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This paper proposes a theoretical model for determining the exchange rate based on the interaction between international bond markets with different maturities. The model accommodates the presence of risk premia between short- and long-term bonds. The difference in risk premium between international bond markets produces imbalances between their yields and is responsible for the differences in equilibrium between the future spot exchange rate and the corresponding forward price. These departures from the expectations hypothesis of the international term structure of interest rates lead to unintended effects on the efficacy of monetary policy in open economies. The existence of imbalances in the risk premium between countries can be considered by monetary authorities as an alternative tool for conducting monetary policy and boosting real output.

The exchange rate is an important macroeconomic instrument fundamental to analyze the relationship between macroeconomic variables such as interest rates, changes in money supply, real output, prices, or the balance of payments, across countries. The exchange rate can also be considered as an asset traded in financial markets (see Hansen and Hodrick [

This paper studies exchange rate determination as the result of the interaction between financial and macroeconomic variables between open economies. Our model is based on rational expectations and absence of arbitrage opportunities. The model explicitly considers the effect of time-varying terms that measure departures from market efficiency in the foreign exchange market and from the expectations hypothesis in international bond markets. These terms can be interpreted as variables measuring the existence of risk aversion in the foreign exchange market, liquidity preferences reflected in the term structure of domestic and foreign interest rates, and ex-ante profitability opportunities reflected in imbalances between international bond markets with the same maturity. This approach is motivated by portfolio balance theories; portfolio balance theorists argue that risk aversion is the predominant motive in investors’ choice between domestic and foreign currency securities. This implies that assets in different markets are not perfect substitutes since investors require a risk premium for investing on the risky market.

The conclusion of our model is that the exchange rate is mainly forward looking. We observe that the failure of the forward exchange rate in predicting the next period spot exchange rate is due to the presence of imbalances in the risk premium between international bond markets with different maturities. These imbalances are reflected, in equilibrium, in differences between the realized differential in international interest rates and the implicit differential obtained from the international term structure of interest rates.

Our theory on exchange rate determination has an immediate applicability to monetary policy. The effects of unanticipated movements in monetary policy between economies differ depending on the term structure of international interest rates. The imbalances in international bond markets have an impact on monetary policies; in particular we observe that the existence of a premium on the foreign short-term bond higher than that on its domestic counterpart tempers the need of monetary measures by the foreign monetary authority. This is done by providing an alternative tool for boosting real output.

The closest contributions to our paper are Obstfeld and Rogoff [

The article is structured as follows. Section 2 sets the theoretical framework by introducing the equilibrium conditions in asset markets and analyzes the effect of departures from the expectations hypothesis for determining the exchange rate in equilibrium. Section 3 extends this theory to analyze exchange rate determination as a result of simultaneous equilibrium in the monetary and output markets. The section also explores the effect of macroeconomic policies affecting money supply, interest rates and prices on the determination of the exchange rate. Section 4 concludes.

We assume two open economies, domestic and foreign, with a floating exchange rate system between their currencies. Interest rates are determined from the interaction between financial and macroeconomic factors and in particular from the clearing of domestic and foreign zero-rate bond markets. In this model supply and demand forces eliminate instantaneously the existence of arbitrage opportunities in asset markets (international debt markets and foreign exchange market). Investors operating in these markets hold rational expectations with respect to the future performance of assets. There is perfect capital mobility between economies implying an infinite free flow of capital to take advantage of investment opportunities arising in both debt markets. Prices fully reflect available information implying market efficiency but make allowance at the same time for the presence of a risk premium derived from investors’ risk aversion. We assume three periods

The notation is the following. Let

Equilibrium in the foreign exchange market is given in the short run by

and in the long run by

with

The assumption of no-arbitrage in financial markets implies no-arbitrage in the foreign exchange market. The no-arbitrage condition is

with

with

Equilibrium in asset markets is completed by equilibrium on international bond markets. We assume a domestic and a foreign market for bonds; each market trades a short and a long term bond. Investors can freely invest in both markets for both maturities. To assess the relation between interest rates in equilibrium we compute the return between time 0 and t of each investment; for simplicity we consider a face value of one monetary unit

for each bond. For the domestic short term bond this is given by

serve a preference for the short term bond in the domestic market; this can be identified with the existence of a preference for liquidity in the market. In order to make the long term bond attractive the market demands a risk premium. Operating with these expressions and using no-arbitrage arguments we observe that in equilibrium domestic interest rates satisfy that

with

currency that will yield a gross expected return of

pected to be more profitable than investing in the domestic bond market if the previous return is higher than

with

From (5), it follows that the term

Expressions (7) and (8) show that under the risk-adjusted uncovered interest parity condition the best predictor of the risk premium on the foreign exchange market is the excess return expected at time t in the international bond market, that is,

Interestingly, we obtain a condition similar in spirit to the uncovered interest parity condition. Investors’ expectations on the exchange rate risk premium

Expression (9) also reveals that for

To study the exchange rate under departures from asset market equilibrium we analyze the impact of a shock to the financial system on the international bond market. A similar analysis can be carried out by studying the impact of the shock to the foreign exchange market. The shock is defined as

This condition together with the no-arbitrage conditions (3) and (4) yield

with

This expression shows that the exchange rate is, as recent literature has highlighted, forward looking. This literature refers to models in which the exchange rate is primarily determined by changes on market expectations, see Engel, Mark and West [

Expression (12) also rationalizes the existence of carry trade strategies. These strategies are given by short positions in the low interest rate country used to invest in the high interest rate country with the expectation of observing an appreciation in the latter currency. For the sake of exposition, assume that the high interest rate country is foreign, assume also that

This formula predicts the profitability of these strategies when the shock to the international bond market produces an unanticipated increase in the realized interest rate differential large enough to offset the implicit interest rate differential at time t and the initial difference of interest rates at time 0. Otherwise, the foreign currency (high interest rate) will depreciate.

The next section analyzes the implications of accounting for the difference between international interest rates differentials in the determination of the exchange rate and real output using monetary models.

The above model for exchange rate determination is based on no-arbitrage conditions and market efficiency. The key factors to determine the exchange rate are unexpected changes in interest rate differentials, the underlying risk premium and potential changes on market expectations on the long run exchange rate. This section studies the determination of the exchange rate from simultaneous equilibrium in the monetary and real output markets. The main difference with previous formulations on exchange rate determination is the expression for the short run exchange rate. In our study expression (12) replaces previous models considering the uncovered interest parity condition as one of the building blocks for determining the exchange rate. In this way our model naturally considers the effect of macroeconomic policies producing departures from equilibrium in the determination of the exchange rate.

The above model also has implications for the determination of interest rates. The main theories entertained in the literature are the monetary approach and the Taylor rule. Central banks usually follow Taylor rules to set nominal interest rates. In our model, international interest rates are determined from equilibrium in international zero-rate bond markets. Although both rates are related it is well known that the base rate set by central banks is a lower bound of the corresponding market rate obtained from bond prices. Moreover, the former rate does not correspond to the return on a tradable asset and does not incorporate a risk premium.

To describe the monetary market, and as in Engel and West [

where

The term gauging departures from the expectations hypothesis in the domestic market,

with

In an open economy, monetary policy cannot be taken independently of other countries’ monetary interventions. The previous equation shows that these policies need to account for investors expectations on the long run exchange rate and for the existence of ex-ante profitability opportunities in international bond markets. Expression (16) suggests that for

The findings of the previous section on the importance of the difference between implicit and realized interest rate differentials have interesting implications for monetary policy. To show this we now consider the exchange rate under departures from equilibrium due to the occurrence of monetary shocks (money expansions/contrac- tions) to the open economy^{1}.

A monetary shock is defined as the difference between the existing real money demand at time t and its conditional expectation. Using the previous expressions, and replacing in (10), we have

that relates monetary shocks to those in output markets and in international bond markets. Now, replacing in (12) we obtain the following decomposition of

with

The exchange rate can be decomposed into three factors. First, a financial factor given by the forward exchange rate, changes in the risk premium and in market expectations on the long run exchange rate. Second, a real factor given by the unexpected increase in real income differentials between economies, and third, a monetary factor that measures cross-country differences in the shocks to real money supply. This model not only describes the exchange rate in equilibrium but also provides the expression for the exchange rate after changes in monetary and real factors. For example, after relative monetary expansions by the foreign monetary authority and presence of risk aversion given by

The exchange rate, modeled as the result of interactions between international asset markets, is forward looking. Our theoretical analysis of the short-run exchange rate highlights the importance of the difference between realized interest rate differentials in international bond markets and the differential predicted by the term structure of interest rates for each economy for determining the exchange rate in equilibrium. This difference is due to the existence of shocks to the international financial system, but more importantly, to imbalances in risk premia between international bond markets. These imbalances have an effect on the spot exchange rate and on the risk premium on the foreign exchange market. These findings also stress the challenges inherent to the choice of the forward exchange rate as an accurate forecast of the spot exchange rate and shed further light on the reasons for the empirical failure of standard regression equations for testing the validity of the uncovered interest parity condition.

Our theory on exchange rate determination has an immediate applicability to monetary policy. The effects of unanticipated movements in monetary policy between economies differ depending on the relation between the term structure of domestic and foreign interest rates and the underlying risk premia in those markets. We observe that the imbalances in international bond markets have an impact on monetary policies. Our model also supports the view that the existence of a premium in the foreign short-term bond higher than that in its domestic counterpart tempers the need of monetary measures by the foreign monetary authority. The risk premium can be interpreted as an alternative tool for boosting real output.