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FX Risk Premia from the Bond Markets

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FX Risk Premia from the Bond Markets FX Risk Premia from the Bond Markets Mi Wu∗ This Draft: November 20, 2017 Abstract This paper proposes a two-country term structure model of joint behavior of bond markets and foreign exchange (FX) markets. With information extracted from local bond markets of G10 currency countries, the model is able to repro- duce the uncovered interest parity (UIP) puzzle as observed in the FX market. Bond market risk factors explain up to 50% of the variations in exchange rate movements at a one-year horizon and over 90% for some countries at a five-year horizon. For currency excess returns, the model-implied time-varying risk pre- mia deliver higher explanatory power than the interest rate differentials. These findings quantify how closely the FX market and the bond markets are inte- grated. The empirical findings also reveal heterogeneity between investment- and funding-currency countries in terms of the risk exposure to the transitory shocks of the bond markets. ∗PhD Candidate, 4-339 Simon Business School, University of Rochester, Rochester, NY, USA 14620. Email: [email protected]; Tel: +1 415-279-6090. I am grateful to my advisor and committee members, Prof. Robert Ready, Prof. Ron Kaniel, and Prof. Robert Novy-Marx, for their invaluable advice. I also thank Prof. Olga Itenberg, Prof. John Long, Prof. Yan Bai, Prof. Andreas Stathopoulos, Prof. Jerry Warner, Dr. Leon Cui and all seminar participants at Simon Business School and University of Sydney Business School for helpful discussions and comments. All remaining errors are mine. 1 1 Introduction In theory, currency trades over any length horizon can be conducted through the bond markets. When there is no arbitrage, capital gains from the interest rate differential between two countries’ sovereign bonds should be eliminated by the relative depreci- ation between the two currencies (uncovered interest rate parity (UIP)). As covered interest parity (CIP) generally holds1, UIP also provides the economic foundation for the forward unbiasedness hypothesis, postulating that the forward exchange rate is an unbiased forecast for the future spot rate. However, a large literature finds the relation violated in the data. High interest rates are usually associated with increasing currency values, which lead to the (in)famous UIP failure (or the forward premium puzzle), and the success of various carry trade strategies in the market. Fama (1984) is among the first to rationalize such observation by incorporating a foreign exchange (FX) risk premium to the UIP model. Recognizing forward rates are usually biased predictors of future spot exchange rates, Fama (1984) and others consider a risk-adjusted UIP, in which the expected exchange rate changes comprise the forward premium and a time-varying FX risk premium. Capturing the FX risk premium accurately is therefore at the heart of understanding the UIP failure puzzle. To measure the FX risk premium empirically, I propose a quantitative approach to construct a proxy for the FX risk premium between any two countries using the risk perception information extracted from the bond markets alone. The approach arises from the strong connection between the bond and the foreign exchange markets. More specifically, when there is no arbitrage, a pricing kernel capturing the effect of systematic risk factors determines the prices of all securities in the economy. 1Akram, Rime, and Sarno (2008) conclude that CIP holds at daily and lower frequencies. This relation was violated during the financial crisis in the fall of 2008 (Baba and Packer, 2009), an extreme time period that is not included in this study. 2 Therefore, any risk factor that drives the term structure of bond prices should also be able to explain the price fluctuations in the foreign exchange markets, i.e., the spot exchange rate movements. If the bond market risk perception is accurately measured, and the bond and the currency markets are highly integrated, a FX risk premium constructed with bond market risk factors should help explain and forecast exchange rate fluctuations and currency excess returns in the foreign exchange markets. The first step is to capture investors’ valuation of the risk from the bond markets of various countries. Cochrane and Piazzesi (2005) find that a single risk factor (henceforth the CP factor) composed of a linear combination of yields and forward rates captures all of the variations in one-year expected excess returns for bonds of one- to five-year maturities in the US market. To study the foreign exchange market, I verify the existence of this single risk factor for the other bond markets. The nine countries whose currencies are the most traded in the FX market (other than the US Dollars) are Australia, Canada, Germany, Japan, New Zealand, Norway, Sweden, Switzerland, and United Kingdom. Together with the US, these countries comprise the list of G10-currency (henceforth G10) countries. G10 countries are all developed market countries, and their nominal interest rates and exchange rates are not exposed to high inflation fluctuations in general. The results from my analysis confirm that the CP factor exists for these bond markets and captures over 95% of the economically interesting variation in one-year expected bond excess returns across one- to ten-year maturities for all G10 countries. Since it is well established in the literature that the first three yield curve principal components provide a good representation of the cross-sectional variation of any country’s yield curves, I augment the orthogonalized CP factor to the three yield risk factors as an unspanned risk factor in the term structure model. Interest rates are fitted by yield factors only 3 under the risk-neutral distribution of the state vector, yet risk associated with the CP factor is still embedded in the FX risk premia under the physical distribution. Under the no-arbitrage condition, and assuming complete markets, exchange rates between any two countries are modeled as the ratio of their stochastic discount factors (SDFs), where each country’s SDF captures the effect of all four risk factors extracted from its local bond market. The fitted exchange rate movements from the two-country term structure model are able to reproduce the UIP failure, or the forward premium puzzle, observed in historical data. In the short term, the fitted exchange rate movements follow the trend of the real exchange rates, but with a lower volatility. As the horizon becomes longer, the fitted exchange rate movements gradually match up with the actual data. According to the model, the exchange rate fluctuations are driven by three components: (1) the difference in the level of interest rates between two countries, (2) a nonlinear time-varying risk premium that captures the effect of risk factors extracted from bond markets, and (3) the difference in shocks to the prices of the risks. Equipped with the two-country term structure model estimation, the time-varying risk premium can be quantified for each country pair. Comparing the explanation power for the exchange rate fluctuations, it is clear that the time-varying risk premium is the main driving force behind exchange rate movements. At the one- year horizon, risk premia extracted from bond markets help explain up to 50% of the variations in exchange rate movements, and up to over 90% at a five-year horizon. Next, I explore the model implication for currency excess returns in the FX markets. Famous anomalies such as carry trade and dollar carry trade refer to the fact that lending in high-interest currencies and borrowing in low-interest curren- cies generate profitable returns. Therefore, positive interest rate differentials are 4 not eliminated by the depreciation of the currency. Instead, the high interest rate currency appreciates. Furthermore, when currency excess returns are regressed on interest rate differentials, although the sign of the coefficient agrees with the carry trade implications, the R2 is close to 0. This suggests that a large portion of the variations in the currency excess returns is not explained linearly by the interest rates. In the two-country term structure model I employ, the currency excess return is composed of the compensations for two layers of risks: (1) the interest rate uncer- tainty and (2) the foreign exchange risk. The first term is captured by the yield term premium and the second term by the nonlinear time-varying risk premium extracted from the bond market. The empirical analysis shows that the nonlinear risk premium is again the key driver behind the variations of the currency excess returns. For the one-month horizon, the time-varying risk premium extracted from the bond markets has an R2 up to 7.3% higher than the interest rate differentials in explaining the cur- rency excess returns and over 50% higher for some countries at a one-year horizon. Finally, the empirical results also point to heterogeneity in risk exposure between the investment currencies and the funding currencies of carry trade strategies. For investment currencies that are featured in the long leg of carry trades, i.e., currencies of Australia, Canada, New Zealand and Norway, the risk premia constructed by the bond market information can successfully explain the fluctuations in the FX market; while for funding currencies such as Japanese Yen and Swedish Krona, ex-post ex- change rate movements and currency excess returns seem to be more disconnected from the risk evaluations in the bond markets. The finding of heterogeneity in risk exposure is consistent with the empirical investigation by Lustig et al. (2011) and Colacito, Croce, Gavazzoni and Ready (2015), among others. Related Literature This paper contributes to the growing macro-finance literature 5 on the joint dynamics of bond and foreign exchange markets. Short-term interest rates, yield curve factors and other macroeconomic fundamentals have been used to explain exchange rate fluctuations; however, there is no consensus on the conclusion so far.
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