Breakdown of covered interest parity: mystery or myth?

That the persistent cross-currency basis is the rational output of a swap dealer adjusting unsecured money market rates for a risk the swap does not carry – so it is “no mystery,” and calling it evidence of market malfunction is a “myth.” The abstract states both halves: “We argue that the phenomenon is no mystery but merely a reflection of the different risks involved between money market and CCBS transactions in the post-crisis era. Empirical results based on seven major currency pairs support our hypothesis that the swap dealer behaves as if he tries to align the risks of the transactions in pricing CCBSs, which causes CIP to break down. We also find that the basis spreads are well arbitraged among the currency pairs, which suggests they are fairly priced. Hence, it is a myth that CCBS basis spreads or CIP deviations are evidence of the market not functioning properly.” Note the load-bearing hedge in the empirical claim: the dealer “behaves as if he tries to align the risks” – a behavioural-equivalence statement, not a claim about dealers’ intentions. The conclusion is careful in the same way: “The breakdown of CIP is more of a myth in the sense that the returns on investing in different currencies are no longer the same even after exchange rate risk is covered. True, exchange-rate-risk-covered returns, taken at face value, are no longer the same because the uncovered returns, as commonly represented by Libors in testing CIP, consist of considerable counterparty and liquidity risk premiums in today’s money market” (Section 7, p. 23). The paper does not claim CIP measured on Libor holds; it claims that measurement is the wrong test.

Because it converts two unsecured money market loans into secured ones, removing exactly the risk that Libor is priced to compensate. “The presence of counterparty risk is extremely important for unsecured lending/borrowing, as the lending party can end up getting nothing back if the other party defaults on the loan. However, swaps are different. They are secured transactions; both parties to the swap do not take counterparty risk. As principals are exchanged at inception, counterparty risk is largely eliminated since the parties effectively hold each other’s loan as collateral” (Introduction, pp. 1-2). The authors qualify this precisely rather than overclaim: “Counterparty risk refers to the risk of default on each other’s loan in this paper. Both parties, however, still take the counterparty risk of the swap itself, which is negligible compared to that of the loan” (fn. 2). They also flag that this is the specific feature distinguishing cross-currency from single-currency swaps: “the cross-currency swap (i.e., FX swap and CCBS) market differs from the single-currency swap (i.e., IRS) market in that principals are exchanged in the former but not in the latter” (p. 3).

Quoting the forward premium. Pre-crisis it was the raw Libor differential; post-crisis it must be adjusted, because the swap is collateralised on both legs. “It was a simple task before the GFC, as there was little concern for counterparty risk. All the dealer had to do was to multiply the spot exchange rate of the two currencies by their interest differential based on benchmark money market rates such as the Libors. In doing so, he is applying CIP” (pp. 1-2). The authors’ reductio: “If the dealer continues to quote the forward premium as he did in the past, then CIP would continue to hold. But this makes no sense, as CIP would then imply that the dealer ignores the fact that the FX swap effectively converts the two unsecured money market loans into secured ones” (p. 2). The symmetry argument that produces the adjustment: a dealer lending against foreign cash collateral “would ceteris paribus be willing to lend at an interest rate that is lower than the benchmark money market rate. But in an FX swap, the dealer also simultaneously borrows from his client in foreign currency. Therefore, he should equally enjoy a lower foreign interest rate… Therefore, in calculating the forward premium, it is only rational for the dealer to adjust the old benchmark interest differential by an amount equivalent to what he judges to be the difference between the two counterparty risk premiums. In this case, the forward premium he quotes for his client differs from what he would quote in the past (unless the two counterparty risk premiums happen to be the same). As a result, CIP does not hold. But this makes sense!” (p. 2). The parenthetical is important: the argument predicts a zero basis exactly when the two counterparty risk premiums coincide, which is why the sign and size of the basis should track the cross-country difference in those premiums.

Through the multi-curve model of interest rate swap pricing, which made the same move for single-currency swaps. “This is consistent with the multi-curve modeling approach to interest rate swap (IRS) pricing in finance literature. The classic single-curve model, which worked fine in the pre-crisis era, no longer works post crisis, as the Libor curve is no longer risk-free. This causes basis to occur even in the single-currency swap market… The multi-curve model tackles the issue by using risk-embedded curves (e.g., Libor-based curves) to calculate the expected future cash flows and a risk-free curve to discount them (Bianchetti, 2010; Mercurio, 2010; Grbac et al., 2015). This pricing methodology dates back to Tuckman & Porfirio (2003) but gains popularity in practice only after the GFC” (p. 3). The authors note the institutional turning point: the multi-curve model “has essentially become the standard market practice after LCH.Clearnet, which operates SwapClear, announced on June 17, 2010 that it would replace the Libor curve with the OIS curve to discount its entire IRS portfolio after extensive consultation with market participants” (fn. 8). They also use this as evidence against a dollar-specific reading: “The fact that bases have also emerged and persisted in the single-currency swap market for practically all currencies provides further evidence that the phenomenon is no privilege of the dollar… Basis is principally an outcome of swapping two interest rates whose underlying risks are not aligned with the nature of the transaction” (fn. 11).

Because the swap swaps liquidity risk rather than eliminating it, and OIS/repo/bond rates contain little of it. “The collateralized nature of the FX swap or CCBS transaction eliminates only the counterparty risks that are priced into the Libors but not the liquidity risks. The fact that both parties to the transaction swap their principals at inception means they still take a liquidity risk for the fund they lend but receive a liquidity premium for the fund they borrow. Hence, as the counterparty risk premiums in the domestic and foreign money market rates are removed, the difference between the liquidity risk premiums and the difference between the risk-free rates are left in the dealer’s equation” (pp. 3-4). The prediction that follows is the explanation for a fact other authors treat as decisive against credit-based stories: “This explains why there is still a basis or deviation when one replaces the Libor-differential in the CIP condition with risk-free or near risk-free interest differentials such as OIS spreads, repo spreads or government bond yield spreads (Bottazzi et al., 2013; Fukuda, 2016; Du et al., 2017). The reason is that these interest rates contain not only minimal counterparty risk premium but also negligible liquidity risk premium” (p. 4). Supporting evidence is cited from outside: “Rime et al. (2017) that CIP deviations based on OIS rates tend to co-move strongly with measures of liquidity premium differentials” (p. 4). The authors also caveat the liquidity premium in collateralised rates: it “depends on the market liquidity of the collateral asset or debt security concerned,” and the problem “will also be compounded by factors that affect the supply of, and demand for, the underlying security other than the opportunity cost of borrowing/lending, e.g., the convenience yield” (fn. 9).

The difference is about whether the driving factors are external to the reference rates or already inside them – and the authors say the accounts are largely compatible, not rival. They characterise the earlier literature: during and after the crisis, foreign institutions needing dollars “found themselves shut off from the Libor market because US financial institutions were concerned about their counterparty risk… As a result, they had to resort to the FX swap and CCBS markets to obtain dollar funding, and paid a premium for it,” so that the basis “essentially reflects this dollar premium”; more recent work ties dollar shortage to “regulatory reforms introduced following the GFC, growing demand for dollar hedging, capital and balance sheet constraints, and even global imbalances, which have singly or jointly resulted in limits to arbitrage” (p. 4). Then the reconciliation: “many of these explanations are not necessarily inconsistent with ours. We concur that the basis is a consequence of certain factors or considerations that did not exist before the GFC. The difference, however, is they believe these factors or considerations are external to the reference interest rates used in the pricing of the swap, while we argue that, if any such factors or considerations exist, they would be translated into counterparty or liquidity risk in money market transactions and hence the reference interest rates” (p. 4). The quarter-end evidence is folded into their reading rather than disputed: “the quarter-end spikes in the basis as observed by Borio et al. (2016) and Du et al. (2017) are totally consistent with the quarter-end jumps we find in the Libor-OIS spread… To them, the greater importance accorded to quarter-end reporting and regulatory ratios following regulatory reforms makes it harder to take arbitrage at those times, which is reflected in the basis. For us, these pressures are detectable in the Libor-OIS spread as they translate into higher funding liquidity risk at quarter ends” (p. 5). This is a reinterpretation of shared evidence, not an alternative prediction that discriminates between the two accounts.

The forward premium regressed in first differences on each currency’s OIS and IRS rates, with two restrictions the theory implies (Section 5.1, pp. 14-15). Because the dependent variable and all four regressors have a unit root, the unrestricted model is in first differences: the change in the forward premium on the changes in foreign and domestic OIS and IRS rates plus a constant. The interpretation of coefficients is structural: “the absolute values of the coefficients of the risk-free rates… represent the shares of counterparty risk premium in the total risk premium… and the absolute values of the coefficients of the interbank borrowing rates… represent the shares of liquidity risk in the total risk premium.” Three hypotheses follow: the constant is zero, and the coefficients on each currency’s IRS and OIS sum to unity (with the appropriate sign). The underlying decomposition is stated as a hypothesis, not an identity: “we hypothesize that Libor (or IRS in the long-run) can be decomposed into three components, namely the risk-free rate, the counterparty risk premium, and the liquidity risk premium” (fn. 20). The authors note they could estimate the basis decomposition directly but choose the forward premium because “the approximate equality will probably generate less-trustworthy results.”

Seven pairs at five-year tenor, roughly late 2009 to mid-2017, with explicit outlier treatment and a documented sensitivity check (Section 5.2, pp. 16-17). “Like most previous studies, this paper focuses on the popular five-year tenor. The sample periods are defined by data availability, ranging from 1887 to 2029 observations in each regression. For USD/CHF and EUR/CHF, the sample period is from January 13, 2010 to June 30, 2017, as the CHF OIS rate is only available from January 13, 2010. For the rest of the currency pairs, the sample period covers September 22, 2009 to June 30, 2017, as the five-year USD IRS rate is only available starting from September 21, 2009.” Outliers “lying five or more standard deviations away from the mean are deleted,” which “still captures 99.0-99.7% of the full sample across all data series,” and cutoffs of three and four standard deviations “change little”; winsorised results at the 0.5/99.5 percentiles are reported as a robustness check and are “broadly consistent” (fn. 26, fn. 31). Non-USD exchange rates are computed from USD rates rather than taken directly, “as data quality for USD exchange rates is much better due to larger trading volumes” (fn. 23), and the three-month JPY IRS – unavailable for lack of an active market – is proxied by subtracting the three-for-six-month basis swap spread from the six-month IRS (fn. 25). The chosen pairs are not arbitrary: “the average daily turnover of CCBS involving these currencies accounted for 79.16% of the total in April 2016, and 78.90% in April 2013” (fn. 22).

Yes, and it tests rather than assumes that OLS is admissible. “The concern about endogeneity arises from simultaneous causality between the forward premium and the four interest rates, as the forward premium may arguably also affect the interest rates.” The authors state their prior – “While the (spot) exchange rate and the interest rates of the two countries concerned are likely to be co-determined, it is hard to imagine the same applies to the relationship between the forward premium (the difference between the spot and forward exchange rates) and the interest rates” – but then test it: they estimate by GMM treating the four rates as endogenous, instrumenting with one- to five-day lags of domestic and foreign government bond yields, domestic and foreign bank CDS spreads and the VIX in first differences, and run a Durbin-Wu-Hausman test. “The results show we cannot reject the null hypothesis that these variables are exogenous at the 10% or higher significance level for the seven currency pairs. This means the estimators in the OLS models are unbiased. Since the OLS estimators are more efficient than those in the GMM, we stick with OLS in our final estimation” (Section 6.2, pp. 20-21).

Broadly, with a documented set of statistical rejections the authors attribute to precision rather than misspecification. “The constant C0 in all regressions are extremely close to zero and statistically insignificant… most coefficients are highly significant in the unrestricted models with signs consistent with our expectation… all four coefficients in each regression fall between zero and one… the sum of the coefficients of IRS and OIS in the same currency is very close to unity.” The sums: “For the four currency pairs with a USD leg… the sum of the shares of counterparty and liquidity risk premiums for USD is 99.2%, 96.1%, 100.2% and 98.0% respectively. For the three currency pairs with a EUR leg… the sum for EUR is 100.3%, 100.1% and 98.5% respectively” (Section 6.2, p. 21). The formal tests are reported honestly: “eight out of the 14 tests show that we cannot reject hypotheses 2a or 2b at the 10% or higher significant levels. For the other six tests, while we can reject the hypothesis, it is worth noting that the rejection is mainly caused by the small size of the standard errors” – a plausible reading, but one the paper asserts rather than demonstrates. Fit is described as “surprisingly good, considering that the variables are in the form of first differences,” with adjusted R-squared “between 0.62 and 0.80 for most regressions except for EUR/CHF (0.36) and EUR/JPY (0.52).”

That the counterparty share is small for the dollar and large for the other currencies, which is what makes the dollar bases negative. Averaged over the four dollar pairs in the unrestricted model, the counterparty risk premium accounts for 22.3 percent of the total risk premium in USD Libor and 75.8 percent in EUR Libor; the restricted model gives 23.7 and 76.7 percent, “which are close to their unrestricted counterparts” (Section 6.2, pp. 21-22). Pair by pair, “the share of counterparty risk premiums for USD is 17.5%, 18.9% and 16.1% when the other leg is the EUR, CHF and JPY respectively; that for EUR is 76.2%, 79.9%, 71.0% and 76.1% when the other leg is USD, GBP, CHF and JPY respectively,” with sterling the outlier: “the share of counterparty risk premium for USD vis-à-vis GBP is 36.8%, which is still small but somewhat larger when compared to the other currencies.” The stability across pairs is itself treated as evidence: “the share of counterparty risk premium associated with any currency is relatively stable regardless of which currency is in the other leg,” suggesting “the share of counterparty risk premium is perceived to be fairly consistent across the non-USD currencies.” The conclusion draws the sign implication: “liquidity risk premium, on average, accounts for a much greater proportion relative to counterparty risk premium for USD, while the other way round is true for the other currencies. Hence, the USD lender (cum foreign currency borrower) tends to receive a greater discount from the foreign currency loan, causing the CCBS bases to be negative” (p. 23). One internal discrepancy is worth the reader’s attention: the introduction presents the 22.3 percent and 75.8 percent figures as pertaining specifically to USD/EUR (“For USD/EUR, for example, we find that, in this period, the counterparty risk premium, on average, accounts for about 22.3% of the total risk premium embedded in the USD Libor”), whereas Section 6.2 reports 17.5 percent for USD in the USD/EUR pair and identifies 22.3 percent and 75.8 percent as the unrestricted-model averages – which is consistent with the four pair-specific USD figures (17.5, 36.8, 18.9, 16.1) and EUR figures (76.2, 79.9, 71.0, 76.1) averaging to exactly those values. The Section 6.2 reading is the one the numbers support.

That the bases across currency pairs are mutually consistent, which the authors read as fair pricing rather than arbitrary pricing. The basis matrix implies “that for any three currencies, the difference between the bases of any two of them vis-à-vis the third one is equal to the basis involving these two currencies,” and the market data bear this out: “the difference between the USD/EUR and USD/GBP bases… is always almost the same as the EUR/GBP basis traded in the market,” and likewise for the franc and yen pairs. “In our view, this is no coincidence. There must be players actively taking arbitrage in the market, which is reminiscent of what occurs in the FX market” (Section 6.1, pp. 17-18). The inference and its limit are both stated: the relationship “suggests that the CCBS market is well arbitraged, though not in the sense of eliminating the basis, and that the bases are not arbitrarily determined but fairly priced,” with the explicit qualification that “the triangular relationship does not imply that CIP holds, as the triangular arbitrage is different from the conventional CIP arbitrage” (fn. 10).

That non-zero bases persist for pairs with no dollar leg, and that the dollar-leg bases differ substantially from one another. “We have also shown that the so-called market anomaly exists not only in the CCBSs with a dollar leg but also in those without one. This finding poses a challenge to the economists who argue that CIP deviation or CCBS basis is attributable to a global shortage of US dollars or reflects the role of the US dollar as a global funding currency, for if it were purely a dollar phenomenon there is no reason why the CCBS bases vis-à-vis USD are considerably different from each other or why cross CCBS bases (i.e., those CCBSs without a dollar leg) are non-zero” (Section 7, p. 24). The same point in the introduction is framed as a challenge to a notion rather than a refutation: “the persistence of the bases (especially those between two non-USD currencies) and the considerable differences among them (even between the currency pairs with a USD leg) challenge the notion that CIP deviation or CCBS basis is essentially a dollar phenomenon” (p. 5). It is worth noting that the euro-leg bases are themselves derived within the same triangular structure as the dollar-leg ones, so their non-zero values are consistent with, rather than independent of, a dollar-centred account.

That limits-to-arbitrage explanations remain possible, and that the Libor-OIS spread is an imperfect measure which likely understates the risks it is being used to decompose. On the first: “We argue that the well-arbitraged non-zero bases are driven by the difference between the counterparty risks of the two money markets concerned but acknowledge the possibility that they are determined by the limits to arbitrage caused by plausible constraints such as capital charges resulting from recent regulatory reforms” (p. 5) – an explicit acknowledgement that the paper’s evidence does not exclude the account it is arguing against. On the second: “an important caveat to the estimates of the shares of these risk premiums is how well the Libor-OIS spread can represent the risks involved for CCBS pricing… Admittedly, the Libor-OIS spread is not a perfect measure of the risks for the CCBS market. First, the Libor scandal is well known and therefore its reliability as a measure of the cost of funding accessible by banks in general seems questionable (Hou & Skeie, 2014). Second, there is a considerable difference in the composition between the Libor and CCBS markets. The Libor market consists of mainly banks, while the CCBS market is composed of a wide range of financial and non-financial institutions, including banks, insurers, investment managers, hedge funds and large corporations. It is clear, therefore, that most of the CCBS market participants are unable to access funds at Libors on an uncollateralized basis. As a result, the risks are likely to be underestimated. Nonetheless, the spread is still arguably the best available measure” (Section 6.2, p. 22).