Adrien Verdelhan | Macro Paper Warehouse

Common Risk Factors in Currency Markets

The starting claim is that currency risk premia are a robust feature of the data, survive transaction costs, and are determined by exposure to a single global risk factor for which the interest rate itself is the measure of exposure. (The figures below come from the freely available NBER working-paper version of June 2008, which is the full text this summary was built from; the published version appeared in the Review of Financial Studies in 2011.) The empirical design is a cross-sectional sort rather than the usual time-series test: at the end of each month all currencies for which forward contracts trade are allocated to six portfolios by their forward discount – which equals the interest differential when covered interest parity holds – so portfolio 1 holds the lowest interest rate currencies and portfolio 6 the highest, and portfolios are rebalanced monthly. This matters for interpretation, because the classic UIP failure documented by Hansen-Hodrick and Fama concerns currencies whose rates are higher than usual, whereas here “our investment strategy only considers whether the currency’s interest rate is currently high.” The sample is 37 currencies from end-1983 to early 2008, growing from 9 countries to 26 with a maximum of 34, with a 15-country developed subsample as a robustness check; returns are computed from spot and one-month forward contracts net of bid-ask spreads. The basic magnitudes: portfolio 1 currencies trade at an average forward discount of -390 basis points but appreciate by only about 100 basis points, giving a log excess return of -290 basis points; portfolio 6 currencies trade at a discount of 778 basis points but depreciate only 188, giving +590 basis points. Net of transaction costs the spread between the first and last portfolio is 483 basis points a year with a Sharpe ratio of 0.54 – against 7.11 percent and a Sharpe ratio of 0.48 for the Fama-French US market excess return over the same period, which does not net out any transaction costs. In the developed-country subsample the long-short Sharpe ratio is 0.39. A principal component analysis of the six portfolio returns yields two factors explaining more than 80 percent of return variation: a level factor (70 percent of common variation, all portfolios loading equally) that is essentially the average portfolio return, labelled the dollar factor RX, and a slope factor (over 12 percent) with monotonically increasing loadings, essentially portfolio 6 minus portfolio 1, labelled HML_FX. Cross-sectional asset pricing on the six portfolios gives an adjusted R-squared of 69 percent with a root mean squared error around 95 basis points and no rejection of the null that pricing errors are zero. The estimated market price of HML_FX risk is 546 basis points per annum against a sample factor mean of 537 – a nine-basis-point gap, which is what linear factor pricing requires since the factor is itself a traded return. HML_FX betas rise monotonically from -0.39 for portfolio 1 to 0.61 for portfolio 6, so low interest rate currencies insure US investors against this risk while high interest rate currencies expose them to it. The dollar factor’s price (135 basis points, mean 136) prices the average level of returns but none of the cross-section. Three further results tie the pieces together: sorting currencies instead on their estimated HML_FX betas recovers monotonically increasing forward discounts and excess returns, so the interest rate really is measuring exposure; the carry factor also prices momentum portfolios, which supports a risk-based rather than characteristic-based reading; and the average forward discount across portfolios predicts returns better than portfolio-specific discounts, with forecast excess returns on medium-to-high interest portfolios moving counter-cyclically against US industrial production, payrolls and help-wanted indices and positively with term and default premia and the VIX. A no-arbitrage exponentially-affine model with a country-specific and a common SDF factor reproduces this, but only under two conditions: a common factor must exist, since it is “the only source of cross-sectional variation in currency risk premia,” and low interest rate currencies must load more on the common factor when the price of common risk is high. Heterogeneity in country-specific loadings alone cannot do the job.

Deviations from Covered Interest Rate Parity

Covered interest rate parity is the no-arbitrage relation that pins the forward exchange rate to the spot rate and the interest differential; the paper’s own description is that it is “presented in all economics and finance textbooks and taught in every class in international finance.” This paper documents that it is systematically and persistently violated among G10 currencies after the 2008 crisis, establishes that the violations are genuine arbitrage rather than compensation for credit risk or transaction costs, and traces them to the cost of using a bank balance sheet. (The magnitudes cited here come from the February 2017 NBER working-paper version, the freely available full text this summary rests on; the published version appeared in the Journal of Finance in 2018.) The scale of the market matters for how surprising this is: $61 trillion notional outstanding and $3 trillion average daily turnover. Over 2010-2016 the average annualised absolute Libor cross-currency basis is 24 basis points at three months and 27 basis points at five years, but those averages conceal a lot – the five-year yen basis was close to -90 basis points at the end of 2015, larger in magnitude than the roughly -70 basis point five-year Libor differential between Japan and the United States. Two moves rule out the standard explanations. The credit-risk story, that interbank panels differ in creditworthiness, is tested directly on panel banks’ CDS spreads and finds little support; more decisively, the authors recompute the basis on instruments with no credit-risk difference at all – general collateral repos, which are fully collateralised, and Kreditanstalt für Wiederaufbau bonds, fully backed by the German government – and the basis survives. The repo basis is persistently and significantly negative for the yen, Swiss franc and Danish krone, ranging from -16 basis points for the euro to -36 for the Danish krone, and the KfW basis is significantly non-zero for the euro, Swiss franc and yen (about -14, -24 and -30 basis points) while being effectively zero for the Australian dollar. Net of measured transaction costs, the resulting arbitrage profits run from 9 to 20 basis points annualised, with standard deviations of 5 to 23 basis points – small numbers, but with zero conditional volatility over the fixed investment horizon, so the Sharpe ratios are infinite. On explanation, the paper advances a two-factor hypothesis: costly post-crisis financial intermediation, which explains why the deviations are not arbitraged away, plus persistent international imbalances in funding supply and investment demand across currencies, which explains why the basis lines up with the level of nominal rates. Four empirical characteristics follow. First, the deviations spike at quarter ends, and the timing is sharp in a way that identifies the mechanism: the one-month deviation jumps exactly one month before quarter end, the one-week deviation exactly one week before, while a three-month contract – which appears on a quarter-end report whenever it is executed – shows no such pattern. Second, using the Fed’s interest on excess reserves in place of Libor/OIS/repo as the direct dollar funding cost, as a proxy for the shadow cost of leverage, explains about one-third of the one-week deviations; also investing at foreign central banks’ deposit facilities shrinks the average basis from -26 (Libor) and -28 (OIS) basis points to -8, which the conclusion describes as accounting for two-thirds of the deviations – while still leaving -12 to -15 basis points for the krone, franc and yen. Third, the basis is positively correlated with the level of nominal interest rates, with a 89 percent correlation between five-year Libor bases and five-year Libor rates across G10 currencies, so the hedged arbitrage trade is long low-rate and short high-rate currencies – exactly the reverse of the unhedged carry trade. Fourth, the basis co-moves with other near-risk-free fixed-income spreads, notably the KfW-over-bund basis and the US Libor tenor basis. The authors are careful about what they have and have not shown: they present “the first international evidence on the causal impact of recent banking regulation on asset prices,” but state that assessing the welfare cost “is behind the scope of this paper; it would necessitate a general equilibrium model.”

Does Incomplete Spanning in International Financial Markets Help to Explain Exchange Rates?

Standard international macro-finance models assume complete spanning, in which case the change in the real exchange rate must exactly equal the difference between the foreign and domestic investor’s marginal utility growth. Almost nobody believes markets really are complete, so this paper asks how much of the exchange rate evidence the missing markets could account for. The authors adopt the perspective of an econometrician who has committed to some model for the domestic and foreign log stochastic discount factors and takes observed macroeconomic quantities as given, and then, following Backus, Foresi, and Telmer (2001), insert a stochastic “FX wedge” between the exchange rate change and the difference in discount factors. To make the exercise an upper bound on what incompleteness can do, they allow the most extreme departure they can write down: domestic investors may hold only the foreign risk-free asset (equivalently, only one-period forward currency contracts), with no access to any foreign risky asset, and symmetrically for foreign investors, so that only two Euler equations discipline the wedge. Those two Euler equations turn out to force the wedge to be procyclical, which means it always lowers exchange rate volatility relative to complete markets – one-for-one in variance. Measured on quarterly data for 15 developed countries over 1973.IV-2014.IV, average annualized bilateral exchange rate volatility is 11 percent (11.21 percent, standard error 0.44), the correlation between real exchange rate changes and relative consumption growth is not statistically different from zero, and the carry trade earns an average annualized excess return of 4.4 percent with a Sharpe ratio of about 0.5. Starting from a maximum Sharpe ratio of 0.50 in each country and a generous cross-country stochastic-discount-factor correlation of 0.50, matching the 11 percent volatility requires a wedge with an annualized standard deviation of 49 percent – as large as the maximum Sharpe ratio itself, and larger still (at least 70 percent) if the discount factors are uncorrelated. That same wedge cuts the model’s currency risk premium from about 12 percent to below 6 percent, and to essentially zero or negative for zero or negative wedge drifts; the drift values large enough to preserve an empirically plausible risk premium make the correlation between exchange rates and consumption growth larger in absolute value than under complete markets (above 0.7 with a risk aversion coefficient of 10), which is the opposite of what the cyclicality puzzle requires. The result survives dropping lognormality: in an entropy-based generalization, and in calibrated Merton (1976) jump and Barro-Rietz consumption-disaster models, no admissible wedge delivers both a plausible exchange rate volatility and a significant risk premium. Imposing dynamic no-arbitrage discipline makes things worse rather than better: in a Cox-Ingersoll-Ross specification the wedge’s drift ceases to be a free parameter, a 50 percent reduction in exchange rate volatility implies a 75 percent reduction in the currency risk premium, and the uncovered-interest-parity slope coefficient is always pushed toward one. The authors are careful about what this does and does not show – they hold the projection of the discount factor on domestically traded assets fixed and so do not claim that incomplete-market models are uninteresting, only that incomplete spanning across borders cannot by itself resolve the three puzzles together.