Fiancial Econometrics Paper - Final Draft

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  1. 1. 1 Financial Econometrics Concerning Carry Trade: Empirical Analysis Francis Dixon
  2. 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 anassets 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 economys rate of inflation, where the inflation rate is denoted as . The mathematical representationof nominal andrealinterestrates are then,i =(1+i) andr= i respectively. The nominal exchange rate,denotedas ,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 = 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 = (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 = (P*/P) would be calculated as 3 = 6*(50/100).
  3. 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 financeseeInternational Economics
  4. 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. 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 assets 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 economys money supply) affects the equilibrium condition in both the domestic money market and the foreign exchange market. Similarly, Figure 6
  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 assets 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. 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 re