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 1.28. 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
c) Not: th way w convntionally dfin th xchang rat can also mak it confusing to talk about changs in th xchang rat, which w call apprciations and dprciations. Apprciation: incras in valu of th givn currncy rlativ to anothr. Say th $/uro rat changd from 1.28 to 1.20, w say th dollar apprciatd rlativ to th uro. Or w could say th uro dprciatd rlativ to th dollar. Not that this can b confusing. Givn how w dfin th xchang rat as hom currncy pr forign, if this gts lowr, it mans that it taks lss hom currncy units to buy a forign currncy unit, and this mans th hom currncy is worth mor. Hnc an apprciation of th hom currncy. d) Multilatral xchang rats: Bilatral xchang rat is btwn on pair of currncis (as abov). Not that somtims th bilatral rat of th dollar with on currncy may apprciat at th sam tim that anothr bilatral rat with anothr currncy may dprciat (S chart from conomist magazin) Nominal ffctiv xchang rat: is a wightd avrag of svral bilatral xchang rats, usually using trad shars as wights to rflct th rlativ importanc of ach of th bilatral pairs involvd. xampl: suppos that: $/pound = - 10%(apprciats 10%), and trad shar of UK in US trad is 40% $/uro = 30%(dprciats 30%), and trad shar of U in US trad is 60% Thn th chang in th nominal ffctiv xchang rat is: = (0.4)(-0.1) + (0.6)(0.3) = +.14 ( dollar dprciats 14% on avrag) Look at th trnds in th valu of th dollar in rcnt yars. Raiss th qustion: why has dollar dprciatd in rcnt yars, and why it movs around so much in gnral? W will dvlop thoris latr to addrss ths qustions. 2) Faturs of forign xchang markt. a) Actors 1) commrcial banks: handl most of th markt transactions - involv a company having its commrcial bank dbit its account, chang into forign currncy and pay a businss partnr by dpositing in its forign bank. Not usually dirct xchang of currncy and coins. Intrbank trading: bank gathrs rqusts of its customrs and ntrs forign xchang markt to xcut trad as a unit, so ar vry larg transactions. ntring markt 2
is a mattr of chcking th postings on a computr ntwork th rats at which othr banks ar willing to trad currncy, thn call on phon and finaliz a pric. 2) corporations: somtims corporations ntr markt dirctly. Incrasingly common and corporations hav plants abroad, or buy componnts from abroad. 3) Nonbank financial institutions: Thr has bn much drgulation of financial markts, so financial institutions othr than banks can compt with banks in providing srvics in markt. On xampl is pnsion funds. 4) Cntral banks. Govrnmnts somtims intrvn in th forign xchang markt to incras or dcras th supply of thir currncy or purposfully affct th xchang rat in th markt. Som countris intrvn to hold th valu of th currncy fixd at a dsirabl lvl (fixd xchang rat) b) Charactristics Volum is normous: ovr a trillion dollars a day. GDP is undr 10 tril in th whol yar of 1994. Cntral bank Banks daling in markt tnd to b concntratd in crtain ky financial citis: know which biggst? London largst, but also NY, Tokyo, Frankfurt and Singapor. Highly intgratd globally: whn on major markt is closd usually anothr is opn, so popl can trad around th clock, moving from on cntr to anothr. Intgration mans xchang rat quots in diffrnt cntrs must b th sam. Is guarantd by arbitrag, dfind as making a risklss profit on a financial trad): NY Frankfurt Suppos that $/ uro < $/ uro : NY offr mor uros for a $ (lowr pric of uros, highr pric of $, $/uro is low) than Frankfurt, thn popl will tak thir $, sll in NY for bunch of uros, thn sll ths in Frankfurt for dollars again and nd up with mor dollars than thy startd. Possibility for you to mak risklss profit? No bcaus short-livd du to arbitrag. Th incrasd dmand for uros in NY would driv up th pric of uros in trms of $ - this is an xchang rat dprciation for th $. Thr ar computrs monitoring such opnings and rady to tak advantag of thm. So gaps clos up vry quickly. Vhicl currncy. Most forign xchang transactions ar btwn banks and tak plac in $, vn if want to chang Swdish kronr for Polish zloty, not dollars. asir to chang kronr first to $ and thn $ to zlotys. Sinc US is so important in world conomy, thr ar many popl willing to trad dollars for kronr and zloty for dollars, to tak th opposit sids of your trad, rathr than th opposit sid of a dirct kronr for zloty trad. uro and Yn ar also usd as vhicls, but lss so at currnt tim. Not that arbitrag ovr thr currncis rquirs: = ( )( ) pound/ uro $/ uro pound /$ 3
c) Spot and forward rats Th xchang transactions talkd about so far tak plac on th spot. Spot rat: xchang rat for currncy transactions that tak plac basically immdiatly. In practic can t b right away bcaus it typically taks two days for th chcks to clar usd to mak th paymnts. Forward xchang rats: Can also arrang currncy trad for som dat in futur. Is on way of hdging against risk of changs. Suppos Bst Buy lctronics is xpcting a shipmnt of Sony TVs in a month, for which it nds to pay yn. Could wait until th shipmnt to buy th yn to pay Sony, but not know what will happn to valu of that yn in mantim. If yn apprciats a lot, th $ pric stor has to pay to gt th TVs could chang a lot. To avoid this risk, th stor can arrang for currncy trad ahad of tim to b xcutd latr at a st xchang rat. This rat is th forward rat. Swaps: anothr possibility is to combin a spot with a forward arrangmnt: i.. A spot sal, thn arrang a rpurchas in th futur at a st rat. Why do this? Say our lctronics stor sold som computrs in Japan and got yn, know will nd thm again in a month to buy Sony TVs, but not want to hang on th mony in yn ovr th month, want to hold it in dollars for domstic xpnss. Might b lowr brokrs fs if arrang both transactions at on tim. Futurs: lik a forward arrangmnt, xcpt you can sll th contract to somon ls. Currncy xchang occurs whn contract coms du, and is dlivrd to whovr is holding th contract in th nd. Usful if your opinions about th xchang rat chang. Som popl just trad ths contracts to mak a profit, bcaus xpct th valu of th contract to chang as xpctations for xchang rat movmnts chang. This is an xampl of currncy spculation. i.. if suddnly looks lik $ will apprciat, a contract spcifying dollars b dlivrd for a givn amount of yn looks mor profitabl, and pric of contact will go up. Options: Call option: hav th right to buy an amount of currncy at a spcifid rat any tim bfor a spcifid dat. Put option: right to sll. Lik futurs, options can thmslvs b bought and sold. 4
3) Asst approach to xchang rats: a) Prviw: Thoris of xchang rat dtrmination Now w com to th qustion of how dos th forign xchang markt dtrmin what th xchang rat will b. Thr two main thoris w wll study hr: 1) Th asst approach which is basd upon intrst rat parity 2) Th montary approach which is basd upon purchasing powr parity ach of ths tlls a logical but somwhat diffrnt story of how th is dtrmind. A gnral thm in th nxt coupl lcturs will b to discuss ths storis, th mpirical vidnc on how wll ach xplains movmnts, and how th two thoris prhaps could b intgratd togthr. Asst Approach: First w discuss th asst approach. Rcall that most forign xchang holdings ar in form of bank dposits, which is a typ of asst, and ths can b analyzd as any othr asst. b) Dtrminants of dmand for assts 1) xpctd Rat of rturn: What ar th dtrminants of th dmand for a financial asst lik a bank account? Th main dtrminant is th rat of rturn that is paid. - In th cas of your saving account in dollars, you car about th intrst rat. - In th cas of a Stock, you car about th dividnd and th capital gain: Suppos you pay 100$ for a shar of Ford, and you gt a dividnd paymnt of 5$ and rsll it for 105$. So you mad a total of 10$ off of th asst; dividd by th initial 100$ invstmnt th implis a rat of rturn of 10%. So to rfin this a bit, not that w may not know ahad of tim what rsal valu will b. So whn you mak a dcision now about buying an asst, you must bas it on th xpctation of what th rturn will b. In addition to th rturn, som savrs car about two othr faturs: risk and liquidity. 2) risk: uncrtainty about rat of rturn. vn if a stock has a highr xpctd payoff than a saving account, th fact that th payoff is uncrtain mans it may b lss dsirabl, bcaus popl not lik risk. 3) liquidity: how asy it is to convrt th asst to cash if you want to buy a diffrnt on or us your savings for consumption. 5
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 1.31. 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 = 1.25 80 uro i $ =10% i uro =5% 110$ $/uro =1.31 84 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
$/ ( 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 = 0.05 + (1.31-1.25)/1.25 = 0.05 + 0.048 = 0.098 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
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 0.500 $/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
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
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