué la discipline, la rigueur et l’amour des études depuis l’école primaire, MERCI. Gnami, ma chérie coco, MERCI de t’être enquise fréquemment de l’évolution de ce travail même si au fond tu ignores le sujet. Plus près de moi, assis dans la pièce d’à côté, Donh KOSSA, B.Eng. Merci Donh de m’avoir réveillé toutes ces fois afin de poursuivre la rédaction du mémoire. Merci de m’avoir écouté parler de toutes ces théories économiques pour lesquelles tu n’avais pas grand intérêt. Donh, mon coach en motivation personnel, j’ai toujours pu compter sur ton aide afin de passer au travers des montagnes russes émotionnelles liées aux études universitaires. Je remercie ma directrice Marise à Desjardins qui m’a offert cet aménagement du temps de travail qui me permit de réussir ma première session de Maîtrise. Je remercie ma directrice Judith et ma manager Glasha pour l’opportunité qu’elles me donnent de travailler à ECCC ainsi que l’ensemble de mes pairs Économistes du Ministère. J’ai une profonde reconnaissance à l’égard de ceux qui ont gentiment accepté de lire et corriger mon anglais: Zeinab, Mankan, Abenco, Robin, Gavin. Je n’oublie pas tous ceux qui ont poliment refusé de relire mon mémoire. Merci à vous tous! Nathan R. Lea, merci pour tes notes de cours, tes anciens examens et tes conseils durant ce cursus. DIEU passe par des hommes pour agir mais au final, à lui la Gloire et la Reconnaissance!
Introduction
Covered Interest Parity (CIP) theory dictates that covered transactions contracted by an American investor in USD or in CAD should provide equivalent returns. For example, consider an investor investing in Canada and in order to cover exchange rate fluctuation, entering in a forward exchange rate contract. As a no-arbitrage condition, CIP states that the gain in interest rate will be offset by an opposite movement of exchange rate.
CIP theory appears to have held until the global financial crisis of 2008. Recent empirical studies show persistent deviations from CIP (Borio et al.,2016;Cerutti et al.,2019;Amador et al.,2019). Early attempts to explain these deviations attributed them to the existence of transaction costs. However, the recent intensity of measured deviations suggests that other factors need to be taken into account. This paper seeks to understand the causes of CIP deviations by linking them to macroeconomic variables such as the money supply and real GDP.
We use Canadian and US data on real GDP, real interest rate, money supply and other financial data, as well as CIP deviations as measured by Bloomberg’s cross-currency swap data. Data are on a monthly frequency and cover the period from June 2009 to June 2019. Our approach is to link the general framework of the CIP to a monetary model of exchange rate,
Ibhagui (2019). To do so, we first perform unit-root tests on the data, to evaluate whether our sample is stationary or non-stationary. Next, we perform cointegration tests, using the Johansen procedure. Finally, we estimate the coefficients in the cointegration relationship using the Fully-Modified OLS (FM-OLS), Dynamic OLS (D-OLS) and Integrated-Modified OLS (IM-OLS) estimators.
This thesis proceeds as follows. The first section reviews the literature on the foreign exchange market and recent studies about CIP deviations. In the second section, we present our theoretical methodology. Section three presents the data used in the study. Two last sections, discuss our results and provide a conclusion.
Chapter 1
Literature Review
This chapter describes the state-of-art of the research on covered interest parity. The first part of this section gives an overview of the foreign exchange market, the second one describes studies on the Unbiased Expectations Hypothesis (UEH). Then, we discuss the relevant literature on CIP.
1.1
Foreign Exchange Market
The foreign exchange market, or FX market, is one of the largest market in the world. It is the place where currencies are traded. The participants in this market are financial institutions and other international banks. In 2016, according to the Triennial Central Bank Survey, the average volume traded was equivalent to 5.1 trillion USD in average per day.1 Many instruments
are traded in this market: spot contracts, forward contracts, future contracts, options, etc. Spot contracts involve two parties which agree to trade a pair of currencies at a fixed price. The settlement date is the next business day. On the other hand, an investor can choose to enter in a forward contract. Common forward contracts are futures currencies and forward exchange contracts. Both of them have the function to cover exchange risk. The difference is that forward contracts are settled at the end of the contract while a future contract is settled on a daily basis. The foreign exchange market is ranked in the category of Over-The-Counter (OTC) markets. In OTC markets, securities are traded "over-the-counter" between two parties without any supervision. In this context, the notion of counterparty risk is very important. The foreign exchange market has grown rapidly over the years. Table 1.1reports the turnover on this market from 2001 to 2016 and by instrument. We can see that the most important instrument in volume are the foreign exchange swaps. Their volume reached the amount of 2378 billions USD in 2016 in average per day. The growth rate of each instrument is more than one hundred percent on average over the fifteen-year. Currency swaps, an important
instrument for analysis represent a growing market, although their quantitative importance remain modest.
Table 1.1: OTC foreign exchange turnover by instrument
OTC foreign exchange turnover 2001 2004 2007 2010 2013 2016
Options and other products 60 119 212 207 337 254
Spot transactions 386 631 1005 1489 2047 1652
Outright forwards 130 209 362 475 679 700
Foreign exchange swaps 656 954 1714 1759 2240 2378
Currency swaps 7 21 31 43 54 82
Total: Foreign exchange instruments 1239 1934 3324 3973 5357 5067
Source: BIS, daily averages in April,
in billions of US dollars.Note: Adjusted for local and cross-border inter-dealer, double-counting.
Non-US dollar legs of
foreign currency transactions were converted into original currency amounts then reconverted into USD
amounts at average April 2016 exchange rates.
As part of our study, we will focus on the Canada/US market. The USD is the most traded currency internationally, so in terms of volume traded, the USD is naturally larger than the CAD. Our interest in the Canada and US markets is due to the fact that they are bordering countries and that the USA is one of the Canada’s main trading partners. Note however that most of literature focuses on relations between the USA and Euro area and the relevant data.
Table 1.2: OTC foreign exchange turnover US and Canada
Year Canada USA
1995 31 266 1998 38 383 2001 44 273 2004 59 499 2007 64 745 2010 62 904 2013 65 1263 2016 86 1272
Source: Bank of International Settlements (BIS) Daily averages, in billions of US dollars
Even if the transaction volume in Canada is smaller compared to the USA in the table 1.2
above, the USD is still the most requested currency in Canada.2
2
Table 1.3 shows a steady evolution of transactions for the USD / CAD pair. USD/EUR, USD/GBP, USD/JPY account for more than 50% of the total OTC foreign exchange turnover (see Table1.3). Table1.3 is an extract, the full table for all the pairs being available in the BIS database. Data are adjusted for local and cross-border inter-dealer double-counting (ie “net-net” basis). Amounts are daily averages in April, in billions of US dollars. Overall, the data thus shows the importance of our two economies, with the US dollar being the most traded currency internationally and also the most traded in Canada.
Table 1.3: OTC foreign exchange turnover by currency pair
Currency pair 2007 2010 2013 2016
Amount % Amount % Amount % Amount %
USD / EUR 892 27 1099 28 1292 24 1172 23 USD / JPY 438 13 567 14 980 18 901 18 USD / GBP 384 12 360 9 473 9 470 9 USD / AUD 185 6 248 6 364 7 262 5 USD / CAD 126 4 182 5 200 4 218 4 Source: BIS
1.2
Unbiased Expectations Hypothesis (UEH)
The expectations of the participants play a key role in forward market. Economists have made several hypotheses about the nature of these assumptions. Sanderson (1984) tested the hypothesis that expectations in the forward market were rational. His approach was to test rational expectations by testing for forward market efficiency and absence of the risk premium. The paper came to the conclusion that the rational expectations hypothesis cannot be rejected. However, the results are not robust because the author only incorporated a narrowly defined information set into the forward rate. Before him, Frankel (1980) concluded a mixed result. For the post-1974 period, the expectation of rational expectations is accepted for the Deutsh Mark. On the other hand, the French franc, the Italian lira, etc. failed many tests. The theory behind rational expectations of forward market is known as the unbiased expectations hypothesis (UEH).Waheed (2009) rejected this theory testing for Pakistan and US currencies. His study covers the period from January 2002 to May 2007. In the mid-1980s, Hsieh (1984), came to the same results. The preferred methodological approach of the authors to test the hypothesis is to perform time series econometrics with cointegration tests.
Even though a broad consensus in the literature supports the rejection of the forward market unbiasedness hypothesis, Krasker (1980) points to the unreliability of the general methodology. He talks about the peso problem, a situation where an unforseen event could potentially cause a large change in the exchange rate (Mexico peso’s problem in 1976 and German hyperinflation
in 1921). Then, the usual statistical test will reject efficiency and rationality even if it is true. He suggests an alternative statistical test, which takes into account the low probability of a large unforseen event. Of course, this alternative will be less powerful than the standard tests. Chen et al.(2014) also explain the failure of the unbiasedness hypothesis by the peso problem. Jardet (2008) showed the evidence that for European countries, the peso-problem is a plausible explanation for the period post 1992. On the other hand, a better explanation is the time-varying term period for the United States.
The failure of the UEH has led economists to develop other theories about the expectations of economic agents. Li et al.(2013a) suggested that agents have heterogeneous expectations, a situation that appears when agents speculate against positions of each other. He built a Markov regime switching model to approximate a Chartists versus Fundamentalists (c&f) model. In a c&f model, the chartists forecast future movements of a forward rate by calibrating on past trends, while fundamentalists make decisions based on economics fundamentals. Some key findings of this paper is that chartists reinforce forward exchange rate movements, while fundamentalists act to revert the prediction of the theory. The author based his empirical studies on USD/EURO and USD/JPY currencies. The debate between chartists and fundamentalists in the forward market led to a thriving literature (Allen and Taylor,1990,Liu,1996,Frankel and Froot, 1990, Prat and Uctum, 2015). Other studies explained the failure of UEH by developing a nonlinear exchange rate model (Bond et al., 2010), Markov switching model (Spagnolo et al.,2005) and a three-factor model (Li et al.,2013b).
1.3
Deviations from CIP
In this section, we discuss the relevant literature for our empirical work. Prior to the financial crisis of 2008-2009, small deviations from CIP were already spotted in the litterature (Clinton
(1988),Atkins(1993),Committeri et al. (1993),Bahmani-Oskooee and Das (1985),Frenkel and Levich (1975)). However, these deviations were of low intensity and the return to equilibrium was quick. Most articles explained these deviations by transaction costs. Since the global financial crisis, persistent deviations and high intensities have brought the subject of CIP back to the fore and a thriving literature tries to explain these departures from CIP.
The influential paper of Du et al.(2018) documents CIP deviations for the postcrisis period among G10 currencies from 2000 to 2016. They reject the common view that the deviations are related to transaction costs, and the authors instead point out that deviations are especially strong for forward contracts that appear on banks’ balance sheets at time when monetary policy shocks are prevalent.
Du et al. (2018) explain CIP deviations as arising from financial intermediaries’ constraints, international imbalances in investment demand, and funding supply across currencies. Then, they document four major characteristics of CIP deviations. The first is that CIP deviations
increase at the quarter-ends, when banks face tighter balance sheet constraints. Second, they used the spread between the Interest rate On Excess Reserves (IOER) and the LIBOR rate as a better proxy for banks’ balance sheet costs. This proxy appears to account for two-thirds of CIP deviations. Third, there is a positive relation between CIP deviations and nominal interest rates (cross section and time series). Fourth, the cross-currency basis is correlated with other near-risk-free fixed income spreads. They point out the evidence for the KfW basis (German government-owned development bank) and the Libor rate basis.
Sushko et al.(2016) found that CIP fails in calm markets. The first cause of this failure accord-ing to the authors is FX hedgaccord-ing demand. Duraccord-ing the financial crisis, unconventional monetary policies led by central banks compressed term and credit spreads. This constrained demand in investment and funding flows. Thus, currency risk causes imbalances in the exchange rate differential and implies a persistent cross-currency basis. The second cause of the deviations is the costs of balance sheet. Since the FX market is imbalanced for exchange rate differential (forward-spot), the balance sheet is committed to arbitrage, which is costly. The study of the authors is based on developed countries currencies: USD, AUD, CAD, GBP, JPY, CHF, DKK and covers the pre and post-crisis period. This paper also addresses the nature of constraints to CIP arbitrage by banks. Although the literature explained this by banks facing balance sheets constraints in the quarter-end and investor’s attention at the same period (Du et al.,2018),
Sushko et al. (2016) found that this could not explain the intensity of deviations observed. They suggest that at a longer maturity, CIP deviations are consistent with bank management of capital constraints.
Our work is also related to the literature on zero lower bound (ZLB) interest policy (as in
Caballero et al.,2015). During the financial crisis, central banks cut interest rates to the lowest bound in order to attract capital inflows. Amador et al. (2019) showed that this situation coupled with the pursuit of an exchange rate policy can lead to deviations from CIP. The authors built a simple monetary model linked with a ZLB policy. Their main finding is that a central banks can cause depreciation to its currency even at the zero lower bound. However, to achieve this, central banks intervene in foreign markets and accumulate foreign reserves. The paper thus suggest deviations from CIP can emerge from this situation.
The collapse of Lehman Brothers significantly increased the counterparty risk of banks in international markets. Previous studies assumed that transaction interest rates between two curriencies were risk-free. This was shown to be less realistic for the postcrisis period. Baba and Packer (2009) built a EGARCH(1,1) model that includes counterparty risk. They show that persistent deviations from CIP during the financial market turmoil of 2008 were caused by asymmetric counterparty risks between European and US financial institutions. Credit default
risk has been widely used by recent literature as a measure of counterparty risk (see Arora et al.(2012),Wang et al. (2013),Eichengreen et al.(2012),Morkoetter et al. (2012), Brown and Hao (2012)). Morkoetter et al.(2012) was interested in pricing of CDS. Through a panel of regression from 2002 to 2009, they showed that market-oriented counterparty risk measures are reflected in the pricing of CDS contracts. They also conclude that for North American banks, the impact of counterparty risk was already incorporated in the loans. For European banks, the financial crisis intensified the impact of CDS pricing. Csávás (2016) interpreted CDS premium as a transaction cost and showed that the cost of counterparty risk resulted in deviations from CIP during GFC.
The link between macroeconomic variables and CIP is less studied in the literature. In a recent paper,Ibhagui(2018) develops a new approach of cross-currency basis swap spreads linked with macroeconomic variables. The author uses a simple monetary model (Frenkel,1976,Dornbusch,
1976) to link his measure of CIP deviations to money supply, real income, and focuses on long run relationships between these variables. The main finding of this paper is that the mechanism behind the return to the equilibrium is driven by an adjustment of cross-currency basis swap. More recently, Cerutti et al. (2019) also discuss the impact of macrofinancial determinants in the failure of CIP. In the paper, they use OLS and IV regressions and include an index of volatility. The authors brought the evidence that recent deviations from CIP could not be explained by regulatory factors only.
Chapter 2
Theoretical Framework
This section provides the structure of our model. The first subsection gives an overview of the CIP condition in the context of an American investor who can buy Canadian or US assets. Next, we present a model of CIP deviations, with a brief analysis of its implications for financial market and the no-arbitrage theory. In the third section, we try to understand the relationship between the deviations from CIP and some macroeconomics determinants, through a version of the monetary model of exchange rates in which we relax the no-arbitrage assumption.
2.1
CIP Model
Consider an investor who can only operate in the US or Canadian market, with the US market considered as the domestic market. Let itbe the interest rate in the domestic market at time t and i∗
t its equivalent in the foreign market. Consider further that the assets in these markets are riskless. Denote St is the spot exchange rate for the foreign currency at time t; St is thus the amount of foreign (Canadian) currency needed to buy 1 USD and an increase of St represents an appreciation of the US dollar. Finally, the investor can enter into a one-period forward contract to hedge the exchange rate risk, with Ftthe forward interest rate agreed at time t for one-period later (t + 1).
The return on investment for our investor is related to her strategy on whether to invest in Canada or the United States. Assume that the investor has $1US to invest at time t. If she invests in the domestic market (US market), the yield generated is $(1 + it) in US dollars. Her second strategy could be to invest in the foreign market, by entering in a forward contract to be implemented at the end of the investment period, i.e time t + 1. The equivalent of $1US on the Canadian market today is St. Investing her $1US then yields St(1 + i∗t) in the foreign market (Canadian market). One period later, she swaps back her gain in the domestic market, at the forward rate Ftagreed at time t; overall the yield on that second strategy will thus be St(1 + i∗t)/Ft.
Covered Interest Parity (CIP) states that the investor should obtain the same return regardless of the investment strategy. As such, one should observe that:
1 + it= St Ft
(1 + i∗t), (2.1)
Which, for small values of i, where 1 + i ' ei, becomes: eit
ei∗t =
St Ft
, (2.2)
or in logs and rearranging :
ft− st= i∗t − it. (2.3)
According to the CIP condition (2.3), the interest rate differential should be equal to the forward premium (ft− st).
2.2
Cross-Currency Basis
In this section, we drop the ideal world of the CIP condition, because significant and persistent deviations from the condition have been observed for most currency pairs after the global financial crisis of 2007-2010. This means that arbitrageurs could potentially take advantage of interest rate differentials to make positive profits.
Let the cross-currency basis be the difference between the direct US interest rate (it) and the synthetic US interest rate (i∗t + st− ft). Algebraically, the cross-currency basis is expressed as follows:
xt= it− [i∗t + st− ft], (2.4) xt= (ft− st) − (i∗t − it) (2.5) In this article, we will use the cross-currency basis data provided by Bloomberg. The amount of profit that can be gained by an arbitrageur is related to the absolute magnitude of the deviations, while the specific strategy to obtain these profits depend on the sign of xt, we consider two scenarios1.
Consider first a negative value for xt. If xt< 0, then i∗t + st− ft> it, so the synthetic foreign interest rate is higher than the direct domestic one. The investor can make profits by investing USD in the foreign market: she borrows USD, which she converts to CAD, invests CAD in the Canadian market to earn the foreign risk-free rate. She then swaps back her benefits in the domestic market at the agreed forward rate contract.
For a positive value of xt, the opposite situation takes place. We have it> i∗t + st− ft so the
1We could have defined S
t in the opposite way, in which case an increase in S represents a depreciation of
direct US rate is higher than the synthetic one. The investor borrows foreign currency that she converts in USD at the spot exchange rate. The synthetic USD obtained is reinvested in the domestic market to earn the dollar risk-free rate. The gain is swapped back at the forward rate contracted to foreign currency.
2.3
Measure of the deviations
The goal of this section is to provide details on available measures of the deviations mentioned above. The cross-currency basis measures are calculated, and provided by Bloomberg. The US currency is considered as the domestic currency. According to Bloomberg, ”Banks are the biggest users of cross currency swaps, while hedge funds and proprietary trading firms rank second. The favored currencies are the dollar, euro and yen. Most contracts involve the dollar. They typically range from 1 to 30 years, reflecting the length of the transactions they fund, such as loans. What makes them unique in the world of swaps is that the parties agree to exchange notional principals, or the face amount used to calculate the payments.”2.
Figure 2.1: Cash flow diagram for CAD/USD 3 months cross-currency basis swap
Figure2.13 above shows the cash flow exchanges of a 3 months CAD/USD cross-currency basis
swap. At the inception, Bank B exchanges 1 USD against StCAD. During the term, on an agreed date, Bank B receives a dollar floating cash flow equal to YLibor,$
t=3 ∗ 1U SDfrom Bank A. Here, YLibor,$
t=3 represents the three-month USD Libor. In the meantime, Bank B pays to Bank A a Canadian dollar floating cash flow equal to (YCDOR,CAD
t=3 + xccyt=3) on the notional CAD St. Yt=3CDOR,CAD is the three-month Canadian CDOR and xccyt=3is the cross-currency basis spread. When the swap contract matures, Bank B receives 1USD from Bank A in exchange for CAD St, undoing the initial transaction. Notice that if xccyt=3< 0 (negative basis), Bank B repays less than what it receives and this is the profit created by the CIP deviation.
2
Source: Bloomberg https://www.bloomberg.com/news/articles/2020-03-17/how-cross-currency-basis-swaps-show-funding-stress-quicktake
3
2.3.1 USD/CAD pair
The pair USD/CAD is the main interest of this paper. Data on cross-currency basis swap were collected on Bloomberg. As mentioned previously, cross-currency basis swap spreads are the benchmark for measures of CIP deviations. The tenors are 3 months, 6 months and 9 months for the short horizons. For the long horizons, we have 1 year, 5-years, 10-years, and 20-years tenors. The data are of monthly frequencies and cover the period from June 2009 to June 2019. Due to data availability constraints, we have not been able to collect data prior to the financial crisis; however the literature provides strong evidence that cross-currency basis swaps were close to zero before the global financial crisis (Clinton,1988;Committeri et al.,1993;Crowder,1995).
Figure2.2shows that all the tenors follow a common trend. In general, values for the USD/CAD cross-currency are negative and the gap is growing over the years. Recall that for a negative basis, the investor should borrow USD and invest it in CAD. This reflects an interest for investors to hold the Canadian currency. Notice that in the last quarter of 2011, cross-currency basis swap spiked to a positive value for all the tenors before decreased throughout the sample. The lowest value is observed in January 2018 for the 3M tenor, at around -45 basis point.
Figure 2.2: Short run USD/CAD cross-currency basis swaps
For longer horizons, Figure2.3 shows that 5Y and 10Y tenors for the USD/CAD cross-currency basis swaps remained positive and relatively modest quantitatively until 2016 but plunged into negative territory afterwards. Generally, higher fluctuations are observed for the 1Y duration. Bases are generally trending down in the sample, which may signal a renewed confidence in the Canadian currency as we move away from the global financial crisis, so that investors borrow USD that they convert in CAD for investment in the Canadian markets.
Figure 2.3: Long run USD/CAD cross-currency basis swaps
2.3.2 Other major pairs of currencies
The situation in other cross-curreny pairs from G10 countries can be used to assess whether the USD/CAD case is an exception or in conformity to deviations observed among G10 countries in the post GFC-crisis. In this section, we show the evidence for five different pairs: USD/EUR (Euro Zone), USD/AUD (Australian dollar), USD/GBP (British pound), USD/JPY (Japanese Yen), and USD/NZB (New Zealand dollar). For the short horizons, we selected 3 months and 6 months tenors, while we use the 5-years tenor for the long horizon.
Over 3-months horizons, Figure 2.4 shows that the measure of the cross-currency basis swap is generally negative among the pairs. For the Eurozone, the sample starts with very negative cross-currency bases with the lowest level reached in November 2011 at -131.25 basis points.4
This level of deviations can be explained by the debt crisis that affected the Eurozone during this period. The European sovereign debt crisis took place in 2009 in many European countries: Portugal, Greece, Cyprus, Ireland, Spain. Figure 2.4 also shows that the return to economic growth in the Eurozone coincides with a gradual rise back towards zero, although, the measurements remain negative over the period. The Japanese Yen and British Pound reported similar situations, with negative cross-currency bases edging towards zero between 2013 and 2015. The scenario for the Australian dollar is the opposite of other G10 countries. Over the period analyzed, the cross-currency basis swap is generally positive and the highest value is reached in February 2012, at 27.5 basis points. The overall picture is similar for the 6-months horizon. The large deviations observed from 2010 on are reduced with the economic recovery of 2014. The lowest point of the cross-currency is observed in the Eurozone in November 2011. From April 2011 to May 2014, the average value of the deviations is -31.98 point in the
4
A very negative basis usually means that investors should borrow in USD and have a strong interest to invest in Euros. The general uncertainty about the Eurozone prevented this to happen.
Figure 2.4: Short run cross-currency basis swaps: 3-months (other G10 countries)
Eurozone, while for British Pound the average is -9.18 point.
Comparing Figures 2.2, 2.4, and2.5 reveals an interesting fact. While the cross-currency basis swaps are getting smaller for other G10 currency pairs over time, the deviations appear to widen for the USD/CAD pair. This situation may be related to the difference in monetary and fiscal policy between countries. For longer horizons (5-years), Figure2.6below shows that most
Figure 2.5: Short run cross-currency basis swap: 6-months (other G10 countries)
currencies have values above or close to zero in general. Values for New Zealand and Australian dollars remain positive. Highest variations are observed for Japanese and Eurozone currencies. For these currencies, the standard deviations are respectively 16.94 and 12.57 . Table 2.1below presents two descriptive statistics that complement figure2.6. The first number is the monthly average and the number in brackets is the standard deviation for each year between 2009 and
2019. For years 2009 and 2019, the results are based on 6 months data. Aggregation on an annual basis allows a smoothing of deviations.
Figure 2.6: Long run cross-currency basis swaps: 5-years (other G10 countries)
Like depicted in Figure 2.6, Table2.1shows that bases for the Euro, the British Pound, and the the Japanese Yen are negative througout the sample while the Australian dollar and the New-Zealand dollar have positive bases.
The economic literature attemptes to explain the deviations by various ways. In the following section, we build a monetary model of exchange rate that we link to the cross-currency basis. Our assumption is that the monetary policy of central banks during the GFC led to persistent deviations from CIP. The impact of monetary policy on the deviations is analyzed by Ibhagui
(2018) and also Cerutti et al. (2019). The model used is based on the work of Eaton and Turnovsky(1984).
2.4
Monetary Model of Exchange Rate
2.4.1 Purchasing Power Parity (PPP)The starting point of most CIP studies is the assumption of Purchasing Power Parity (PPP). PPP is a macroeconomic theory of price and exchange rate determination. It compares the currencies of two countries through a basket of goods. According to this theory 5, the
exchange rate is determined by the relative price levels between two countries. This theory was popularized by the Swedish economist Gustav Cassel at the beginning of the 20th century
5Recent other research has suggested that the principle of PPP is sometimes violated (seePelagatti and
Colombo,2015;Elliott and Pesavento,2006;Lee and Yoon,2013;Afat et al.,2015). Pelagatti and Colombo
(2015) provided this evidence through simulations but also empirical tests. The reasons for PPP’s failure are diverse and vary according to the study conducted by the authors. Common reasons are speculation on some goods, restrictions of capital movements, central banks interventions, etc.
Table 2.1: Mean and standard deviations of cross-currency basis swap - 5-years horizon
EURO AUD GBP JPY NZB
2009 -21.51(4.91) (13.23)27.93 -25.35(7.63) -34.88(3.69) (13.26)21.43 2010 -26.70(7.09) (4.83)26.17 -12.10(7.6) -40.00(9.31) (6.41)37.34 2011 (15.58)-30.83 (4.31)18.23 (7.23)-1.16 (15.89)-59.65 (4.96)33.32 2012 -40.14(9.6) (3.17)30.23 (4.51)-7.68 -71.97(8.64) (3.37)42.33 2013 -21.13(5.68) (0.87)26.61 (4.35)-8.42 -59.91(5.36) (3.06)30.82 2014 (4.62)-9.24 25.94(3.1) (1.89)-1.69 -48.59(6.79) (2.47)23.17 2015 -33.01(3.78) (2.79)23.44 (2.67)-5.61 -73.45(7.93) 22.23(1.6) 2016 -45.03(2.84) (1.44)20.86 -12.04(3.23) -85.89(6.58) (3.05)26.86 2017 -35.42(2.77) (1.51)21.85 (1.84)-9.35 -67.17(9.21) (2.72)27.02 2018 -21.00(6.05) (4.11)27.84 (6.76)3.94 -48.48(3.51) (3.28)33.13 2019 -16.06(2.53) (3.05)28.58 (1.66)5.52 -44.38(2.37) (2.07)28.54
(seeCassel,1916;Cassel,1918).
There are two versions of PPP, absolute and relative. The absolute version refers to nominal values of variables while the relative version is about percentage changes. In this thesis, we assume that PPP holds and focus our work on absolute PPP, which states that:
S = P ∗
P , (2.6)
where recall that P would be the price level in the United States and P∗ its counterpart in the foreign country, i.e Canada. Taking logs of (2.6) gives
st= p∗t − pt. (2.7)
2.4.2 Monetary Models
Another component of CIP modelling is the monetary model of exchange rates. Monetary models are based on the assumption of perfect mobility of goods and assets, a plausible
assumption for the USA and Canada markets, which experience relative freedom of movements for goods, services, and capital across borders.
First we use conventional money demand equations to state the relationship between real money balances, prices, gross output and interest rates as:
mt− pt= αit+ βyt, (2.8)
m∗t− p∗t = αi∗t + βyt∗, (2.9) where mt, pt, it and yt are respectively the money supply, price level, interest rate and real income at time t, while asterisks designate foreign counterparts.
The natural assumptions about the parameters of money demand are β > 0 and α < 0, as represented notably by Frenkel(1976) and Bilson (1978). As such, the expansionary monetary policy is used as a tool by central banks to raise asset prices, and stimulate the economy (see
Bordo and Lando-Lane,2013; Rawdanowicz et al., 2013; Fisera and Kotlebova,2020). An increase in the demand for the domestic currency lowers the interest rate (Frankel, 1982). However, it may occur that actual empirical work suggests that α > 0, as in Frankel(1979). In that case, an increase of the interest rate makes the domestic currency more attractive and increases its demand.
Differencing (2.8) and (2.9) gives:
(m∗t − mt) − (p∗t − pt) = α(i∗t − it) + β(yt∗− yt) (2.10) Next, assuming that PPP holds, as in equation (2.7), and substituting (p∗
t− pt)out of equation (2.10), one gets:
st= (m∗t − mt) − α(it∗− it) − β(y∗t − yt) (2.11) Now, if CIP holds, then (ft− st) = (i∗t − it), and equation (2.11) becomes
st= (m∗t − mt) − α(ft− st) − β(yt∗− yt) (2.12) The equation above is the Flexible Price Monetary Model (FLPM).6. The coefficient of relative
money supply is one because of money neutrality. According to the FLPM, the coefficient β is assumed to be positive. The rationale behind this is that growth of real income will increase money demand, and that real income’s growth thus causes exchange rate devaluation.
Now consider a case where CIP does not hold, combining the monetary model (2.11) with CIP deviations (2.4) gives: xt= 1 α − 1 st− 1 α m∗t− mt +β α yt∗− yt + ft. (2.13)
6The Real Interest Differential Model (RIDM) is another version of monetary model developed byFrankel
(1979) It emphasizes the role of expectations and rapid adjustment in capital markets. RIDM is reduced to FLPM in the long run. Moreover, RIDM takes into account the Keynesian assumption of sticky prices.
Discussion on the coefficients Taking the first derivative of the previous equation gives: ∂xt ∂st =1 α− 1 ∂xt ∂(m∗t − mt) = − 1 α ∂xt ∂(yt∗− yt) = β α ∂xt ∂ft = 1
We see that the interpretation of these derivatives depends on the sign of the coefficients. We first assume that α < 0 and β > 0, as in Frenkel(1976) and Bilson(1978), then:
∂xt ∂st = 1 α − 1 <> 0 ∂xt ∂(m∗t − mt) = − 1 α > 0 ∂xt ∂(y∗t − yt) = β α < 0 ∂xt ∂ft = 1 > 0
Thus, an increase of money supply is more likely to tighten the deviations of cross-currency basis. Yet, an increase of real income tends to widen the deviations. For the exchange rate, the impact on the cross-currency depends on whether α < 1 or α > 1. We could also have both α and β positive as inFrankel (1979). Then a similar analysis would yield the opposite of the previous scenario. The rationale behind the signs of coefficients α and β is discussed by
Frankel (1979), Frenkel(1976) andBilson (1978).
Our empirical framework is a simplified version of equation (2.13). This model allows us to apply long-run tests on the cointegration of our variables. Our empirical application below uses the following equation:
xt= λ0+ λ1(m∗t − mt) + λ2(yt∗− yt) + λ3st+ λ4ft+ t (2.14)
Discussion on the expected signs of the coefficients
1. α < 0 and β > 0 (Frenkel,1976and Bilson,1978) Here, λ1> 0 ; λ2< 0 ; λ3< 0 ; and λ4> 0 2. α > 0 and β > 0 (Frankel,1979)
Thus, depending on the sign of α, we expect the relative money supply to widen or tighten the deviations. For the relative output and the spot exchange rate, the interpretation is the same. In both cases, the sign of the forward points variable is positive. These theoretical predictions will be assessed in the empirical application of Chapter 4.
Chapter 3
Data
This section describes the other data used in our analysis, in addition to the cross-currency basis swap already discussed. First, forward points were collected on Bloomberg. According to the description of Bloomberg, forward foreign exchange transactions involve the purchase of a specified amount of one currency and selling of another on an agreed date in the future. Forward exchange rates are determined by using the arbitrage free price relationship between the interest rates of the two currencies and the current spot rate. These data are measured in points, i.e the difference between the forward and spot rates in basis points. As such, they correspond to (f −s) in our analysis. We cover the period from June 2009 to June 2019 for short and long run maturities. In addition, we collected the actual spot exchange rates i.e the price of 1 USD in CAD. For a better visualization, we developed charts of the forward basis points and the spot exchange rate separately. Other financial tools involved in the cross-currency basis swap calculations are forward premia and interest rates of foreign and domestic countries.
Figure 3.1 shows that short horizons, forward points spike in 2010 then reach a plateau that remains until 2015. During the period 2011 to 2015, forward points fall temporarily in 2011, but that is quickly followed by a return to the plateau value. From 2016 onwards, forward points fall drastically and take negative values until the end of the period. The decline is more pronounced for 9M forward points. For their part, 10Y and 5Y forward points follow very similar patterns; before 2015, forward points are generally positive with a high fluctuation level. After 2015, the opposite trend is observed. One-year forward points are steady over the period and values are close to zero. Yet, a sharp decline is observed in the post 2015 period. Since forward points are expressed as the difference in the forward rates relative to the spot rate, negative values in Figure
3.1mean that f < s, so that the domestic currency (US dollar) is expected to depreciate in the future. On the other hand, for f > s, the domestic currency is expected to appreciate in the fu-ture. In the rest of our empirical analysis, the symbol f will designate the forward point (f −s).
Figure 3.1: Forward points USD/CAD
Figure 3.2: Spot exchange rate USD/CAD
Let us turn now to the spot rate. Figure3.2shows that the USD faced a sustained depreciation until 2011Q4. Possibly as a long lasting consequence of the GFC, in September 2011 the average USD/CAD spot exchange rate was as low as 0.9552. Following the economic recovery, the US currency appreciated strongly and its value has remained above 1.2 CAD since January 2015..
On Bloomberg, the data on cross-currency basis swaps underlying Figures 2.2 and 2.3 are based on interest rates with similar risk. For Canada, they use the Canadian Dollar Offered Rate (CDOR), the benchmark for Canadian bankers’ acceptances, which is determined from a daily survey provided by seven majors banks. For the US currency, the preferred interest rate is US LIBOR. The London InterBank Offered Rate (LIBOR) is the benchmark interest rate
for global banks. Data is provided by InterContinental Exchange (ICE). On a daily basis, ICE asks each bank the rate it would charge to another bank for a loan. The CDOR and LIBOR graphs are presented in AnnexB.1
Turning now to the macrofinancial determinants of CIP deviations, we collected both Canada’s money supply and real GDP from Canadian Socio-Economic Information Management System (Statistics Canada). For monthly US GDP, data are from the Federal Reserve and the Energy Information Association (EIA). The money supply category selected is M2, a measure of money supply which includes currency outside banks, chartered bank demand and notice deposits, chartered bank personal term deposits. For real output, we used data expressed in 2012 chained dollars, seasonally adjusted, and sata are expressed in billions of dollars.
In Figure 3.3 below, for both Canadian and American currencies, we expressed the levels of money supply as a ratio from its 2009 values and then created the difference (m∗− m). The reference period is the first observation in the data: June 2009. A positive value means that the Canadian money supply growth rate is higher than its American counterpart.1 From 2009
to 2011, the curve increases rapidly, reaching a peak in the mid-2010 and decreases afterward. Until 2016, the difference is close to zero with a unsteady variation. For the remainder period, the curve remains above zero so that the Canadian money supply grows quicker than its US conterpart. A positive value of the relative money supply means that the growth rate of Canadian money supply is higher than that of the USA.
Figure 3.3: Relative money supply between the United and States and Canada
Figure3.4 shows relative output between Canada and the United States. We computed the relative output as we did previously for relative money supply. Here again, a positive value means a higher growth rate of the Canadian GDP, the Canadian economy performs better
than US conterpart. We first observe an upward trend from 2009 to 2014, then the curve plunges until 2016. The Canadian GDP’s contraction over this period is due to the 2014 oil shock. In general, we see that the Canadian GDP’s growth rate is higher than that of the United States. Furthermore, periods of contraction in Canadian GDP are short and followed by a rapid recovery.
Chapter 4
Empirical Strategy and Results
4.1
Econometric methodology
Our model is designed to explain the intensity of CIP deviations, as measured by data on currency basis swaps. The goal is to quantify the causal relationship between cross-currency basis swaps and our macroeconomic variables. The usual methodology is to regress the independent variables on the dependant ones using OLS. However, this approach can be misleading and lead to so-called ”Spurious regression” problems. Spurious regressions occur when we use non-stationary time series variables in a linear regression and we find significant relationships between variables where none might exist. In the OLS regression, we assume that our time series are stationary, which imply that the mean, variance, correlations of these time series are independent of time. To overcome this potential problem, the first step in our empirical strategy is to conduct unit root tests, which will determine if our series are stationary or not.
4.1.1 Unit-root tests
The first test we conducted is the Augmented Dickey Fuller (ADF) test. Its null hypothesis is that the variable is non-stationary. The ADF test includes p lags of the variable to rid the residuals of serial correlation. For a large value of p, the power of the test is weakened but if p is too small, serial correlation in the errors is likely to bias the test. In R, the p-order lag chosen is 4. The second test we conducted is the Phillips-Perron (PP) test, where the null hypothesis is that a time series is integrated of order 1. It is a non-parametric so there is no assumption on the functional form of the error process. It is a good alternative to the ADF test, but since the test relies on asymptotic theory, it may not perform well in finite samples. The last unit root test performed is the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. The null hypothesis of this test is different from the two preceding ones and evaluates the hypothesis of stationarity against the alternative of non-stationarity. In practice, each test has advantages and disadvantages and it is common to conduct different tests and check if the
Table 4.1: Unit Root Tests
Variables ADF Test KPSS Test Phillips-Perron Test
At Level At Difference At Level At Difference At Level At Difference
m∗-m -0.827 -5.308 0.637 0.19 -3.558 -78.941 (0.956) (0.01) (0.01) (0.1) (0.91) (0.01) y∗-y -2.41 -5.19 0.506 0.308 -6.684 -95.949 (0.40) (0.01) (0.04) (0.1) (0.72) (0.01) s -2.267(0.46) (0.01)-5.40 (0.01)2.091 (0.1)0.27 -12.13(0.41) -129.2(0.01) f (0.44)-2.33 (0.01)-4.71 (0.01)1.75 0.177(0.1) (0.314)-13.84 -89.855(0.01) 5y xccy (0.09)-3.18 (0.01)-5.73 (0.01)2.31 (0.1)0.03 -24.804(0.02) -109.28(0.01) 10y xccy (0.08)-3.24 (0.01)-5.59 (0.01)1.86 (0.1)0.05 -23.92(0.02) -113.9(0.01) 20y xccy (0.289)-2.69 (0.01)-6.01 0.208(0.1) 0.093(0.1) -19.41(0.07) -103.09(0.01)
results are coherent. This would be a proof of the robustness of our conclusions.
The results of our tests are in Table 4.1 above. The values in brackets correspond to the p-value, which we compare to the threshold of 5%. We conducted the three tests both on the level and the first difference of each series. The results of the different tests on the levels show the evidence that our time-series are non-stationary and our variables are I(1). This conclusion is reinforced by the fact that the tests carried out on first difference data reject the null hypothesis of non-stationarity. Even though some tests produce contradictory results, we are confident with our conclusion of I(1) variables since the majority of tests go in this direction.
4.1.2 The Johansen cointegration test
Since our variables are I(1), we cannot apply common econometric methods. Before estimating the coefficients of the regression, we need to ensure that all five variables [x, s, (m∗− m), (y∗− y), f ] move in the same direction in the long-run. To do so, we test for a cointegration relationship among these variables. We conducted the Johansen cointegration test and the
results are reported in Table 4.2 below. The null hypothesis is that our variables are not cointegrated. In Table 4.2, both the Eigen and Trace statistics support the evidence that our variables are cointegrated.1 Comparing both Eigen and Trace test statistics to the fifth
percentile suggests the presence of up to 2 or 3 cointegration relationships. The absence of any cointegrating relationship (last row of the table) is rejected very clearly. Tests performed on 10 and 20 years cross-currency basis swap confirm this result (see Annex B.1).
Table 4.2: Johansen Cointegration test - 5 years cross-currency basis swaps Eigen Test 10pct 5pct 1pct Trace Test 10pct 5pct 1pct r ≤ 4 10.88 10.49 12.25 16.26 10.88 10.49 12.25 16.26 r ≤ 3 15.74 16.85 18.96 23.65 26.62 22.76 25.32 30.45 r ≤ 2 37.60 23.11 25.54 30.34 64.22 39.06 42.44 48.45 r ≤ 1 52.14 29.12 31.46 36.65 116.36 59.14 62.99 70.05 r = 0 58.89 34.75 37.52 42.36 175.25 83.20 87.31 96.58 4.1.3 Estimation
The last step of our approach is to estimate the coefficients of our parameters. We use different regression methods since we know that for non-stationary and cointegrated variables, the OLS regression is no longer appropriate. The first regression uses Fully-Modified OLS (FM-OLS) developed byPhillips and Hansen(1990). This semi-parametric method modifies the usual OLS regression to take into account the endogeneity arising from the cointegrating relationship in the regressors. The second approach is Dynamic OLS (DOLS), proposed byStock and Watson
(1993), which is a parametric approach for estimating long-run equilibria within integrated regressors. To get rid of potential bias among regressors, DOLS includes leads and lags of first differences of the regressors. More recently, Vogelsang and Wagner (2011) proposed Integrated modified OLS (IM-OLS) estimation of the parameters. The authors document that IM-OLS has a better performance than FM-OLS in terms of bias reduction and Root Mean Square Error (RMSE). Another advantage of IM-OLS is that compared to FM-OLS and DOLS, it does not require estimation of long run variance matrices and there is no need to choose tuning parameters (kernels, bandwidths, lags).
4.2
Regressions results
In this section, we provide the results of our regressions. For comparing purposes, we also provide the results of the OLS regression. The results are detailed in Table 4.3 below. The values in brackets correspond to the standard deviation. Recall that the data on money
supply and real GDP are normalized, with June 2009 as a reference, before computing the difference between the Canadian and the American data. This process is a good approxi-mation of the logarithm function. Since we have a lot of negative values, we cannot apply directly the logarithm function on the data. Spot exchange rates are in logs, the forward point variable is in levels and the dependent variable is measured in levels. In definitive, our model is measured in level-log and the result reported in the Table4.3are per basis point change.
The first observation is that the sign of the different coefficients is consistent with the discussion in Section2.4.2. In general, the coefficient of the relative money supply is positive and that of the relative output is negative. Thus, an increase of money supply tends to widen the deviations of CIP and an increase of real output tends to lessen the deviations. The coefficients of the spot exchange rate and the forward rate also suggest a similar movement between them and cross-currency basis swap. However, for all the variables, the standard deviation of the coefficients is larger than the value of the coefficients.
Table 4.3: Regression results
Parameters FM-OLS D-OLS IM-OLS OLS
m∗− m −0.318 0.491 0.397 −0.933∗∗∗ (0.675) (0.72) (0.83) (0.176) y∗− y −0.688 −1.531 −4.15∗ −3.31∗∗∗ (1.23) (1.98) (1.99) (0.359) s 0.27 0.238 1.09 −1.90∗∗∗ (0.52) (0.738) (0.797) (0.189) f 0.043∗ −0.04. 0.076∗∗ −0.009. (0.017) (0.02) (0.025) (0.005) Intercept 0.223∗∗∗ (0.0165) Signif. codes: 0‘∗∗∗00.001‘∗∗00.01‘∗00.05‘.00.1‘01
4.2.1 Discussion on the results
Let us recall the equation (2.14), the main empirical specification for our tests: xt= λ0+ λ1(m∗t − mt) + λ2(yt∗− yt) + λ3st+ λ4ft+ t
OLS and FM-OLS regressions). The highest value is the coefficient of D-OLS: 0.491 with a standard deviation of 0.72. The interpretation is that an increase in the relative money supply between two currencies by one point of percentage is likely to widen the basis by 0.491. Positive values for the coefficient of m∗− m are consistent with theFrenkel (1976) and Bilson (1978) assumptions about the monetary model. They might also agree with economic intuition. Indeed, during the financial crisis, most central banks accelerated the growth rate of money supply to support the economy. This could be a reason for the persistent deviations observed. For the FM-OLS regression, the negative value of the money supply coefficient tends to favor theFrankel(1979) view, as per our discussion of section2.4.2. However, we cannot rely on these results since the estimates are not statistically significant because of high standard deviations. The coefficients of the real output are negative for all the regressions. This means that the difference in real output between two countries tends to lessen the deviations. The real output is a measure of the health of an economy, so this result was expected. This tends to favor the
Frenkel (1976) andBilson (1978) view of the model. An increase of 1% of y∗− y, lessens the deviations by 4.15 points of percentage (IM-OLS regression). The US dollar is a safe haven so investors are more likely to invest in the US market. However, the increase of our GDP variable is the signal that the Canadian economy is performing well. Thus, the investments are redirected to the foreign market. In the long term, a country in poor economic health cannot maintain the attractiveness of its financial system. It is the situation where the synthetic foreign interest rate is higher than the domestic direct one. D-OLS and FM-OLS regression’s coefficients are not significant while IM-OLS regression’s coefficient is significant at 5%. In general, the coefficients of the spot exchange rate are positive. This is more supportive of theFrankel (1979) view. Yet, here again, the coefficients are not significant and the standard deviations are high. The coefficients of the forward points are significant and positive for FM-OLS and IM-FM-OLS regressions. In the long term, the expectation of the US dollar appreciation is likely to widen the deviations.
Even though the OLS regression is not suitable for long-term analysis, we have included the results of this regression in Table 4.3 above. We observe that the value of the coefficients is significantly different from that of the other regressions. The results of this regression exaggerate the real impact of these parameters on the deviations and bias the analysis of the long-term effect.
4.2.2 Robustness Checks
Results provided in Table 4.2refer to cointegration tests between the dependent variable and all the regressors taken together. An alternative is to take each regressor and determine the level of cointegration with the dependent variable. The results of these tests are provided in Table 4.4.
Table 4.4: Johansen Cointegration test - by variable
Eigen Test 10pct 5pct 1pct Trace Test 10pct 5pct 1pct
m∗− m r ≤ 3 15.74 16.85 18.96 23.65 26.62 22.76 25.32 30.45 r ≤ 2 37.60 23.11 25.54 30.34 64.22 39.06 42.44 48.45 r ≤ 1 52.14 29.12 31.46 36.65 116.36 59.14 62.99 70.05 r = 0 58.89 34.75 37.52 42.36 175.25 83.2 87.31 96.58 y∗− y r ≤ 1 7.41 10.49 12.25 16.26 7.41 10.49 12.25 16.26 r = 0 10.34 16.85 18.96 23.65 17.75 22.76 25.32 30.45 s r ≤ 1 3.65 10.49 12.25 16.26 3.65 10.49 12.25 16.26 r = 0 5.79 16.85 18.96 23.65 9.45 22.76 25.32 30.45 f r ≤ 1 3.20 10.49 12.25 16.26 3.20 10.49 12.25 16.26 r = 0 10.16 16.85 18.96 23.65 13.35 22.76 25.32 30.45 VIX r ≤ 1 7.12 10.49 12.25 16.26 7.12 10.49 12.25 16.26 r = 0 14.68 16.85 18.96 23.65 21.80 22.76 25.32 30.45
relationship between 5 years cross-currency basis and our variables except money supply. This result is not counterintuitive. Indeed, it is the proof that the calculation of the cross-currency basis includes the spot and forward rates variables. Thus, considered singularly, the cointegration’s analysis of these variables is not significant. On the other hand, for the money supply variable, the cointegration level is at least 2 for the different test statistics (Eigen and Trace). This result confirms the precedent and justifies the use of D-OLS, FM-OLS, IM-OLS regressions for parameter’s estimation.
In the previous section, we performed the cointegrating tests on 5 years cross-currency basis swap. To check the robustness of our results, we use longer terms: 10 and 20 years cross-currency basis swap. The goal is to check whether shocks to macroeconomic variables during the financial crisis have an impact on very long-run cross-currency basis swap. We also add a new regressor, which is the Volatility index (VIX). VIX estimates the 30 day implied volatility of S&P 500 index options. There is a negative correlation between VIX and S&P 500 index options: the expectation of uncertainty in the market increases the volatility (VIX).
The first observation from Table4.5 is that while most coefficients are significant at 5 and 10 years horizons, on a longer horizon (20 years cross-currency basis) most of the coefficients are not significant. The coefficient of the money supply differential is negative for 10-years and 20-years horizon in this alternative specification. For the real output, the sign of the coefficients remains negative, and the effect on the cross-currency at 20-years horizon is lower than that of 10-years horizon. Even though, the money supply and the real GDP have the same effect on the cross-currency basis, we find that that of real GDP is stronger.
For spot exchange rate, the coefficient at 5-years horizon is higher than that of 10-years horizon. The effect of the exchange rate on cross-curency is less significant over a longer horizon. Furthermore, the standard deviation is low for all the regressions.
In general, the VIX coefficients are positive and significant. Another interesting result in this alternative specification is that the variations implied by the standard deviation is low. Thus, we are more confident with the results reported in this table below.
Table 4.5: Regression results - alternative specification
5 years xccy 10 years xccy 20 years xccy FM-OLS m∗− m −0.967 ∗∗∗ −1.06∗∗ −1.23∗ (0.258) (0.40) (0.53) y∗− y −2.97 ∗∗∗ −2.54∗∗ −1.42 (0.52) (0.80) (1.06) s −1.95(0.25)∗∗∗ −0.87(0.16)∗∗∗ −0.04(0.21) f −0.017(0.007)∗ VIX 0.182(0.019)∗∗∗ 0.16(0.02)∗∗∗ (0.03)0.06∗ D-OLS m∗− m −0.50 . −0.24 −0.098 (0.28) (0.53) (0.72) y∗− y −2.74 ∗∗∗ −3.93∗∗∗ −2.39. (0.55) (0.93) (1.26) s −2.73(0.37)∗∗∗ −0.75(0.17)∗∗∗ (0.23)0.33 f −0.04(0.01)∗∗∗ VIX 0.21(0.021)∗∗∗ 0.16(0.025)∗∗∗ (0.034)0.037
5 years xccy 10 years xccy 20 years xccy IM-OLS m∗− m −1.19 ∗∗∗ −0.93. −0.99 (0.33) (0.51) (0.68) y∗− y −3.108 ∗∗∗ −3.55∗∗ −2.24 (0.641) (1.05) (1.39) s −2.54(0.0.34)∗∗∗ −0.74(0.18)∗∗∗ (0.25)0.36 f −0.03(0.01)∗∗ VIX 0.22(0.02)∗∗∗ 0.17(0.02)∗∗∗ (0.037)0.06 Signif. codes: 0‘∗∗∗0 0.001‘∗∗00.01‘∗00.05‘.00.1‘01
Conclusion
The puzzling and persistent violations to the CIP theory motivated this thesis. The failure of this theory is a major concern since this means that there are opportunities for arbitrage in the forward market between two currencies. This thesis, we attempts to address the causes of the long run deviations by attributing them to macrofinancial variables, through the lens of the monetary model of exchange rates.
This approach is a simple framework to estimate the impact of money supply and real GDP deviations across countries to CIP deviations. Our results document that for long horizons (5-years tenors), the money supply differential between two economies is more likely to lessen the deviations. The same effect is observed in the case of the real GDP differential. These results are identical over a longer horizon (10-years and 20-years horizons). In addition, the extension of our model with a volatility index confirmed the previous results and was significant. This thesis uses only a limited number of macrofinancial variables, and did not address the impact of different monetary policy choices. This reduces the scope of the analyzes we can draw from our results. Also, this paper does not explicitly address the mechanisms of return to the equilibrium. An interesting pattern for further research should be to address the shortcomings of this thesis.
Appendix A
Data sources
Table A.1: Data source
Variable Notation Source Notes
Cross-currency basis swap xccy Bloomberg 3M, 6M, 9M 1Y, 5Y, 10Y, 20Y
Forward points, Spot exchange rate f − s, s Bloomberg
Canadian Dollar Offered Rate CDOR Bloomberg
London Inter-bank Offered Rate LIBOR Bloomberg
Volatility Index VIX Bloomberg US VIX
Canada Money supply m∗ CANSIM Money M2
US money supply m FRED Money M2
Canada Real Output y∗ Statistics Canada Real GDP
Appendix B
Tables & Graphs
Table B.1: Johansen Cointegration tests - 5, 10, and 20 years horizons 5 years cross-currency basis
Trace test 10pct 5pct 1pct Eigen test 10pct 5pct 1pct r ≤ 4 10.88 10.49 12.25 16.26 10.88 10.49 12.25 16.26 r ≤ 3 26.62 22.76 25.32 30.45 15.81 15.74 18.96 23.65 r ≤ 2 64.22 39.06 42.44 48.45 37.60 23.11 25.54 30.34 r ≤ 1 116.36 59.14 62.99 70.05 52.14 29.12 31.46 36.65 r = 0 15.25 83.2 87.31 96.58 58.89 34.75 37.52 42.36 10 years cross-currency
Trace test 10pct 5pct 1pct Eigen test 10pct 5pct 1pct r ≤ 4 11.01 10.49 12.25 16.26 11.01 10.49 12.25 16.26 r ≤ 3 29.62 22.76 25.32 30.45 18.62 16.85 18.96 23.65 r ≤ 2 67.81 39.06 42.44 48.45 38.19 23.11 25.54 30.34 r ≤ 1 124.86 59.14 62.99 70.05 57.05 29.12 31.46 36.65 r = 0 184.70 83.2 87.31 96.58 59.84 34.75 37.52 42.36 20 years cross-currency
Trace test 10pct 5pct 1pct Eigen test 10pct 5pct 1pct r ≤ 4 10.83 10.49 12.25 16.26 10.83 10.49 12.25 16.26 r ≤ 3 23.67 22.76 25.32 30.45 12.84 16.85 18.96 23.65 r ≤ 2 65.21 39.06 42.44 48.45 41.54 23.11 25.54 30.34 r ≤ 1 112.71 59.14 62.99 70.05 47.50 29.12 31.46 36.65 r = 0 173.42 83.2 87.31 96.58 60.71 34.75 37.52 42.36
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