Deviations from Covered Interest Rate Parity

It is the difference between the direct dollar interest rate from the cash market and the synthetic dollar rate obtained by swapping a foreign currency into dollars; a non-zero value means two payoff-identical strategies have different prices (Introduction, pp. 1-2). The arbitrage logic: an investor can deposit dollars for a month, or convert to a foreign currency, deposit there, and lock in the reconversion with a one-month forward. “If both U.S. and foreign currency deposit rates are default-free and the forward contract has no counterparty risk, the two investment strategies are equivalent and should thus deliver the same payoffs,” so the interest differential should equal the log forward-spot difference (p. 1). The basis measures the gap: “A positive (negative) currency basis means that the direct dollar interest rate is higher (lower) than the synthetic dollar interest rate. When the basis is zero, CIP holds” (p. 2). The authors are explicit about the scope of the puzzle: “Our findings are a puzzle for all no-arbitrage models in macroeconomics and finance. Since the arbitrage opportunities exist at very short horizon, such as overnight or one-week, our findings are also a puzzle for the classic limits-of-arbitrage models that rely on long-term market risk à la Shleifer and Vishny (1997)” (p. 1).

G10 currencies, 2010-2016, with an average absolute Libor basis of 24 basis points at three months and 27 at five years – and much larger values in specific cases (Introduction, p. 2). The ten currencies are the Australian, Canadian and New Zealand dollars, the Swiss franc, the Danish and Norwegian krone, the euro, the pound, the yen and the Swedish krona, with total daily turnover above $2 trillion. The averages “hide large variations both across currencies and across time. In the current economic environment, the cross-currency basis can be of the same order of magnitude as the interest rate differential. For example, the five-year basis for the Japanese yen was close to -90 basis points at the end of 2015, which was even greater in magnitude than the difference (of about -70 basis points) between the five-year Libor interest rate in Japan and in the United States” (p. 2). The authors situate this against the pre-crisis consensus that CIP held (Frenkel and Levich; Akram, Rime and Sarno) and the crisis-period literature that documented large bases while “the interbank markets became impaired and arbitrage capital was limited” – their own contribution being that the deviations “persist after the global financial crisis… and remain large in magnitude,” i.e. outside conditions of financial distress (p. 2).

Two independent reasons: the panel CDS evidence does not support it, and the basis survives on instruments where cross-currency credit differences are absent by construction. The credit story, attributed to Tuckman and Porfirio (2004), is that if yen interbank lending carries more credit risk than dollar interbank lending, “the lender should be compensated for the credit risk differential… and thus the cross-currency basis needs not be zero” (p. 3). The direct test: “Studying the credit default spreads of banks on interbank panels in different currencies, we do not find much support for this explanation of the CIP deviations” (p. 3). The stronger argument is instrumental. Repos “are fully collateralized and thus do not exhibit any credit risk”; KfW bonds “are fully backed by the German government and thus exhibit very minimal credit risk, without differences in credit risk across currencies”; and the two cover different parts of the curve – “Repo and forward contracts highlight the CIP deviations at the short-end of the yield curves, while KfW bonds and swaps focus on longer maturities” (p. 3). A further piece of evidence appears in the cross-sectional section: the mean CDS spread of the interbank panel has a correlation of -33 percent with the five-year Libor basis, against +89 percent for the interest rate level (Section 5.4.1, p. 40) – the wrong sign and much weaker than the rate relationship.

Between roughly 8 and 22 basis points annualised depending on the instrument and cost assumption, with zero conditional volatility over the strategy’s fixed horizon. The headline range in the introduction is “9 to 20 basis points on average in annualized values,” with standard deviations “range[ing] from 5 to 23 basis points,” and the authors emphasise the risk profile rather than the size: “the conditional volatility of each investment opportunity is naturally zero and Sharpe ratios are thus infinite for the fixed investment horizon of the strategy” (p. 4). By instrument, the repo-based strategy yields “average annualized profits range from 11 to 19 basis points after taking into transaction costs. The profits vary over time, with standard deviations ranging from 13 basis points to 27 basis points. The arbitrage profits are positive for the majority of the sample window” (Section 3.2, p. 21). The KfW strategies yield 10 to 22 basis points, and net of the bid-ask and other fees prevailing on the transaction day, “average profits range from 8 to 20 basis points, with standard deviations ranging from 5 to 11 basis points” (Section 3.3). The authors are deliberately conservative on costs, using a US repo bid-ask spread of about 9 basis points – “significantly higher than the 4 basis points bid-ask spread quoted on Tullett Prebon” – and a total swap transaction cost averaging about 5 basis points since 2009. The trade is described concretely: “borrow at the U.S. dollar repo rate or short U.S. dollar-denominated KfW bonds and then earn risk-free positive profits by investing in repo rates or KfW bonds denominated in low interest rate currencies… while hedging the foreign currency risk using foreign exchange forwards or swaps” (p. 3).

Costly intermediation explains persistence; cross-currency imbalances explain the pattern. Either alone would predict a zero basis (Section 4, p. 4). “If financial intermediaries were unconstrained, the supply of currency hedging should be perfectly elastic, and any CIP deviations would be arbitraged away. Similarly, if the global funding and investment demand were balanced across currencies, there would be no client demand for FX swaps to transform funding liquidity or investment opportunities across currencies, and thus the cross-currency basis would also be zero regardless of the supply of currency hedging.” The two do different explanatory work: “Costly financial intermediation can explain why the basis is not arbitraged away post crisis. The imbalances in savings and investment across currencies can explain the systematic relationship between the basis and nominal interest rates” (p. 4).

By giving a contract that must sit on the quarter-end balance sheet a treated-versus-untreated comparison within the same market. “We find that the one-month CIP deviation increases exactly one month before the quarter ends, at the time when a one-month forward contract has to appear on the quarter-end balance sheet. Likewise, the one-week CIP deviation increases exactly one week before the quarter ends. Meanwhile, a three-month CIP trade, which has to appear on a quarter-end report regardless of when it is executed, does not exhibit any particular dynamics” (Section 5.1, pp. 4-5). The design is described in those terms: the one-month and one-week forwards crossing quarter ends “are the ’treated’ assets, subject to higher balance sheet costs due to regulatory filings, while the three-month forward contract is the ’non-treated’ asset. Our simple difference-in-difference experiments exploits different lags before the quarter ends and different horizons of the forward contracts. The term structure of short-term CIP deviations suggest that banking regulations have a causal impact on asset prices” (p. 5). The word choice in the introduction – “pointing to a causal effect of banking regulation on asset prices” – and the conclusion’s “the first international evidence on the causal impact of recent banking regulation on asset prices” bracket the strength of the claim.

Sizeable post-crisis, larger again after January 2015, and essentially absent pre-2007 (Section 5.1.1, p. 35). For one-week contracts, “the quarter-end CIP deviation relative to the mean deviation in the rest of the quarter is on average 10 to 22 basis points higher in the post-2007 sample than over the pre-2007 sample,” and “compared to the post-2007 sample, the quarter-end weekly CIP deviation increases by another 30-40 basis points on average since January 2015.” For one-month contracts based on Libor and OIS, “the month-end deviation relative to the rest of the quarter is on average 4 to 5 basis point higher post-crisis than the level pre-crisis and increases by another 8 basis point in the post-2015 sample”; for one-month repo the post-2015 coefficient is not significant but the post-crisis one “is highly significant and equals 13 basis points.” The pre-period check is explicit: “coefficients on QendW and QendM are very small and largely insignificant, suggesting that there is very little quarter end effect before 2007.”

Because they answer two different questions: substituting the IOER for the US funding leg explains about one-third of the one-week deviations, while also investing at foreign central banks explains roughly two-thirds. The first step replaces Libor/OIS/repo with the IOER as the direct dollar funding cost, which “is equivalent to assuming… that banks borrow at the Libor (or OIS) rates and that the difference between the IOER minus the Libor (or OIS) rate proxies for the banks’ balance sheet costs.” The reductions are 6 basis points against the Libor basis, 12 against the OIS basis and 8 against the repo basis, so “the gap between the IOER and OIS/Libor/repo in the U.S. can explain about one-third of the one-week CIP deviations” (Section 5.2, pp. 36-37). The second step also invests at the foreign central bank’s deposit facility, justified because central bank balances “are considered safer and more liquid than any private market alternatives even before being codified as the Level-1 HQLA by the Basel liquidity coverage ratio requirement.” That gives an average IOER basis of -8 basis points, “much closer to zero than the Libor and OIS basis at -26 and -28 basis points, respectively” (p. 37) – and the conclusion summarises the combined exercise as “proxies for the banks’ balance sheet costs account for two-thirds of the CIP deviations” (p. 43). The abstract and introduction, referring to the US-side proxy, say “about one third to one half.”

No. It “significantly reduces the size of the CIP deviations, but it does not eliminate them.” For the Danish krone, Swiss franc and yen, “the CIP deviations still range from -12 to -15 basis points on average,” and the authors spell out what that residual means: “Such CIP deviations imply risk-free arbitrage opportunity for global depository institutions that can borrow U.S. dollars in wholesale cash funding market, and deposit at the foreign central bank deposit facility while hedging currency risk, even after proxying for their balance sheet costs. Banks are either factoring in higher shadow costs, or they are willing to forego some extra” profit (Section 5.2, p. 37). They also note a sign asymmetry with a behavioural implication: “The bases based on the IOER can be positive, while the Libor basis is always negative. A positive IOER basis would lead U.S. banks to park excess reserves at the Fed, as opposed to lending out in U.S. dollars as suggested by a negative Libor basis. Increasing reserves at the Fed further reduces the bank flows to arbitrage the Libor basis” (fn. 24).

Low-rate currencies have the most negative bases and high-rate currencies less negative or positive ones, so the hedged arbitrage is the reverse of the unhedged carry trade (Section 5.4.1, pp. 39-41). The pattern “holds across Libor, OIS, Treasuries, KfW and other multinational bonds,” and “the relationship is particularly strong at long maturities, with the correlation between five-year Libor bases and Libor rates equal to 89 percent for G10 currencies.” The trading implication: “there exist arbitrage opportunities for going long in low interest rate currencies, short in high interest rate currencies with the currency risk hedged using exchange rate swaps. The direction of the arbitrage trade is exactly the opposite of the conventional unhedged carry trade.” The authors put the two effects on the same scale rather than letting the comparison stand as a puzzle: “the average CIP deviations and average carry trade excess returns differ by an order of magnitude: less than 50 basis points for the CIP deviations, and more than 500 basis points for average carry trade excess returns” (fn. 29). The same pattern shows in issuance behaviour: relative to non-financial issuers, “supranational issuers issue more in high-basis and high-interest-rate currencies, such as the Australian and New Zealand dollars, and issue less in low-basis and low-interest-rate currencies, such as the Swiss franc, the Danish Krone, and the Japanese yen” (p. 41). In the time series, the basis relationship is established “using a high-frequency event study of a narrow window around the ECB monetary policy” announcements, with the basis tending “to increase with interest rate shocks” (Section 5.4.2; Introduction, p. 5).

It points at intermediaries and correlated dollar-funding demand rather than at anything specific to currency markets. “The cross-currency basis is correlated with other liquidity spreads, especially the KfW over German bund basis and the U.S. Libor tenor basis, the price of swapping the one-month in exchange of the three-month U.S. Libor rates. The co-movement in bases measured in different markets points to the role of financial intermediaries and correlated demand shocks for dollar funding and other forms of liquidity” (Introduction, pp. 5-6). The quarter-end behaviour is shared too: a related spread “largely varies between 5-20 basis points outside quarter ends, and can reach 100 basis points at quarter ends. Same as the CIP deviations” (fn. in Section 5.3).

With intermediary-based asset pricing, while noting that existing models were not built for this fact pattern. Garleanu and Pedersen (2011) “build a margin-based asset pricing model and use it to study the deviations from CIP during the crisis”; Gabaix and Maggiori (2015) provide “a tractable and elegant model of exchange rate determination in the presence of moral hazard,” with “a variant of their model, presented in their Appendix,” that encompasses CIP deviations (p. 6). The authors’ own reading: “Our evidence on the impact of banking regulation points towards models of intermediary-based asset pricing, as those of He and Krishnamurthy (2012, 2013) and Brunnermeier and Sannikov (2014) in the tradition of Bernanke and Gertler (1989) and Holmstrom and Tirole (1997)” (p. 6). They also place the pre-crisis literature carefully: CIP appears “in Lotz (1889) and much more clearly in Keynes (1923),” was tested extensively in the 1970s and 1980s, and “up to the recent global financial crisis, the consensus was that the CIP condition holds in the data” (fn. 2).

Any welfare estimate, and any general-equilibrium interpretation. The conclusion sets out the implications the authors think follow – that deviations “occur in one of the largest and most liquid markets in the world after the crisis in the absence of financial distress, suggesting that other arbitrage opportunities exist elsewhere”; that although “trading in exchange rate derivatives is a zero-sum game, the CIP deviations may have large welfare implications because of the implied deadweight cost borne by firms seeking to hedge their cash flows”; and that the wedge between cash- and swap-market rates “affects the external transmission of monetary policy.” But the boundary is stated plainly: “The welfare cost of the CIP deviation is behind the scope of this paper; it would necessitate a general equilibrium model. Yet, even without such model, the CIP condition is a clean laboratory to test the impact of financial frictions in a very general framework” (Section 6, p. 43).