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.

Nikolai Roussanov | Macro Paper Warehouse

Common Risk Factors in Currency Markets