Long-term foreign exchange risk premia and inflation risk

As highlighted by recent literature, long-term foreign exchange risk premia (FRP) of a currency pair tend to covary negatively with short-term real interest rate differentials (RIRD) of the pair. We fit an affine term structure model for 9 major currencies against the US dollar and estimate two components of this covariance: the real risk premia (RRP) component and the inflation risk premia differential (IRPD) component. We find that the IRPD component is significantly negative for all currency pairs in our sample. We propose a macro-finance model to understand the types of shocks that generate such covariance.     

Expectations of Exchange Rates and Differential Inflation Rates: Further Evidence on Purchasing Power Parity in Efficient Markets

The paper tests the null hypothesis of ex ante purchasing power parity. The empirical evidence obtained is inconsistent with the null for major industrialized countries over the current floating exchange rate regime. Expected nominal exchange rate changes appear to deviate systematically from expected inflation rate differentials over the same holding period even though real exchange rate changes appear to be serially uncorrelated. This supports the presence of time-varying risk premia in foreign exchange markets and real determinants of exchange rate movements as suggested by equilibrium theories of international asset markets.     

A Habit-Based Explanation of the Exchange Rate Risk Premium

This paper presents a model that reproduces the uncovered interest rate parity puzzle. Investors have preferences with external habits. Countercyclical risk premia and procyclical real interest rates arise endogenously. During bad times at home, when domestic consumption is close to the habit level, the representative investor is very risk averse. When the domestic investor is more risk averse than her foreign counterpart, the exchange rate is closely tied to domestic consumption growth shocks. The domestic investor therefore expects a positive currency excess return. Because interest rates are low in bad times, expected currency excess returns increase with interest rate differentials.     

Nonlinear dynamics in foreign exchange rates

This paper investigates whether the behavior of real and nominal foreign exchange rates as well as interest rates are governed by nonlinear dynamics; it also explores whether observed deviations from parity conditions exhibit nonlinear dependence. Standard statistical tests for randomness, such as autocorrelation tests, have low power against a large class of deterministic, nonlinear processes. Discerning nonrandomness of innovations in exchange rates is important for a variety of reasons. For example, many models of international asset pricing assume exchange rates to follow a random walk. Furthermore, nonlinear patterns in deviations from various exchange rate parities have implications for the existence of a time-varying foreign exchange risk premium. With the use of the BDS statistic and a correlation dimension analysis, this paper's primary findings are that (1) foreign exchange markets have become increasingly complex and therefore less amenable to forecasting over time; (2) although forward exchange risk premia are statistically significant and display a deterministic structure, this structure is complex and therefore not easily discernible; and (3) innovations in real exchange rates are consistent with a Purchasing Power Parity equilibrium.     

Which Fundamentals Drive Exchange Rates? A Cross‐Sectional Perspective

Standard present‐value models suggest that exchange rates are driven by expected future fundamentals, implying that exchange rates contain information about future fundamentals. We test this key empirical prediction of present‐value models in a sample of 35 currency pairs ranging from 1900 to 2009. Employing a variety of tests, we find that exchange rates have strong and significant predictive power for nominal fundamentals (inflation, money balances, nominal GDP), whereas predictability of real fundamentals and risk premia is much weaker and largely confined to the post–Bretton Woods era. Overall, we uncover ample evidence that future macrofundamentals drive current exchange rates.     

The impact of jump risks on nominal interest rates and foreign exchange rates

This article investigates the relationship between the nominal interest rate and inflation and also the forward exchange rate under a general specification of the underlying processes govering the foreign exchange rate. There are three distinct risks that affect the relation between the real rate of interest and the nominal rate namely, consumption risk, diffusion risk, and the existence of jump risks of inflation. Jump risks lower the nominal interest rate because of jump hedging of a nominal bond. The forward exchange rate depends on the expected depreciation of the domestic currency as well as these three risks. As the domestic jump risks increase, the domestic nominal interest rate decreases and the forward exchange rate decreases.     

Rational speculation and exchange rates

Models of exchange rates have typically failed to produce results consistent with the key fact that real and nominal exchange rates move in ways not closely connected to current (or past) macroeconomic variables. Models that rely on the same shocks to drive fluctuations in macroeconomic variables and exchange rates typically imply counterfactually-strong co-movements between them. We develop a model in which new information leads agents to change their rational beliefs about risk premia on foreign exchange markets. These changes in risk premia work through asset markets to cause real and nominal exchange rates to change without corresponding changes in GDP, productivity, money supplies, and other key macro variables.     

Interest Rates as Options

Since people can hold currency at a zero nominal interest rate, the nominal short rate cannot be negative. The real interest rate can be and has been negative, since low risk real investment opportunities like filling in the Mississippi delta do not guarantee positive returns. The inflation rate can be and has been negative, most recently (in the United States) during the Great Depression. The nominal short rate is the “shadow real interest rate” (as defined by the investment opportunity set) plus the inflation rate, or zero, whichever is greater. Thus the nominal short rate is an option. Longer term interest rates are always positive, since the future short rate may be positive even when the current short rate is zero. We can easily build this option element into our interest rate trees for backward induction or Monte Carlo simulation: just create a distribution that allows negative nominal rates, and then replace each negative rate with zero.     

Can interest rate factors explain exchange rate fluctuations?

The level, slope, and curvature of the yield curve reflect time variation in investors’ risk premia and are known predictors of excess bond returns and economic activity. In this paper, I develop a term structure model under complete markets and no arbitrage to relate these interest rate factors to exchange rate fluctuations. The Gaussian properties of the stochastic discount factors imply non-linearities in exchange rate risk premia that are shown to account for up to half of the in-sample variation in one-year currency returns for different country pairs during the 1980s–2015 period. I find that interest rate factors help explain exchange rate fluctuations in and out of sample, particularly at longer horizons, and yield profitable currency portfolios relative to standard carry trade strategies.     

Forecasting Emerging Market Exchange Rates from Foreign Equity Options

The use of derivatives to infer future exchange rates has long been a subject of interest in the international finance literature. With the recent currency crises in Mexico, Southeast Asia, and Brazil, work on exchange rate expectations in emerging markets is of particular interest. For some emerging markets, foreign equity options are the only liquid exchange‐traded derivatives with currency information embedded in their prices. Given that emerging markets sometimes undergo currency realignment with discrete jumps in their exchange rate, estimation of risk‐neutral probability density functions from foreign equity option data provides valuable evidence concerning market expectations. To illustrate the use of foreign equity options in estimating market beliefs, we consider Telmex options around the 1994 peso devaluation and find evidence that markets anticipated the change in the Mexican government's foreign exchange policy.     

Real Rates, Expected Inflation, and Inflation Risk Premia

This paper studies the term structure of real rates, expected inflation, and inflation risk premia. The analysis is based on new estimates of the real term structure derived from the prices of index-linked and nominal debt in the U.K. I find strong evidence to reject both the Fisher Hypothesis and versions of the Expectations Hypothesis for real rates. The estimates also imply the presence of time-varying inflation risk premia throughout the term structure.     

The Share of Systematic Variation in Bilateral Exchange Rates

Sorting countries by their dollar currency betas produces a novel cross section of average currency excess returns. A slope factor (long in high beta currencies and short in low beta currencies) accounts for this cross section of currency risk premia. This slope factor is orthogonal to the high‐minus‐low carry trade factor built from portfolios of countries sorted by their interest rates. The two high‐minus‐low risk factors account for 18% to 80% of the monthly exchange rate movements. The two risk factors suggest that stochastic discount factors in complete markets' models should feature at least two global shocks to describe exchange rates.     

Real Sector Shocks and Monetary Policy Responses in a Financially Vulnerable Emerging Economy

When analyzing the appropriate response for monetary policy during a currency crisis, it is important to keep in mind two distinct channels: the effect of raising interest rates on exchange rates and the direct effect of exchange rate changes on output. The first pertains to the monetary side of the economy as given by the interest parity condition. The second pertains to the real side of the economy. The interaction between these two parts of the economy derives the equilibrium output and exchange rate in the economy. This paper expands on the Aghion et al. (2000) monetary model with nominal rigidities and foreign currency debt, to examine the interaction between the real and monetary sides of the economy and to analyze the effect of monetary policy on the real economy. We find that the effect of monetary policy on exchange rate and output is theoretically ambiguous. This in turn suggests that the appropriate monetary policy response could vary among countries at any point in time, or for a particular country between two different periods.     

Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

In this paper, we study inflation risk and the term structure of inflation risk premia in the United States' nominal interest rates through the Treasury Inflation Protection Securities (TIPS) with a multi-factor, modified quadratic term structure model with correlated real and inflation rates. We derive closed form solutions to the real and nominal term structures of interest rates that drastically facilitate the estimation of model parameters and improve the accuracy of the valuation of nominal rates and TIPS prices. In addition, we contribute to the literature by estimating the term structure of inflation risk premia implied from the TIPS market. The empirical evidence using data from the period of January 1998 through October 2007 indicates that the expected inflation rate, contrary to data derived from the consumer price indices, is very stable and the inflation risk premia exhibit a positive term structure.     

Exchange Rates and the Conversion of Currency‐Specific Risk Premia

How do the risk factors that drive asset prices influence exchange rates? Are the parameters of asset price processes relevant for specifying exchange rate processes? Most international asset pricing models focus on the analysis of asset returns given exchange rate processes. Little work has been done on the analysis of exchange rates dependent on asset returns. This paper uses an international stochastic discount factor (SDF) framework to analyse the interplay between asset prices and exchange rates. So far, this approach has only been implemented in international term structure models. We find that exchange rates serve to convert currency‐specific discount factors and currency‐specific prices of risk – a result linked to the international arbitrage pricing theory (IAPT). Our empirical investigation of exchange rates and stock markets of four countries presents evidence for the conversion of currency‐specific risk premia by exchange rates.     

An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for pricing currency options based on a third order asymptotic expansion scheme; we do not model a foreign exchange rate’s variance such as in Heston [(1993) The Review of Financial studies, 6, 327–343], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. Finally, numerical examples are provided and the pricing formula are applied to the calibration of volatility surfaces in the JPY/USD option market.     

Valuation effects and long-run real exchange rate dynamics

This paper uses the Johansen test for cointegration to check the prediction of a portfolio balance model that predictable valuation effects are associated with a saddle-path dynamic relationship between the net foreign asset position and the real exchange rate. The analysis uses newly constructed quarterly series on the net foreign position as a percentage of the nominal gross domestic product, together with data on real effective exchange rate indices for a sample of developed countries which borrow in their own currency. The results indicate that the net foreign asset position and the real exchange rate are not cointegrated for all the countries in the sample. The rejection of saddle-path dynamics suggests that predictable valuation effects are quantitatively small in developed countries. The rejection of cointegration suggests that the net foreign asset position is not a determinant for long-run real exchange rates in developed countries.     

The equilibrium pricing of exchange rates and assets when trade takes time

When trade takes time, there are systematic deviations of the exchange rate from its Law of One Price value; these depend on the real interest rate in terms of the importable good. There is no systematic tendency for the spot rate to attain its LOP value in the long run. This means that agents in different countries price the same cash flows by using different risk premia, with agents in the ‘foreign’ country pricing the asset by adding a risk premium related to foreign exchange risk.     

The high-frequency response of exchange rates and interest rates to macroeconomic announcements

The joint movements of exchange rates and U.S. and foreign term structures over short-time windows around macro announcements are studied using a 14-year span of high-frequency data. In order to evaluate whether the joint effects can be reconciled with conventional theory, the implications of these joint movements for changes in expected future exchange rates and changes in foreign exchange risk premia are deduced. For several real macro announcements, a stronger than expected release appreciates the dollar today, and must either (i) lower the risk premium for holding foreign currency rather than dollars, or (ii) imply net expected dollar depreciation over the ensuing decade.     

Interest rates and risk premia in the stock market and in the foreign exchange market

This paper documents common empirical regularities in the foreign exchange market and in the US stock market. We find that increases in interest rates are associated with predictable increases in the volatility of returns in both markets, and that expected returns both in the stock market and in the foreign exchange market are negatively correlated with nominal interest rates.We show that not taking into account the time variation of second moments may seriously affect tests of asset pricing models. Using a numerical example based on the static capital asset pricing model, we are able to produce fluctuations in risk premia similar to those observed empirically. Finally we show that the overidentifying restrictions of the latent variable capital asset pricing model are not rejected when beats are assumed to be correlated with nominal interest rates.