1) The document examines international currency exchange markets and drivers of deviations from purchasing power parity in the short run through econometric analysis. It establishes key terms and notation used, and reviews equilibrium conditions in domestic money markets and their relationship to foreign exchange markets.
2) Graphs and equations are used to show the relationship between nominal exchange rates, interest rates, income levels, price levels, and money supplies in domestic and foreign economies. Shifts in supply and demand curves are explained by changes in these factors.
3) The paper analyzes how permanent changes in money supplies affect equilibrium conditions in domestic money markets and foreign exchange markets in both the short run and long run, with a focus on how movements toward purchasing power parity occur
This document provides an overview of international financial markets and linkages, including:
- The Eurodollar market, which began in the 1950s and increased in importance due to factors like oil shocks in the 1970s.
- International bond and stock markets, which have facilitated greater international capital mobility and interdependence as well as spread of financial crises.
- Basic models of international financial linkages based on interest rate parity and how a change in domestic interest rates would impact markets.
- Derivatives markets that have emerged to hedge foreign exchange and interest rate risk, though cannot eliminate risk as shown by the global financial crisis.
The objective of this paper is to test the exchange rate dynamics by measuring the speed of adjustment of prices. In this overshooting model, we assume price stickiness (gradual adjustment). If the prices are adjusted instantaneously, we will have the monetarist view; otherwise, the overshooting one, due to slow adjustment of prices and consequently, it affects all the other variables and slowly the exchange rate. We outline, here, an approach of testing the dynamic models of exchange rate determination. This approach is based upon the idea that it is difficult to measure directly the process by which market participants revise their expectations about current and future money supplies. On the other hand, it is possible to make indirect inferences about these expectations through a time series analysis of related financial and real prices. Empirical tests of the above exchange rate dynamics are taking place for four different exchange rates ($/€, $/£, C$/$, and ¥/$). Theoretical discussion and empirical evidence have emphasized the impact of gradual adjustment and “overshooting” that it is taking place. Only for the $/€ exchange rate the monetarist model is correct.
This document discusses several exchange rate theories, including the traditional or elasticities approach, purchasing power parity (PPP), and interest rate parity (IRP).
The traditional approach assumes an equilibrium exchange rate where a country's imports balance its exports. If imports exceed exports, the exchange rate will fall to make the country's exports cheaper and imports more expensive, balancing trade.
PPP has both an absolute and relative form. In absolute PPP, similar goods should have the same price in different currencies. Relative PPP recognizes market imperfections but holds that inflation rates between countries will offset exchange rate changes over time.
IRP links exchange and money markets, stating that interest rate differences between countries should equal forward exchange
The foreign exchange market allows companies to convert one currency into another. It provides insurance against risks from unpredictable exchange rate changes that could harm sales and profits. Companies use the market when paying or receiving funds in foreign currencies. Firms can hedge against exchange rate risk by entering forward contracts to set future exchange rates. Spot rates are current rates while forward rates are set for future dates. Currency swaps also allow companies to temporarily exchange one currency for another without exchange rate risk. The global foreign exchange market is a network of banks and dealers that trade currencies 24/7. Exchange rates are determined by supply and demand and factors like inflation rates and interest rates that can impact currency values. Managers must consider various types of exchange rate risk for their
1. The document discusses goods market equilibrium using the Keynesian cross model. It shows how equilibrium occurs at the point where aggregate demand equals real output (Y).
2. It then derives the IS curve, showing the combinations of interest rates (i) and output (Y) that maintain equilibrium in both the goods market and foreign exchange market. The IS curve slopes downward, as lower interest rates increase investment and the trade balance via currency depreciation.
3. Similarly, the LM curve is derived from money market equilibrium, showing the combinations of i and Y that balance money demand and supply. The LM curve slopes upward, as higher output increases money demand and requires higher interest rates to maintain equilibrium.
The document summarizes key concepts about foreign exchange rates and their determinants. In the 1980s, the strong dollar made US goods expensive abroad, hurting competitiveness. By the 2000s, as the dollar weakened, US goods became cheaper and competitiveness increased. Exchange rates are determined by supply and demand in the market. In the long run, factors like relative price levels and productivity affect exchange rates, while in the short run, interest rates and expected future exchange rates drive exchange rate movements through interest rate parity.
The document provides an overview of the Mundell-Fleming model, which analyzes the effects of fiscal and monetary policy in a small open economy with perfect capital mobility. It describes the IS* and LM* curves and how they determine equilibrium income and exchange rates. Key points covered include: fiscal policy cannot affect output, while monetary policy impacts output by changing the exchange rate; floating exchange rates allow monetary policy flexibility; and fixed rates make fiscal policy more effective at changing output.
This document provides an overview of international financial markets and linkages, including:
- The Eurodollar market, which began in the 1950s and increased in importance due to factors like oil shocks in the 1970s.
- International bond and stock markets, which have facilitated greater international capital mobility and interdependence as well as spread of financial crises.
- Basic models of international financial linkages based on interest rate parity and how a change in domestic interest rates would impact markets.
- Derivatives markets that have emerged to hedge foreign exchange and interest rate risk, though cannot eliminate risk as shown by the global financial crisis.
The objective of this paper is to test the exchange rate dynamics by measuring the speed of adjustment of prices. In this overshooting model, we assume price stickiness (gradual adjustment). If the prices are adjusted instantaneously, we will have the monetarist view; otherwise, the overshooting one, due to slow adjustment of prices and consequently, it affects all the other variables and slowly the exchange rate. We outline, here, an approach of testing the dynamic models of exchange rate determination. This approach is based upon the idea that it is difficult to measure directly the process by which market participants revise their expectations about current and future money supplies. On the other hand, it is possible to make indirect inferences about these expectations through a time series analysis of related financial and real prices. Empirical tests of the above exchange rate dynamics are taking place for four different exchange rates ($/€, $/£, C$/$, and ¥/$). Theoretical discussion and empirical evidence have emphasized the impact of gradual adjustment and “overshooting” that it is taking place. Only for the $/€ exchange rate the monetarist model is correct.
This document discusses several exchange rate theories, including the traditional or elasticities approach, purchasing power parity (PPP), and interest rate parity (IRP).
The traditional approach assumes an equilibrium exchange rate where a country's imports balance its exports. If imports exceed exports, the exchange rate will fall to make the country's exports cheaper and imports more expensive, balancing trade.
PPP has both an absolute and relative form. In absolute PPP, similar goods should have the same price in different currencies. Relative PPP recognizes market imperfections but holds that inflation rates between countries will offset exchange rate changes over time.
IRP links exchange and money markets, stating that interest rate differences between countries should equal forward exchange
The foreign exchange market allows companies to convert one currency into another. It provides insurance against risks from unpredictable exchange rate changes that could harm sales and profits. Companies use the market when paying or receiving funds in foreign currencies. Firms can hedge against exchange rate risk by entering forward contracts to set future exchange rates. Spot rates are current rates while forward rates are set for future dates. Currency swaps also allow companies to temporarily exchange one currency for another without exchange rate risk. The global foreign exchange market is a network of banks and dealers that trade currencies 24/7. Exchange rates are determined by supply and demand and factors like inflation rates and interest rates that can impact currency values. Managers must consider various types of exchange rate risk for their
1. The document discusses goods market equilibrium using the Keynesian cross model. It shows how equilibrium occurs at the point where aggregate demand equals real output (Y).
2. It then derives the IS curve, showing the combinations of interest rates (i) and output (Y) that maintain equilibrium in both the goods market and foreign exchange market. The IS curve slopes downward, as lower interest rates increase investment and the trade balance via currency depreciation.
3. Similarly, the LM curve is derived from money market equilibrium, showing the combinations of i and Y that balance money demand and supply. The LM curve slopes upward, as higher output increases money demand and requires higher interest rates to maintain equilibrium.
The document summarizes key concepts about foreign exchange rates and their determinants. In the 1980s, the strong dollar made US goods expensive abroad, hurting competitiveness. By the 2000s, as the dollar weakened, US goods became cheaper and competitiveness increased. Exchange rates are determined by supply and demand in the market. In the long run, factors like relative price levels and productivity affect exchange rates, while in the short run, interest rates and expected future exchange rates drive exchange rate movements through interest rate parity.
The document provides an overview of the Mundell-Fleming model, which analyzes the effects of fiscal and monetary policy in a small open economy with perfect capital mobility. It describes the IS* and LM* curves and how they determine equilibrium income and exchange rates. Key points covered include: fiscal policy cannot affect output, while monetary policy impacts output by changing the exchange rate; floating exchange rates allow monetary policy flexibility; and fixed rates make fiscal policy more effective at changing output.
Relationships between Inflation, Interest Rates, and Exchange Rates ICAB
The document discusses purchasing power parity (PPP) theory and the international Fisher effect (IFE) theory. PPP theory states that inflation rate differentials between countries will lead to changes in exchange rates as the high inflation country's currency depreciates. IFE theory similarly argues that interest rate differentials, which often correlate with expected inflation differentials, will cause the high interest rate currency to depreciate. Both theories predict that the currency experiencing higher inflation or interest rates will lose value against other currencies. The document also provides derivations of the PPP and IFE formulas to calculate expected exchange rate changes based on inflation or interest rate differentials.
The document provides an overview of foreign exchange including:
1. It defines foreign exchange as the conversion of one country's currency into another. It also discusses how foreign exchange is important for paying import bills.
2. It outlines some fundamentals of foreign exchange including that each country has its own currency and conversions occur through banks and credit instruments.
3. It discusses factors that influence foreign exchange rates such as supply and demand, interest rates, inflation rates, balance of trade, government debt, and political/economic stability.
A study on the impact of global currency fluctuations with a special focus to...Aman Vij
The paper discusses about the factors influencing and impact of currency fluctuations on global economy. Then we shift our focus to Indian rupees factors which causes the Rupee fluctuations has been discussed. In the end we discuss about the steps taken by the RBI and the government and what else can be done by investors to lessen the impact of Global currency fluctuations and what can be done to prevent Indian Rupee fluctuation.
Does Misaligned Currency Affect Economic Growth? – Evidence from Croatia Nicha Tatsaneeyapan
The document examines the relationship between currency misalignment and economic growth in Croatia from 2001 to 2013. It estimates the fundamental equilibrium exchange rate of the Croatian kuna using techniques like cointegration and VAR models. The findings show the kuna was undervalued from 2000 to 2007 and overvalued from 2008 to 2013. For the whole sample period, currency misalignments Granger caused GDP growth, but no causality was found for the two sub-periods. The research also finds the misalignments over this period were relatively small.
BAFI 3200- International Finance- Group 2- Team LChau Vuong Minh
This document analyzes and forecasts the exchange rate between the USD and AUD from 1996 to 2015 using quantitative and qualitative analysis.
Quantitatively, regression models are used to analyze the relationship between macroeconomic factors and the exchange rate change. The final model found money supply, unemployment rate differential, and time series to be the most significant factors.
Qualitatively, recent economic events are expected to cause the AUD to depreciate against the USD in December. These include expected interest rate cuts by the RBA, an interest rate hike by the Fed, higher Australian GDP growth, a rising US trade deficit, and falling iron ore prices.
Based on the quantitative and qualitative analysis, the forecast exchange rate on December
The document discusses key concepts related to foreign exchange including:
- The meaning of foreign exchange as the conversion of one country's currency into another at exchange rates.
- How foreign exchange markets operate as global online networks where traders buy and sell currencies.
- The factors that influence exchange rates such as exports, imports, capital flows, inflation, and monetary policy.
- The difference between fixed and floating exchange rate systems and how governments intervene to maintain fixed rates.
Determination of exchange rate chapter 6Nayan Vaghela
Determination of exchange rate, mint par theory, balance of payment theory, Purchasing power parity theory, Absolute version and relative version, Criticisms
Unit 2.2 Exchange Rate Quotations & Forex MarketsCharu Rastogi
This presentation deals with exchange rate quotations, common currency symbols, direct and indirect quotes, American terms, European terms, cross rates, Bid and Ask rates, Mid rate, Spread and its determinants, Spot markets, Forward Markets, Premium and Discounts, various practices of writing quotations, calculating broken period forward rates, Speculation and arbitrage, Forex futures and Currency Options.
This document discusses open economy macroeconomics concepts including the roles of net exports, capital flows, and trade balances. It covers how interest rates are determined in closed versus open economies and how fiscal and investment policies at home and abroad can influence real exchange rates. Graphs and equations are presented showing how real exchange rates are determined and how policies can impact them. Contact information is also provided for the United World campus locations in Ahmedabad and Kolkata, India.
- The foreign exchange market involves the trading of one country's currency for another. It determines exchange rates through supply and demand.
- In the long run, exchange rates are determined by theories like purchasing power parity which says exchange rates will adjust over time to reflect differences in inflation. The law of one price also applies to keep identical goods priced the same globally.
- In the short run, exchange rates are the price of one country's bank deposits in terms of another's. The current and expected future exchange rates determine demand for each country's deposits and set the equilibrium exchange rate where supply meets demand.
Firms forecast exchange rates for hedging decisions, short-term financing decisions, capital budgeting decisions, and long-term financing decisions. There are two main approaches - fundamental analysis, which studies macroeconomic variables like inflation and GDP growth, and technical analysis, which analyzes historical exchange rate data. Factors like inflation rates, purchasing power parity, GNP growth, monetary policy, and relative economic strength between countries can influence exchange rate forecasts. No single approach can perfectly predict future exchange rates.
In this paper we evaluate critically the popular Mundell-Fleming model from the standpoint the exogenous interest rate heterodox approach. We criticize the assumptions of exogenous money supply, "perfect" international capital markets and inelastic exchange rate expectations. We show that in a more realistic framework none of the main results of the Mundell-Fleming model on the relative effectiveness of fiscal and monetary policies are valid, either in floating and fixed exchange rate regimes. We conclude that ,within certain very asymmetric bounds, the central bank has the power to determine the domestic interest rate exogenously even in open economy with free capital mobility and that there is no automatic market mechanism to ensure the automatic adjustment of the interest rate and exchange rate to sustainable levels.
The foreign exchange market determines exchange rates and facilitates international trade and investment. It is a decentralized global market where multiple currencies are traded. Participants include banks, central banks, companies, investors and more. The purpose is to allow businesses to convert one currency to another to facilitate international trade. Under a fixed exchange rate system, a country's central bank pegs its currency value to another currency and intervenes to maintain the peg. A floating system allows market forces to determine exchange rates without central bank intervention. Countries consider factors like financial depth, trade openness and volatility when deciding their exchange rate regime.
O
Where S = Savings, T = Taxes, I = Investment, G = Government spending, X = Exports,
M = Imports. According to this approach, the balance of payments equilibrium requires that
the excess of domestic savings over domestic investment plus the excess of taxes over
government spending plus the excess of imports over exports should be equal to zero.
C
The document summarizes the key concepts of foreign exchange management including:
ZA
D
1) The sources of demand and supply of foreign exchange including import/export companies,
foreign investors, and speculators. There is an inverse relationship between exchange rates
and demand and a positive relationship between exchange rates and
1. The document discusses foreign exchange rates and policies regarding differentiating between bank selling rates (BSR) and bank buying rates (BBR).
2. It provides examples to show that BSR is the rate at which banks sell foreign currency to tourists, while BBR is the rate at which banks buy foreign currency from tourists.
3. Tourism is an important source of foreign currency for South Africa, contributing to GDP and employment. However, a strong rand negatively impacts tourism while a weak rand makes South Africa a more affordable destination.
- The document discusses Mongolia's money market and defines different types of money, including cash money, time deposits, and non-cash money.
- It describes Mongolia's money supply and how it is aggregated into different categories (M0, M1, M2) based on liquidity and inclusion of various types of assets and deposits.
- Mongolia's central bank, the Bank of Mongolia, is responsible for monitoring and managing the country's money supply to achieve price stability and sustainable economic growth.
This document discusses different types of exchange rate systems and how exchange rates are determined. It outlines fixed exchange rates where a government sets the rate, floating/flexible rates where market forces determine the rate, and managed rates where a government intervenes to influence the rate. It then provides details on how demand and supply impact exchange rate equilibrium and can cause currency appreciation or depreciation under flexible systems.
The purchasing power parity (PPP) theory compares the average costs of goods and services between countries using exchange rates. PPPs are useful for inter-country comparisons of GDP in real terms and economic data expressed in national currencies. PPPs are calculated at the product group level by comparing consumption baskets, then aggregated to GDP levels using weights. PPP exchange rates are meant to converge with actual exchange rates over the long run, though various factors can cause short-term deviations. PPPs are useful for output and productivity comparisons, while market exchange rates are better for trade-related analyses.
The document provides information about the foreign exchange market (FOREX). It explains that currencies are traded between countries and factors like preferences, quality, prices, incomes, and interest rates can impact currency exchange rates. The FOREX is represented worldwide and currencies are subjected to supply and demand. When factors change, it can cause one currency to appreciate or depreciate relative to another currency, impacting exports and imports between the two countries.
Estimation of parameters of linear econometric model and the power of test in...Alexander Decker
1) The document discusses using Monte Carlo simulations to estimate parameters of a linear econometric model and test the power of statistical tests in the presence of heteroscedasticity.
2) Two forms of heteroscedasticity (h(x)=X1/2 and h(x)=X) were introduced into the model. Sample sizes of 20, 50, and 100 were used with 50 replications each.
3) The bias, variance, and root mean square error of ordinary least squares (OLS) and generalized least squares (GLS) estimators were examined across sample sizes and heteroscedasticity forms. Both estimators were found to be unbiased but neither was consistently more efficient.
Relationships between Inflation, Interest Rates, and Exchange Rates ICAB
The document discusses purchasing power parity (PPP) theory and the international Fisher effect (IFE) theory. PPP theory states that inflation rate differentials between countries will lead to changes in exchange rates as the high inflation country's currency depreciates. IFE theory similarly argues that interest rate differentials, which often correlate with expected inflation differentials, will cause the high interest rate currency to depreciate. Both theories predict that the currency experiencing higher inflation or interest rates will lose value against other currencies. The document also provides derivations of the PPP and IFE formulas to calculate expected exchange rate changes based on inflation or interest rate differentials.
The document provides an overview of foreign exchange including:
1. It defines foreign exchange as the conversion of one country's currency into another. It also discusses how foreign exchange is important for paying import bills.
2. It outlines some fundamentals of foreign exchange including that each country has its own currency and conversions occur through banks and credit instruments.
3. It discusses factors that influence foreign exchange rates such as supply and demand, interest rates, inflation rates, balance of trade, government debt, and political/economic stability.
A study on the impact of global currency fluctuations with a special focus to...Aman Vij
The paper discusses about the factors influencing and impact of currency fluctuations on global economy. Then we shift our focus to Indian rupees factors which causes the Rupee fluctuations has been discussed. In the end we discuss about the steps taken by the RBI and the government and what else can be done by investors to lessen the impact of Global currency fluctuations and what can be done to prevent Indian Rupee fluctuation.
Does Misaligned Currency Affect Economic Growth? – Evidence from Croatia Nicha Tatsaneeyapan
The document examines the relationship between currency misalignment and economic growth in Croatia from 2001 to 2013. It estimates the fundamental equilibrium exchange rate of the Croatian kuna using techniques like cointegration and VAR models. The findings show the kuna was undervalued from 2000 to 2007 and overvalued from 2008 to 2013. For the whole sample period, currency misalignments Granger caused GDP growth, but no causality was found for the two sub-periods. The research also finds the misalignments over this period were relatively small.
BAFI 3200- International Finance- Group 2- Team LChau Vuong Minh
This document analyzes and forecasts the exchange rate between the USD and AUD from 1996 to 2015 using quantitative and qualitative analysis.
Quantitatively, regression models are used to analyze the relationship between macroeconomic factors and the exchange rate change. The final model found money supply, unemployment rate differential, and time series to be the most significant factors.
Qualitatively, recent economic events are expected to cause the AUD to depreciate against the USD in December. These include expected interest rate cuts by the RBA, an interest rate hike by the Fed, higher Australian GDP growth, a rising US trade deficit, and falling iron ore prices.
Based on the quantitative and qualitative analysis, the forecast exchange rate on December
The document discusses key concepts related to foreign exchange including:
- The meaning of foreign exchange as the conversion of one country's currency into another at exchange rates.
- How foreign exchange markets operate as global online networks where traders buy and sell currencies.
- The factors that influence exchange rates such as exports, imports, capital flows, inflation, and monetary policy.
- The difference between fixed and floating exchange rate systems and how governments intervene to maintain fixed rates.
Determination of exchange rate chapter 6Nayan Vaghela
Determination of exchange rate, mint par theory, balance of payment theory, Purchasing power parity theory, Absolute version and relative version, Criticisms
Unit 2.2 Exchange Rate Quotations & Forex MarketsCharu Rastogi
This presentation deals with exchange rate quotations, common currency symbols, direct and indirect quotes, American terms, European terms, cross rates, Bid and Ask rates, Mid rate, Spread and its determinants, Spot markets, Forward Markets, Premium and Discounts, various practices of writing quotations, calculating broken period forward rates, Speculation and arbitrage, Forex futures and Currency Options.
This document discusses open economy macroeconomics concepts including the roles of net exports, capital flows, and trade balances. It covers how interest rates are determined in closed versus open economies and how fiscal and investment policies at home and abroad can influence real exchange rates. Graphs and equations are presented showing how real exchange rates are determined and how policies can impact them. Contact information is also provided for the United World campus locations in Ahmedabad and Kolkata, India.
- The foreign exchange market involves the trading of one country's currency for another. It determines exchange rates through supply and demand.
- In the long run, exchange rates are determined by theories like purchasing power parity which says exchange rates will adjust over time to reflect differences in inflation. The law of one price also applies to keep identical goods priced the same globally.
- In the short run, exchange rates are the price of one country's bank deposits in terms of another's. The current and expected future exchange rates determine demand for each country's deposits and set the equilibrium exchange rate where supply meets demand.
Firms forecast exchange rates for hedging decisions, short-term financing decisions, capital budgeting decisions, and long-term financing decisions. There are two main approaches - fundamental analysis, which studies macroeconomic variables like inflation and GDP growth, and technical analysis, which analyzes historical exchange rate data. Factors like inflation rates, purchasing power parity, GNP growth, monetary policy, and relative economic strength between countries can influence exchange rate forecasts. No single approach can perfectly predict future exchange rates.
In this paper we evaluate critically the popular Mundell-Fleming model from the standpoint the exogenous interest rate heterodox approach. We criticize the assumptions of exogenous money supply, "perfect" international capital markets and inelastic exchange rate expectations. We show that in a more realistic framework none of the main results of the Mundell-Fleming model on the relative effectiveness of fiscal and monetary policies are valid, either in floating and fixed exchange rate regimes. We conclude that ,within certain very asymmetric bounds, the central bank has the power to determine the domestic interest rate exogenously even in open economy with free capital mobility and that there is no automatic market mechanism to ensure the automatic adjustment of the interest rate and exchange rate to sustainable levels.
The foreign exchange market determines exchange rates and facilitates international trade and investment. It is a decentralized global market where multiple currencies are traded. Participants include banks, central banks, companies, investors and more. The purpose is to allow businesses to convert one currency to another to facilitate international trade. Under a fixed exchange rate system, a country's central bank pegs its currency value to another currency and intervenes to maintain the peg. A floating system allows market forces to determine exchange rates without central bank intervention. Countries consider factors like financial depth, trade openness and volatility when deciding their exchange rate regime.
O
Where S = Savings, T = Taxes, I = Investment, G = Government spending, X = Exports,
M = Imports. According to this approach, the balance of payments equilibrium requires that
the excess of domestic savings over domestic investment plus the excess of taxes over
government spending plus the excess of imports over exports should be equal to zero.
C
The document summarizes the key concepts of foreign exchange management including:
ZA
D
1) The sources of demand and supply of foreign exchange including import/export companies,
foreign investors, and speculators. There is an inverse relationship between exchange rates
and demand and a positive relationship between exchange rates and
1. The document discusses foreign exchange rates and policies regarding differentiating between bank selling rates (BSR) and bank buying rates (BBR).
2. It provides examples to show that BSR is the rate at which banks sell foreign currency to tourists, while BBR is the rate at which banks buy foreign currency from tourists.
3. Tourism is an important source of foreign currency for South Africa, contributing to GDP and employment. However, a strong rand negatively impacts tourism while a weak rand makes South Africa a more affordable destination.
- The document discusses Mongolia's money market and defines different types of money, including cash money, time deposits, and non-cash money.
- It describes Mongolia's money supply and how it is aggregated into different categories (M0, M1, M2) based on liquidity and inclusion of various types of assets and deposits.
- Mongolia's central bank, the Bank of Mongolia, is responsible for monitoring and managing the country's money supply to achieve price stability and sustainable economic growth.
This document discusses different types of exchange rate systems and how exchange rates are determined. It outlines fixed exchange rates where a government sets the rate, floating/flexible rates where market forces determine the rate, and managed rates where a government intervenes to influence the rate. It then provides details on how demand and supply impact exchange rate equilibrium and can cause currency appreciation or depreciation under flexible systems.
The purchasing power parity (PPP) theory compares the average costs of goods and services between countries using exchange rates. PPPs are useful for inter-country comparisons of GDP in real terms and economic data expressed in national currencies. PPPs are calculated at the product group level by comparing consumption baskets, then aggregated to GDP levels using weights. PPP exchange rates are meant to converge with actual exchange rates over the long run, though various factors can cause short-term deviations. PPPs are useful for output and productivity comparisons, while market exchange rates are better for trade-related analyses.
The document provides information about the foreign exchange market (FOREX). It explains that currencies are traded between countries and factors like preferences, quality, prices, incomes, and interest rates can impact currency exchange rates. The FOREX is represented worldwide and currencies are subjected to supply and demand. When factors change, it can cause one currency to appreciate or depreciate relative to another currency, impacting exports and imports between the two countries.
Estimation of parameters of linear econometric model and the power of test in...Alexander Decker
1) The document discusses using Monte Carlo simulations to estimate parameters of a linear econometric model and test the power of statistical tests in the presence of heteroscedasticity.
2) Two forms of heteroscedasticity (h(x)=X1/2 and h(x)=X) were introduced into the model. Sample sizes of 20, 50, and 100 were used with 50 replications each.
3) The bias, variance, and root mean square error of ordinary least squares (OLS) and generalized least squares (GLS) estimators were examined across sample sizes and heteroscedasticity forms. Both estimators were found to be unbiased but neither was consistently more efficient.
This study uses regression analysis to examine the relationship between state-level firearm death rates in the US and several independent variables representing prevailing theories about the causes of gun deaths. The analysis finds that states with weaker gun laws and higher unemployment rates have statistically significant higher firearm death rates, while personal income, mental illness rates, and income inequality were not significant predictors. This provides support for the argument that lax gun regulation and poor economic conditions contribute to higher rates of gun deaths in the US.
Married men earn significantly more than unmarried men, around 20-40% more according to studies. This paper analyzes whether this "marital premium" differs between the public and private sectors using data on over 40,000 men. The results show a 20.6% marital premium overall but the premium is smaller, 10.6% less, for married men working in government compared to the private sector. The authors conclude that while marital status benefits men's earnings, the effect is less pronounced in government work.
This document summarizes a research study that uses econometric models to analyze factors that influence whether television shows are renewed for a second season. The study uses panel data on the top 100 television programs from 2010 to 2014 to examine how characteristics like lead characters, parental ratings, genre, episode number, and broadcast format relate to renewal chances. Previous related studies focused on capital investment or viewer demographics. The models used are ordinary least squares regression and binary choice regression. The results found parental ratings of TVY7, TVPG, and TVMA along with comedy, drama and reality genres as most significant, as well as cable subscription numbers, in influencing second season renewal.
BlackBerry was once a leader in the smartphone market with 70% market share in North America in 2008, but has since fallen to just 5% market share by 2011. A shift in consumer preferences towards touchscreen smartphones with more functionality like the iPhone created strong competition for BlackBerry. BlackBerry's focus on engineers and lack of understanding of customers led to failures to adapt to the changing market demands for more affordable, full-featured smartphones. As a result, BlackBerry lost significant ground and is no longer considered in the smartphone market.
This document discusses research into factors that influence the domestic box office success of films between 1980-2016. It presents two regression models to analyze the relationship between films' domestic gross (adjusted for inflation) and variables like budget, theaters, weeks in release, ratings and MPAA ratings. The preliminary model had a low adjusted R-squared of 0.370. The adjusted model omitted insignificant variables like sequels and improved fit. Empirical results found all variables in the adjusted model were statistically significant in explaining films' domestic box office successes.
The document describes a study that uses panel data from 1994-2010 to create an econometric model to predict poverty rates in Canada. The study finds that the pooled OLS model best predicts poverty rates. The strongest predictors are low income transition exit and entry rates, average market income, and persons with 0-8 years of schooling. The study also finds that in 2001 the poverty rate saw a decrease, and that Ontario generally has a higher poverty rate than other provinces.
11.exploring the link between poverty pollution-population (0003www.iiste.org...Alexander Decker
This document examines the link between poverty, population growth, and air pollution (carbon dioxide emissions) in Pakistan from 1975 to 2009. It finds:
1) Population growth and air pollution significantly contribute to increasing poverty in Pakistan based on OLS regression analysis. However, poverty is not found to be a major direct cause of environmental degradation.
2) There is a stable long-run relationship between population, poverty, and pollution in Pakistan according to bounds testing.
3) Unidirectional causality is found from population to carbon dioxide emissions based on causality testing.
4) Poverty in Pakistan increased during the post-reform period due to ineffective pro-poor policies, and population growth also
This document examines potential socioeconomic factors that could explain differences in Olympic medal counts between countries. It reviews previous research finding correlations between higher GDP, GDP growth, healthcare spending, education levels, population size, and income levels and higher medal counts. The authors develop a model using multiple linear regression to analyze the relationship between three independent variables - GDP per capita, population size, and literacy rate - and the dependent variable of total medals won for 33 countries at the 2012 London Olympics. While all three independent variables are expected to have a positive correlation, the analysis aims to determine if socioeconomic factors can predict and influence a country's Olympic success.
The world's population exceeded 7 billion in 2011 and is projected to increase by 40% over the next 40 years. Egypt's population grew rapidly from 20 million in 1948 to 80 million in 2011, adding 20 million people every 20 years. Rapid population growth is increasing environmental pollution like air, water, noise, and waste as finite resources are used up more quickly and fossil fuels are burned, releasing greenhouse gases.
- The paper examines the relationship between team payroll and success in Major League Baseball from 2011-2015. It builds on previous studies that found a weak positive relationship.
- The empirical model finds no statistically significant relationship between payroll and wins. However, it does find that earned run average and runs scored have strong relationships with wins, while stolen bases has a weak negative relationship.
- Playing in the American League is associated with more wins, likely due to the designated hitter position. Overall, the results do not support the hypothesis that increased payroll leads to more wins in MLB.
The document summarizes an econometrics project analyzing the effect of advanced degrees on income for white male economics graduates in the United States. Regression analyses found:
1) On average, men with an advanced degree earn $48,256 more per year than those with just a bachelor's degree.
2) When controlling for age, marriage, children and work hours, men with an advanced degree earn $11,124-$24,000 more annually.
3) Both earnings and the advanced degree earnings premium increase with age but at a diminishing rate, with peak earnings around age 44 for those with an advanced degree and 43 for bachelor's degree holders.
Multiple Regression worked example (July 2014 updated)Michael Ling
The document describes using regression analysis to predict daily ice cream sales based on temperature and humidity. A base model found temperature and humidity explained 62.9% of sales variance. An interaction model adding a temperature*humidity term explained 77.3%, a significant improvement. Graphs show humidity moderates the temperature-sales relationship, and temperature moderates humidity-sales. The analysis validates both models with adequate sample size and meets statistical assumptions.
This document summarizes a regression analysis project examining the relationship between nutritional factors (total fat, carbohydrates, protein) and calorie content in various chip products. Nutritional data for different chip types was compiled and compared. Scatterplots and a histogram were generated comparing calories to each nutrient factor. Regression analysis found total fat to have the strongest correlation (83.2%) to calories, while carbohydrates and protein had weaker correlations. The conclusion was total fat has a direct relationship with calories in chips.
Econometrics notes (Introduction, Simple Linear regression, Multiple linear r...Muhammad Ali
Econometrics notes for BS economics students
Muhammad Ali
Assistant Professor of Statistics
Higher Education Department, KPK, Pakistan.
Email:Mohammadale1979@gmail.com
Cell#+923459990370
Skyp: mohammadali_1979
This document discusses the methodology of econometrics. It begins by defining econometrics as applying economic theory, mathematics and statistical inference to analyze economic phenomena. It then outlines the typical steps in an econometric analysis: 1) stating an economic theory or hypothesis, 2) specifying a mathematical model, 3) specifying an econometric model, 4) collecting data, 5) estimating parameters, 6) hypothesis testing, 7) forecasting, and 8) using the model for policy purposes. As an example, it walks through Keynes' consumption theory using U.S. consumption and GDP data to estimate the marginal propensity to consume.
Aleksey Narko
II year Management
Econometrics Final Project
I took the data set about the wealth of nations and in particular the dependence between the population and total wealth of the country (nation).
Source: http://data.worldbank.org/data-catalog/wealth-of-nations
2011 WSB-NLU
Professor: Jacek Leskow
Urbanization and its effect on environmentHILLFORT
Urbanisation and its effect on environment explains both positive and negative impacts in a broad sense. I took help from many study materials available over internet and library and tried to make a brief out of them. Hope, this presentation will help new learners to visualise the real scenario. Students of Urban Planning, Architecture, Environmental Planning, Law and sociology can use it for their reference.
The objective of this paper is to test the exchange rate dynamics by measuring the speed of adjustment of prices. In this overshooting model, we assume price stickiness (gradual adjustment). If the prices are adjusted instantaneously, we will have the monetarist view; otherwise, the overshooting one, due to slow adjustment of prices and consequently, it affects all the other variables and slowly the exchange rate. We outline, here, an approach of testing the dynamic models of exchange rate determination. This approach is based upon the idea that it is difficult to measure directly the process by which market participants revise their expectations about current and future money supplies. On the other hand, it is possible to make indirect inferences about these expectations through a time series analysis of related financial and real prices. Empirical tests of the above exchange rate dynamics are taking place for four different exchange rates ($/€, $/£, C$/$, and ¥/$). Theoretical discussion and empirical evidence have emphasized the impact of gradual adjustment and “overshooting” that it is taking place. Only for the $/€ exchange rate the monetarist model is correct.
The document discusses foreign exchange rates and several theories related to how exchange rates are determined. It provides the following key points:
1. Foreign exchange rates refer to the rate at which one country's currency can be converted into another's. The rate expresses the external purchasing power of a currency.
2. In foreign exchange markets, rates are determined by the supply and demand of currencies. Demand comes from imports, exports, and other cross-border transactions while supply comes from exports, investments, and remittances.
3. Equilibrium exchange rates occur when supply and demand are equal. Changes in supply or demand can cause fluctuations in the exchange rate.
The document discusses the asset approach model of exchange rates. It begins by introducing the idea that currencies can be viewed as assets, with the exchange rate being the price of one currency in terms of another. It then presents the uncovered interest parity equation, which is the fundamental equation of the asset approach model. This model uses interest rates and expected future exchange rates as inputs to predict the current spot exchange rate. The document provides examples of how changes in interest rates or expected exchange rates would lead to adjustments in the spot exchange rate to maintain equal expected returns across currencies.
The choice of the exchange policies in the primary commodity exporting countr...Alexander Decker
This document analyzes the exchange rate policies of Morocco and estimates the equilibrium real exchange rate of the Moroccan Dirham. It uses an autoregressive distributed lag model to estimate the long-run relationship between the real exchange rate and macroeconomic fundamentals like terms of trade, degree of openness, government expenditure, and net capital flows. The results suggest that Morocco's fixed exchange rate regime adopted in 1973 is not responsible for its trade deficit or low export growth, as the Dirham's value is close to its equilibrium level. However, other factors may be contributing to Morocco's low economic performance. The document examines theories on how exchange rates and macroeconomic variables interact and equilibrium exchange rates are estimated.
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Effect on the Foreign Exchange Market of an lncreased Demand for Euros
$1.27
1.25
Arbitrageurs-dealers who take advantage of any
d.ifference in exchange rates belvreen markets by
buying low and selling high-ensure this equality.
Their actions help to equalize exchange rates across
markets. For example, if one euro costs $r.24 in New
York but $r.25 in Frankfurt, an arbitrageur could buy,
say, $r,ooo,ooo worth of euros in New York and ai
the same time sell them in Frankfurt for $r,oo8,o6o,
thereby earning $8,o6o minus the transaction costs of
the trades.
Because an arbitrageur buys and sells simulta-
neousiy, little risk is invoived. In our example, the
arbitrageur increased the demand for euros in New
York and increased the supply
of euros in Frankfurt. These
actions increased the doilar
price of euros in New York
and decreased it in Frankfurt,
thereby squeezing down the
difference in exchange rates.
Exchange rates may still
change because of market
forces, but they tend to change
in all markets simultaneously.
The demand and supply of
foreign exchange arises from
many sources-from import-
ers and exporters, investors
in foreign assets, central
banks, tourists, arbitrageurs,
and speculators. Speculaiors
buy or sell foreign exchange
in hopes of profiting by trad-
ing the currency at a more
favorable exchange rate iater.
By taking risks, speculators aim io profi.t
from rnarket fluctuations-they try to buy
lcv"' and sell high. In contrast, arbitrageurs
take less risk, because they simultaneously
buy currency in one market and sell it in
another.
Finrlhr nannle in nnrrntrioc crrffo#no
from economic and political turmoil, such
as occurred in Russia, Indonesia, and the
Phiiippines, may buy hard currency as a
hedge againsi the depreciation and insta-
bility of their own currencies. The dollar
has long been accepted as an international
rnedium of exchange. It is also the currenry
of choice in the world markets for oii and
six times easier to smuggie euro notes than U.S. notes
of equal value.
Psdrchasimg Fcwren FarFty
As iong as trade across borders is unrestricted and as
long as exchange rates are allowed to adjust freely,
the purchasing power parity {PPP} theoiV predicts
that the exchange rate between two currencies wiil
adjust in the long run to reflect price differerrces
between the two currency regions. A given basket
of internationally traded good.s should therefore sell for
about the same around the world (except for differences
reJlecting transportotion costs and the like). Suppose a
basket of internationaily traded goods that seiis for
$ro,ooo in the United States seils for 8,ooo euros in
the euro area. According to the purchasing power
parity theory the equiiibrium exchange rate should
be $r.25 per euro. If this were not the case-if ihe
exchange rate were, say, $r.2o per euro-then you
could exchange $9,5oo for 8,ooo euros, with which
you buy the basket of commoditie ...
Foreign Exchange
Rate Deterrntnatton
and Forecastlng
The herd instinct among forecasters makes sheep
look like
independent thinkets- -Edgar R Fiedler'
LEARNING OBJECTIVES
*E,xaminehowthesupplyanddemandforanycunencycanbeviewedaSanassetchoice
issue within the portfolio of investors'
{& -bxplore how the three malor approaches to excnange rate determlnatron-pailty con-
ditioot, the balance of payments, and the asset approach-combine to explain the
numerous emerging market currency crises experienced in recent yeals.
* Observe how forecasters combine technical analysis with the three major theoretical
approaches to forecasting exchange rates'
What determines the exchange rate between currencies? This has proven to be a very diffi-
cult question to answer. Companies and agents need foreign currency for buying imports, or
*uy
"urn
foreign currency by exporting. Investors, investing in interest-bearing instruments
in ioreign
"orrntri"5
and currencies, fixed-income securities like bonds, shares in publicly
traded cimpanies, or other new types of hybrid instruments in foreign markets, all need for-
eign currenty. Tourists, migrant workers, speculators on currency movements-all of these
ec;nomic agents buy and sell and supply and demand currencies.every day.This chapter
offers somJ basic theoretical frameworks to try to organize these elements, forces, and
principles.'
Cirapter 7 described the international parity conditions that integrate exchange rates
with inflation and interest rates and provided a theoreticai framework for both the globai
financial markets and the management of international financial business. Chapter 4 pro-
vided a detailed analysis of how an individual country's international economic activity, its
balance of payments, can impact exchange rates. This chapter extends those discussions of
exchange rate determination to the third school, the asset market approach.
gxiiOit 9.1 provides an overview of the many determinants of exchange rates. This road
map is first organized by the three major schools of thought (parity conditions, balance of
payments appioach, asset market approach), and second by the individual drivers within
i6or" uppro*hes. At first glance the idea that there are three sets of theories may appear
daunting, but it is important to remember that these are not competing theories, but rather
contplementary theories.Without the depth and breadth of the various approaches combined-
out ubility to capture the complexity of the global market for currencies is lost. The chapter
concludes with the Mini-Case, The Japanese Yen Intervention of 2010, detailing Japan's
return to its guidance of market value.
234
cHAPTER I Foreign Exchange Rate Determination and Forecasting
The Determinants of Foreign Exchange Rates
Parity Conditions
1. Reiative inflation rates
2. Relative interesl rates
3. Forward exchange rates
4. lnterest rate parity
235
ls there a well-developed
and liquid money and capi.
This document appears to be a student project on interest rate parity submitted for a university course. It includes a title page with the student's name and details, a declaration signed by the student, an acknowledgements section thanking the professor for guidance, and a table of contents listing the various sections of the project. The sections discuss concepts like covered and uncovered interest rate parity, the assumptions of interest rate parity, and covered interest rate parity specifically. Diagrams and equations are provided to illustrate the concepts.
The document discusses exchange rate determination theories from international economics. It covers the purchasing power parity theory, including absolute and relative PPP. It then covers the monetary approach to exchange rates and the balance of payments under both fixed and flexible exchange rate systems. The monetary approach views exchange rates as primarily determined by monetary factors in the long run.
bothSolutions.docx1 The Empirics of Purchasing Power Parity an.docxhartrobert670
both
Solution
s.docx
1 The Empirics of Purchasing Power Parity and
Exchange Rates
The foreign exchange intervention by the French government involves the sale of a
U.S. asset, the dollars it holds in the United States, and thus represents a debit item in
the U.S. financial account. The French citizens who buy the dollars may use them to
buy American goods, which would be an American current account credit, or an
American asset, which would be an American financial account credit
Suppose the company issuing the traveler’s check uses a checking account in France to
make payments. When this company pays the French restaurateur for the meal, its
payment represents a debit in the U.S. current account. The company issuing the
traveler’s check must sell assets (deplete its checking account in France) to make this
payment. This reduction in the French assets owned by that company represents a
credit in the American financial account.
2 The QQ-DD Model
The DD-curve in the Netherlands, a smaller and more open economy than the US, is atter than the DD-curve in the US because of the following QQ-DD diagram
3 Import Tariffs and the Current Account
output growth volatility tends to increase temporarily as an economy transitions from a steady-state with a low level of capital and high markups to a steady-state with high level of capital and low markups.
Equation can be written as CA = (Sp - I) + (T - G).
Higher U.S. barriers to imports
may have little or no impact upon private savings, investment, and the budget deficit.
If there were no effect on these variables then the current account would not improve
with the imposition of tariffs or quotas. It is possible to tell stories in which the effect
on the current account goes either way. For example, investment could rise in
industries protected by the tariff, worsening the current account. (Indeed, tariffs are
sometimes justified by the alleged need to give ailing industries a chance to modernize
their plant and equipment.) On the other hand, investment might fall in industries that
face a higher cost of imported intermediate goods as a result of the tariff. In general,
permanent and temporary tariffs have different effects. The point of the question is that
a prediction of the manner in which policies affect the current account requires a
general-equilibrium, macroeconomic analysis.
4 Monetary and Fiscal Policy under Different
Exchange Rate Regimes
Figure can be used to show that any permanent fiscal expansion worsens the
current account. In this diagram, the schedule XX represents combinations of the
exchange rate and income for which the current account is in balance. Points above and to the left of XX represent current account surplus and points below and to the
right represent current account deficit. A permanent fiscal expansion shifts the DD
curve to D'D' and, because of the effect on the long run exchange rate, the AA curve
shifts to A'A'. The equilibrium point moves from 0, where the current a ...
This document provides an overview of international economics and the balance of payments. It discusses:
1) The balance of payments accounts record international transactions and whether an economy is a net lender or borrower based on current and capital account balances.
2) Historically, exchange rates were fixed under the Bretton Woods system but countries now choose between fixed and floating rates.
3) Exchange rates affect trade by determining the prices of internationally traded goods and services. Fluctuations impact producers and financial asset holders.
1) The document discusses the monetary model of exchange rates and its predictions. The model predicts that exchange rates will follow the relative money supplies and inflation rates of the two currencies.
2) The model assumes that real money demand is constant, but evidence shows that money demand decreases with higher interest rates. This means the original model is too simplistic.
3) When updated to reflect interest rate effects on money demand, the model implies exchange rates, inflation rates, and interest rates will equalize in the long run between countries according to purchasing power parity and uncovered interest rate parity.
- The document discusses various theories of exchange rate determination, including supply and demand, purchasing power parity, balance of payments, monetary approach, and portfolio balance approach.
- It also examines factors that influence exchange rates like inflation differentials, interest rates, money supply, and diversification of investor portfolios.
- Forecasting exchange rates is difficult due to many influencing factors and uncertainty around data used in formulas; the foreign exchange market may not be fully efficient.
Covered interest parity a law of nature in currency marketsGE 94
CIP is a cornerstone principle in international finance. First described by John Maynard Keynes in 1923, the idea that FX forward rates must reflect interest rate differentials between currencies has long been considered one of the best tested theories in financial economics. If a market participant is willing to swap a higher yielding currency for a lower yielding currency over some time horizon, he must be compensated for the difference in yield via an adjusted forward price. Otherwise an arbitrage opportunity arises until prices and interest rates align again.
The financial crisis and direct aftermath revealed cracks in the armour of CIP. In a market environment with scarce liquidity and high credit risks in forward markets, dealers were constrained in their ability to profit from what was previously regarded as an almost risk-free arbi¬trage trade. But as conditions in financial markets slowly normalised after the crisis, CIP deviations remained and cross-currency basis never returned to its pre-crisis levels. After narrowing for some time, it started to widen again across most G10 pairs since approximately 2015. Increasingly, FX forward markets seemingly do not reflect what would be expected given the observed interest rate differentials. Figure 1 illustrates these dynamics by depicting the magnitude of G10 cross-currency basis over time for an exemplary three-month tenor.
Linkages between extreme stock market and currency returnsNicha Tatsaneeyapan
1) The document investigates the empirical link between extreme events in local stock and currency markets for 26 countries using daily return data from 1996-2005.
2) Preliminary results show that in some emerging markets, an extreme stock market decline increased the probability of an extreme currency depreciation on the same day.
3) For currency markets, there is evidence of spillover of extreme events within regions, but limited influence across regions. Extreme events in stock markets are more globally interconnected, especially when originating from the US.
This document discusses currency exchange rates and economic growth. It provides details on how exchange rates are determined between currencies, including factors that affect exchange rate spreads. It also outlines several economic theories related to what drives long-term economic growth, such as investment in physical and human capital, as well as productivity gains from technological development. Key growth accounting relationships are presented, linking output growth to contributions from capital deepening, increases in the labor force, and improvements in total factor productivity.
This document provides an overview of monetary policy tools and frameworks in Pakistan. It discusses the monetary policy tools used by the State Bank of Pakistan including monetary base, reserve requirements, discount window lending, and interest rates. It also explains key monetary policy frameworks like the money market, goods market equilibrium, money market equilibrium, and the ISLM model. The goals of monetary policy are outlined as price stability, high employment, economic growth, interest rate stability, financial market stability, and foreign exchange market stability. Key monetary policy concepts like the money market, goods market equilibrium, and liquidity trap are also summarized.
Basis risk refers to the mismatch in performance between a position hedged using a futures contract versus the underlying asset. The more dissimilar the hedged position and underlying asset are, the greater the basis risk. Factors like interest rates, yields, and the composition of a portfolio can cause the hedge to be imperfect, resulting in basis risk. Basis is the difference between the futures and spot price, and is impacted by costs like storage and interest rates. Unexpected changes in basis over the hedging period represent basis risk.
This paper will show the endogenous channel of monetary policy under a Sraffian
context. That is, assuming a distributive variable as exogenous. In this case we say that
the interest rate is determined by constitutional features and is set exogenously by the
central bank to the level that it wants.
In this scheme, banks have a central role. The possibility of extending credit without
the need for prior deposits, makes them a key driver of economic growth. Since the
loan amount is determined by the demand for credit rather than deposits, the concept
of effective demand cannot be dissociated from the analysis.
The implications of monetary and fiscal policy should also not be ignored.
This document summarizes a study that examines how agents in an artificial currency market evolve their forecasting rules over time using a genetic algorithm. It finds that when agents are allowed to adopt misspecified forecasting rules, it can lead to persistent exchange rate dynamics. Specifically:
1) The model considers an artificial currency market with two currencies where agents use a genetic algorithm to evolve their forecasting rules for the exchange rate over time.
2) When agents are restricted to using correctly specified linear forecasting rules, learning tends to converge. But when agents can adopt misspecified nonlinear rules, it can result in unstable exchange rate dynamics over long periods.
3) This occurs because misspecified rules may appear reasonable
Similar to Fiancial Econometrics Paper - Final Draft (20)
2. 2
Part 1: Purpose, Notation, and an Introduction into International Currency Exchange Markets
The purpose of this paper is to examine--from an econometric approach--the metrics at play in
international currencymarkets, the potential drivers of the frictionbetweenthese marketswhich cause
deviation from Purchase Power Parity in the short run, theorized statistical methods through which
economists generate exchange rate forecasts and investors exploit arbitrage opportunities, and an
analysisof the empirical resultsof these statistical instruments.We will conclude withanexplanationof
our findingsfroma strictlyempirical perspective. Letusfirstlay the foundation forthis study by defining
the keyterms andgeneral notations thatwill be usedthroughoutthispaper,and byreviewingtheof short
andlongrunequilibrium conditionof domesticmoneymarketsaswellastheirrelationshiptoequilibrium
in foreign exchange markets.
The notation to specify the time interval associated with a “holding period” will be represented
by subscripts. The beginningof anasset’s holdingperiodwill be denotedbysubscript(t),withthe endof
that the holding period denoted by subscript (t+1).
The notationtospecifywhetheravariable isa characteristicof the domesticeconomyoraforeign
economywillbe representedbysuperscripts.Domesticvariablesof interestwillbedenotedbysuperscript
(*), withforeignvariablesof interest will be denotedbylackof a subscript. The domesticeconomy willbe
the economyinwhichanassetisfunded,andthe foreigneconomywill be the economyinwhichanasset
is borrowed. For simplicity strictlywhen generating formulas or expressions the domestic economy will
be the United States, and the foreign economy will be Europe, unless noted otherwise.
The nominal interestrate,denoted asi,represents the interestearnedon financial assetsheldin
an economy.The real interestrate,denotedasr, representsthe interestearnedonfinancial assetsheld
in an economy less that economy’s rate of inflation, where the inflation rate is denoted as π. The
mathematical representationof nominal andrealinterestrates are then,i =(1+i) andr= i –π respectively.
The nominal exchange rate,denotedas ϵ,isthe price of oneUSdollarintermsof foreigncurrency.
For Example,if itcostsone andahalf unitsof foreigncurrencytopurchase one unitof domesticcurre ncy,
the nominal exchange rate would equal 1.5€/$ or ϵ = 1.5. The real exchange rate, denoted as q, is the
price of one unitof US goodsin termsof foreigngoods,wherethe domesticprice levelwill be denotedas
P*, and the foreign price level will be denoted as P. The mathematical expression for the domestic real
exchange rate is then, q = ϵ(P*/P).For Example, If a US shirt costs 50 dollars, the nominal exchange rate
is 6, and a European shirt costs 100 euros, then q = ϵ(P*/P) would be calculated as 3 = 6*(50/100).
3. 3
These terms are essential in understanding the dynamics between the short run supply of and
demand for domestic and foreign currency, as well as how short run equilibrium is determined in the
nominal exchange market.1
Review Figure 1, which plots the nominal exchange rate on the vertical axis
and the quantityof currency exchanged onthe horizontal axis. The upwardslopingcurve representsthe
supply of domestic currency to foreign investors. To understand why it slopes upward, notice when the
nominal exchange rate rises the purchasing power of domestic currency rises relative to that of foreign
currency(makingdomesticimportsof foreigngoodsandservicescheaper).The downwardslopingcurve
represents the demand for domestic currency by foreign investors. To understand why it slopes
downward,notice whenthe nominalexchange rate falls the purchasingpowerof domesticcurrencyfalls
relative to that of foreign currency (making foreign imports of domestic goods and services cheaper).
Short run equilibrium in the nominal exchange market is the point where the supply of and demand for
the domestic currency intersect. This equilibrium, shown in Figure 1, relates the quantity of domestic
currencyexchangedforforeigncurrencyatanygivennominal exchangerate. Note thatinthismodel,the
nominal exchange rate is measured as €/$.
Supply in the nominal exchange market is essentially a combination of domestic demand for
foreigngoodsandservices,anddomesticdemandforforeignfinancial assets (suchasreal estate,mines,
factories,bankaccounts,stocks,bondsand treasurybills).There are twocausesof shiftsinthe supplyof
domesticcurrency:achange inthe domesticlevelof income,andchange inforeignnominal interestrate.
Anincrease todomesticincome shiftsthe supplyof domesticcurrencytothe right,asdomesticinvestors
1 For more information on international financesee“International Economics”
4. 4
will have the ability to buy more foreign goods and services. Rising foreign interest rates also shiftsthe
supplyof domesticcurrency rightward.Thisis because domesticinvestorswill wanttoholdmore assets
inforeigncurrency. A rightwardsupplyshiftresultsinadecreasethe domesticnominal exchangerate and
an increase indomesticoutput.The resultingdecreaseinthe domesticnominalexchangerate represents
a domestic currency depreciation.
Similarly,demandinthe nominalexchange marketisessentiallyacombinationof foreigndemand
for domestic goods and services, and foreign demand for domestic financial assets (such as real estate,
mines, factories, bank accounts, stocks, bonds and treasury bills). There are two causes of shifts in the
demandfor domesticcurrency:a change in the foreignlevel of income andchange in domesticnominal
interest rate. An increase to foreign income shifts the demand for domestic currency to the right, as
foreign investors will have the ability to buy more domestic goods and services. Demand for domestic
currencyalsoshiftsrightif domesticinterestratesrise.Thisis because foreigninvestorswillwanttohold
more assetsindomesticcurrency. A rightwarddemandshiftresultsinanincreasesthe domesticnominal
exchange rate and domestic output. The resulting increase in the domestic nominal exchange rate
represents a domestic currency appreciation.
Using Figure 1 which relates the nominal exchange rate to the short run equilibriumquantityof
currencyexchange atthe intersectionof the supplyof anddemandforcurrency,we are able toconstruct
a graphicrepresentationthatrelatesthe nominalexchangerates tothelevel ofdomesticeconomicoutput
inthe short run inFigure 2. Here the DD schedule isderivedfromall potential combinationsof the supply
of and demandforcurrency inthe shortrunequilibrium conditionwe discussedinFigure 1.Ourobjective
isnowto relate the domesticmoneymarkettothe foreignexchange market.InFigure 3, the AA schedule
represents all possible combinationsof real exchange rates and output levels that keep the domestic
money market and foreignexchange market in equilibrium. Figure 4 combines these schedules, relating
these two markets. Creating this graphic representation, we are able to better understand how foreign
exchange rates relate to interest rates, the level of income, the price level, and the money supply.
5. 5
It is important to understand the factors that cause the AA and DD schedule to shift. The DD
schedule will shift rightward in reaction to an increase in domestic government spending,a decrease in
domestictaxes,anincrease ininvestmentdemand,adecrease inthe domesticprice level relative tothe
foreign price level, a decrease in domestic savings, and an increase in demand for domestic goods and
services.The AA schedulewillshiftsrightwardinreactiontoanincrease inthe domesticmoneysupply,a
decrease in the domestic price level,an increase in the expectedexchange rate at the end of an asset’s
holdingperiod,anincrease inthe foreigninterestrate,anda decrease indomesticreal money demand.
Itisobviousatthispointof the natural linkbetweenthe moneymarketsandthe foreignexchange
markets.We are able to showgraphicallythislinkthroughFigures5and6, where we take acloserlookat
the twocauses of marketfluctuationwe discussedinFigure 1. Figure 5 displayshow a change in foreign
interest rates (due to an increase in the foreign economy’s money supply) affects the equilibrium
condition in both the domestic money market and the foreign exchange market. Similarly, Figure 6
6. 6
displays how an increase in the domestic level of income (outward shift in the money demand curve)
affects the equilibrium condition in the domestic money market and foreign exchange market.
Understandinghowthese marketsrelate toone anotherisessential inforecastingtheequilibrium
conditionof these markets inthe longrun.Now we willlook atthe longruneffectof apermanentchange
in the moneysupply,which as statedpreviously drivesfluctuationin bothmarketsby changingthe level
of inflation (therefore changing the expected exchange rate) at the end of an asset’s holding period.
Figure 7 showsthe relationship betweenthe foreignexchange marketandthe moneymarketin
longrun equilibrium where the purchasingpowerparityconditionholds.Figure 8displaysmovementto
short run equilibrium inresponse toapermanentincrease inthe domesticmoneysupply onthe leftside
of the graph, as well as movement from this short run equilibrium to long run equilibrium on the right
side of the graph.
Let us look more closely at Figure 8. Note that in this model, the exchange rate is measuredas
$/€. Initially the markets are in long run equilibriumat point 1. If the domestic central bank were to
permanently increase the money supply by raising the rate of monetary growth (engaging in easy
monetarypolicies),there wouldbe animmediate increaseinthesupplyof domesticcurrency,whichshifts
the real domestic money supply downward. Observe how the increase in the domestic money supply
7. 7
shiftsdomesticMSdownward fromMS1
US toMS2
US, and causesthe domesticrate of returnshiftleftward,
a decrease fromR1
$ to R2
$ in the domesticmoneymarket.To understandwhy,rememberour definition
of the real interest rate is the nominal interest rate less the inflation rate. Permanently increasing the
money supply would then permanently increase the expected rate of inflation, resulting in the lower
return to domestic assets. Because the return to domestic currency has decreased, the expected return
to foreigncurrencyincreases,whichisrepresentedinthe rightwardshiftinthe expectedeuroreturn.The
resulting short run equilibrium is now at point 2, where the equilibrium exchange rate has increased in
the foreign exchange market.The increase in the exchange rate associate with point 2 is a depreciation
of domestic currency against the foreign currency.
In the long run,pricesbecome flexible sothatthe domesticprice level adjuststothe permanent
change in the money supply. As this process takes place, the real domestic money supply shifts back
upward to its initial level do to the increase in P1
US to P2
US, which increases the return to assets held
domesticallyfromR2
$ back to itsinitial level atR1
$ as well.The curve that representsthe expectedreturn
to foreign currency, however, is not affected by the increase in the domestic price level. The long run
equilibrium therefore decreases to point 4. Therefore, in the long run the permanent increase in the
money supply has no effect on the domestic money market, but results in a permanent increase in the
exchange rate in the foreign exchange market: the domestic currency has permanently depreciated
against the foreign currency.
8. 8
Part 2: Spot Transactions, Futures Contracts, and the Three Purchase Interest Parity Conditions
Now that we have an understanding of what factors drive the fluctuation of exchange
rates,we can beginanalyzinghowarbitrage opportunitiesarise.The “Law of One Price”statesthatwhen
convertedintoacommoncurrency,the pricesof identical goodsandservicessoldindifferent economies
shouldhave the same value.2
Recall fromPart1 thatthe real exchange rate equalsthe nominal exchange
rate adjusted for difference in the price levels of two economies, q = ϵ(P*/P). To convert the different
price levelsintoone commoncurrency.Byrearrangingthe termsof this formulatosolveforthe domestic
price level. This conditioncreates what economist and currency investors refer to as “Purchasing Power
Parity”(PPP). Figure9exhibitshowthe conceptof purchasepriceparityrelatestothe longrunequilibrium
of money markets and foreign exchange markets:
2 For details on the link between interest rates, exchange rates, and the parity conditions see“A note on Parity
Conditions (CIRP,“FP”, UIRP, PPP) and Carry Trades”
9. 9
Our studyof the manyvariantsof purchase powerparity beginsbydefiningabsolute andrelative
PPP. If absolute PPP holds, the real exchange rate should equal one. In practice, absolute PPP at many
times will fail to hold true for some goods and most services. Relative PPP, a less restrictive variation,
claimsthat the differentinthe twoeconomies inflationrateswill measure the degree of appreciationor
depreciationin acurrencyalongthe holdingperiod.Relative PPP,iscomputed mathematicallyas Δϵ / ϵ =
π – π*, where Δϵ represents the change in the nominal exchange rate, π represents the rate of foreign
inflationand π*representstherate of domesticinflation. WhereasinabsolutePPP,if the law failstohold
the real exchange rate fluctuatesaround1, with relative PPPthe real exchange rate remainsconstantas
movementsinpricelevelsare offsetbymovementsinthe nominalexchange rate.Inpractice,relative PPP
has proven empirically to the more accurate measure in explaining exchange rate fluctuation in the
medium to long run.
It is also important to understand two types of currency transactions: spotsand futures. A spot
transactionwill be denotedas ϵ for simplicity,because the transactionsprice of aspot transactioninthe
currenttime period issame asthe nominalexchange rate.Withfuturescontracts,denotedasF,the buyer
and seller of the currency instrument agree to reverse the transaction at a future date, but hold the
repaymentprice paidatthe endof the holdingperiod atthe currentnominal exchangerate.Thisholding
period could be a week, month, years,etc. It is important to understand in a futures contract, investors
have potential tospeculate and hedge againstrisk,because the future nominal exchange rate may have
increasedordecreased.The difference inthese transactions fostertwoPPPconditions we willfindtobe
major elements in our study: covered and uncovered interest parity.
Covered Interest Parity takes place in the presence of futures contracts. It states that a trader
investingatthe domesticnominal interestrate (i*) mustearnthe same return as an investorexchanging
domestic currency for foreign currency in the current time period, earning the foreign interest rate (i)
during the holding period, and converting the investment back to domestic currency at the end of the
holding period at the nominal interest rate locked in by the futures contract. There are two ways to
express covered interest parity mathematically: CIP exact and CIP approximate.
CIP exactis measuredas CIPexact = 1 + i = (ϵ*
t/F)(1 + i). It is typicallymore accurate to use the CIP
exact when forecasting against developing economies due to the significantly high interest rates
associated with emerging markets. A more commonly used expression known as CIP approximate is
measuredas CIPapproximate = (F – ε*
t/ ε*
t) = i – i*. WhenCIPholds,as itshould,there shouldbe noexistence
of arbitrage opportunities.If conditionsprovoke CIPtofail,traderstendtoborrow assetsatlow domestic
10. 10
interestratesandfund assetsat the higherinterest ratesof foreigneconomies. The exploitationof these
arbitrage opportunities exerts pressure on price levels in the two economies until CIP is restored.
Uncovered Interest Parity takes place when there is no presence of a futures contract. It states
thatonaverage,tradersinvestingindomesticcurrencyshouldmakethesame returnontheirinvestments
as investors buying foreign currency, earning the foreign nominal interest rate, and converting their
investmentsback to domesticcurrencyat the domesticnominal interestrate at the time of maturity,or
(ε*
t+1). The mathematical representationof uncoveredinterestparity is then, UIPapproximate = (E(ε*
t+1) – ε*
t/
ε*
t) = i – i*, where E(ε*
t+1) denotesthe expectedvalue of the domesticnominal exchangerate at the end
of the holding period.
Part 3: The “Forward Premium Puzzle” and the Theories that Seek Explain its Existence
The formof currencytradingof we will focusonforthe durationof thispaperiscarrytrade.Carry
traders concentrate their investments in high-yielding currencies in an attempt to profit from the yield
spread. One of the most basic principles of financial econometrics states that on average a zero-cost
investment, suchascarry trade, shouldgenerate zeroexpectedreturn. However,historicallythisformof
trading generates small positive returns the majority of the time it is executed. Our study in Part 2
explained twovariantsof PPP, coveredand uncoveredinterestparity.The UIP conditionstatedthat the
degree of appreciationof the fundedcurrencyneededtoeliminate arbitrage isdirectlyrelatedtothe yield
spreadbetweenthe twoeconomies,where the yieldspreadisconsideredtobe an unbiasedpredictorof
fluctuation in the spot exchange rate. The CIP condition stated that due to forward contracts, there is a
natural link between the spot and forward exchange rates, where the forward exchange rate acts an
unbiased predictor as well. As we stated, these conditions are compared to the PPP condition, the
observationthatnationalprice levelsshouldequaloneanotherwhenconvertedtoone commoncurrency.
Most economists agree that the UIP and CIP conditions should hold, meaning a trader investing
inforwardcontractswithdevelopingcountriesthathave relativelyhigherinterestratesshouldexpectthe
funded currency to depreciate along the holding period (eliminating arbitrage opportunities). However,
empirical studies have indicated the exact opposite: high interest rate countries tend to appreciate
creating the positive average returns captured in carry trade. This is the basis of one of the largest
international financial economic anomalies today, known as the “Forward Premium Puzzle.” Over the
recent decades, many economists have sought to solve this puzzle. While some economists have been
able to partially explain potential causes of this anomaly, none have succeeded in deriving a complete
11. 11
explanation for deviations from the law of one price. Before we begin discussing how to exploit the
forward premium puzzle, it is important to cover a few of these economist’s findings. Generally, the
researchof economiststhatsucceedsin explainingdeviationinthe short run, fail to explaindeviationin
the long run. Likewise, research that succeeds in explaining deviation in the long run, fails to explain
deviation in the short run.3
First,letuslookat the shortrun. One explanationisthe existence of transportationcosts,tariffs,
andnontariff barrierscreate frictioninthe international markets.Transportationcostshave the potential
to create differences in domestic and foreign price levels.Over the last decade the level of worldtariffs
have beendramaticallyreduced,yetsome remaininplace andwill inevitablydiscourage assetallocation
relative to a hypothetical tariff free environment. With nontariff barriers, exporters operating with a
limited supply must charge a premium price in order to offset the costs of initially surmounting the
barriersaswell asgainingsomeof the rentsassociatedwithinternationaltrade whengovernmentforeign
exchange policy fails to prohibit rent seeking among private entities. Many economists succeeded in
proving empirically that nontariff barriers can partially explain some of the deviation from PPP.
Another way to explain the failure of short run PPP is through price stickiness. Price stickiness,
however,failstocompletelyexplaindeviationsfromPPPinthe longrun.Afteraperiodof abouttwoyears
prices typically become flexible, but convergence to long run PPP usually takes much longer. One of the
most popular economists today, Paul Krugman, explainssome of this puzzle through a concept called
“pricing the market.” Pricing the market takes place with monopolistic firms that refuse to provide
warranty services for goods to consumers in one country who have purchased the goods in another
country. By limiting arbitrage this way, producers then have the ability to discriminate prices across
internationalmarkets. While manyattemptstolimitmonopoliesabilitytoprice the marketthroughfiscal
policies, pricing the market does occur and continues to create some deviation in the short term.
Anotherhypothesisisknownasthe Balassa-SamuelsonHypothesis focusesmore onthe longrun.
This theoryarguesthat whenall price levelsare convertedintodollarsusingthe nominal exchange rate,
there are higher price levelsassociated with rich countries relative to poor countries because wealthier
countriestendto be more productive inthe traded goodssectorof theireconomies.Insmall developing
countries,the price levelof the tradedgoodssectoristiedtothe worldprice level.Therefore,anincrease
inproductivityinthesecountriesresultsinanincrease inwagesearnedbylaborersof tradedgoods.If the
3 For more information on the theories discussed in this section,see“The PurchasingPower Parity Puzzle”
12. 12
non-tradedgoodssectorsfail to increase inproductivityatthe same rate as the tradedgoodssector,the
only way that wages will remain competitive across sectors would be to increase prices. Under the
assumption that there is one constant component and one increasing component of the CPI, thiswould
inevitably cause the CPI of the developing country to increase. If both components were to increase in
productivitysimultaneously,there wouldbe norelative price effect,andtherefore nochange tothe real
exchange rate. Compared to the theory of stick priceswhich was a short term explanations in deviation
from PPP, the Balassa-Samuelson theory partially explains long term deviations. Through shifts in the
terms of trade, we are able to account for significant movements in real exchange rates.
A similarlongrun theorypredictsthatrichcountrieswill havehigherexchangerate adjustedprice
levelsduetothe factthattheircapital-laborratiosare higherrelative topoorcountries,ratherthanbeing
dependentonthe assumptionof higherproductivity.Since highercapital-laborratiosimplieshigherwage
rates, labor is cheaper in poor countries. Through the study of international trade there is evidence of
poor countries being labor intensive relative to wealthy capital intensive countries. Coupled together,
these twofactslead us again to the conclusion that wealthy countries should have higher price levels.
Another long run theory takes account deficits into consideration.The argument here is that
sustaineddeficitsare directlyrelatedwithreal exchangerate depreciation.While these twovariablesdo
exhibitempirical correlation,there ismuchdebate as to whetherthiscorrelationisa resultof causation
due to the fact that there are manycausesof currentaccount deficitsthatare not directlyrelatedtoreal
exchange rates.Proponentsof thistheoryare quickto emphasize correlationandcausationbecause the
borrowingandlendingbetweencountriesthat isassociatedwithsustainedcurrentaccountdeficitsleads
to a transfer of wealth across countries. Government spending has also been considered as a potential
cause for fluctuation in the real exchange rate. Because government spending tends to fall more on the
non-traded goods sector, a rise in government spending at many times leads to increases in the real
exchange rate. Proponents argue when taxes are used to finance government spending programs, it is
possible for fiscal policy to cause fluctuation in real exchange rates.
All of these theories can partially explain deviation from PPP, but all fail to provide a complete
explanationof the forwardpremiumpuzzle inthe short,medium, andlongrun. We conclude that inthe
short run, PPP does not hold, and convergence to PPP in the long run can take many years. Most
explanationsthattendtofocuson monetaryand fiscal policiesare able toexplainthe puzzleinthe short
run, but fail to provide evidence for the long run. The theories that focus on shocks to productivity, and
consumer preferences are able to explain some of the long run convergence back to PPP, but fail to
13. 13
provide evidence for exchange rate volatility in the short run. In reality a complete explanation of
deviationof PPPwillbe amultivariatemodelcontainingmanyof these theoriessimultaneously,assuming
some variablestobe purelytemporaryandotherspermanent.Everydayinternationalgoodsmarketsare
continuing to become more integrated, but until they become as integrated as domestic goods market
segments these markets will continue to generate various sources of friction among international
economies.
Part 4: The Exploitation of Arbitrage Opportunities and the “Trader’s Decision Problem”
Now that we have created a solid understanding of the dynamics of international currency
marketsas well as howarbitrage opportunitiesarise inthem, the questionbecomes“whatmethodscan
be used bythe carry traderto capture returninthe market.Let usbeginbyrecallingone of the principles
of econometric analysis: a zero cost investments, such as carry trade, should generate zero expected
return on average (assuming the absence of arbitrage opportunities). Throughout our discussion, the
econometricmodelswe will builduponrepresent stochasticprocesses.The modelswe buildwillthenbe
used in generating forecasted outcomes of financial variables of interest.4
Let Et denote the expected
value of returnatthe currenttime period,andletxt+1 denote thereturntoazerocostinvestmentstrategy
for a risk-neutral investor in the absence of arbitrage. We can then express this econometric principle
mathematically by:
What this expressionimpliesisthaton average,one wouldexpecta return of zero to theircarry
portfolio.Nowwe addastochasticdiscountfactorwhichwillsummarize the interactionof outcomesand
consumerpreferences.Thisfactor representsthe potential combinationof pseudo-probabilitiesimplied
bythe investor’schoice of consumption,andisdeterminedbythe outcomesthesepreferences associated
withthe conditionof worldmarketsandothersourcesof risksothatthe value of the trader’sinvestment
is dependent on its ability to generate return at the current condition of the world markets. This
expression, where mt+1 represents the stochastic discount factor, then becomes:
4 For more information on the expressions derived in this section as well as the characteristicsof stochastic
processes see “Carry Trade”
14. 14
To geta betterideaof whatthisformulaimplies,assume wehave borrowedone unitof domestic
currency at the domestic interest rate by selling the domestic security short, then we purchase the
equivalentunitof foreigncurrencywiththe same date of maturitythatyieldsthe foreigninterestrate.At
the time of maturity, the transaction is reversed.
For those not familiar with Investment jargon, selling a currency short means it is not currently
ownedbyaninvestor,andthereforemustreturnthe same securitytothe lenderatanagreedupondate.
This strategyis usedwhenanticipatinga decline invalue,resultinginrepaymentof the securitylessthe
depreciated value which leaves the difference as return to the investor who sold short. By the same
measure, the investment of foreign currency would be a process known as going long.
At the time of maturity,the fundedforeigncurrencyistransformed backtodomesticcurrencyat
the spot exchange rate,denotedas ε*
t+1. Alongthe term, the returngeneratedbythe foreignsecurity is
equal to the foreign interest rate, so that return is represented mathematically by (1 + it). Proceeds will
then be used to repay the borrowed principle as well as the interest associated with it. We will denote
the value of this interest payment as it+1. Remembering this form of investment should generate zero
expectedreturn onaverage, the expressionwithwhich we can measure the expectedcarrytrade return
of a spot transaction is then:
With respect to the stochastic process, we must then take the natural logarithms, using the
approximation ln(1 + it) ≈ it, denoting ln(ε*
t) = et, and Δet+1 = et+1 – et. The stochastic expression for the
expected carry trade return of a spot transaction is then:
Assuming the trade is operating under risk-neutrality and assuming the absence of arbitrage implies:
This measure also expresses uncovered interest parity in that:
Reverting back to and modifying expression (3) for the expected carry trade return of a spot
transaction, we can express the expected carry trade return of an investor who instead purchased a
15. 15
futurescontract,denotedasFt.Holdingthe assumptionthatthe investorhasriskneutralpreferences,this
measure expresses covered interest parity where the forward rate is again an unbiasedpredictor of the
spot exchange rate at the time to maturity. The expected carry trade return of a futures transaction is
then:
To complete the trinityof parity conditions,wemodify versionof ourexpressionforthe expected
carry trade returnof aspottransaction once more toreflectthe valueof the expectedreturn inrealrather
than nominal terms.Let the real interestrate,denotedrt, equal the nominal interestrate in the current
time period less the inflation over the course of the holding period, so that r*t = i*t – π*t+1 where π*t+1 =
Δp*t+1 an letp*t = ln(P*t).Let the same notation methodapplyfor foreign economies so that rt
= it
– πt+1
where πt+1 = Δpt+1 and by letting pt = ln(Pt). With respect to the stochastic process, the logarithm of the
real exchange rate, denoted as qt+1, would be measured by qt+1 = et+1 + (pt+1 – pt+1).
The stochasticconditionknownas “first orderweaklystationary”statesthat for a processto be
firstorder weakly,all randomvariablesmusthave the same meanor expectedvalue.Forthisexpression
tobecome aweaklystationaryprocess,wedenotethe fundamentalequilibriumexchange rate (FEER) that
the natural logarithmof the real exchange rate (qt+1) revertsto inthe longrun as, ɋ. The expression then
becomes qt+1 = ɋ + Ø(pt+1 – p*t+1).
Now expression(4) which weobtainedbytakingthenatural logarithmof theexpected carrytrade
return of a spot transaction can be rewritten as:
Again,assumingthe absenceof arbitrage,the degreeof expectedreal exchangerate appreciationequals
the expected value of the spread between the real interest rates, that is, Et(qt+1) = Et(rt – r*t).
We can nowuse interactionof interestrates, exchangerates,andlongrunequilibrium condition
under purchasing power parity as a stochastic process regressed against the nominal exchange rate to
generate forecasts for future time intervals. Review the stationary random vector for Δyt+1 below:
16. 16
If the stochasticprocessof thissystemislinear,we use the VectorErrorCorrectionModel (VECM). VECM
is one of the most common models used among economists and currency traders. There are four
characteristics of VECM models that differentiate them from other statistical models. First, they are
bivariate systems,wherewe modeltwostochasticprocessesjointly.Second,eachequationhasthe same
regressorsaswell asthe same numberof lags,builtuponan autoregressive structure.Third,all variables
onthe leftandrighthandside of the equationare stationaryduetothe cointegrationthatexistsbetween
them. Fourth, there must be at least one adjustment coefficient different from zero (otherwise there
wouldn’tbe cointegration). The first order of the vector error correction model for the system is then:
Comprised within this expression are three “signals” that can be analyzed individually by carry
traders:the carry signal,the value signal,andthe momentumsignal.Thesesignalsare sub-strategiesthat
can be used individually based on the carry trader’s preferences. Collectively, CMV signals are the
foundation from which entire VCM portfolios have been built. Let us look at each of the three sub-
strategies individually before covering the VECMmodel in more detail.
The carry strategy (C) can be expressed mathematically as Δět+1 = 0. This strategy focuses solely
on the expectedvalue of the real domesticinterestrate lessthe real foreigninterestrate indetermining
which currency should be sold short, and which to go long in. The momentum strategy (M) can be
expressedmathematicallyasΔět+1 =βeΔet. Assumingβe to be equal tozero,thisstrategyusesthe value of
the nominal exchange rate inthe current periodto be the best forecastof the exchange rate at the end
of the term. The value strategy (V) can be expressed mathematically as Δět+1 = ϒ(qt - ɋ), and is used to
forecast the degree of currency appreciation or depreciation via the value of the PPP signal. The VECM
model is used in forecasting deviations of the real exchange rate from the fundamental equilibrium
exchange rate,andisoneof themostaccurate methodswithwhichwe canexpresstheuncoveredinterest
parity.
The currencies which an investor should borrow and which an investor should fundcan then be
taken by inputting the results from any of these strategies into the expression (10). This expression
represents the direction of a carry trade for it to be profitable at the end of the holding period. In this
expression, xt+1 is the VECMstrategy result:
17. 17
The ex-post realized return of the investment is then:
Expressions(10) and (11) reveal a veryimportantcharacteristicof carry trade.The probabilityof
generatinga positive investment ismore dependent onthe investor’sabilitytoforecastthe directionof
the trade correctly than the investor’s ability to accurately forecast the expected change in the real
exchange rates (Δet+1) at the end of the holding period.
All of these trading strategiesare generatedthrough statistical modelsusingthe propertiesof an
asset’s first and second moments. The “Trader’s Decision Problem” is that an investor must, however,
develop aninvestmentstrategythatreliesmore heavilyongenerating performance criteriathatappeals
to aportfolio’s requiredreturnwhilerespectingthe degreeof riskassociatedwithindividualperformance
preferences. We beginhow to solve this problem by modifying the expressions we coveredin Part 4 to
determine the direction of a carry trade as well ascalculate ex-postrealizedreturns.We will use amore
general notation knownas a “genericscoringclassifier,”whichenables the analysisof multiple classifiers
to generate forecasts,ratherthanjustusingthe conditional momentsof ourinformationset.The implied
increase in independent variables is simply the transformation of our information set to a multi-variant
econometric model. Incorporate this scoring classifier, the trade directionexpressionthen will become:
dt+1
= sign(δt+1
– c), where δt+1
represents the classifier and c is a scalar that can take any value in the
interval cЄ {-∞,∞}. Incorporatingthisnotation, the total numberof observations thatencompassacarry
portfoliocanbe expressedbyeachindividual forecast(decision) andtheirassociatedoutcomes.Observe
Figure 10:
In thistable,TN(c) refersto the true classificationratesof negative outcomes,while TP(c) refers
to the true classificationratesof positive outcomes.Likewise,FN(c) referstothe false classificationrates
18. 18
of negative outcomes, while FP(c) refers to the false classification rates of positive outcomes. Negative
rates andpositive ratesare representative of currencysoldshortandcurrency fundedlong,respectfully.
Aswe wouldexpect mathematically,the sumof TN(c) andFP(c) is equal toone,andthe sumof FN(c) and
TP(c) is equal toone. If we letthe total numberof observationsinaportfolio(N),equalsthe sumof total
shorts (S) and the total numberof longs(L),then N = S + L. Throughthese denotations,we cancompute
the empirical values of TN(c) and TP(c) as:
All possiblecombinationsof true outcomescanbe representedgraphicallyinthe same mannera
production possibilities frontier is constructed. This PPF is shown in Figure 11, where the Correct
Classification Frontier (CC Frontier) represents all possible combinations of true outcomes. The Perfect
ClassifierFrontierextendshorizontallyfromthe Y-axisat the value of 1 and verticallyas well asX-axisat
the value of 1, and represents the points along the frontier in which all realized outcomes matchedan
investor’s trade directionpredictions.The UninformativeClassifierFrontier,representsaclassifierwhere
TP(c) = FP(c) =1 – TN(c) foranyscalarvalue.Thislineisoftenreferredtoasthe “coin-toss”diagonal. Utility
optimization, as we would expect, occurs at the point of tangency along the CC frontier. In equilibrium
(pointof tangency) the marginal rate of substitutionbetweenprofitable longsand shortswouldbe equal
to -1.
19. 19
We are then able to define the utility of classification using the expression:
With the point of tangency along the utility classification function calculated as:
Another useful statistic is the Kolmogorov-Smirnoff statistic (KS) which compares the average
correct classificationabilityof aclassifieragainstacoin-tosser.The KSstatisticis measuredbythe vertical
distance between the CC frontier and the coin-toss diagonal. The formula used in measuring the KS
statistic is calculated:
The area underthe CC frontier,the AUC,is an alternative tothe KS statisticthat summarizesthe
characteristicsof the CCfrontierwithbetterdefinition.Inthe graph,the AUCforaperfectclassifierequals
1, and for a coin-tosserequals.5.Inpractice,mostportfoliosresultinanAUC value somewhere between
perfectclassificationandcoin-toss.The KSstatisticandAUCare bothmeasuresof aninvestor’ssuccessin
forecasting the direction of the trades that makeup a carry portfolio.
In practice, the trades that make up a carry portfolio are not identical in term length, quantity
exchanged,orwhentrades are made with differingamountsof leverage.Therefore,the weightedvalue
of each trade must be adjusted to generate an accurate measure of a currency portfolio’s profitability.
Using modifiedstatistics toadjustforthese differences,we definethe total portfolioreturnequal to the
sum of total returnto short trades (BS) and total returnto long trades(BL).These totalsare measuredby
the following two expressions:
These measurements are used to adjust for the difference in weights of each positive and negative
outcome so that the return to BS and BL after being adjusted for their respective weight is calculated by
the following two expressions:
20. 20
We these statisticswe can measure the valuesof TN(c) and TP(c) adjustedfor weight,which are
needed in generating a KS statistic and AUC that also reflect return-weighted directional performance.
Thus the adjusted measurements of TN(c) and TP(c) are expressed by:
By normalizing net portfolio profit by total potential portfolio profit we can measure portfolio
performance in terms of total portfolio gainsand losses. Let gains(G) equal the product of total returns
to shorts and the return-weightedstatisticfortotal numberof true negative classificationratesplusthe
product of total returns to longs and the return weighted statistic for total number of true positive
classificationrates. Likewise,let losses(L) equal the product of total returns to shorts and the return-
weightedstatisticfortotal numberof false positive classificationratesplusthe productof total returnsto
longs and the return weighted statistic for total number of true negative classification rates. Net profit
would then be the value of gains less losses where:
Using the expressions for a portfolio’s gains and losses, we can then normalize portfolio profit by total
potential portfolio profit to express a portfolio’s utility. This measure of utility would then be:
Because thisfunctionforportfolioutilitycanbe expressedintermsof the portfolio’sgains-losses
ratio, maximizingthe ratioof gains to lossesisthe same as maximizingaportfolio’sutility.The portfolio
utility function in terms of portfolio gains and losses is expressed by:
21. 21
Using this adjusted functionfor portfolio utility, we define the point at which optimal portfolio utilityis
being achieved. At this point, the slope of the CC frontier, represented by –BS/BL, again equals -1. The
followingderivativerepresentsthe pointalongthe portfolioutilityfunction where utility is maximized:
In practice, portfolio returnsare rarely symmetric even in the presence of risk neutrality.This is
due to a number of external factors such as leverage limits and transaction costs. Assuming that an
investor’s portfolio return is symmetrically distributed, then the gain-loss ratio that maximizes utility
coincides with the point at which the KS statistic adjusted for return-weight is calculated so that:
Inthe absence of arbitrage opportunitiesaportfolio’sexpectedreturniszero,where the valueof
total portfolio gains is the same as the value of the total portfolio losses.This implies the gain-lossratio
wouldbe equal to one.In the presence of arbitrage,thisratio can take any approximationinan interval
from negative infinityto positive infinity where a gain-loss ratio of positive infinity would imply perfect
classification.
Part 5: Empirical Analysis Assuming the Existence of Arbitrage and Concluding Research
Historically, the empirical analysis of the results generated by these models exhibits positive
average returns to carry trade portfolios. One theory as to how this is possible argues that carry trade
returns are, in fact, compensation for risk. Proponents of this theory argue that shocks to supply and
demandinthe currency marketsencourage investorstoreduce theirholdingsof riskyassets,resultingin
potential losses in the short run via the order flow effect which impacts the price of trades.
Orderflowis a standardpractice inthe brokerage industry where brokeragefirmsreceive asmall
per-share rebate on orders routed to certain market makers for the execution of their transaction. In
addition, compensation may be rewarded that is not directly related to specific per-share values from
marketcenters,butbased onotherfactorssuchasquantity,quality,and type of the orderflow presented
tothe market. Statistical analysisindicates,however,thanorderflow doesnotcompletelyaccountforthe
positive average returns.
22. 22
Another potential explanation is in the context of a certain class of consumption-based asset
pricing models. The argument here is that brokers make infrequent adjustments to their portfolio
decisions because the losses incurred are insignificant relative to portfolio management fees. The very
structure of our financial system provokes infrequent portfolio adjustments by investors because many
of the majorfinancial instrumentsthatmake upour marketscan be boughtand soldat any pointintime
while others cannot.
Part 3 of this paper elaborated upon the existence of deviation from the PPP condition, which
createsfrictionbetweeninternational economiesresultinginarbitrageopportunities.Understandingthat
the arbitrage opportunities do in fact exist in these markets fosters an environment where generating
positive average returns becomes a possibility.
The potential positiveexpectedreturnstocarrytrade strategiescanbe improvedfurtherthrough
strategiesthatallowaninvestortoremaininacashpositionif theyexpectreturnstobe small oruncertain,
such as an optimally designed portfolio. While carry trade is inarguably a risky form of financial
investment, returns to carry portfolios are hardly justified on the basis of trader’s preferences of risk
exposure alone.
To validate this study we will build a model that focusesexclusivelyon the carry sub-strategyof
the VECM model.5
In this model we regress excess return to three different currencies on the current
differences in interest rates between their respective economies. Because of the short memory
characteristicof financial forecasts,wewillbe forecastingatamonthlyfrequencyaswell asataquarterly
frequency. The trade direction will be an investment in the Brazilian Real, the Canadian Dollar, and the
Chinese Yuan from the United States Dollar. The Regression will then be:
In the calculationof excessreturn,the variable∆st+1 representsthe change inthe logexchange rate from
one periodto the next.Make note that inthismodel the measure of exchange rate isin termsof foreign
currency per United States Dollar and that i* denotes the “funded” economy (The U.S. Dollar nominal
interest rate is denoted by i) that the carry trade will invest in. After running the regression, we will use
the descriptive statisticsgeneratedintestingforstatistical significance. Uncoveredinterestparityimplies
5 For details on this model see “Infrequent Portfolio Decisions:A Solution to the Forward DiscountPuzzle”
23. 23
the value of excess return to be equal to one. We are testing if the difference in interest rates has
predictive powerinthe excessreturninthe nextperiod.There willbe predictivepowerif βisstatistically
differentfromzero.The testwillthenbe onthe null hypothesisthatβ=0, andthe alternative will be that
β < 0. The model estimation results at monthly and quarterly frequencies are as follows:
Monthly Predictable Excess Returns
qt+1 = α + β(it – it*) + Ɛt+1
Currency β σ(β) R2
T-Statistic P-Value
CanadianDollar -1.071980 .063570 .356183 -16.86309 .00000
BrazilianReal -.967640 .067705 .551669 -14.29203 .00000
Chinese Yuan -.986021 .009943 .983402 -99.17174 .00000
Average -1.01 0.05 0.63 -43.44 0.00
Let us focus on the resultsof our model at the monthlyfrequency. All three tradesresultedina
negative expectedvaluesof excess return.Consideringthe large t-statisticsaswell asthe low p-valuesof
all three processes,the resultsindicate the predictabilitycoefficientsare statisticallydifferentfromzero.
All three processesrejectthe null hypothesisinfavorof the alternative,thusthe modelsexhibitpredictive
power. The R2
, which measures the “goodness of fit” of the model indicates how much the regression
capturesthe variation of the dependentvariable.We cansayat a monthlyfrequency,the model we have
builtexplains35.62%of the returnto the CanadianDollar,55.17% of the returnto the BrazilianReal,and
24. 24
98.34% of the returnto the Chinese Yuan. Consideringourmodelsonlycapture interestrate differentials
inexplaininginterestrate fluctuation,one mightinquire astohow the variationof the Chinese Yuanisso
high (a near perfect fit), but the reason is actually quite simple. Currencies with fixed exchange rates
againstthe dollar(suchas the Yuan) generate a value of close to zero in the coefficient∆st+1.This causes
the equation to become –(i – i*) = α + β(it – it*) + Ɛt+1.
Quarterly Predictable Excess Returns
qt+1 = α + β(it – it*) + Ɛt+1
Currency β σ(β) R2
T-Statistic P-Value
CanadianDollar -.998531 .118277 .295403 -8.442313 .00000
BrazilianReal -.902532 .245386 .200329 -3.678014 .00005
Chinese Yuan -.976701 .042434 .907501 -23.01711 .00000
Average -0.96 0.14 0.47 -11.71 0.00
Now let us examine the results of our model at a three month frequency. Again, all three
processesresultedinanegativeexpectedvaluesof excessreturn,large t-statistics,andlowp-values.With
the t-statistics statistically different from zero, we once again reject the null hypothesis in favor of the
alternative inall three cases.Thisiswhat we wouldexpect,asthe change in frequencyshouldhave little
effect on the statistical significance of the regression parameters. The R2
, measures have all decreased
from their monthly values, which reflects the additional movement in the variables over the additional
twomonthsof marketactivitybetweentrades.Forecastingatquarterlyhorizons, the modelwe havebuilt
explains 29.54% of the return to the Canadian Dollar, 20.03% of the return to the Brazilian Real, and
90.75% of the return to the Chinese Yuan.
Using the descriptive statisticsof these processeswe are able to graphthe fittedline againstthe
realized returns to generate the residual series for each process:
25. 25
All six time series seem to exhibit the stochastic properties we are looking for. To inquire as to
whether the residuals are white noise processes, we compute their autocorrelation and partial
autocorrelation functions as follows:
The resultsindicate,however,thatall of our processesexhibitsome lineardependence.Inall six
series,there isone to three spikesinthe PACFand a slow decay towardzeroin the ACF.This impliesthe
dependent variable would be better explained through an autoregressive structure of higher order
(depending on the series) that includes lagged values of the regressors. This is very much expected
consideringwe’ve alreadydiscussedmany sourcesof deviationfromUIP thatcan cause wedgesbetween
price levelsforyearsatatime. Manyfinancial time seriesare improvedbyincluding laggedvaluesof their
regressive variables due tononsynchronoustrading,andinfrequentportfoliodecisions.Aswe nowknow,
the equilibrium expected returnsare positive and time varying, with portfolios optimally designed,one
can hedge against changes to future expected returns.
To conclude our study, we observe the β coefficients of our empirical analysis.In each of our
models, the β coefficients were all statistically different from zero. This proves not only that UIP fails to
hold in the short run, but also that there are variables such as interest rates that yield predictive power
over the deviation in UIP. Executing carry trades based on models such as this carry strategy will, on
average,be successful ingeneratingpositive portfolioreturns.Includingothervariables(assuggestedin
the VECM) will only increase the accuracy of the models used to forecast carry trade.
26. 26
Footnote References
1
International Economics:TheoryandPolicy
Paul R. Krugman; Maurice Obstfeld;Marc J.Melitz
Textbook, Part3
Stable URL:
http://www.acsu.buffalo.edu/~twang28/Krugman-%20International%20Economics%209ed%202011.pdf
2
A note on ParityConditions(CIRP,“FP”,UIRP,PPP) andCarry Trades
Michel A.Robe
WorkingPaper, Kogod School of Business,AmericanUniversity,Washington,DC
Stable URL:
http://www1.american.edu/academic.depts/ksb/finance_realestate/mrobe/302/Handouts/IRP_note.pd
f
3
Exchange Rate DynamicsRedux
Maurice Obstfeld;KennethRogoff
The Journal of Political Economy,Vol.103, No.3. (Jun.,1995), pp.624-660.
Stable URL:
http://links.jstor.org/sici?sici=0022-3808%28199506%29103%3A3%3C624%3AERDR%3E2.0.CO%3B2-6
4
Carry Trade
Òscar Jordà
WorkingPapers,Universityof California,Departmentof Economics,No.10, 18. (2010)
Stable URL:
http://hdl.handle.net/10419/58381
5
InfrequentPortfolioDecisions:A Solutiontothe ForwardDiscountPuzzle
Bacchetta,P. and E. van Wincoop
WorkingPapers,CEPRand NBER, (2007)
Stable URL:
http://www.hec.unil.ch/pbacchetta/PDF/forexnew51-1.pdf