BIS Working Papers
No 590
The failure of covered
interest parity: FX
hedging demand and
costly balance sheets
by Vladyslav Sushko, Claudio Borio, Robert McCauley,
and Patrick McGuire
Monetary and Economic Department
October 2016
JEL classification: F31, G15, G2
Keywords: Covered interest parity, FX swaps, currency
basis, limits to arbitrage, US dollar funding, currency
hedging.
BIS Working Papers are written by members of the Monetary and Economic
Department of the Bank for International Settlements, and from time to time by other
economists, and are published by the Bank. The papers are on subjects of topical
interest and are technical in character. The views expressed in them are those of their
authors and not necessarily the views of the BIS.
This publication is available on the BIS website (www.bis.org).
©
Bank for International Settlements 2016. All rights reserved. Brief excerpts may be
reproduced or translated provided the source is stated.
ISSN 1020-0959 (print)
ISSN 1682-7678 (online)
The failure of covered interest parity: FX hedging demand and
costly balance sheets∗
Vladyslav Sushko§ Claudio Borio† Robert McCauley† Patrick McGuire‡
First version: 30 June, 2016
This version: 30 October, 2016
∗
We would like to thank Wenxin Du, Enisse Kharroubi, Catherine Koch, Aytek Malkhozov, Michael
Moore, Andreas Schrimpf, Hyun Song Shin, Nikola Tarashev, and the participants of the BIS research
seminar for their comments and suggestions. We have also benefited from conversations with representatives
of major dealer banks as well as supranational and agency debt issuers. An earlier version from June 2016
was titled “Whatever happened to covered interest parity? Hedging demand meets limits to arbitrage.” The
views expressed in this paper are those of the authors and do not necessarily reflect those of the Bank for
International Settlements (BIS).
§
Economist, Monetary and Economic Department, BIS; [email protected].
†
Head of Monetary and Economic Department, BIS; [email protected].
†
Senior Adviser, Monetary and Economic Department, BIS; [email protected].
‡
Head of International Data Hub, BIS; [email protected].
The failure of covered interest parity: FX hedging demand and
costly balance sheets
Abstract
The failure of covered interest parity (CIP), or, equivalently, the persistence of the
cross currency basis, in tranquil markets has presented a puzzle, as there has been
mounting evidence that post-crisis CIP deviations cannot be explained by bank credit
and liquidity factors. Focusing on the basis against the US dollar (USD), we show
that the CIP deviations are closely associated with the demand to hedge USD forward.
Fluctuations in FX hedging demand matter because committing the balance sheet to
arbitrage is costly. With limits to arbitrage, CIP arbitrageurs charge a premium in the
forward markets for taking the other side of FX hedgers’ demand in proportion to their
balance sheet exposure. We find that measures of FX hedging demand, combined with
proxies for the risks associated with CIP arbitrage, improve the explanatory power of
standard regressions.
JEL Classification: F31, G15, G2
Keywords: Covered interest parity, FX swaps, currency basis, limits to arbitrage, US dollar
funding, currency hedging.
I.
Introduction
One of the most notable financial market anomalies in the post-great financial crisis (GFC)
period has been the persistent violation of the no-arbitrage condition known as covered interest rate parity (CIP), or, equivalently, the persistence of a cross-currency basis. In the past,
CIP deviations were arbitraged almost instantly (Akram, Rime, and Sarno, 2008),1 with the
exceptions of temporary episodes when arbitrage was inhibited by bank counterparty risks,
during the Japan banking crisis (the “Japan premium”, Hanajiri (1999)) and, in addition,
by wholesale US dollar funding strains, particularly during the GFC (Baba, McCauley, and
Ramaswamy (2009), Coffey, Hrung, and Sarkar (2009), McGuire and von Peter (2012), Baba
and Packer (2009), Cetorelli and Goldberg (2011) and Cetorelli and Goldberg (2012)) and
during the euro area sovereign debt crisis (see Bottazzi, Luque, Pascoa, and Sundaresan
(2012) and Ivashina, Scharfstein, and Stein (2015)). The basis then narrowed again when
central banks provided US dollar funding and banks’ credit risk improved. Ivashina, Scharfstein, and Stein (2015) present a model where CIP deviations can arise when banks shift some
of their funding away from wholesale funding markets due to default risk premia. However,
the CIP deviations in the post-2012 period have not coincided with a rise in bank credit risk
or wholesale USD funding strains.2
We derive the cross-currency basis in a simple setup with limits to arbitrage (eg Shleifer
and Vishny (1997), Gromb and Vayanos (2010)) to show that fluctuations in net currency
hedging demand can cause CIP violations even in calm markets. This is because the balance
sheet commitment to take the other side of net FX hedging imbalances so as to trade against
CIP violations is costly. While balance sheet capacity has a number of dimensions, we focus
on a specific setup that emphasizes the costs stemming from risks involved in taking exposures
1
Before 2008, the USD basis was slightly negative (positive) against currencies with lower (higher) yields,
such as JPY (AUD), indicating greater demand to hedge US dollar assets out of lower yielding currencies
than the demand to hedge lower yielding assets by US investors and vice versa. However, controlling for
transaction costs, the CIP deviations where not wide enough to generate persistent profits (see Frenkel and
Levich (1981) for even earlier periods). In fact, Akram, Rime, and Sarno (2008) document that in the
pre-crisis period profitable CIP deviations on average lasted from 30 seconds to less than four minutes.
2
The re-emergence of CIP deviations and US dollar funding premiums in currency swap markets for
major currencies since mid-2014 have been highlighted in, among others, BIS (2015a,b); BOJ (2015, 2016);
J.P.Morgan (2015); Barclays (2015a,b).
1
to FX derivatives. This is because, regardless of the many ways in which CIP arbitrage can
be funded, or foreign currency invested for the duration of the trade,3 all arbitrageurs would
have to take positions in FX swaps or similar instruments.
Balance sheet costs have become a binding constraint post-GFC. Prior to the crisis, for
instance, the standard practice in the industry was to mark derivatives portfolios to market
without taking the counterparty’s credit quality into account (Zhu and Pykhtin (2007)). This
gave rise to bank trading models such as the “flow monster”, because balance sheets could be
expanded virtually unconstrained in response to new flows hitting the swap trading desks.
Following the crisis period of 2008-2011, the flow model has been replaced by a more cost
sensitive approach of balance sheet management.4 In FX derivatives, this means that market
risk and counterparty risk are being priced-in at all times, even when measured risks are
low.5 Indeed, industry reports indicate that banks have been applying greater credit charges
to swap pricing.6
Our theoretical setup seeks to capture these changes. The balance sheet costs of CIP
arbitrage arise endogenously due to a combination of counterparty and market risk. This is
because if the counterparty defaults on the forward leg an FX swap, then a CIP arbitrageur
will face market risk from exposure to foreign currency collateral. As long as markets clear,
the aggregate CIP arbitrageurs’ balance sheet exposure to FX swaps will exactly offset the
net demand for FX swaps by those seeking to hedge currency risk. As a result, the currency
basis responds to demand shocks to hedge currency risk forward and CIP can fail even in
calm markets.
3
For example, CIP arbitrage can be conducted by asset managers using T-bills, by banks using banks
deposits and interbank funding markets (Aliber (1973) and Frenkel and Levich (1975)), by hedge funds using
repo markets (Mancini Griffoli and Ranaldo (2012)), by banks using excess reserves (Bräuning and Ivashina
(2016) and Du, Tepper, and Verdelhan (2016)), and by supranational and agency bond issuers using foreign
currency bond funding (Du, Tepper, and Verdelhan (2016)).
4
See, for example, Kaminska, I. (2014, May 30). The Europe-based flow monster is under siege. FT
Alphaville. Retrieved from http://ftalphaville.ft.com/2014/05/30/1866432/the-europe-based-flow-monsteris-under-siege.
5
Consistent with higher post-crisis counterparty risk concerns among traditional FX market participants,
Levich (2012) finds that trading in interbank currency forwards has declined in favour of currency futures.
Because futures are traded on an exchange and counterparties post margins, they involve significantly lower
counterparty risks than forward contracts, which are over-the-counter.
6
See, for example, “Small fish big prize: the market markers out to eat the banks’ lunch”, Euromoney
magazine, December 2015.
2
Empirically, we show that CIP deviations closely track the fluctuations in the net FX hedging demand. Following Borio, McCauley, McGuire, and Sushko (2016), the typical sources
for USD forward hedging demand include banks’ funding business models, institutional investors’ strategic hedging decisions and firms’ opportunistic securities issuance. These drivers
are largely insensitive to the size of the basis (at least in the medium term), thereby representing an exogenous demand for forward USD hedges. This demand pushes down the dollar
price of foreign currency in spot markets and pushes up the dollar price of foreign currency
in the forward markets. On the other side of the market, the balance sheet costs of meeting
net FX hedging demand to arbitrage the resulting currency basis are priced into the forward
exchange rates by CIP arbitrageurs, and therefore prevent CIP from being fully restored.
While it is difficult to quantify how financial institutions’ own risk management or regulatory requirements translate into the cost of CIP arbitrage, it is fairly straightforward to use
market data to proxy for the key fundamental risks involved. For counterparty risk, we rely
on Libor-OIS spreads.7 For the perceived market risk of foreign currency collateral, we rely
on FX option-implied volatility. As can be seen particularly clearly in Figure 1, right-hand
panel, the currency basis against the USD widened significantly starting in mid-2014. Figure
2, left-hand panel, shows that Libor-OIS spreads have remained well below their crisis levels during this period. However, Figure 2, right-hand panel, shows that FX option-implied
volatility rose sharply at the time the currency basis began to widen in 2014. This points
to the link between the riskiness of foreign currency collateral and CIP deviations. In our
derivations of the currency basis from first principles with risk-averse arbitrageurs, the association comes from CIP arbitrageurs’ pricing their balance sheet exposure to FX collateral
by taking the other side of the FX hedging demand.
[Figures 1 and 2, about here]
Our study includes both time-series and panel analysis.
7
In addition to credit risk, Libor-OIS spreads can also contain a liquidity risk premium. Liquidity risk
has been found to play an especially significant role during crises and for short maturities; by contrast, for
longer maturities and at lower frequency, credit risk has been found to play a more important role. See
McAndrews, Sarkar, and Wang (2008), Michaud and Upper (2008) and Gefang, Koop, and Potter (2011).
3
In the time-series, we focus on the JPY/USD currency pair, which exhibits by far the
largest CIP deviations post-GFC. We find that two factors can explain the variation in the
JPY/USD basis of different maturities after controlling for bank credit risk and transaction
costs.
The first factor, which accounts for most of the common variation in the JPY/USD basis,
is closely associated with our measure of aggregate net demand to hedge the US dollar forward
out of the yen.
The second factor is closely associated with funding conditions in the yen and US dollar
repo markets, capturing the additional CIP arbitrage costs that stem from the reliance on
collateralised funding, for example by hedge funds. This is also consistent with what Bottazzi,
Luque, Pascoa, and Sundaresan (2012) refer to as the “scalability constraint” which operates
when USD collateral is scarce or more expensive, and with funding liquidity’s continued
central role in the pricing of financial instruments, a mechanism described in Brunnermeier
and Pedersen (2009).
The time-series regression results show that the demand for forward USD hedges is a
significant driver of the JPY/USD basis. If the demand for forward USD hedges is omitted
from the regressions, then the short-term (eg 3-month) basis will appear to be driven almost
exclusively by Libor-OIS spreads and measures of funding (repo spreads) and market liquidity
(FX bid-ask spreads). This is because the short-term FX swap basis is more volatile than the
long-term cross-currency basis, and widens particularly in crisis times. However, this masks
the importance of the size of the associated balance sheet exposure (FX hedging demand).
When the currency hedging demand and its interaction with credit and market risk measures
are added to the explanatory variables, the linear association of Libor-OIS spreads with the
currency basis becomes insignificant.
For the long-term basis (eg 2-year), the effects of demand shocks dominate even in the
simple linear specification. This is because longer-term cross currency swaps are primarily
used to hedge currency risks of long-term funding and investment flows and not for liquidity
management. The effect of FX hedging demand on the 2-year JPY/USD basis is further
amplified by its interaction with balance sheet costs. We also find that accounting for FX
4
hedging demand restores the cointegrating relationship between the actual JPY/USD forward
rate and that implied by CIP.
In the panel analysis, we include major liquid currencies not subject to capital controls
or other major structural distortions: AUD, CAD, CHF, DKK, EUR, GBP, JPY, NOK,
and SEK.8 Here, owing to data limitations, we need to restrict our measure of FX hedging
demand to that coming from banks and corporate bond issuers. The panel regression results
also show that this demand is a significant determinant of the sign and size of the basis.
Our paper is one among several concurrent studies motivated by the re-emergence of CIP
violations since mid-2014. Du, Tepper, and Verdelhan (2016) formally establish the CIP
arbitrage opportunities that cannot be explained away by credit risk or transaction costs.
They infer the impact of balance sheet costs from quarter-end anomalies and IOER-Fed funds
arbitrage, and provide empirical findings that the basis is correlated to interest rates and
monetary policy shocks. Borio, McCauley, McGuire, and Sushko (2016) offer a framework to
think about CIP violations in non-crisis times, stressing the combination of hedging demand
and tighter limits to arbitrage. They find a close empirical relationship between measured FX
hedging demand and cross-currency basis, and quantify arbitrage flows by banks and bond
issuers taking advantage of the basis in select currencies. Liao (2016) attribute CIP deviations
primarily to the activities of foreign currency bond issuers. Pinnington and Shamloo (2016)
focus on the behaviour of the basis in light of the reduction in FX market liquidity due to
the shock stemming from the Swiss National Bank’s decision to abandon the currency peg in
January 2015. Wong, Ng, and Leung (2016) explore the relationship between CIP deviations
in tranquil times and the counterparty and liquidity risk premia in money market rates.
Iida, Kimura, and Sudo (2016) find that return spreads have replaced measures of banks’
creditworthiness as drivers of CIP deviations in JPY/USD and JPY/EUR pairs. These
authors use sign restrictions to identify supply and demand shocks in the Tokyo FX swap
market. Their theoretical setup is based on an extension of Ivashina, Scharfstein, and Stein
(2015), who model global banks’ USD funding and lending, combined with capital-constrained
8
Hence, our analysis abstracts from currencies for which capital controls, political risk premia or pegged
exchange rate regimes cause further deviations from CIP; see eg Frenkel and Levich (1977), Dooley and Isard
(1980) and Hutchison, Pasricha, and Singh (2012).
5
CIP arbitrageurs.9 Avdjiev, Du, Koch, and Shin (forthcoming) explore a link between the
US dollar exchange rate and cross-currency basis, against a backdrop that the former relates
to the shadow price of bank leverage.
10
In light of this emerging literature, one of our contributions is to base the empirical
analysis on the highest quality empirical proxies for the demand-driven pressure on hedging
costs in FX swap markets following Borio, McCauley, McGuire, and Sushko (2016). Instead of
modelling banking sector’s FX swap demand, we estimate it following McGuire and von Peter
(2012). We then augment the estimates of net demand for FX swaps stemming from banks by
bringing-in FX hedging demand of institutional investors and corporate bond issuers. Thus,
our measurement is grounded in consolidated bank balance sheet positioning and a flow of
funds approach, rather than interest rates or national savings and investment imbalances.
In addition, in the derivation of the currency basis, and in the regression analysis, we take
account of the interaction of counterparty and market risks inherent in FX swaps and similar
instruments. These have an end-effect of limiting CIP arbitrage in ways that are similar to
imposing risk-based capital constraints. Using a simple setup with limits to arbitrage, we
show that the market impact of these risks is scaled by the size of the associated positions.
The resulting risk premia will cause market-clearing forward exchange rates to remain out of
line with CIP when FX hedging demand is large and imbalanced, even though measured risks
may be low. We view our approach as useful in better understanding CIP deviations at longer
maturities, which are associated with the use cross-currency markets for the purpose of foreign
currency funding and long-term foreign currency investment management. This is important,
because, as shown in Figure 1, non-crisis deviations from CIP have been particularly stark
for longer maturities.
We also address CIP deviations for shorter tenors, but, at these maturities, factors associated with short-term liquidity management that are largely beyond the scope of this paper
9
A similar theoretical framework is also used in He, Wong, Tsang, and Ho (2015) to study the implications
of monetary policy divergence on international dollar credit; however, these authors take the cross-currency
basis as exogenous to international banks’ US dollar funding.
10
See also Arai, Makabe, Okawara, and Nagano (2016) for conjunctural evidence of increased demand for
US dollars in FX swaps against the background of diverging monetary policies, reduced appetite for marketmaking and arbitrage by global banks, and the developments in the flow of arbitrage capital in FX swap
markets.
6
take greater precedence. Even then, the association of the FX swap-implied basis with measures such as Libor-OIS spreads arises primarily due to the interaction with the aggregate
demand for currency hedges, which banks have to meet as CIP arbitrageurs.
Finally, our paper contributes to the debate on the nature of possible capital constraints
limiting CIP arbitrage by banks. While, in some specifications, we do find evidence consistent
with a contribution of leverage constraints at quarter-ends, broad evidence is more consistent
with banks’ management of capital constraints due to risk-based exposures considerations.
The rest of the paper is organised as follows. Section II reviews the CIP condition, how
it relates to forward points and to instruments such as FX swaps and cross-currency swaps.
It also describes the institutional setting of cross-currency funding markets and motivates
our quantitative proxies for the institutional demand for USD forward hedges. Section III
shows the derivation of the currency basis in a stylised limits-to-arbitrage setting. Demand
shocks for USD forward hedges affect risk-averse pricing of FX swaps, thereby moving forward
exchange rates out of line with CIP. Section IV applies the framework to JPY/USD basis,
using both factor analysis and time-series regressions. Section V presents the panel regression
results using nine major currency pairs. Section VI concludes.
II.
CIP and currency risk hedging using FX swaps
A. Forward points and CIP
CIP is a textbook no-arbitrage condition according to which the interest rate on two otherwise
identical assets in two different currencies should be equal once the currency hedging cost
is taken into account. Given two benchmark interest rates, for example Libor rates, the
relationship between the FX spot and forward rates should be as follows:
FtB
=
StA
1 + rt
1 + rt∗
(1)
where FtB is the forward bid rate for foreign currency, in units of US dollars; StA is the
corresponding spot ask exchange rate; rt is the US dollar on-shore rate; and rt∗ is the foreign
7
on-shore rate. CIP fails when (1) does not hold.
Since the underlying interest rates, rt and rt∗ , are determined in the much deeper respective
money and fixed income markets, the degree to which CIP holds mainly depends on where
Ft is relative to St ; that is, by supply and demand conditions in the markets for currency
forwards, FX swaps,11 and cross currency swaps.12,13
B. Exogenous demand for currency swaps vs CIP arbitrage
An interesting aspect of the failure of CIP concerns the lengthening of the maturity of the
contracts. This is consistent with the fact that the currency swap markets have been increasingly used to hedge long-term funding and investment flows. Accordingly, the maturity of
outstanding FX derivatives has risen considerably in recent years, as can be gleaned from
the rising share of notional principal outstanding of currency swaps compared to currency
forwards and FX swaps (Figure 3, left-hand panel). One key factor at work has been central bank purchases of long-dated government bonds, which have triggered rebalancing by
11
An FX swap is a contract in which one party borrows one currency from, and simultaneously lends
another to, the second party; at the spot rate (StA ), in the units of US dollar per foreign currency. At
B
maturity, m, the amount borrowed is repaid at the pre-agreed FX forward rate (Ft,m
). The basis can be
B
A
inferred by comparing the forward points, (Ft,m − St ), with the chosen interest rate benchmark, typically
Libor rates in the two currencies. A textbook covered arbitrage borrowing in USD to invest in EUR is
B
∗
∗
B
− StA )/(StA )
+ (Ft,m
), where the difference between rt,m and rt,m
− StA )/(StA ) > (rt,m − rt,m
profitable if (Ft,m
constitutes the basis. FX swaps can be viewed as collateralised borrowing and lending. FX swaps are shortterm. Baba, Packer, and Nagano (2008) provide a more detailed exposition of the cash flows in FX swaps
and cross-currency swaps.
12
Cross-currency swaps are FX derivatives in which two parties borrow from, and simultaneously lend to,
each other an equivalent amount of money denominated in two different currencies for a predefined period
of time. A cross-currency basis swap is a floating/floating swap where the reference rates are Libor rates
in the two currencies. At maturity date t + m, the amount borrowed is exchanged back at the same spot
exchange rate St . Thus, unlike an FX swap, which is priced off of the forward exchange rate, a cross-currency
basis swap is priced off the respective Libor rates, whereby one counterparty stands to pay US dollar Libor
plus (or minus) the basis, bt,m , for borrowing US dollar in exchange for its currency for a period m. Crosscurrency basis swaps tend to be longer-term. By a no-interest arbitrage condition, an FX swap desk’s offer
price for forward points will satisfy the following relationship with the currency basis for the case of m = 1:
∗
) − St .
Ft,1 − St = St × (1 + rt,1 + bt,1 )/(1 + rt,1
13
Taking logs of both sides of Equation (1), a textbook covered arbitrage borrowing in USD to invest in
∗
B
A
EUR is profitable if ftB − sA
t > rt − rt . FX swap desks quote prices in terms of forward points, ft − st ,
while currency swaps are priced by quoting the basis on top of the reference interest rates.By a no-interest
arbitrage condition between FX swaps and currency swaps, the basis is equal to the difference between rt
and rt∗ + (ftB − sA
t ).
8
investors and corporate borrowers.14 Du, Tepper, and Verdelhan (2016) show a positive correlation between ECB policy announcements and longer-term EUR/USD basis in the 2010
to 2015 period. Similarly, Borio, McCauley, McGuire, and Sushko (2016) show that central
bank announcements have been associated with the widening of the longer-term basis since
2014 in EUR/USD and JPY/USD markets. This stands in sharp contrast to the crisis periods of 2008 and 2011-12, when the short-term basis, rather than long-term basis, widened
markedly as a US dollar liquidity squeeze pushed non-US banks into FX swap markets for
US dollar funding (see also Figure 1, left-hand panel, above).
Demand for currency hedges. Cross-currency investments and funding tend to flow
out of the currencies where yields and spreads are low and into the currencies where yields
and spreads are relatively high. Borio, McCauley, McGuire, and Sushko (2016) describe the
institutional aspects of the three main sources of FX hedging demand: demand by banks,
institutional investors and non-financial corporates. We apply the same framework to proxy
the fraction of the cross-currency positions that are hedged for currency risk. Banks and institutional asset managers that use the cross-currency market to swap out of home currencies
to fund long-term US dollar assets exert negative pressure on the dollar basis. Corporates
can also go through cross-currency markets to swap out of cheap foreign currency funding.
For these types of swap market users, the currency basis represents a cost of putting on a
currency hedge. We will refer to these exogenous flows as demand for USD forward hedges.
BIS reporting banks’ net USD liabilities (the amount by which the total on-balance sheet
USD assets exceeds the total on-balance sheet USD liabilities, or “funding gap”) can be used
to proxy for banks’ USD funding needs in FX swap markets (McGuire and von Peter (2012)).
In aggregate, post-GFC, non-US banks’ USD funding gap increased from about $400 billion
to close to $1 trillion by 2014 (Figure 3, right-hand panel).15
14
See Borio and Zabai (2016) for a review of evidence on the transmission of unconventional monetary
policies to bond yields, as well as output and inflation.
15
Part of the greater bank reliance on FX and currency swaps is also driven by less ample wholesale
USD funding following the withdrawal of US money market funds (MMFs). First, US MMFs have become
increasingly sensitive to foreign banks’ credit quality following the European sovereign risk crisis of 201112. Second, assets under management have migrated from prime funds to government MMFs on the back
of regulatory reform that went into effect in October 2016. The shift in investment allocations has largely
affected foreign banks, and some have lost a significant portion of their wholesale USD funding.
9
[Figure 3, about here]
The close association between BIS reporting banks’ USD dollar “funding gap” and the
currency basis is shown in Figure 4, left-hand panel. For example, in the yen (red dots) and
the euro (dark blue dots), banks’ funding of dollar assets reinforces the pressures on the basis,
as these banks are on the same side of the swap market as institutional investors that hedge
their dollar securities. In contrast, Australian banks raise foreign currency abroad to fund
domestic currency mortgages, thus supplying US dollars via swaps to Australian institutional
investors that need to borrow dollars to hedge their dollar bonds.16
[Figure 4, about here]
Corporate bond issuance in foreign currencies affects the currency basis through the associated hedging. US corporates that issue in foreign currency because of a credit-risk adjusted
funding cost advantage generally swap the proceeds back into US dollars, creating demand
for forward USD hedges. Hence, the currency basis is more negative for currencies where
the corporate option-adjusted spread (OAS) differential with the USD, OAS U S − OAS LC ,
is higher, Figure 4, right-hand panel).17 Swapping the associated EUR proceeds into USD
would have exerted a negative (widening) pressure on the basis.18
[Figure 5, about here]
CIP arbitrage. Bank FX swap desks that clear the demand for USD forward hedges push
the currency basis in the opposite direction (less negative against the US dollar). Banks and
16
Bertaut, Tabova, and Wong (2013) document that Australian, as well as Canadian, banks have been
able to sustain robust issuance of high-grade USD bonds.
17
OAS is the spread of a risky fixed-income security relative to a riskless security of a similar maturity,
typically taken as a government bond. When spreads relative to government bonds are lower in a local
currency relative to the USD, US corporates have an incentive to borrow in that currency and then swap the
funding into US dollars. Equally, when such risk spreads in local currencies are compressed, local investors
have an incentive to seek yield by investing in foreign, including US, securities, thus swapping their home
currency for US dollars as they put on a currency hedge. More generally, the OAS provides a broad measure
of the level of risk spreads in a currency, thus indicating the direction in which the marginal funding and
investment flows should go, all else equal.
18
The outliers, blue dots in Figure 4, right-hand panel, lower-left quadrant, are observations during the
euro area sovereign debt crisis when the currency basis widened and spreads in the euro area exceeded those
in the US.
10
hedge funds may also enter cross-currency markets as archetypical CIP arbitrageurs when
the basis is wide enough. In addition, highly rated supranational and sovereign agencies
can effectively engage in CIP arbitrage by raising long-term US dollar funding to swap for
currencies that pay the basis in cross-currency swaps (Du, Tepper, and Verdelhan, 2016).
Central banks can also be reasonably active in FX swaps, mostly as lenders of their US
dollar reserves. For these users, the currency basis represents a profit opportunity. Hence,
such flows are more sensitive to price conditions in cross-currency markets, and can be thought
of as responding to the exogenous demand for USD forward hedges.19 We will refer to such
flows as CIP arbitrage.
Clearing currency hedging demand via FX swaps. Figure 5 illustrates the cash
flows in an FX swap between currency hedgers and CIP arbitrageurs. Banks, institutional
investors, and corporates demand a total of DXC of USD via FX swaps to hedge their USD
exposure forward. Since they do not have USD on hand in period t = 0, they swap DXC /S
of local currency for xf,t of USD supplied to the swap market by CIP arbitrageurs, such as
banks, hedge funds, official reserve managers, and supranational and agency bond issuers.
Markets clear, therefore xf,t = DXC . At the expiration date, t = 1, currency hedgers repay
the borrowed USD amount with interest given by the forward points: F/S × xf,t , where
F > S, and receive back DXC /S of the local currency collateral they had used in the swap.
On the other side of the swap market, CIP arbitrageurs effectively charge more in the forward
leg for the foreign currency that they sell back to currency hedgers, earning the forward points
(F − S)/S per dollar lent via the swap.
III.
Derivation of currency basis with limits to arbitrage
Textbooks describe CIP arbitrage as a self-financing strategy with exchange rate risk fully
hedged. In such a setting, demand shocks have no impact on prices because demand shocks
are offset by arbitrage, with the latter being profitable up to the point at which CIP is
restored. In this section we show that even small counterparty and market risks of FX
19
Borio, McCauley, McGuire, and Sushko (2016) and Arai, Makabe, Okawara, and Nagano (2016) quantify
arbitrage flows by banks and other types of investors since the basis widened in the EUR and JPY in mid-2014.
11
swaps give rise to balance sheet costs that make it unprofitable to arbitrage CIP deviation
unless these are large enough. The no-arbitrage bounds increase with the size of the balance
sheet exposed to the trade. Since markets have to clear, the balance sheet exposure of CIP
arbitrageurs is exactly equal to net FX hedging demand.
Balance sheet capacity has a number of dimensions, but we only focus on the specific
implications of the costs of FX swaps when CIP arbitrageurs are risk-averse. Hence, we
abstract from other potentially important frictions.20 We derive the currency basis by solving
a constrained optimisation problem that takes account of the interaction of counterparty and
market risks inherent in FX swaps and similar instruments. These have an end-effect of
limiting CIP arbitrage in ways that are similar to imposing risk-based capital constraints.
A. CIP arbitrageur’s objective
Suppose CIP arbitrageurs are risk-averse, have an exponential utility function, −Et [exp (−ρWt+1 )],
and choose the amount of dollars to supply via FX swaps, xt,f so as to maximise the utility
from next-period wealth, Wt+1 . Although the interest rates in the two currencies, rt and rt∗
and the currency forward rate, ft are known at time t,21 there is uncertainty stemming from
the counterparty risk in the swap. The risk of counterparty default to payback the dollars at
date t + 1 at rate ft introduces a (small) probability, θt , that the CIP arbitrageur will end
up stuck holding the foreign currency collateral at the expiration of the contract that would
have to be converted into dollars at prevailing exchange rate st+1 . The CIP arbitrageur’s
expected end-period wealth can be expressed as follows:
B
∗
A
Et [Wt+1 ] = Wt + (Wt − xt,f )rt + [1 − θt ]xt,f (ftB + rt∗ − sA
t ) + θt xt,f (Et [st+1 ] + rt − st ) (2)
if ft − st > rt − rt∗ ; and,
20
As discussed in Borio, McCauley, McGuire, and Sushko (2016), first, counterparty risks and exposure
limits in the funding and investment legs of arbitrage transactions, can further inhibit arbitrage; second,
institutions may be concerned about the overall balance sheet leverage.
21
We work with log approximation to CIP arbitrage payoff: F/S − (1 + r)/(1 + r∗ ) ≈ f − s + r∗ − r, where
f ≡ log(F ) and s ≡ log(S).
12
B
A
∗
∗
0
+ [1 − θt ]xt,f (ftA + rt − sB
] = Wt∗ + (Wt∗ − xt,f )rt,1
Et [Wt+1
t ) + θt xt,f (Et [st+1 ] + rt − st ) (2 )
if ft − st < rt − rt∗ . ftB and ftA denote the forward bid and ask rates, and Wt is the
arbitrageur’s starting wealth in period t.22
Let us focus now on the case for ft − st > rt − rt∗ with the budget constraint Equation
(2) (we return to the opposite case, Equation (20 ), at the end of the section).
The case θt = 0 corresponds to riskless arbitrage, in which the CIP arbitrageur’s balance
sheet commitment would be driven only by the relative return of (ft − st + rt∗ ) − rt compared
to investing all of Wt into dollar assets yielding rt . The case θt > 0 introduces an additional
risk-return trade-off of marking to market the associated position in FX swaps taking the
counterparty credit quality into account.
B. Relationship to risk management and regulatory constraints
In fact, the difference between the risk-free derivatives portfolio value and the true portfolio
value taking the possibility of counterparty default into account is what is known as credit
value adjustment (CVA); see, for example Assefa, Bielecki, Crépey, Jeanblanc, Brigo, and
Patras (2009) and Pykhtin (2009). For our CIP arbitrageur, adjusting for market risk of the
FX swap exposure in the presence of counterparty credit risk amounts to accounting for:
∗
Et [Wt+1 |θt > 0] − Et [Wt+1 |θt = 0] = [1 − θt ]xt,f (ftB − sA
t + rt − rt )
A
∗
+ θt xt,f (Et [sB
t+1 ] − st + rt − rt )
∗
− xt,f (ftB − sA
t + rt − rt )
B
= θt xt,f (Et [sB
t+1 ] − ft )
22
(3)
In this setting, the problem faced by a CIP arbitrageur is analogous to that faced by an FX swap dealer
trading with its own funds, in that both provide the other side of the trade to the hedgers of currency risk.
13
A unilateral CVA is given by the product of the probability of counterparty default and
the exposure (contract value) at the time of default. If θt equals the true probability, then
the adjustment in Equation (3) will result in outcomes that are actuarially fair. In our
case, the fluctuations in the contract value arise from changes in the dollar value of foreign
currency collateral. According to Zhu and Pykhtin (2007), for years the standard practice
in the industry was to mark derivatives portfolio to market without taking the counterparty
credit quality into account. However, following the crisis period of 2008-2011, market risk
and counterparty risk have been reflected more accurately in the valuation of derivatives
exposures.
C. Shadow balance sheet cost
Substituting Equation (2) into the utility function and assuming investors treat the next
period exchange rate as log-normally distributed, Et [st+1 ] ∼ N (ft , σs2 ), the objective function
reduces to the following certainty-equivalent:
ρ 2 2
∗
Wt (1 + rt ) + xt,f (ftB − sA
t + rt − rt ) − θt xt,f σs
2
(4)
The last term on the right-hand side of Equation (4) is a very simple way of capturing
the impact of risk premia on the arbitrageurs’ budget constraint without the complexity of
default or value-at-risk (VaR) models. The coefficient of absolute risk aversion, ρ , can also
be interpreted as the Lagrange multiplier on a VaR constraint. This follows Zigrand, Shin,
and Danielsson (2010) and Shin (2010), who show that optimal risky asset portfolio choices of
mean-variance optimising risk-averse investors are equivalent to those for risk-neutral banks
that face a VaR constraint. In the latter case, the degree to which the leverage constraint
is binding is captured by a term that plays the same role as the risk aversion coefficient of
mean-variance investors.
In sum, ρ2 θt x2t,f σs2 can be interpreted as the shadow balance-sheet cost for FX swap exposure of size xt,f . In a setting with multiple counterparties, ρ can also vary depending on the
CIP arbitrageurs’ (in this case a bank) tolerance to exposure to a particular counterparty, or
14
a country, for that matter.23 Duffie (2010) provides a comprehensive framework in which the
risk aversion or limited capital of financial intermediaries leads them to charge a premium to
absorb supply and demand shocks.
Market clearing forward rate. Maximizing Equation (4) with respect to xt,f and
imposing market clearing xt,f = DtXC yields an equation for the price of currency forwards:
2 XC
∗
ftB = sA
t + rt − rt + θt ρσs Dt
(5)
The last term in Equation (5) indicates that demand shocks, DtXC , will drive forward
exchange rates away from spot exchange rates, and hence the basis, as long as credit and
market risks are being priced into the balance sheet costs of open FX derivatives exposures.
Without appealing to the microfoundations of investor decisions, market participants simply
refer to θt ρσs2 DtXC as “hurdle rates”. Hurdle rates are used to represent, in a generic way, the
many factors that could determine the “attractiveness” of the resulting trade combination in
addition to a positive return: the use of resources (credit lines, capital), its role in balance
sheet restrictions, the relative attractiveness of other business opportunities, etc. While both
θt and ρσs2 have been low since 2014, the currency basis has widened. This puts the onus on
the FX hedging demand.
24,25
23
In practice, FX swap desks of financial institutions would optimise taking into account the exposure limits
to particular institutional counterparties, instruments, or currencies set by their risk control department.
24
The hurdle associated with mark-to-market risk becomes more binding as the maturity of the exposures
increases. This is because of mark-to-market changes in banks’ foreign currency collateral as FX spot rates
fluctuate, raising the risk of ending up severely out of the money at the expiration of the contract. This
would bias the intermediation away from longer term FX swaps and cross-currency basis swaps, allowing the
longer-term basis to persist.
25
That CIP arbitrageurs will be including a premium proportional to the size of their balance sheet
commitment into the pricing for the forward leg of the swap, ftB , is a rather general feature that need not
depend on the specific assumptions about counterparty risks. An alternative approach would have been to
impose a leverage constraint. Then, additional add-on factors for derivatives exposures under the leverage
constraint could play a similar role to the management of counterparty credit risk described in the text.
Specifically, banks would allocate additional capital in proportion to their total FX derivatives exposure
xf,t by the multiplier γ. This is known as the potential future exposure (PFE) adjustment factor. Using
regulatory requirements as an example, under both Basel and US standards, γ = 0.05 for FX and gold
derivatives with maturity 1-5 years. Following Maccario and Zazzara (2002), suppose banks’ cost of equity
funding is ke = Et [EP St+1 ]/Pt , where Pt is bank’s share price and EP St+1 is next period earnings per share.
2
∗
2
XC
Assuming Et [epst+1 ] ∼ N (µeps , σeps
), Equation (5) modifies to ftB = sA
; where L
t + rt − rt + Lγρσeps Dt
denotes the assumed leverage ratio and γ denotes the PFE adjustment factor.
15
D. Liquidity-constrained arbitrageurs and short-selling costs
A fraction of arbitrageurs may be liquidity-constrained. For example, hedge funds would
typically need to establish a position in repo markets: borrowing some of the needed US
dollar cash to lend via FX swaps by posting securities as collateral (Mancini Griffoli and
Ranaldo, 2012). In such a case, in aggregate arbitrageurs maximise the objective augmented
by short-selling costs:
ρ 2 2
REP O
∗
c
Wt + (Wt − xt,f (1 − c))rt + xt,f (f B − sA
t + rt ) − θt xt,f σs − xt,f rt
2
(6)
where c is the fraction of arbitrage funded via repo markets, and rtREP O denotes the
corresponding repo rate.26 Solving again for the optimal xt,f and imposing market clearing:
∗
2 XC
ftB = sA
+ c(rtREP O − rt )
t + rt − rt + θt ρσs Dt
(7)
where the last term in Equation (7) captures the additional cost stemming from the
reliance on repo funding.
It is straightforward to generalise the setup to a symmetric setting, whereby repo rates
in both currencies factor into the arbitrage cost. This is because CIP arbitrageurs funding
themselves in US dollar repo would lend the swapped foreign currency in foreign currency
repo markets for the duration of the swap. The equation for the forward rate becomes:
∗
2 XC
ftB = sA
+ c[(rtREP O − rt ) − (rt∗,REP O − rt∗ )]
t + rt − rt + θt ρσs Dt
(8)
Hence, the forward exchange rate will be driven by the weighted average of the two
types of relevant funding and investment rates in both currencies. In the regime where the
26
For simplicity, we have assumed that liquidity-constrained arbitrageurs do not face uncertainty in their
repo position, and therefore do not assign a risk premium to their position in repo markets. This assumption
is a reasonable first approximation given that both legs in a repo transaction are in the same currency
involving cash and a risk-free bond government bond. In other words, the volatility of r and r∗ is assumed
away in our setup. Put less abstractly, repo transactions may have implications for the liquidity position of
an investor, but not so much for an investor’s exposure to credit or market risk.
16
size of the demand shocks bind, the secured funding markets are more likely to become
the marginal source of arbitrage funding. The importance of the short-selling constraint,
i
h
XC
, is similar to the
c (rtREP O − rt ) − (rt∗,REP O − rt∗ ) in the presence of demand shocks, Di,t
setup of Gromb and Vayanos (2010), in which repo funding costs bind when the demand
shock is positive.
E. Cases with a positive covered interest differential and no-arbitrage bounds
Repeating the steps in Equations (4) through (8) for the case of a positive covered interest
rate differential which induces arbitrage if ft − st < rt − rt∗ subject to the budget constraint
Equation (20 ), yields the following solution for the forward ask rate:
∗
2 ∗,XC
ftA = sB
+ c[(rt∗,REP O − rt∗ ) − (rtREP O − rt )]
t − rt + rt + θt ρσs Dt
(80 )
where the demand shock is defined as Dt∗,XC ≡ −DtXC , indicating the investor hedging
demand when the foreign-currency asset yields a higher yield r∗ (swapping out of rt assets)
when rt∗ > rt .
Finally, solving for the observable basis, b̂t , and expressing the mid spot and forward rates
as a function of bid and ask rates yields an expression for the no-arbitrage bounds within
which the positive and negative basis can persist. The currency basis, b̂t , is a function of
risk premia and uncertainty (or, equivalently, cost of capital), demand shocks, repo market
spreads (cost of secured funding), and bid and ask spreads (transaction costs; here, we use:
A
B
(ft − st ) ≡ 1/2 × [((ftB − sA
t ) + (ft − st )]):
17
≡ rt − (rt∗ + ft − st )
b̂−
t
≥ −
h
i
θt ρσs2 DtXC
− c (rtREP O − rt ) − (rt∗,REP O − rt∗ )
| {z }
|
{z
}
Balance sheet costs of FX derivatives Secured funding costs/funding liquidity
B
A
[(ftB − sA
t ) − (ft − st )]/2
|
{z
}
Transaction costs/market liquidity
= b−
t
−
(9)
if (rt∗ + ft − st ) − rt < 0, and
b̂+
≡ rt − (rt∗ + ft − st )
t
h
i
∗,REP O
2 ∗,XC
∗
REP O
B
A
≤ θt ρσs Dt
+ c (rt
− rt ) − (rt
− rt ) + [(ftA − sB
t ) − (ft − st )]/2
= b+
t
(10)
if (rt∗ + ft − st ) − rt > 0. Equations (9) and (10) determine the no-arbitrage bounds:
+
b−
t ≤ b̂t ≤ bt
(11)
According to Equations (9) and (10), CIP deviations can also arise in non-crisis times, eg
when readings of θt and ρσs2 are negligible, as long as the market for FX forwards and swaps
is hit by sufficiently large demand shocks, DtXC , raising the total balance-sheet costs for CIP
arbitrageurs.
IV.
The yen-dollar basis
JPY/USD is the currency pair with the largest deviations from CIP in the post-crisis period.
Statistically, we show that two factors can explain the variation in the JPY/USD basis of
18
different maturities after controlling for bank credit risk and transaction costs: (i) forward
USD hedging demand from banks, life insurance companies and corporate issuers; and (ii)
relative funding conditions in the yen and US dollar repo markets. We then test the predictions based on Equation (9) using time-series regressions and cointegration tests. We find
that the demand for FX hedges is a significant driver of the currency basis as specified in
Equations (9) and (10).
A. Quantifying demand shocks
Table I lists the three sources of demand shocks for FX forwards and swaps along with the
price and quantity proxies that can be used in the empirical analysis.
[Table I, about here]
Data. We construct the quantity measure by adding together three variables: a measure
of Japanese banks’ USD funding gap, derived from the BIS international banking statistics;
(ii) Japanese life insurers’ FX bond holdings adjusted by time-varying hedge ratios; and (iii)
US non-financial corporates’ outstanding yen-denominated bonds.27
Following McGuire and von Peter (2012), Japanese banks’ USD funding gap is constructed
by taking the difference between the consolidated on-balance sheet USD assets and liabilities.
Assuming that the banks do not run open FX positions, when the corresponding assets exceed
the liabilities, the gap is a proxy for the funding of these assets using swaps to convert JPY
funding into USD, Bank XC . In practice, this measure also includes USD bonds in Japanese
banks’ trust accounts, therefore it will overstate the actual USD swap positions by the amount
of these holdings that are not FX hedged. Figure 14 (below) shows that Japanese banks’
USD funding gap (inverted scale) is considerably larger than that of other banking systems
and has tracked the evolution of the long-term, eg 2-year and 5-year, basis closely following
the GFC.
27
See Borio, McCauley, McGuire, and Sushko (2016) for a detailed discussion of the limitations of these
proxies.
19
We use the BIS international debt securities statistics to construct the stock of JPYdenominated bonds issued by US corporates (reverse yankee bonds). The currency hedges
put on top of reverse yankee bonds will contribute to the aggregate USD forward hedging
demand, CorpXC (see also Figure 14, below, red bars inverted scale). US corporate issuance
of reverse yankee bonds has been a minor factor for JPY/USD swaps because of low volumes.
Moving to institutional investors, the hedge ratios of Japan’s pension funds are low, and
therefore ought not to affect the basis materially. However, Japan’s life insurers hedge more
than half of their foreign asset portfolios; Barclays (2015a) reported a hedging ratio of 66%
as of September 2015.
[Figure 6, about here]
We benchmark Japanese life insurers’ low-frequency stock numbers of foreign currency
bond holdings by using the annual reports of the Life Insurance Association of Japan. We
then construct the corresponding monthly series using monthly flows from the Japan Ministry
of Finance flow of funds, which reports insurance sector purchases and sales of foreign longterm debt securities broken down by residence. Finally, we use the currency hedge ratios as
provided by Barclays Research.
Since 2014, monthly flows by Japan’s life insurers into international long-term debt (predominantly USD) have often exceeded JPY 500 billion (Figure 6, left-hand panel). These
institutions’ associated position in currency derivatives, InstXC , stood at USD 190-200 billion
(Figure 6, right-hand panel).
The proxy for the aggregate demand for USD forward hedges out of JPY, DXC , is then
constructed by adding Bank XC , InstXC , and CorpXC . Since the BIS banking statistics are
not available at monthly frequency, we use a simple linear interpolation to add the banking
data to the aggregate DXC series. Admittedly, this is a shortcoming for monthly analysis,
so we also conduct robustness checks using the price-based measure of DXC – the corporate
spread differentials (OAS U S − OAS JP ). OAS provides a broad measure of the level of risk
spreads in each currency, thus indicating the direction in which the marginal funding and
investment flows should go, all else equal.
20
B. Demand shocks, funding liquidity, and JPY/USD OIS basis
In logs, the deviation from CIP, or equivalently Libor-based basis, can be decomposed as
follows:
LIBOR
bLIBOR
= (rt∗,LIBOR + ftB − sA
t
t ) − rt
h
i
= (rt∗,OIS + ft − st ) − rtOIS
h
i
+ (rt∗,LIBOR − rt∗,OIS ) − (rtLIBOR − rtOIS )
A
B
+ (ftB − sA
t ) − (ft − st ) /2
(12)
where the first term is the OIS-based CIP deviation while the second is the relative
riskiness of the two Libor panels (eg difference in bank credit risk in the US and Japan).
Adopting a similar approach to Pinnington and Shamloo (2016), the last term captures the
contribution of bid-ask spreads – a proxy for transaction costs.
Figure 7, upper left-hand panel, shows the time-series of the JPY/USD OIS basis, bOIS
t,m ≡
∗,OIS
OIS
− (rt,m
+ ft,m − st ), for maturities, m, ranging from 1-month to 5-years. A regime
rt,m
switch post-crisis is apparent, marked with a vertical dashed line: the basis of different
maturities becomes wider, more persistent, and exhibits roughly parallel movements. In
addition, although the basis of different maturities tends to co-move in parallel, the shorterterm basis, eg 1-month, has widened at quarter-ends well in excess of the long-term basis
beginning mid-2014. Moreover, the effects have strengthened over time.
[Figure 7, about here]
Figure 7, upper right-hand panel, shows the time-series of the first and second principal
components (P Cs) based on PCA decomposition of the variation in the OIS basis of the
seven maturities for the post-2008 sample. The first P C explains 83.6% of the variation,
while the first and second P Cs together explain 94.5%. The first P C appears to load more
on the level of the longer-term basis, while the second appears to be stationary, loading more
21
on the quarter-end effects visible in the shorter-term basis.
Hedging demand is clearly important in explaining the yen-dollar basis. This is shown
in Figure 7, lower left-hand panel, which plots the first P C along with our estimate of
institutional US dollar funding via yen/dollar swaps. The inverse movement of the two series
suggests that bank, insurer, and corporate funding and hedging activities via yen/dollar
swaps are indeed related to the level of the JPY/USD OIS basis.
The second factor, explaining another 10.9% of the common variation, appears to load
more on the short-term OIS basis, particularly on the quarter-end turn that appeared in
late 2014. Figure 7, lower right-hand panel, shows this component along with the difference
between US and Japan repo spreads. The graph points to the presence of “short-selling
constraints”, whereby the rising (increasingly negative) repo spreads in the US dollar (the
yen) have made it increasingly costly to fund CIP arbitrage to close the negative USD/JPY
basis.
[Figure 8, about here]
The quarter-end widening of repo spreads is related to the timing of the reporting of
financial statements and regulatory ratios. These dynamics became particularly stark for
shorter-term, eg 1-week, tenors beginning in 2014 (Figure 8, left-hand panel), when banks
gradually started to adhere to the new supplementary leverage ratio rules.28 Indeed, Du,
Tepper, and Verdelhan (2016) interpret quarter-end widening of 1-week and 1-month basis
as evidence of tighter balance sheet constraints. Similarly, Arai, Makabe, Okawara, and
Nagano (2016) take the fact that FX swap spreads and GC repo spreads widen at quarterends while Tri-party repo spreads do not widen as evidence of bank balance sheet management
under the leverage ratio. This is because FX swap markets and GC repo markets rely on
arbitrage-trading and market-making by banks, whereas the Tri-party repo market gets US
dollar supply also from real money investors not subject to the leverage ratio. While these
effects contribute to CIP deviations, and tighter USD funding liquidity conditions are also
28
For example, the Basel standards required public disclosure of the leverage ratio by international banks
as of January 2015, although the leverage ratio will become a mandatory part of the Basel III Pillar 1
requirements only in January 2018, after a period of monitoring and final calibration.
22
visible for longer-term, eg 3-month, contracts (Figure 8, right-hand panel), they explain only
a fraction (10.9% in the case of JPY/USD basis) of deviations from CIP.29
In sum, the principle component analysis of the yen-dollar basis indicates that demand
shocks, DtXC , can account for the majority of the common variation of CIP deviations in
JPY/USD calculated using the respective OIS rates. The remaining fraction of the common
variation us closely associated with limits to arbitrage stemming from short-term liquidity
management and short-selling costs, (rtREP O − rt ) − (rt∗,REP O − rt∗ ).
C. Regression results
Table II reviews the notation for the variables in the regression. We proxy counterpaty risks,
θ, using the Libor-OIS spread. We proxy the risk-neutral expectation of the market risk of
FX collateral, ρσr2 , using currency options-implied volatility of the same maturity.
[Table II, about here]
As a robustness check, we also use the option-adjusted spread (OAS) differential of corporate issuers in the US and Japan (defined as OASU S -OASJP ) as the price-based proxy of the
fluctuations in the demand to swap out of yen funding into dollar investments (see Section
1). We proxy short-selling constraints with repo spreads in the two currencies, using the
USD and JPY general collateral (GC) repo rates, the fed funds rate and the JPY call rate,
h
i
specifically (rtREP O − rt ) − (rt∗,REP O − rt∗ ) .
Our monthly regression specification based on Equations (9) and (10) then becomes:
29
Furthermore, these quarter-end anomalies largely reflect not so much the leverage ratio itself, as the
uneven application of the leverage regulation, where some non-US banking systems are only required to
report their quarter-end numbers, which gives rise to the window-dressing behavior. Indeed, this anomaly
may disappear entirely by 2019, when the daily leverage computation of the leverage ratio will apply to
non-US banks as well.
23
2
2
× ∆DtXC ]
+ βD × ∆DtXC + βθ×σ×D × [∆θt × ∆ρσs,t
∆bt = βθ × ∆θt + βσ × ∆ρσs,t
h
i
+ βRepo × ∆ (rtREP O − rt ) − (rt∗,REP O − rt∗ )
B
A
+ βbid−ask × ∆[(ftB − sA
t ) − (ft − st )]/2 + α + t
(13)
where ∆ is the first-difference operator. The variables comprising the interaction terms,
θt ρσs2 DtXC , also enter the regression in levels to ensure that the coefficient βθ×σ×D is unbiased.
Since the regression specification of Equations (9) and (10) also includes a linear contribution
of Libor-OIS spreads, ∆θt , it also nests a specification based only on the prices of interbank
credit and liquidity risk premia (for example, Libor-OIS enters linearly in specifications of
Baba and Packer (2009) and Mancini Griffoli and Ranaldo (2012)). A departure from the
existing literature is the coefficient βθ×σ×D , which captures non-linearities stemming from the
interaction between risk premia and dealers’ aggregate balance sheet size.
The FX swap-implied short-term basis. Most of the empirical literature on CIP
deviations has focused on short maturities, given that it was the short-term basis that fluctuated most widely during crisis periods (see also Figure 1, above). We thus first examine
the drivers of the 3-month FX swap-implied basis.
[Table III, about here]
Table III shows the regression results. The variables have been standardised to z-scores
(zero mean, unit variance) to facilitate the comparison and interpretation of the size of the
coefficients (Appendix Table VIII shows the raw results). The baseline specification (1)
corresponds to a standard CIP regression, where the basis widens in response to heightened
risks in interbank funding markets, tighter funding liquidity, and worse market liquidity or
transaction costs. The coefficient on ∆θ indicates that a 1 standard deviation increase in
Libor-OIS spreads is associated with widening of 3-month JPY/USD basis by 0.9 standard
deviation, making it more negative. This confirms that CIP deviations tend to increase when
risks in the interbank funding markets worsen.
24
Consistent with factor analysis of the JPY/USD basis, we find that the JPY/USD basis
widens when US dollar repo market conditions tighten relative to yen repo market conditions.
The coefficient on ∆Repo spread diff. indicates that a 1 standard deviation widening of USD
GC repo spreads relative to JPY GC repo spreads is followed by a 0.26 standard deviation
wider USD/JPY basis. This points at the continued importance of liquidity constraints. It is
also noteworthy that the Federal Reserve has moved to a corridor-type system during the exit
from the zero-lower bound, with rates on its reverse repo (RRP) facility acting as a floor, and
those on the overnight excess reserves (IOER) as a ceiling, to the federal funds rate target.
Hence, in addition to collateralised CIP arbitrage, the close association of the currency basis
with repo spreads may also reflect the importance of underlying central bank rates, as global
banks can engage in CIP arbitrage based directly on central bank deposit and funding rates
(Du, Tepper, and Verdelhan, 2016).
The coefficient on the FX bid-ask, defined according to the direction of CIP arbitrage
A
B
A
B
B
A
([(ftB − sA
t ) − (ft − st )]/2 for negative basis, and [(ft − st ) − (ft − st )]/2 for positive
basis), indicates that a 1 standard deviation rise in the bid-ask spreads is associated with the
widening of the basis by 0.4 standard deviations.
Accounting for the interaction of the size of the demand shocks with measures of bank
balance sheet risks improved the overall regression fit. Columns (2) and (3) in Table III
add the balance sheet size component to the credit risk component of CIP arbitrageurs’
FX derivatives exposures. The introduction of the interaction term between ∆θ and ∆DXC
changes the results materially. The coefficient on the linear impact of ∆θ, as proxied by
changes in Libor-OIS spread, turns insignificant. Instead, the effect of ∆θ on the 3-month
basis appears to work via its interaction with demand shocks, ∆DXC . The coefficient β̂θ×D =
−1.14 indicates that a 1 standard deviation increase in the product of Libor-OIS spreads
and currency hedging demand is associated with a 1.14 standard deviations wider 3-month
currency basis. Compared to the baseline specification, the R-squared rises from 0.68 to 0.80.
Finally, the interaction with the market risk component of CIP arbitrageurs’ FX derivatives exposures is also significant. The coefficient on the interaction of CIP arbitrageurs’
balance sheet size, DXC , with credit risks, θ, and market risks, ρσs2 , is negative and signifi-
25
cant, indicating that a 1 standard deviation increase in this measure is associated with a 0.9
standard deviation widening of the currency basis (column 4).30
The long-term cross-currency swap basis Table IV shows regression results for CIP
deviations based on the prices of longer-term, eg 2-year, cross currency basis swaps.31
[Table IV, about here]
Compared with those for the 3-month basis, the coefficients on ∆θ are approximately
two times smaller in magnitude, indicating that the longer-term currency basis is less driven
by the immediate funding risks in interbank markets than the short-term FX swap basis.
In addition, the 2-year currency basis is insensitive to the changes in the bid-ask spreads,
suggesting that market liquidity factors do not affect the pricing of longer-term instruments
to the same extent as the pricing of shorter-term FX swaps.
Instead, the 2-year currency basis exhibits a more direct association with demand shocks
for hedging currency risk. As indicated by the statistically significant coefficients on ∆DXC
in specifications (2), (3), and (4) of Table IV, the fluctuations in currency hedging demand
and the associated pressures on CIP arbitrageur’s balance sheets have a direct linear effect
on the 2-year JPY/USD basis. The estimated impact of a 1 standard deviation increase
in DXC ranges from a 0.2 to 0.3 standard deviations widening in the 2-year basis. This is
consistent with the close association of DXC and bt in levels shown in Figure 9. In addition,
the interaction between the aggregate size of CIP arbitrageurs’ balance sheet necessary to
clear currency hedgers’ demand with measures of credit and market risks, θ and ρσs2 , doubles
the total impact of ∆DXC on the basis.
Finally, the ability of liquidity-constrained arbitrageurs to raise funding to arbitrage the
long-term basis is also a significant factor. The coefficients on repo spread differential range
30
Appendix Table IX shows robustness checks using the price-based proxy for DXC measures, ie the OAS
spread differential. The results are consistent with those using the quantity-based measure. They support
the finding that the importance of risk spreads as drivers of the short-term currency basis can be overstated
when the size of the aggregate demand on dealers’ balance sheets is not taken into account.
31
The ADF test fails to reject the null of a unit root for the currency basis of 2-year maturity and higher;
therefore, we include the dependent variables in first-differences.
26
from -0.7 to -0.9, indicating an almost one-to-one transmission to the currency basis.32
Overall, the results shown in Tables III and IV suggest some differences between the
determinants of the long-term and short-term basis. Changes in the longer-term, eg 2-year,
JPY/USD basis follow closely the fluctuations in the demand for forwards USD hedges,
whereas those in the short-term, eg 3-month, JPY/USD basis tend to be more sensitive to
the fluctuations in credit and liquidity conditions in interbank markets and in market liquidity
in FX markets. Even then, the effects of high Libor-OIS spreads on the short-term basis are
due to their interaction with the size of the demand shocks. This is consistent with the
forward exchange rates including a risk premium that is proportional to the net FX hedging
demand scaled by balance sheet risk factors captured by metrics such as Libor-OIS spreads.
D. Cointegration tests
Figure 9 shows the strong association in levels between the longer-term JPY/USD basis and
our measure of the demand for USD forward hedges.
[Figure 9, about here]
Cointegration tests provide another way to test for the link between the currency basis
and FX hedging demand. Specifically, the additional premia priced into currency forwards
and forward legs of FX swaps are expected to lead to the breakdown of the cointegration
relationship between the currency forward rate, Ft , and the forward rate consistent with CIP,
F̄t ≡ St (1 + rt )/(1 + rt∗ ). Since the extra cost that currency hedgers face is proportional to
the size of the CIP arbitrageurs’ balance sheet commitment, as long as markets clear, the
wedge between Ft and F̄t reflects the size of currency hedging demand. Consistent with this
implication, below we show that the cointegration relationship can be recovered by accounting
for DtXC .
[Table V, about here]
32
Appendix Table XI shows robustness checks using the price-based proxy for DXC measures, ie. the OAS
spread differential. The results are consistent with those using the quantity-based measure.
27
OIS,JP
OIS,U S
),
)/(1 + rt,2y
We focus on 2-year currency forwards Ft,2y and F̄t,2y ≡ St (1 + rt,2y
where we use 2-year OIS rates in the US and Japan to obtain the CIP-implied forward rate.
Since both Ft,2y and F̄t,2y contain a unit root, we can proceed to test for cointegration of
several linear combinations, both excluding and including DtXC .
As expected, the 2-year JPY/USD forward exchange rate, Ft,2y , is in fact not cointegrated
with the corresponding CIP-implied forward rate (Table V). This confirms what we already
know: the 2-year JPY/USD basis, is large, persistent, and non-stationary. However, adding
a linear combination with our measure of forward USD hedging demand, DtXC , restores the
cointegration with Ft,2y (line 2 in Table V). The cointegrating relationship with DtXC is
even stronger when we consider the deviation of the forward rate from its CIP-implied rate,
Ft,2y − a − bF̄t,2y , or just the actual 2-year basis (lines 3 and 4 in Table V).
V.
Panel of currencies
The cross-currency basis is also expected to be wider for currencies exhibiting greater FX
hedging imbalances versus the US dollar and those where credit and market risk factors, that
interact with net FX hedging demand to limit CIP arbitrage, are higher. In this section we
extend our analysis to a panel of currencies: AUD, CAD, CHF, DKK, EUR, GBP, JPY,
NOK and SEK (Figures 10 to 12). These currencies are free of capital controls. In addition,
XC
sufficient data to construct a measure of Di,t
are available because the respective central
banks report to the BIS international banking statistics.
[Figure 10 through 12, about here]
Figures 10 to 12 show that the widening of the basis for most currencies since mid-2014
(left-hand panels) has been associated with the rise in option-implied currency volatility
(right-hand panels). This is consistent with the role of market risks of foreign currency
collateral, ρσs2 , as a factor driving the market-clearing forward exchange rates and, hence,
the currency basis.
28
XC
A. Using BIS data as quantity proxies for Dt,i
In the panel analysis, the measurement of currency hedging demand is incomplete because
we lack comprehensive data on hedged dollar positions of institutional investors. Therefore,
XC
the proxy of Dt,i
is limited to BIS reporting banks’ USD funding gaps (BankXC
t,i ) and US
corporates reverse yankee bond liabilities (CorpXC
t,i ).
[Figure 13 through 15, about here]
Figures 13 through 15, blue bars, show BankXC for each banking system. A positive value
indicates that banks have more on-balance sheet US dollar liabilities than assets, and hence
are in a position to supply the difference via swaps to institutional and corporate hedgers.
This is the case for Australian banks, hence the AUD/USD basis is positive. A negative
value indicates that banks have more on-balance sheet US dollar assets than liabilities, and
hence have to make up for the difference via swaps, putting them on the same side of the
swap market as institutional and corporate hedgers. This is the case for Canadian, Swiss,
UK, and Japanese banks. Hence, the CAD/USD, CHF/USD, GBP/USD, and JPY/USD
basis is negative. Euro area banks have tended to be mostly on the US dollar supplying side
prior to 2008-2012 crisis period, but since then have, on the margin, also been raising USD
via swaps.
Scandinavian currencies and banking systems are an exception, with the DKK/USD,
NOK/USD, and SEK/USD basis mostly negative despite their banks supplying USD via FX
swaps. As explained in Borio, McCauley, McGuire, and Sushko (2016), this reflects the fact
that the FX swap euro market, rather than the dollar market, is the marginal funding source
for excess lending in these currencies, since swapping out of euros is more expensive than
out of dollars. Accordingly, the picture for Sweden resembles that for Australia once the
SEK/USD basis is considered. Hence, the inclusion of Scandinavian currencies biases against
finding a significant result. Still, since the regression analysis is conducted in first-differences,
it is ultimately the changes in these positions rather than their absolute sign that matters
for our regression analysis.
29
Figures 13 through 15, red bars, show the stock of bonds denominated in each currency
issued by US non-financial corporates. Here, following the same sign convention, a negative number indicates a positive stock of outstanding reverse yankee bond liabilities. When
US corporates hedge their associated bond liabilities in foreign currencies, they exert negative/widening pressure on the currency basis. As the figure shows, cross-currency funding
activities by US corporates pale in comparison to banks’ cross currency off-balance sheet
funding in most jurisdictions.
The euro area is a major exception. US corporates have issued large amounts of reverse
yankee bonds in order to take advantage of term and credit spread compression in the euro,
most recently on the back of the ECB’s asset purchase programmes. Hence, the EUR/USD
basis is much more negative than euro area banks’ consolidated USD position alone would
suggest. Although euro area banks’ USD funding gap recovered from minus 100 billion USD
in late 2014 to close to plus 50 billion USD by the end of 2015, it falls far short of clearing
the demand for USD via swap of up to 220 billion USD coming from US corporates’ reverse
yankee issuance (see Borio, McCauley, McGuire, and Sushko (2016) for further details).
B. Regression results
The FX swap-implied short-term basis. Table VI shows the quarterly frequency panel
regression results for the 3-month basis. As in the time-series benchmark results, the variables
have been standardized to z-scores (zero mean, unit variance); see Appendix Table XII for
the raw results. To be consistent with the sign convention used in the previous regression
XC
results, a positive change in Dt,i
corresponds to a more negative USD funding gap (eg greater
reliance by banks and bond issuers on FX swaps to raise US dollars), and vice-versa.
[Table VI, about here]
The panel regression results are consistent with the JPY/USD time-series results. Accounting for the interaction of ρσs2 and θ with DXC improves the explanatory power of the
regressions. The coefficient on the interaction term in specification (4) indicates that a one
standard deviation increase in ρσs2 × θ × DXC is associated with the widening of the 3-month
30
currency basis by 0.1 standard deviations. In addition, both credit and market risk measures
have a statistically significant association with a wider basis. A one standard deviation in
crease in Libor-OIS spreads, θ, goes hand-in-hand with a widening of the 3-month currency
basis by 0.5 standard deviations; and a one standard deviation in crease in the 3-month
option-implied FX volatility, ρσs2 , with a widening of the 2-year currency basis by 0.3 standard deviations.
The long-term cross-currency swap basis. Our main focus, however, is to explain
the long-term currency basis, given its relatively larger deviations from CIP in the non-crisis
period. Figure 16 shows the relationship between the 3-year currency basis and our proxy
of DtXC . The figure points to a clear cross-sectional difference between jurisdictions where
banks and corporate bond issuers swap out of the local currency into the US dollar (Figure
16, lower-right quadrant) and those where they swap out of the US dollar into the local
currency (Figure 16, upper-left quadrant). As discussed in Section II, Japanese banks and
US corporates funding themselves in the yen are in the lower-right quadrant, because they
demand US dollars via swaps, while Australian banks are in the upper-left quadrant, because
they fund themselves directly by issuing USD debt securities and then supply US dollars via
swaps.
[Figure 16, about here]
[Table VII about here]
Panel regression results with long-term currency basis as the dependent variable confirm
the significance of the interaction of FX hedging demand with balance sheet costs, but evidence concerning linear impact of FX hedging demand on the basis is somewhat mixed. Table
XC
VII column (2) shows that the demand for USD forward hedges out of each currency, Di,t
,
has a linear association with the basis (Appendix Table XIII shows the coefficients of the
regressions using non-standardized variables). Since panel regressions use fixed effects, the
XC
significant coefficient on Di,t
is not entirely due to the cross-sectional variation. This results
is also consistent with the time-series analysis of JPY/USD basis (see Table IV, above). The
XC
terms involving Di,t
become insignificant when the interaction with credit risk is included,
31
column (2), but turn significant once the interaction with market risk is added to the controls,
column (4). The coefficient on the interaction term in specification (4) indicates that a one
standard deviation increase in ρσs2 × θ × DXC is associated with the widening of the 2-year
currency basis by 0.2 standard deviations.33
VI.
Conclusion
The failure of covered interest parity (CIP) despite low volatility and risk premia runs contrary to most of the existing literature. We derive the currency basis in a simple limits-toarbitrage setup and show that CIP can fail even in calm markets due to two factors.
First, the basis opens up because of large and imbalanced FX hedging demand. In particular, the compression of term and credit spreads, largely due to unconventional monetary
policies in major currency areas, has resulted in cross currency investment and funding flows
being more one-sided. Hedging these flows for currency risks puts pressure on the forwardspot exchange rate differential, causing the basis to open up.
Second, the basis does not close because balance sheet commitment to take the other side
of net FX hedging imbalances so as to trade against CIP violations is costly. While balance
sheet capacity has a number of dimensions, our stylised setup emphasizes the costs stemming
from risks involved in taking exposures to FX derivatives. The market impact of these risks
is scaled by the size of the associated positions. The resulting risk premia will cause the
market-clearing forward exchange rates to remain out of line with CIP when FX hedging
demand is large and imbalanced across currencies.
Empirically, we find that proxies for hedging demand combined with indicators of possible
balance sheet costs of trading against CIP violations help explain the currency basis. While
the exact balance sheet costs of CIP arbitrage are unobservable, natural limits to arbitrage
33
In addition, unlike the JPY/USD time-series results, the panel regressions indicate a statistically significant linear association between the implied FX volatility, ρσs2 , and the currency basis. While, in our
framework, uncertainty about the future exchange rate affects the currency basis only to the extent that
CIP arbitrageurs’ balance sheets are exposed to the risk, eg via the interaction of ρσs2 with θ × DXC , in the
cross-section currency risks may affect CIP arbitrage because of broader effects of exchange rate uncertainty
on banks’ risk-taking (see the recent papers by Bruno and Shin (2015), Hofmann, Shim, and Shin (2016),
and Avdjiev, Du, Koch, and Shin (forthcoming) in this context).
32
arise from the risk management, and, possibly, complementary regulatory requirements in
place. These can be indirectly proxied using standard financial market data. For credit
risk we use Libor-OIS spreads and for the market risk of foreign currency collateral we use
option-implied currency volatility.
The results hold in both time-series and panel settings: empirical proxies for FX hedging
demand improve substantially the performance of standard regressions. The pricing of longterm cross-currency swaps responds directly to the fluctuations in FX hedging demand. In
addition, consistent with our theoretical framework, in most specifications accounting for
market risk of foreign currency collateral using option-implied volatility is significant and
improves the explanatory power of the regressions.
We view our approach as useful in better understanding CIP deviations at longer maturities, which are associated with the use cross-currency markets for the purpose of foreign
currency funding and long-term foreign currency investment management. That said, we also
address CIP deviations for shorter tenors, but, at these maturities, factors associated with
short-term liquidity management that are largely beyond the scope of this paper take greater
precedence. Hence, the pricing of shorter-term FX swaps responds more to measures of interbank credit and liquidity risks than the pricing of long-term cross currency swaps. However,
even then, the impact of measures such as Libor-OIS spreads on the FX swap-implied basis
arises predominantly due to the interaction with the aggregate demand for currency hedges,
which banks have to meet as CIP arbitrageurs. Hence, the underlying risk are scaled by the
total balance sheet exposures even at shorter tenors.
Finally, our paper contributes to the debate on the nature of possible constraints limiting
CIP arbitrage by banks. Although the appearance of quarter-end widening of short-term
lending spreads in FX swap markets has coincided with banks beginning to report their
leverage ratios according to the new regulatory templates, we find that these effects can only
account for a small fraction of CIP deviations in the time-series. In contrast, we show both
theoretically and empirically that CIP deviations at longer maturities, which are particularly characteristic of the post-2014 period, are consistent with bank management of capital
constraints due to risk-based exposures considerations.
33
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Figures
(a) 3-month basis: b3m
(b) 3-year basis: b3y
Figure 1. Dollar basis for select currency crosses and maturities
(b) 3-month FX option-implied volatility: ρσs2
(a) 3-month Libor-OIS spreads: θ
Figure 2. Measures of bank risk, volatility and uncertainty
39
(a) Notional principal of FX forwards & FX swaps vs cross (b) BIS reporting banks’ consolidated USD fund gap (BIS
currency swaps (BIS semi-annual OTC derivatives statistics) banking statistics)
Figure 3. The rising maturities of cross currency funding instruments and USD
cross-currency funding of global banks
(a) Banks’ USDF funding gap & 3-year basis
(b) Corporate spread differentials & 3-year basis
Figure 4. Banks’ USD funding gaps, cross-country spread differentials, and 3-year cross
currency basis vs USD; Sample: Q1/2009 - Q4/2015.
Note: AU = Australia, CA = Canada, CH = Switzerland, DK = Denmark, GB = United Kingdom, JP =
Japan, NO = Norway, SE = Sweden, XM = Euro area.
40
Figure 5. Flows in the FX swap market when net demand from currency hedgers for USD
is positive
41
(a) Stock of FX bonds and hedge ratio
(b) Hedged FX bond holdings, expressed in USD and JPY.
Figure 6. Proxy for USD forward hedges of JP life insurers: InstXC
t
(a) OIS-basis, 1-month to 5-year
(b) PC1 and PC2 of OIS-basis
(d) (rtREP O − rt ) − (rt∗,REP O − rt∗ ) and PC2 of OIS basis
(c) DtXC and PC1 of OIS basis
Figure 7. Common factors of JPY/USD OIS basis, FX hedging demand, and repo spreads
42
(a) 1-week tenors:
JPY/USD basis
(rtREP O − rt ) − (rt∗,REP O − rt∗ ) and (b) 3-month tenors: (rtREP O − rt ) − (rt∗,REP O − rt∗ ) and
JPY/USD basis
Figure 8. Repo market funding conditions and JPY/USD basis; 1-week (left) and 3-month
(right)
(a) Time-series of bt,3y and DtXC
(b) Scatter plot of bt,3y and DtXC
Figure 9. Levels of USD cross-currency funding out of JPY and 3-year JPY/USD basis
43
(a) AUD/USD basis
(b) AUD/USD implied vol
(c) CAD/USD basis
(d) CAD/USD implied vol
(e) CHF/USD basis
(f) CHF/USD implied vol
Figure 10. Left: Cross-currency basis, bt ; Right: option-implied currency volatility, ρσs2 .
44
(a) DKK/USD basis
(b) DKK/USD implied vol
(c) EUR/USD basis
(d) EUR/USD implied vol
(e) GBP/USD basis
(f) GBP/USD implied vol
Figure 11. Left: Cross-currency basis, bt ; Right: option-implied currency volatility, ρσs2 .
45
(a) JPY/USD basis
(b) JPY/USD implied vol
(c) NOK/USD basis
(d) NOK/USD implied vol
(e) SEK/USD basis
(f) SEK/USD implied vol
Figure 12. Left: Cross-currency basis, bt ; Right: option-implied currency volatility, ρσs2 .
46
(a) AUD/USD
(b) Net AUD/USD positioning
(c) CAD/USD
(d) Net CAD/USD positioning
(e) CHF/USD
(f) Net CHF/USD positioning
Figure 13. Left: Cross-currency basis, bt ; Right: US dollar funding gap of BIS reporting
banks & US corporate reverse yankee bond liabilities (BankXC +CorpXC ), in units of USD
billions.
47
(a) DKK/USD
(b) Net DKK/USD positioning
(c) GBP/USD
(d) Net GBP/USD positioning
(e) JPY/USD
(f) Net JPY/USD positioning
Figure 14. Left: Cross-currency basis, bt ; Right: US dollar funding gap of BIS reporting
banks & US corporate reverse yankee bond liabilities (BankXC +CorpXC ), in units of USD
billions.
48
(a) NOK/USD
(b) Net NOK/USD positioning
(c) SEK/USD
(d) Net SEK/USD positioning
(e) EUR/USD
(f) Net EUR/USD positioning
Figure 15. Left: Cross-currency basis, bt ; Right: US dollar funding gap of BIS reporting
banks & US corporate reverse yankee bond liabilities (BankXC +CorpXC ), in units of USD
billions.
49
(a) bt,3y and DtXC
Figure 16. Sum of banks’ USD funding gap, BanktXC , and US corporates’ reverse Yankee
bonds outstanding, CorpXC
t , in each currency jurisdiction plotted against the 3-year basis
vs USD.
Note: AU = Australia, CA = Canada, CH = Switzerland, DK = Denmark, GB = United Kingdom, JP =
Japan, NO = Norway, SE = Sweden, XM = Euro area.
50
Tables
Table I. FX hedging demand: DtXC
Sector & activity:
Proxy
Source:
Banks’ use of FX swaps
to fund USD lending
BIS banks’ USD
funding gap (BankXC )
BIS IBS
(consolidated)
Insurers’ use of FX swaps
to hedge USD bonds portfolio
USD bond holdings
× hedge ratio (InstXC )
National and
commercial data
US Corporates’ use of FX swap
US corporates’ FX bonds
to convert cheap FX funding into USD outstanding (CorpXC )
Aggregate incentive to swap out of
FX funding into USD investment
BIS IDS
Asset swap spread differential Barclays
(OASU S -OASF X )
Table II. Baseline regression variable description
Proximate source:
Notation
Proxy
DtXC (prices)
(OASU S -OASJP );
DtXC (quantities)
BankXC +InstXC +CorpXC
XC
− 1)
100 × (DtXC /Dt−1
∆DtXC (quantities)
Bank credit risk:
θ
Libor-OIS spreads
FX option-implied IV
Implied FX volatility: ρσs2
∗,REP O
REP O
∗
Short-selling costs:
(rt
− rt ) − (rt
− rt ) GC repo spreads, US minus JP
A
B
Transaction costs:
[(ftB − sA
)
−
(f
−
s
)]/2
Spot and forward bid-ask spreads
t
t
t
FX hedging demand:
51
Table III. JPY/USD: Drivers of 3-month JPY/USD CIP deviations, controlling for
interactions between balance sheet risks and demand shocks
(DXC =(BankXC +InstXC +CorpXC )).
2
2
b̂t = βθ × ∆θt + βσ × ∆ρσs,t
+ βD × ∆DtXC + βθ×σ×D × [∆θt × ∆ρσs,t
× ∆DtXC ] + βRepo ×
i
h
∗,REP O
∗
A
B
REP O
− rt−1
) + βbid−ask × [(ftB − sA
∆ (rt−1
− rt−1 ) − (rt−1
t ) − (ft − st )]/2 + α + t
3-month JPY/USD basis
θ
(1)
(2)
(3)
(4)
-0.909***
(0.216)
-0.905***
(0.206)
-0.150
(0.107)
0.001
(0.271)
-0.132
(0.101)
-1.138***
(0.340)
-0.128
(0.270)
-0.123
(0.114)
DXC
θ × DXC
ρσs2 × θ × DXC
-0.255*
(0.149)
0.397***
(0.136)
-0.270*
(0.154)
0.430***
(0.128)
-0.388***
(0.118)
0.380***
(0.096)
-0.941***
(0.345)
-0.053
(0.108)
-0.429***
(0.151)
0.408***
(0.112)
-0.315***
(0.100)
-0.249**
(0.100)
-0.227***
(0.083)
-0.214***
(0.079)
72
0.679
67
0.725
67
0.794
67
0.776
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Notes: The table reports coefficients based on regressions using standardized variables (zero mean,
unit variance). Monthly frequency, 12/2007 to 04/2016. Unit root (ADF) test rejects the null
in levels for 3-month currency basis (test stat=-13.265, 1% critical value=-3.482, p-value=0.000),
therefore the dependent variable specified in levels. AR(1) not significant. Robust standard errors
in parentheses: *** p<0.01, ** p<0.05, * p<0.1
52
Table IV. JPY/USD: Drivers of 2-year JPY/USD CIP deviations, controlling for
interactions between balance sheet risks and demand shocks
(DXC =(BankXC +InstXC +CorpXC )).
2
2
∆b̂t = βθ × ∆θt + βσ × ∆ρσs,t
+ βD × ∆DtXC + βθ×σ×D × [∆θt × ∆ρσs,t
× ∆DtXC ] + βRepo ×
i
h
∗,REP O
∗
A
B
REP O
− rt−1
) + βbid−ask × ∆[(ftB − sA
∆ (rt−1
− rt−1 ) − (rt−1
t ) − (ft − st )]/2 + α + t
2-year JPY/USD basis
θ
(1)
(2)
(3)
(4)
-0.463***
(0.172)
-0.480***
(0.127)
-0.292**
(0.125)
-0.296
(0.386)
-0.281**
(0.123)
-0.228
(0.454)
-0.382***
(0.109)
-0.221*
(0.120)
DXC
θ × DXC
ρσs2 × θ × DXC
-0.759***
(0.201)
-0.381
(0.970)
-0.839***
(0.194)
-0.714
(0.936)
-0.857***
(0.192)
-0.588
(0.920)
-0.228*
(0.132)
0.104
(0.164)
-0.709***
(0.254)
-0.372
(0.925)
-0.004
(0.134)
-0.066
(0.131)
-0.059
(0.132)
-0.047
(0.126)
72
0.425
67
0.506
67
0.509
67
0.531
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Notes: The table reports coefficients based on regressions using standardized variables (zero mean,
unit variance). Monthly frequency, 12/2007 to 04/2016. Unit root (ADF) test fails to reject the
null in levels for 2-year currency basis (test stat=-1.425, 1% critical value=-3.479, p-value=0.570),
therefore the dependent variable specified in levels. AR(1) not significant. Robust standard errors
in parentheses: *** p<0.01, ** p<0.05, * p<0.1
53
Table V. JPY/USD: Cointegration between the actual 2-year currency forward rate, Ft
and the 2-year currency forward rate consistent with CIP, accounting for the demand for
forward USD hedges, DtXC
Johansen cointegration
t
t
t
t
trace stat
critical value
max rank
9.581
31.5651*
6.3788*
16.4755*
15.41
29.68
3.760
15.41
0
1
2
1
McKinnon p-val
Lag-order
p-val
0.5687
0.7097
0.5702
1
1
2
0.000
0.000
0.000
= Ft,2y − a − bF̄t,2y is I(0)
= Ft,2y − a − bF̄t,2y − cDtXC is I(0)
= [Ft,2y − F̄t,2y ] − a − cDtXC is I(0)
= bt,2y − a − cDtXC is I(0)
Diagnostics
Ft,2y
F̄t,2y
bt,2y
Notes: Monthly frequency, 12/2007 to 12/2015.
54
Table VI. Panel of currencies: Drivers of the 3-month CIP deviations, controlling for
interactions between balance sheet risks and demand shocks (DXC =(BankXC +BondXC ).
2
XC
2
XC
b̂t,i = βθ × ∆θt,i + βσ × ∆ρσs,t,i
+ βD × ∆Dt,i
+ βθ×σ×D × [∆θt,i × ∆ρσs,t,i
× ∆Dt,i
] + βRepo ×
h
i
∗,REP O
REP O
∗
B
A
B
∆ (rt,i
− rt ) − (rt−1,i
− rt−1,i
) + βbid−ask × [(ft,i
− sA
t,i ) − (ft,i − st,i )]/2 + αi + t,i
3-month currency basis
θ
(1)
(2)
(3)
(4)
-0.545***
(0.088)
-0.545***
(0.089)
-0.003
(0.012)
-0.528***
(0.106)
0.033
(0.018)
-0.120***
(0.019)
-0.529***
(0.100)
0.047*
(0.019)
DXC
θ × DXC
ρσs2 × θ × DXC
0.314
(0.397)
0.561***
(0.101)
-0.127***
(0.017)
0.318
(0.398)
0.562***
(0.101)
-0.127***
(0.017)
0.316
(0.410)
0.556***
(0.099)
-0.126***
(0.017)
-0.102**
(0.029)
-0.265**
(0.097)
-0.174
(0.386)
0.525***
(0.095)
-0.127***
(0.016)
281
0.269
7
yes
yes
277
0.270
7
yes
yes
277
0.282
7
yes
yes
275
0.329
7
yes
yes
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Currency pairs
Fixed effects
Clustered standard errors
Notes: The table reports coefficients based on regressions using standardized variables (zero mean,
unit variance). Quarterly frequency, Q1/2000 to Q4/2015; currencies included: AUD, CAD, DKK,
EUR, GBP, JPY, and SEK; size of the cross-section limited by the availability OIS rates and CG
repo rates. Unit root (ADF) tests reject the null in levels for 3-month currency basis, therefore the
dependent variable specified in levels. AR(1) not significant. Clustered robust standard errors in
parentheses: *** p<0.01, ** p<0.05, * p<0.1
55
Table VII. Panel of currencies: Drivers of the 2-year CIP deviations, controlling for
interactions between balance sheet risks and demand shocks (DXC =(BankXC +BondXC ).
2
XC
2
XC
∆b̂t,i = βθ × ∆θt,i + βσ × ∆ρσs,t,i
+ βD × ∆Dt,i
+ βθ×σ×D × [∆θt,i × ∆ρσs,t,i
× ∆Dt,i
] + βRepo ×
h
i
∗,REP O
REP O
∗
B
A
B
∆ (rt,i
− rt ) − (rt−1,i
− rt−1,i
) + βbid−ask × ∆[(ft,i
− sA
t,i ) − (ft,i − st,i )]/2 + αi + t,i
2-year currency basis
θ
(1)
(2)
(3)
(4)
-0.641**
(0.180)
-0.627**
(0.171)
-0.073**
(0.028)
-0.621***
(0.163)
-0.061
(0.038)
-0.040
(0.029)
-0.455**
(0.142)
0.030
(0.063)
DXC
θ × DXC
ρσs2 × θ × DXC
-0.601
(0.601)
0.629**
(0.248)
-0.014***
(0.004)
-0.585
(0.592)
0.625**
(0.247)
-0.009
(0.006)
-0.587
(0.600)
0.626**
(0.250)
-0.009
(0.006)
-0.197**
(0.058)
-0.286*
(0.138)
-0.994
(0.645)
0.660**
(0.268)
-0.014*
(0.006)
247
0.341
7
yes
yes
243
0.352
7
yes
yes
243
0.353
7
yes
yes
195
0.414
7
yes
yes
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Currency pairs
Fixed effects
Clustered standard errors
Notes: The table reports coefficients based on regressions using standardized variables (zero mean,
unit variance). Quarterly frequency, Q1/2000 to Q4/2015; currencies included: AUD, CAD, DKK,
EUR, GBP, JPY, and SEK; size of the cross-section limited by the availability OIS rates and CG repo
rates. Unit root (ADF) tests fail to reject the null in levels for 2-year currency basis, therefore the
dependent variable specified is first-differenced. AR(1) not significant. Clustered robust standard
errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
56
A.
Extra tables and robustness checks
Table VIII. JPY/USD: Drivers of 3-month JPY/USD CIP deviations, controlling for
interactions between balance sheet risks and demand shocks
(DXC =(BankXC +InstXC +CorpXC )).
2
2
× ∆DtXC ] + βRepo ×
+ βD × ∆DtXC + βθ×σ×D × [∆θt × ∆ρσs,t
b̂t = βθ × ∆θt + βσ × ∆ρσs,t
i
h
∗,REP O
B
A
∗
REP O
) + βbid−ask × [(ftB − sA
− rt−1 ) − (rt−1
− rt−1
∆ (rt−1
t ) − (ft − st )]/2 + α + t
3-month JPY/USD basis
θ
(1)
(2)
(3)
(4)
-113.620***
(26.952)
-113.102***
(25.800)
-1.731
(1.230)
0.064
(33.889)
-1.526
(1.163)
-44.481***
(13.285)
-15.961
(33.734)
-1.417
(1.318)
DXC
θ × DXC
ρσs2 × θ × DXC
-29.301*
(17.148)
2.160***
(0.737)
-31.026*
(17.714)
2.338***
(0.694)
-44.696***
(13.631)
2.069***
(0.524)
-2.525***
(0.925)
-0.464
(0.944)
-49.354***
(17.417)
2.220***
(0.610)
-19.420***
(2.535)
-16.621***
(2.373)
-15.487***
(2.326)
-10.352
(9.686)
72
0.679
67
0.725
67
0.794
67
0.776
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Notes: Monthly frequency, 12/2007 to 04/2016. Unit root (ADF) tests reject the null in levels for
3-month currency basis, therefore the dependent variable specified in levels. AR(1) not significant.
Robust standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
57
Table IX. JPY/USD: Drivers of 3-month JPY/USD CIP deviations, controlling for
interactions between balance sheet risks and demand shocks (DXC = OAS U S − OAS JP )).
2
2
b̂t = βθ × ∆θt + βσ × ∆ρσs,t
+ βD × ∆DtXC + βθ×σ×D × [∆θt × ∆ρσs,t
× ∆DtXC ] + βRepo ×
h
i
∗,REP O
REP O
∗
A
B
∆ (rt−1
− rt−1 ) − (rt−1
− rt−1
) + βbid−ask × [(ftB − sA
t ) − (ft − st )]/2 + α + t
3-month JPY/USD basis
θ
(1)
(2)
(3)
(4)
-113.620***
(26.952)
-112.440***
(28.476)
-1.769
(12.643)
-42.195***
(13.518)
-3.752
(7.542)
-92.246***
(10.298)
-34.265*
(17.186)
-7.464
(7.568)
DXC
θ × DXC
ρσs2 × θ × DXC
-29.301*
(17.148)
2.160***
(0.737)
-29.955
(19.867)
2.177***
(0.776)
-42.413***
(12.768)
0.835
(0.502)
-6.687***
(0.912)
1.112
(0.716)
-42.537***
(13.798)
0.978**
(0.474)
-19.420***
(2.535)
-19.379***
(2.583)
-20.239***
(2.376)
-31.549***
(7.433)
72
0.679
72
0.679
72
0.815
72
0.818
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Notes: Monthly frequency, 12/2007 to 04/2016. Unit root (ADF) tests reject the null in levels for
3-month currency basis, therefore the dependent variable specified in levels. AR(1) not significant.
Robust standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
58
Table X. JPY/USD: Drivers of 2-year JPY/USD CIP deviations, controlling for
interactions between balance sheet risks and demand shocks
(DXC =(BankXC +InstXC +CorpXC )).
2
2
∆b̂t = βθ × ∆θt + βσ × ∆ρσs,t
+ βD × ∆DtXC + βθ×σ×D × [∆θt × ∆ρσs,t
× ∆DtXC ] + βRepo ×
i
h
∗,REP O
∗
A
B
REP O
− rt−1
) + βbid−ask × ∆[(ftB − sA
∆ (rt−1
− rt−1 ) − (rt−1
t ) − (ft − st )]/2 + α + t
2-year JPY/USD basis
θ
(1)
(2)
(3)
(4)
-15.675***
(5.825)
-16.228***
(4.303)
-0.913**
(0.390)
-10.023
(13.069)
-0.879**
(0.383)
-2.415
(4.798)
-12.905***
(3.682)
-0.691*
(0.376)
DXC
θ × DXC
ρσs2 × θ × DXC
-23.634***
(6.252)
-0.093
(0.237)
-26.114***
(6.027)
-0.174
(0.229)
-26.674***
(5.979)
-0.144
(0.225)
-1.632*
(0.943)
0.608
(0.957)
-22.074***
(7.905)
-0.091
(0.226)
-0.312
(0.776)
-0.252
(0.759)
-0.143
(0.809)
-0.010
(0.759)
72
0.425
67
0.506
67
0.509
67
0.531
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Notes: Monthly frequency, 12/2007 to 04/2016. Unit root (ADF) tests reject the null in levels for
3-month currency basis, therefore the dependent variable specified in levels. AR(1) not significant.
Robust standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
59
Table XI. JPY/USD: Drivers of 2-year JPY/USD CIP deviations, controlling for
interactions between balance sheet risks and demand shocks (DXC = OAS U S − OAS JP )).
2
2
∆b̂t = βθ × ∆θt + βσ × ∆ρσs,t
+ βD × ∆DtXC + βθ×σ×D × [∆θt × ∆ρσs,t
× ∆DtXC ] + βRepo ×
h
i
∗,REP O
REP O
∗
A
B
∆ (rt−1
− rt−1 ) − (rt−1
− rt−1
) + βbid−ask × ∆[(ftB − sA
t ) − (ft − st )]/2 + α + t
2-year JPY/USD basis
θ
(1)
(2)
(3)
(4)
-15.675***
(5.825)
-12.316*
(6.280)
-4.745
(3.784)
-0.845
(5.633)
-5.611*
(3.299)
-15.233***
(4.361)
-4.470
(4.301)
-3.778
(3.420)
DXC
θ × DXC
ρσs2 × θ × DXC
-23.634***
(6.252)
-0.093
(0.237)
-25.570***
(6.740)
-0.072
(0.243)
-26.716***
(5.823)
-0.047
(0.235)
-9.940***
(2.465)
0.623
(0.763)
-23.268***
(6.922)
-0.020
(0.230)
-0.312
(0.776)
-0.364
(0.776)
0.272
(0.765)
0.265
(0.775)
72
0.425
72
0.446
72
0.506
72
0.505
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Notes: Monthly frequency, 12/2007 to 04/2016. Unit root (ADF) tests reject the null in levels for
3-month currency basis, therefore the dependent variable specified in levels. AR(1) not significant.
Robust standard errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
60
Table XII. Panel of currencies: Drivers of the 3-month CIP deviations controlling for
interactions between balance sheet risks and demand shocks (DXC =(BankXC +BondXC ).
2
XC
2
XC
b̂t,i = βθ × ∆θt,i + βσ × ∆ρσs,t,i
+ βD × ∆Dt,i
+ βθ×σ×D × [∆θt,i × ∆ρσs,t,i
× ∆Dt,i
] + βRepo ×
h
i
∗,REP O
REP O
∗
B
A
B
∆ (rt,i
− rt ) − (rt−1,i
− rt−1,i
) + βbid−ask × [(ft,i
− sA
t,i ) − (ft,i − st,i )]/2 + αi + t,i
3-month currency basis
θ
(1)
(2)
(3)
(4)
-92.810***
(15.061)
-92.714***
(15.078)
-0.002
(0.009)
-89.811***
(18.063)
0.026
(0.014)
-0.281***
(0.045)
-90.087***
(16.953)
0.037*
(0.015)
DXC
θ × DXC
ρσs2 × θ × DXC
6.738
(8.530)
1.425***
(0.256)
-13.954***
(1.823)
6.833
(8.554)
1.426***
(0.257)
-13.934***
(1.860)
6.789
(8.812)
1.413***
(0.252)
-13.621***
(1.855)
-0.015**
(0.004)
-2.742**
(1.002)
-3.745
(8.286)
1.334***
(0.241)
12.868
(10.457)
281
0.269
7
yes
yes
277
0.270
7
yes
yes
277
0.282
7
yes
yes
275
0.329
7
yes
yes
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Currency pairs
Fixed effects
Clustered standard errors
Notes: Quarterly frequency, Q1/2000 to Q4/2015; currencies included: AUD, CAD, DKK, EUR,
GBP, JPY, and SEK; size of the cross-section limited by the availability OIS rates and CG repo
rates. Unit root (ADF) tests reject the null in levels for 3-month currency basis, therefore the
dependent variable specified in levels. AR(1) not significant. Clustered robust standard errors in
parentheses: *** p<0.01, ** p<0.05, * p<0.1
61
Table XIII. Panel of currencies: Drivers of the 2-year CIP deviations, controlling for
interactions between balance sheet risks and demand shocks (DXC =(BankXC +BondXC ).
2
XC
2
XC
∆b̂t,i = βθ × ∆θt,i + βσ × ∆ρσs,t,i
+ βD × ∆Dt,i
+ βθ×σ×D × [∆θt,i × ∆ρσs,t,i
× ∆Dt,i
] + βRepo ×
h
i
∗,REP O
REP O
∗
B
A
B
∆ (rt,i
− rt ) − (rt−1,i
− rt−1,i
) + βbid−ask × ∆[(ft,i
− sA
t,i ) − (ft,i − st,i )]/2 + αi + t,i
2-year currency basis
θ
(1)
(2)
(3)
(4)
-29.948***
(7.384)
-29.096***
(6.854)
-0.015**
(0.006)
-28.791***
(6.496)
-0.013
(0.007)
-0.023
(0.015)
-21.249***
(5.064)
0.002
(0.013)
DXC
θ × DXC
ρσs2 × θ × DXC
-1.056
(3.440)
0.220**
(0.067)
-0.749***
(0.056)
-0.842
(3.484)
0.219**
(0.068)
-0.728***
(0.066)
-0.785
(3.517)
0.220**
(0.068)
-0.699***
(0.071)
-0.037**
(0.011)
-1.079*
(0.465)
0.746
(3.298)
0.234**
(0.069)
-0.860***
(0.076)
262
0.352
7
yes
yes
258
0.362
7
yes
yes
258
0.364
7
yes
yes
206
0.412
7
yes
yes
ρσs2
Repo spread diff.
FX bid-ask
Constant
Observations
R-squared
Currency pairs
Fixed effects
Clustered standard errors
Notes: Quarterly frequency, Q1/2000 to Q4/2015; currencies included: AUD, CAD, DKK, EUR,
GBP, JPY, and SEK; size of the cross-section limited by the availability OIS rates and CG repo
rates. Unit root (ADF) tests fail to reject the null in levels for 2-year currency basis, therefore the
dependent variable specified is first-differenced. AR(1) not significant. Clustered robust standard
errors in parentheses: *** p<0.01, ** p<0.05, * p<0.1
62
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