FX carry trading strategies only use short-term interest rates (and forward basis) as signal. Yet both theoretical and empirical research suggests that the whole relative yield curve contains important information on monetary policy and risk premia. In particular, the curvature of a yield curve indicates – to some extent – the speed of adjustment of the short rate towards a longer-term yield. Since relative curvature between two countries is therefore a measure of the relative trajectory of monetary policy it is a valid directional signal for FX trading. Indeed, recent empirical research suggests that this signal is statistically significant. A curvature-based trading rule produces higher Sharpe ratios and less negative skewness than conventional FX carry strategies.

*The post ties in with SRSV’s summary lecture on systematic value through macro trends, particular the section on using financial data.
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*The below are quotes from the paper. Emphasis, cursive text and the curvature graph have been added.*

### From carry trade to “curvy” trade

“High interest rate currencies are found to appreciate rather than depreciate over the short-term…__Carry trades exploit the empirical failure of uncovered interest parity__ by borrowing at low interest rates in one currency and investing the proceeds into a higher yielding currency…Traditional carry trade strategies do not account for any information embedded in the respective yield curves beyond short-term interest rates…This… stands somewhat in contrast to a __growing body of evidence which suggests that the yield curve contains… signalling power for future interest rates__… and…the exchange rate.”

“We offer an intuitive economic interpretation of the outperformance of curvy trade returns that is line with recent interpretations of the curvature factor.”

*N.B.: Curvature here is the amount by which a curve deviates from being a straight line: curvature is the rate of change of the slope or the rate at which a curve turns.*

“The yield curve’s curvature bears an unambiguous and forward-looking interpretation. Abstracting from term premia, __the curvature factor proxies the speed at which the short-rate converges to the long-rate (at a given level and slope)__ and can thus be related to the stance of monetary policy with a higher curvature indicating a more hawkish outlook for monetary policy and vice versa…In the same vein…an idiosyncratic shock to the curvature predicts an increase in short-term rates [*relative to previous expectations*] and hence a tightening of monetary policy over the quarters ahead.”

*N.B. High positive curvature also is consistent with a central bank expected to “over-tighten”, i.e. to raise rates so aggressively that short-term rates further in the future are expected to decrease again. Similarly, high negative curvature is consistent with a central bank expected to “over-ease”, i.e. to cut rates so aggressively that short-term rates further in the future are expected to rise again.*

“__If the domestic curvature is higher than the foreign curvature, domestic short-term interest rates are more likely to rise in the period ahead, even beyond expectations inherent in the expectation hypothesis__ of the term structure, forcing the domestic currency to appreciate vis-a-vis the foreign currency subsequently. This interpretation is consistent with the principle of uncovered interest parity (UIP) under exchange rate stationarity, according to which the level of the exchange rate today is determined by the expectation about future short term interest rate differentials.”

### Empirical evidence for the curvature signal

“The signals to buy and sell currencies are based on summary measures of the yield curve, the Nelson-Siegel factors…Nearly all __information embedded in the yield curve can be approximated by three nearly orthogonal factors… the level, slope and curvature__…We extract the three Nelson-Siegel factors from period-by-period OLS regressions.”

“Five additional exchange rate predictors are considered. The three global factors…capture the moving three-months change in the average intra-month volatility of the daily G10 exchange rate returns, the moving three-months return of the CRB spot commodity index, and the average bid-ask spread of the G10 spot dollar exchange rate. While exchange rate volatility and illiquidity are found to be associated with an appreciation of the US dollar along with other so-called safe haven currencies, higher commodity prices typically coincide with a surge in the value of currencies with higher risk premia (vis-a-vis the US dollar)…In addition, we include measures of exchange rate momentum and value as currency-specific predictors.”

“We first show that __the relative curvature factor has some signalling power for unexpected currency movements one to six months ahead__. The lower the domestic curvature relative to the US curvature, the higher the average depreciation against the US dollar.”

“The significant predictability of exchange rates based on relative Nelson-Siegel yield curve factors when controlling for other global and country-specific predictors of exchange rates widely used in the carry trade literature __complements the existing evidence [ provided by previous academic papers] on the predictive content of yield curve factors for a number of currencies against the US dollar__.”

“__The period of the zero lower bound has materially weighed on the forward-looking capacity of the curvature factor__. With medium-term yields being close to short-term rates, the curvature bears hardly any information that stretches beyond the signals that can be derived from the slope coefficient, which, in turn, is shown to carry little predictive content for future currency excess returns. However, with monetary policy normalisation being under way, the curvature may soon regain its signalling information for future monetary policy and exchange rates.”

### Trading strategies based on yield curvature

“We sort currencies into portfolios based on the relative curvature factor, __short-selling currencies with a relatively low curvature and investing into currencies with a relatively high curvature__…We take the perspective of a US investor. Funding currencies are sold against the US dollar, and the US dollar proceeds are invested into a third currency. The resulting exposure is neutral with respect to the dollar…All carry trade strategies are symmetric, i.e. the number of funding currencies is equal to the number of investment currencies in each portfolio…We take into account transactions costs, distinguishing between bid and ask spreads in order to work with net portfolio returns.”

“We show that __an investment strategy based on the relative curvature factor, the curvy trade, yields higher Sharpe ratios…than traditional carry trade strategies__…Higher economic returns of curvy trade portfolios relative to traditional carry trade strategies can be ascribed to higher returns from movements in the exchange rate that tend to offset lower interest rate returns.

“Moreover, we find that __the negative skewness of carry trade returns does not apply to the curvy trades__…Building currency portfolios based on prospective exchange rate movements yields return distributions which are less skewed and thus less subject to tail risks…The lower negative return skewness…reflects the different set of funding and investment currencies. For instance, curvature trades build less upon the typical carry trade funding currencies, like the Japanese yen and the Swiss franc, and are hence less susceptible to crash risk. In line with that, standard pricing factors of traditional carry trade returns, such as exchange rate volatility, fail to explain curvy trade returns in a linear asset pricing framework.”