The Dollar, Bank Leverage, and Deviations from Covered Interest Parity

The puzzle is the persistence of riskless arbitrage in the deepest market in finance; the flaw is that the textbook argument has no banks in it. “CIP is perhaps the best-established principle in international finance, and states that the interest rates implicit in foreign exchange swap markets coincide with the corresponding interest rates in cash markets. Otherwise, someone could make a riskless profit by borrowing at the low interest rate and lending at the higher interest rate with currency risk fully hedged. However, the principle broke down during the height of the 2008-2009 crisis. After the Great Financial Crisis (GFC), CIP deviations have persisted and have become more significant recently, especially since mid-2014” (Introduction, p. 1). The diagnosis: “In competitive markets, market participants are price takers, and can take on any quantity of goods at the prevailing market price… The failure of CIP would thereby open up the possibility of unlimited riskless profits. However, in textbooks, there are no banks. In practice, though, such arbitrage typically entails borrowing and lending through banks, and the competitive assumption is violated due to balance sheet constraints that place limits on the size of the exposures that can be taken on by banks. Even for non-banks, their ability to exploit arbitrage opportunities rely on banks to provide leverage. Hence, if deviations from CIP persist, it must be because banks do not or cannot exploit such opportunities” (p. 1). That last sentence is the paper’s pivot: it converts a pricing anomaly into a question about bank balance sheet capacity.

That the dollar spot exchange rate is a barometer of risk-taking capacity, and hence a determinant of bank leverage. “The key message of our paper is that the value of the dollar plays the role of a barometer of risk-taking capacity in capital markets. In particular, it is the spot exchange rate of the dollar which plays a crucial role. Deviations from CIP turn on the strength of the dollar; when the dollar strengthens, the deviation from CIP becomes larger. To the extent that CIP deviations turn on the constraints on bank leverage, our results suggest that the strength of the dollar is a key determinant of bank leverage” (Introduction, p. 1). The conditional clause is load-bearing – the inference to bank leverage runs through the assumption that CIP deviations reflect leverage constraints, which is an interpretation the paper argues for rather than a measured quantity. The descriptive fact is stated plainly: the cross-currency basis “is the mirror image of dollar strength. When the dollar strengthens, the CIP deviations widen. This is especially so in the last 24 months, reflecting the stronger dollar” (p. 2).

Ten currencies with daily turnover above $2 trillion, 1 January 2007 to 2 February 2016, with a mostly negative basis (Section 3.1, pp. 9-10). The currencies are “the Australian dollar, the Canadian dollar, the Swiss franc, the Danish krone, the euro, the British pound, the Japanese yen, the Norwegian krone, the New Zealand dollar, and the Swedish krona,” with raw data from Bloomberg. The basis is defined “as the difference between the US Libor and the implied dollar interest rate by swapping foreign currency into dollars.” On average it is negative, “which suggests that the dollar interest rate in the cash market is lower than the implied dollar interest rate in the swap market, and banks can borrow dollars in the cash market and lend dollars in the swap market to make arbitrage profits.” The exceptions matter later: “The average three-month basis is positive for the Australian and the New Zealand dollar, but negative for all other currencies, ranging from -11 to -62 basis points. The average five-year basis is positive for the Australian, the New Zealand, and the Canadian dollar, and negative for all other currencies.”

A one percentage point dollar appreciation goes with a 2.1 to 2.6 basis point narrowing of the basis, against a daily standard deviation of about 7 basis points (Section 3.2.1, p. 11). “The coefficient estimate on the change in the dollar is negative and significant across all specifications, suggesting that a dollar appreciation is associated with a more negative cross-currency basis, and, hence, greater CIP deviations. In terms of the magnitude, the coefficient estimate… in Column 1 (excluding additional control variables) implies that a one percentage point appreciation of the US dollar is associated with a 2.6 basis point decrease in the cross-currency basis… After including all controls, a one percentage point appreciation of the dollar is associated with a 2.1 basis point decrease… Given that the standard deviation for daily changes in the cross-currency basis is about 7 basis points, the impact of the broad dollar index on the basis is not only statistically significant but also economically meaningful.” The authors add a methodological remark in their own favour: “These results are especially remarkable, because they draw on daily changes in the cross-currency basis and spot exchange rates, which are notoriously noisy.”

Yes, and the dollar alone accounts for about a fifth of the variation in the five-year basis (Section 3.2.2, pp. 13-14). “The significantly negative correlation between changes in the cross-currency basis and the strength of the dollar is not restricted to short-dated contracts at the daily frequency… the coefficient on the change in the dollar is significantly negative in all specifications ranging from -1 to -1.4. Thus, a one standard deviation increase of quarterly changes in the broad dollar index (3%) corresponds to a 3-4 basis point reduction in the five-year cross-currency basis. In addition, the change in the dollar as a standalone variable already explains 19% of time series variations in the changes of the five-year basis.” The control variables behave differently at the two frequencies, which the authors report rather than smooth over: “the level and changes of the VIX index do not enter significantly,” and “most of the other control variables that are significant in our daily regressions lose their significance in quarterly regressions,” while the Treasury yield spread “remains significant, but with the opposite sign compared with the daily regression.”

No – the authors rerun everything from January 2009 and get similar or stronger results, though they report this as unreported regressions. “In unreported regressions, we find that these results are not driven by the GFC. We repeat all daily and quarterly regression specifications for the subsample starting in January 2009 and obtain negative coefficient estimates on the change in the dollar of similar magnitude at even higher levels of statistical significance. In sum, we find that when the dollar appreciates, the cross-currency basis becomes more negative, which entails larger arbitrage opportunities of borrowing dollars in the cash market and lending dollars via the FX swap market” (Section 3.2.2, p. 14).

That dollar betas price the cross-section of CIP arbitrage returns, because the trade carries mark-to-market risk correlated with the dollar even though its terminal payoff is certain (Section 3.3, pp. 15-16). Currency-specific betas come from regressing changes in each basis on changes in the broad dollar index; “the dollar beta is significantly negative for most currencies,” with the Australian dollar excepted at three months, and the Australian, Canadian and New Zealand dollars excepted at five years. The pricing test regresses the mean basis on the beta, and the reasoning for expecting a positive slope is set out carefully: “an arbitrageur’s expected return on the CIP trade, which consists of borrowing the dollar and investing in the foreign currency, is equal to the negative of the basis. However, the return on the strategy is certain only if the arbitrageur holds the trade until maturity. During the life of the trade, the arbitrage strategy is subject to mark-to-market risks, which are in turn correlated with the strength of the dollar to different extent. If the dollar is a global risk factor in the arbitrageur’s pricing kernel, higher systematic loadings on the dollar factor (a more negative dollar beta) require higher expected returns, or a more negative cross-currency basis.” This is the paper’s reconciliation of “risk-free arbitrage” with a risk premium: the profit is riskless only to a holder who can sit on the position, and the constraint is precisely that banks cannot.

Very strong, with correlations of 85 and 97 percent and a slope the authors translate into expected returns (Section 3.3.1, p. 16). “We can see a strong positive relationship between the average basis and the dollar beta with a bivariate correlation equal to 85% for the three-month basis and 97% for the five-year basis… An increase in the magnitude of the dollar beta by 1 corresponds to an increase in the expected returns of 11 basis points based on three-month CIP deviations and 26 basis points based on five-year CIP deviations. Taking together, these findings suggest that the aggregate dollar exchange rate acts as a risk factor that is priced in the cross section of CIP arbitrage returns. The cross-currency basis with more systematic exposure to the dollar tends to have higher expected returns for the CIP trade.” Note the calibration: the dollar “acts as a risk factor that is priced,” which is a statement about a cross-sectional relationship in ten currencies, not an identified causal claim.

That the currencies most exposed to the dollar factor are the safe havens, not the carry currencies. “The CIP deviations of different currencies have differing exposures to the dollar factor. Interestingly, we document a reversal of roles. The classical ‘safe haven’ currencies, such as the Japanese yen and the Swiss franc, have the highest exposure to the dollar factor, and high-yielding ‘carry’ currencies, such as the Australian dollar and the New Zealand dollar, have the lowest exposure to the dollar factor. Currencies with higher exposure to the dollar factor exhibit larger CIP deviations and thereby offer greater potential arbitrage profits for banks” (Introduction, p. 2). This is a reversal relative to the currency risk-premium literature, where the carry currencies are the risky ones – here the ranking on the dollar factor runs the other way.

A genuine out-of-sample test with a sharp, documented result: the basis widened for every G10 currency and the post-event dollar beta correlated 98 percent with the basis. “Our main sample ended before the U.S. presidential election on November 8, 2016. The appreciation of the dollar after the election presents an opportunity to put the main predictions to an out-of-sample test” (Section 3.3.2). The addendum reports that “the broad dollar index of the Federal Reserve rose by 3.9% between 8 November and 29 November. During the same period, the cross-currency basis widened for all G10 currencies. The largest movement was for the yen, with the basis widening from -70.3 basis points to -90.5 basis points. For the post-election period, the ‘dollar beta’ is defined as the ratio of the change in the cross-currency basis (in basis points) over changes in the broad dollar index (in percentage points). In line with the findings in Avdjiev, Du, Koch and Shin (2016), the dollar beta is highly correlated with the basis itself. The correlation coefficient is 98%.” The pattern in the reported table is monotone in the expected way: the Australian and New Zealand dollars, with positive bases, have positive betas (0.64 and 0.70), while the yen, krone and franc, with the most negative bases, have the most negative betas (-5.18, -4.14, -3.97). One caveat the reader should carry: with the beta here defined as a ratio of the two changes over a single episode, the high correlation with the level of the basis is a cross-sectional fact about ten points rather than an independent statistical test.

That it falls when the dollar strengthens, and that the broad index matters beyond the bilateral rate (Section 4.1, pp. 22-23). The benchmark panel regresses quarterly growth in dollar-denominated cross-border lending to a borrowing country on changes in the broad dollar index and the bilateral dollar rate, with borrowing-country fixed effects to “control for heterogeneity on the demand side of cross-border credit.” Results are reported for Q1 2002-Q3 2015 and Q1 2007-Q3 2015: “When entering the regression as a standalone variable, the estimated coefficient on the dollar index is negative and statistically significant. The same is true for the coefficient on the bilateral dollar exchange rate. Moreover, both of the above variables remain negative and strongly statistically significant even when jointly entering the regression. Our results therefore show that the dollar index has explanatory power over and above the bilateral dollar exchange rate for cross-border bank lending. This finding strongly supports our previous hypothesis that the dollar is a global risk factor, which affects the risk-taking capacity of banks, and, ultimately, the supply of cross-border bank lending. The above results hold not only for lending to all sectors but also for distinct subsamples of bank and non-bank lending.” A rolling-window exercise shows the relationship “has been strong throughout the sample period,” having “gradually strengthened over the decade leading up to the GFC and reached a peak in 2008 during the acute phase of the crisis” (Introduction, p. 3). A structural panel VAR over Q1 2002-Q3 2015 traces the response of cross-border lending to a one standard deviation exchange rate shock, with 95 percent confidence intervals from 1,000 Monte Carlo draws.

By the joint sign pattern: credit quantity falls while the price of balance sheet capacity rises, which demand alone would not deliver. “This empirical regularity has several potential drivers, both on the demand for dollar credit on the part of borrowers as well as on the supply of dollar credit by lenders. The negative relationship between dollar credit, a proxy for bank leverage, and the magnitude of CIP deviations, the price of balance sheet capacity, point in favor of supply drivers” (Introduction, p. 4). The mechanism invoked is the risk-taking channel: “When there is potential for valuation mismatches on borrowers’ balance sheets arising from exchange rate changes, a weaker dollar flatters the balance sheet of dollar borrowers, whose liabilities fall relative to assets. From the standpoint of creditors, the stronger credit position of borrowers reduces tail risks in the credit portfolio and creates spare capacity for additional credit extension even with a fixed exposure limit through a value-at-risk (VaR) constraint or economic capital constraint.” A simple model is sketched “to illustrate that a stronger dollar increases the shadow cost of bank balance sheet capacity, and therefore reduces the supply of dollar credit and increases CIP deviations” – illustrative rather than estimated. The borrowing-country fixed effects in the lending panel are the design element carrying the demand-side control.

That a stronger dollar hurts bank equity, and hurts it most where the basis is most negative (Section 6, p. 33). The sample is 51 internationally active banks in G10 currency areas, in panel regressions with bank fixed effects of local-currency equity returns on quarterly broad dollar movements. “A 1% appreciation of the broad dollar index is associated with a 2% decline in bank equities. Once we control for the market returns… the change in the broad dollar remains significant: a 1% appreciation of the broad is still associated with 0.27% decline in bank equities.” The interaction test is the one that supports the mechanism: “The coefficient on the interaction term is significantly positive, which indicates that bank equities in countries with a more negative cross-currency basis respond more negatively to a dollar appreciation. The coefficient on the change in the broad dollar is very small and no longer significant once the interaction term is added. This suggests that for countries with the cross-currency basis equal to zero (e.g. the United States), bank equities are not significantly correlated with movements in the dollar after controlling for the market returns. For countries with a positive basis, such as the Australia, bank equities actually respond positively to a dollar appreciation after controlling for benchmark equity index returns.” The sign flip for positive-basis countries is a real prediction of the mechanism rather than a nuisance, which is why it is worth carrying.

Post-crisis, no – the euro exhibits the same triangle, but other major currencies do not. “We show that similar relationship between the exchange rate, the cross-currency basis and cross-border bank lending can also be found for the euro in the post-crisis sample. This is the case despite the fact that the triangular relationship is absent for other major currencies, which points to the unique role of international funding currencies in affecting leverage and risk-taking via fluctuations in exchange rate valuations” (Introduction, p. 4). The euro result is also time-varying in a way that supports the funding-currency reading: “During the pre-crisis (2002-2007) period, the impact of fluctuations in the euro exchange rate on cross-border bank lending denominated in euros was not statistically significant (and, at times, was even positive). Nevertheless, the post-crisis period has seen a sustained dive of the estimated impact coefficients into negative territory… In summary, in the post-crisis sample, we find a triangular relationship for the euro that is similar to the one that exists for the US dollar” (Section 4.3, pp. 26-27). The conclusion states it as an emergence rather than a parity: “we also find evidence that the euro has started to exhibit characteristics of a global funding currency in the period after the Great Financial Crisis” (Section 7, p. 35).

It runs the other way, which is the paper’s broader point for macroeconomics. “One possible explanation for our results is related to the financial channel of exchange rates, through which fluctuations in the strength of the dollar set in motion changes in capital market intermediation spreads that respond at a high frequency. The net exports channel of exchange rate changes is standard in open economy macro models, but the financial channel is less standard, and may operate in the opposite direction to the net exports channel. Under the net exports channel, it is when the domestic currency depreciates that real economic activity picks up. By contrast, the financial channel appears to operate in the opposite direction; it is when the domestic currency appreciates, financial conditions in that country loosen, and CIP deviations narrow” (Introduction, pp. 2-3). Note the hedges the authors keep: this is “one possible explanation,” and the channel “appears to operate” in that direction. The conclusion states the interpretation as an argument rather than a measurement: “We interpret the magnitude of CIP deviations as the price of bank balance sheet capacity and dollar-denominated credit as a proxy of bank leverage, and argue that such a triangular relationship exists because of the impact of the dollar on the shadow price of bank leverage” (Section 7, p. 35).