# Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13

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1 Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions a) Dfin xchang Rats: Df of xchang rat: pric of on currncy in trms of anothr. Th convntional way of rporting this in conomics is hom currncy pr forign. In th U.S. this is \$ pr forign currncy. For xampl, currntly it would tak about \$1.28 to buy on uropan uro ( \$/uro ) This is th convntion in conomics and will b usd in this class. Somtims you will har quotd th othr way around, oftn calld uropan trms. i: 1/1.28 = 0.78 \$/uro. b) xchang rats ar important for trad bcaus thy allow you to compar th cost of imports to that of domstic goods in common trms. Thr was a priod whn Amricans wr going to Grmany to buy Mrcds and bring thm hom, rathr than buying thm in th U.S. xampl: Considr th Mrcds: suppos th going pric is 60 thousand uros in Grmany and 60 thousand dollars in th US. Would popl flock to Grmany? Dpnds on th xchang rat - comparing \$ and uro is lik comparing appls and orangs. Suppos th \$/uro xchang rat is So th cost in Grmany rportd in dollar units is: 60 thousand uros * (1.28 \$/uro) = \$76,800 At this xchang rat, looks lik it is chapr to buy th car in th U.S. How know using th rat not upsid down? Look at units: hav uro, want dollars, so multiply by \$/uro and uro cancls out, and you lft with units in dollars. 1

6 c) Forign currncy assts What is th xpctd rturn for th larg bank accounts typically usd in forign xchang markt transactions? Th typically do pay an intrst rat. An additional fatur with an account in a forign currncy is that changs in th xchang rat whil holding th currncy also affct th valu of th asst whn you switch it back to domstic currncy trms. So whn you ar dciding whthr to hold your assts in \$ accounts or uro accounts, you nd to considr th intrst rats on ach dposit option and th xpctd chang in th xchang rat in th mantim. xampl (whr intrst parity holds) Lts say you hav a 100\$ and nd to dcid whthr hold in \$ or ruo account: Dfin: i \$ : nt intrst on a \$ account = 10%. i uro : nt intrst on a uro account = 5%. Is uro bttr? Rprsnt th currnt spot xchang rat as \$/uro and suppos this starts at 1.25 So convrt 100 \$ into 80 uro. Gt 5% intrst so hav 84 uro at nd of yar. But thn you nd to convrt ths back to \$ in th nd. Rprsnt th xpctation for th futur spot xchang rat as \$/uro and suppos this is So whn you ar rady to convrt back to \$ ths uro ar worth mor than thy usd to b; 84 uro ar worth 110 \$. \$ account URO account 100\$ \$/uro = uro i \$ =10% i uro =5% 110\$ \$/uro = uro 4) Intrst parity condition: a) Thr is a simpl rul to shortn this calculation: Writ total gross \$ rturn on URO asst as consisting of two parts: th URO intrst rat plus th prcnt apprciation of th URO currncy, this is: 1+ i Total gross rturn on URO dposit = ( ) \$/ uro uro \$/ uro In th xampl abov, this xactly quals th gross rturn on th \$ dposit, so: In quilibrium: Total gross rturn on \$ dposit = Total grossrturn on URO dposit (in \$ trms) 6

7 \$/ ( 1+ i ) = ( 1+ i ) \$ uro uro \$/ uro W can writ this in trms of nt rturns instad of gross rturns, as an approximation: Dfin th prcntag xpctd apprciation of th uro as: \$/ uro \$/ uro \$/ uro = \$/ uro \$/ uro This allows us to writ th UIP condition as: \$/ uro ( 1+ i\$ ) = ( 1+ iuro ) 1+ \$/ uro \$/ uro \$/ uro = 1+ iuro + + iuro \$/ uro \$/ uro Sinc th last trm in brackts is two small numbrs multiplid by ach othr, w can drop it and still hav a good approximation: \$/ uro ( 1+ i\$ ) = 1+ iuro + i \$ = iuro + Which mans nt rturn on \$ asst \$/ uro \$/ uro \$/ uro = total nt rturn on uro asst = uro nt intrst rat + xpctd uro apprciation Th ida is that th Grman intrst rat might b lowr than th \$ intrst rat, but th total rturn will b incrasd by an xpctd apprciation of th URO currncy whil holding th URO dposit in that currncy. This quation is calld th uncovrd intrst rat parity condition. xampl from abov: 0.10 = ( )/1.25 = = b) quilibrium in th Forign xchang Markt W will tak this intrst rat parity condition to b a dscription of quilibrium in th forign xchang markt. Givn a crtain intrst rat on \$ dposits (i \$ ) and a crtain intrst rat on URO dposits (i URO ), and givn crtain xpctations about th futur xchang rat ( \$/URO), thn th intrst parity condition tlls us what th currnt spot xchang rat has to b in ordr for thr to b no xcss dmand or supply in th forign xchang markt. 7

8 quilibrating procss: For xampl, suppos a cas whr th total rturn on URO assts ar l ss than on \$ assts, givn th currnt spot xchang rat and givn our xpctation for th futur spot xchang rat. In this cas, holding URO assts is lss attractiv than holding \$ assts, and popl will try to sll thir URO and buy \$. This xcss supply of URO will immdiatly bid down th currnt valu of URO and bid up th valu of \$; in othr words th currnt spot xchang rat \$/URO will fall. But sinc w still ar xpcting th sam futur valu of th xchang rat in th futur, \$/URO, th fact that th currnt spot rat is lowr mans w xpct a largr URO apprciation ovr th tim w ar holding th URO asst. This vry fact raiss th total rturn on th URO asst, and maks it mor attractiv than bfor. This procss will continu until th currnt spot rat falls nough that th xpctd URO apprciation ovr tim maks th total URO rturn xactly quals th rturn on th \$ asst. At this point thr is no xcss supply of URO forign xchang, and th spot xchang rat has rachd its quilibrium lvl. xpctd rats of rturn (in units of \$) i \$ Rturn on \$ dposits Rturn on URO dposits \$/UR c) ffct of changing intrst rats: If any of th undrlying conditions chang, thn this will rquir a chang in th spot xchang rat. If i \$ riss, this shifts th horizontal lin (dollar rturns) upward, which mans th quilibrium xchang rat \$/URO is lowr (th URO is worth lss). Th intuition gos lik this: a ris in i \$ maks \$ dposits mor attractiv than bfor, so thr is an xcss dmand for dollars which drivs up th currnt valu of th dollar and drivs down th currnt valu of th URO ( \$/URO falls). Similarly, if R URO riss, this shifts th URO-rturns curv upward. Now th URO assts bcom mor attractiv and thr is xcss dmand for URO. This bids up th currnt valu of th URO, which is a ris in \$/URO. In gnral w s that if th intrst rat riss in a country, thn this tnds to rais th valu of that country s currncy. W can also considr th ffcts of a chang in th xpctd futur xchang rat. If \$/URO riss, this shifts th URO-rturn curv upward just lik cas abov and raiss th currnt spot xchang rat. Th ida is that if you xpct URO 8

9 currncy to ris in valu ovr tim, URO assts bcom mor attractiv for this rason, and thr is xcss dmand for URO, which bids up thir currnt valu. In futur sssions, w will discuss som of th conomic rasons for why ths cass might aris, that is, why intrst rats or xpctations might chang. 9

10 d) mpirical tsts on intrst parity. It is difficult to tst th intrst rat parity condition, bcaus it is difficult to gt a masur of popl s xpctations. Som conomists hav usd th actual futur xchang rat as a proxy for xpctations in th past, assuming that popl corrctly prdict th futur rat. Som conomists hav usd survy data on xpctations thy call popl who tak part in th forign xchang markt and ask thm what rats thy xpct. Both sts of tsts tnd to find th intrst parity condition dos not hold wll. But this may simply rflct th fact that th xpctd futur xchang rat componnt of th quation was masurd with rror, not that th thory was wrong. Anothr rason why th tsts may rjct th intrst parity condition is th rol of risk. Thr is som risk involvd bcaus you do not know ahad of tim what th futur xchang rat will b; if your xpctations turn out to b wrong, th payoff from your invstmnt schm may b diffrnt from what you xpctd. This may mak popl rquir an xtra xpctd rturn on URO dposits as compnsation for uncrtainty. In this cas thr would b an xtra trm in th intrst parity quation: RP rprsnting th risk prmium: i \$ = i URO + ( \$/URO - \$/URO )/ \$/URO - RP (Not: RP can in principl b ithr positiv or ngativ, dpnding on how th risk is prcivd both by popl trading URO for \$ and thos trading \$ for URO, sinc both groups ar xposd to risks of diffrnt typs). ) COVRD intrst parity. If xchang risk is th problm, isn t thr a way w know to gt rid of that? Us forward contract. Crat a risk-fr vrsion of th intrst parity rlation. Dnot th forward rat: F \$/URO This suggsts a risk-fr vrsion of intrst rat parity: calld covrd intrst rat parity: i \$ = i URO + (F \$/URO - \$/URO )/ \$/URO Th old quation thn is oftn calld uncovrd intrst rat parity. mpirical vidnc supports covrd intrst parity. In fact, it sms this is how forward rats ar dtrmind. Dalrs scan currnt and Forward rats F, and if s immdiat arbitrag, tak advantag of it, which closs it. Dos this imply that th forward rat F is th xpctd futur valu of th spot xchang rat? (Dos F \$/URO = \$/URO?) This is tru only if both uncovrd and covrd intrst rat parity conditions hold. 10

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