Problem 7.1 Starbucks in Croatia Starbuck% opene it% fir%t %tore in Zagreb& Croatia Croatia in 'ctober *+ ,he price of a tall vanilla latte in Zagreb i% -+.kn+ "n Ne York York Cit0& Cit0& the price of a tall vanilla latte i% $+1-+ ,he exchange rate beteen Croatian kuna% (kn) an +S+ ollar% i% kn-+122/$+ Accoring to purcha%ing purcha%ing poer parit0& i% the Croatian kuna overvalue or unervalue3 unervalue3 Assumptions Spot exchange exchange rate (Kn/$) Price of vanilla latter in Zagreb (kn) Price of vanilla latter in NYC ($)
Actual price of Croatian latte in S! "#plie PPP of Croatian latte in S! Percentage overvaluation (po%itive) or unervaluation (negative)
Value 5.6288 25.70 2.65
4.57 9.70 112.408
Problem 7.2 Crisis at t!e "eart o# Carna$al ,he Argentine pe%o a% fixe through a currenc0 boar at P%*+/$ t hroughout the *99%+ "n 5anuar0 the Argentine pe%o a% floate+ 'n 5anuar0 9& 6 it a% traing at P%6+/$+ !uring that one 0ear perio Argentina;% inflation rate a% < on an annuali8e ba%i%+ "nflation in the nite State% uring that %a#e perio a% +< annuali8e+ a+ 4hat %houl have been the exchange rate in 5anuar0 6 if PPP hel3 b+ 70 hat percentage a% the Argentine pe%o unervalue on an annuali8e ba%i%3 c+ 4hat ere the probable cau%e% of unervaluation3 Assumptions Spot exchange rate& fixe peg& earl0 5anuar0 (P%/$) Spot exchange rate& 5anuar0 9& 6 (P%/$) S inflation for 0ear (per annu#) Argentine inflation for 0ear (per annu#)
Value 1.0000 %.2000 2.20 20.00
a. &!at s!oul' !a$e been t!e e(c!an)e rate in *anuar+ 200% i# PPP !el',
7eginning %pot rate (P%/$) Argentine inflation S inflation PPP exchange rate
1.00 20.00 2.20 1.17
b. -+ !at percenta)e as t!e Ar)entine peso un'er$alue' on an annuli/e' basis,
Actual exchange rate (P%/$) PPP exchange rate (P%/$) Percentage overvaluation (po%itive) or unervaluation (negative)
%.20 1.17 6%.%07
c. &!at ere t!e probable causes o# un'er$aluation,
,he rapi ecline in the value of the Argentine pe%o a% a re%ult of not onl0 inflation& but al%o a %evere cri%i% in the balance of pa0#ent% (%ee Chapter :)+
Problem 7.% ra$elin) on 3n'er ,err0 >a#oreaux ha% ho#e% in both S0ne0& Au%tralia an Phoenix& Ari8ona+ ?e travel% beteen the to citie% at lea%t tice a 0ear+ 7ecau%e of hi% fre@uent trip% he ant% to bu0 %o#e ne& high @ualit0 luggage+ ?e;% one hi% re%earch an ha% ecie to go ith a 7rigg% Bile0 bran three= piece luggage %et+ ,here are retail% %tore% in both Phoenix an S0ne0+ ,err0 a% a finance #aor an ant% to u%e purcha%ing poer parit0 to eter#ine if he i% pa0ing the %a#e price no #atter here he #ake% hi% purcah%e+ a+ "f the price of the 6=piece luggage %et in Phoenix i% $2- an the price of the %a#e 6=piece %et i n S0ne0 i% $96& u%ing purcha%ing poer parit0& i% the price of the luggage trul0 e@ual if the %pot rate i% A$*+9:*/$3 b+ "f the price of the luggage re#ain% the %a#e in Phoenix one 0ear fro# no& eter#ine hat the price of the luggage %houl be in S0ne0 in one=0ear ti#e if PPP hol% true+ ,he S "nflation rate i% *+*-< an the Au%tralian inflation rate i% 6+*6<+ Assumptions Price of 6=Piece >uggage %et in S$ Price of 6=Piece >uggage %et in A$ Spot exchange rate& (A$/$) S inflation for 0ear (per annu#) Au%tralian inflation for 0ear (per annu#)
Value 850.00 9%0.00 1.0941 1.15 %.1%
a. s t!e spot rate accurate )i$en bot! lu))a)e prices,
Price of 6=Piece >uggage %et in S$ Price of 6=Piece >uggage %et in A$ Spot rate a% eter#ine b0 PPP Spot rate = Price in A$ / Price in US$
2-+ 96+ 1.0941
a. &!at s!oul' be t!e price o# t!e lu))a)e set in A in 1+ear i# PPP !ol's,
7eginning %pot rate (A$/$) Au%tralian inflation S inflation PPP exchange rate Price of 6=Piece >uggage %et in S$ PPP exchange rate Price of 6=piece luggage %et in S0ne0 (A$)
*+9:* 6+*6< *+*-< 1.1155
2-+ *+**-948.19
However, purchasing power parity is not always an accurate predictor of exchange rate movements, particularly in the shortterm!
Problem 7.4 akes!i ama'a CA *apan ,ake%hi Ka#aa& a foreign exchange traer at Creit Sui%%e (,ok0o)& i% exploring covere intere%t arbitrage po%%ibilitie%+ ?e ant% to inve%t $-&& or it% 0en e@uivalent& in a covere intere%t arbitrage beteen +S+ ollar% an 5apane%e 0en+ ?e face the folloing exchange rate an intere%t rate @uote%+ Assumptions Arbitra)e #un's a$ailable Spot rate ;<=> 180'a+ #orar' rate ;<=> 180'a+ 3.S. 'ollar interest rate 180'a+ *apanese +en interest rate
Value 5:000:000 118.60 117.80 4.800 %.400
en ui$alent 59%:000:000
Ar"itrage #ule of hum"% &f the difference in interest rates is greater than the forward premium/discount, or expected change in the spot rate for U&A, invest in the higher interest yielding currency! &f the difference in interest rates is less than the forward premium 'or expected change in the spot rate(, invest in the lower yielding currency! i##erence in interest rates ; i < i > ?orar' premium on t!e +en CA pro#it potential
1.400 1.%58 0.042
,hi% tell% ,ake%hi Ka#aa that he %houl borro 0en an inve%t in the higher 0ieling currenc0& the +S+ ollar& to lock=in a covere intere%t arbitrage (C"A) profit+
U.S. dollar interest rate (180 days) 4.800
5:000:000 @ @ @ @ @ Spot ;<=> 118.60 @ @ @ 59%:000:000.00 *apanese +en SA
D
D
1.0240
D
D
B 180 'a+s B
D
D
1.0170
D
%.400 Japanese yen interest rate (180 days)
D
5:120:000 ?orar'180 ;<=> 117.80 60%:1%6:000 60%:081:000 55:000 D
,ake%hi Ka#aa generate% a C"A profit b0 inve%ting in the higher intere%t rate currenc0& the ollar& an %i#ultaneou%l0 %elling the ollar procee% forar into 0en at a forar pre#iu# hich oe% not co#pletel0 negate the intere%t ifferential+
Problem 7.5 akes!i ama'a 3A *apan ,ake%hi Ka#aa& Creit Sui%%e (,ok0o)& ob%erve% that the E/$ %pot rate ha% been holing %tea0& an both ollar an 0en intere%t rate% have re#aine relativel0 fixe over the pa%t eek+ ,ake%hi oner% if he %houl tr0 an uncovere intere%t arbitrage ("A) an thereb0 %ave the co%t of forar cover+ Fan0 of ,ake%hi;% re%earch a%%ociate% == an their co#puter #oel% == are preicting the %pot rate to re#ain clo%e to E**2+/$ for the co#ing *2 a0%+ %ing the %a#e ata a% in the previou% proble#& anal08e the "A potential+ Assumptions Arbitra)e #un's a$ailable Spot rate ;<=> 180'a+ #orar' rate ;<=> (pecte' spot rate in 180 'a+s ;<=> 180'a+ 3.S. 'ollar interest rate 180'a+ *apanese +en interest rate
Value 5:000:000 118.60 117.80 118.00 4.800 %.400
en ui$alent 59%:000:000
Ar"itrage #ule of hum"% &f the difference in interest rates is greater than the forward premium/discount, or expected change in the spot rate for U&A, invest in the higher interest yielding currency! &f the difference in interest rates is less than the forward premium 'or expected change in the spot rate(, invest in the lower yielding currency! i##erence in interest rates ; i < i > (pecte' )ain ;loss> on t!e spot rate 3A pro#it potential
1.400 1.017 0.%8%
,hi% tell% ,ake%hi Ka#aa that he %houl borro 0en an inve%t in the higher 0ieling currenc0& the +S+ ollar& to potentiall0 gain on an uncovere ba%i% ("A)+
U.S. dollar interest rate (180 days) 4.800 5:000:000 @ @ @ @ @ Spot ;<=> 118.60 @ @ @ 59%:000:000.00 *apanese +en SA
D
D
1.0240
D
D
B 180 'a+s B
D
D
1.0170
D
%.400 Japanese yen interest rate (180 days)
D
5:120:000 (pecte' Spot ate in 180 'a+s ;<=> 118.00 604:160:000 60%:081:000 1:079:000 D
a) ,ake%hi Ka#aa generate% an uncovere intere%t arbitrage ("A) profit of E*&.9& if hi% expectation% about the future %pot rate& the one in effect in *2 a0%& prove correct+ b) ,he ri%k ,ake%hi i% taking i% that the actual %pot rate at the en of the perio can theoreticall0 be an0thing& better or or%e for hi% %peculative po%ition+ ?e in fact ha% ver0 little Giggle roo#&G a% the0 %a0+ A %#all #ove#ent ill co%t hi# a lot of #one0+ "f the %pot rate en% up an0 %tronger than about **.+.9/$ (a %#aller nu#ber)& he ill lo%e #one0+ (Herif0 b0 inputting E**.+./$ in the expecte %pot rate cell uner a%%u#ption%+)
Problem 7.6 *apanese=3nite' States parit+ con'itions !erek ,o%h i% atte#pting to eter#ine hether S/5apane%e financial conition% are at parit0+ ,he current %pot rate i% a flat ¥89+/$& hile the 61=a0 forar rate i% ¥84.90/$+ Ioreca%t inflation i% *+*< for 5apan& an -+9< for the S+ ,he 61=a0 euro=0en epo%it rate i% :+.<& an the 61=a0 euro=ollar epo%it rate i% 9+-<+ a+ !ia ra# an calculate hether international arit conition% hol beteen 5a an an the nite State%+ b+ Iin the foreca%te change in the 5apane%e 0e%/+S+ ollar (E/$) exchange rate one 0ear fro# no+ Assumptions Ioreca%t annual rate of inflation for 5apan Ioreca%t annual rate of inflation for nite State% 'ne=0ear intere%t rate for 5apan 'ne=0ear intere%t rate for nite State% Spot exchange rate (E/$) 'ne=0ear forar exchange rate (E/$)
Value 1.100 5.900 4.700 9.500 89.00 84.90
a. Appro(imate ?orm
Forward rate as an unbaised predictor (E)
J
J
J
J
!nternational Fisher E""ect (#)
?orar' premium on #orei)n currenc+ 4.8 ;*apanese +en at a premium>
!nterest rate parity ($)
?orecast c!an)e in spot e(c!an)e rate 4.8 ;ollar e(pecte' to eaken>
J
i##erence in nominal interest rates 4.8 ;!i)!er in 3nite' States>
J
Purchasing power parity ()
?orecast 'i##erence in rates o# in#lation 4.8 ;3S !i)!er t!an *apan>
J
J
Fisher e""ect (%)
A% i% the ala0% the ca%e ith parit0 conition%& the future %pot rate i% i#plicitl0 foreca%t to be e@ual to the forar rate& the i#plie rate fro# the international Ii%her effect& an the rate i#plie b0 purcha%ing poer parit0+ Accoring to Ya88ie;% calculation%& the #arket% are inee in e@uilibriu# == parit0+
b.
Spot exchange rate (E/$) 'ne=0ear forar exchange rate (E/$) Iorca%te change in exchange rate%
29+ 2:+9 4.8
')urrent Spot #ate *orward +xchange #ate( / '*orward +xchange #ate(
Problem 7.7 Corolla (ports an' Pass!rou)! A%%u#e that the export price of a ,o0ota Corolla fro# '%aka& 5apan i% E&*-&+ ,he exchange rate i% E2.+1/$+ ,he foreca%t rate of inflation in the nite State% i% +< per 0ear an i% +< per 0ear in 5apan+ %e thi% ata to an%er the folloing @ue%tion% on exchange rate pa%% through+ a+ 4hat a% the export price for the Corolla at the beginning of the 0ear expre%%e in +S+ ollar%3 b+ A%%u#ing purcha%ing poer parit0 hol%& hat %houl the exchange rate be at the en of the 0ear3 c+ A%%u#ing *< pa%%=through of exchange rate& hat ill the ollar price of a Corolla be at the en of the 0ear3 + A%%u#ing .-< pa%%=through& hat ill the ollar price of a Corolla be at the en of the 0ear3 Steps "nitial %pot exchange rate (E/$) "nitial price of a ,o0ota Corolla (E) Lxpecte S ollar inflation rate for the co#ing 0ear Lxpecte 5apane%e 0en inflation rate for t he co#ing 0ear !e%ire rate of pa%% through b0 ,o0ota a. &!at as t!e e(port price #or t!e Corolla at t!e be)innin) o# t!e +ear, Year=beginning price of an Corolla (E) Spot exchange rate (E/$) Year=beginning price of a Corolla ($) b. &!at is t!e e(pecte' spot rate at t!e en' o# t!e +ear assumin) PPP, "nitial %pot rate (E/$) Lxpecte S$ inflation Lxpecte 5apane%e 0en inflation Lxpecte %pot rate at en of 0ear a%%u#ing PPP (E/$) c. Assumin) complete pass t!rou)!: !at ill t!e price be in 3S in one +ear, Price of Corolla at beginning of 0ear (E) 5apane%e 0en inflation over the 0ear Price of Corolla at en of 0ear (E) Lxpecte %pot rate one 0ear fro# no a%%u#ing PPP (E/$) Price of Corolla at en of 0ear in ($) '. Assumin) partial pass t!rou)!: !at ill t!e price be in 3S in one +ear, Price of Corolla at en of 0ear (E) A#ount of expecte exchange rate change& in percent (fro# PPP) Proportion of exchange rate change pa%%e through b0 ,o0ota Proportional percentage change Lffective exchange rate u%e b0 ,o0ota to price in S$ for en of 0ear Price of ,o0ota at en of 0ear ($)
Value 87.60 2:150:000 2.200 0.000 75.000
2:150:000 87.60 24:54%.%8
87.60 2.20 0.00 85.71
2:150:000 0.000 2:150:000 85.71 25:08%.%%
2:150:000 2.200 75.000 1.6500 86.178 24:948.%4
Problem 7.8 Copen!a)en Co$ere' ;A> ?eii ?Mi 5en%en& a foreign exchange traer at 5+P+ Forgan Cha%e& can inve%t $- #illion& or the foreign currenc0 e@uivalent of the bank;% %hort ter# fun%& in a covere intere%t arbitrage ith !en#ark+ %ing the folloing @uote% can ?eii #ake covere intere%t arbitrage (C"A) profit3 Assumptions Arbitra)e #un's a$ailable Spot e(c!an)e rate ;kr=> %mont! #orar' rate ;kr=> 3S 'ollar %mont! interest rate anis! kroner %mont! interest rate
Value 5:000:000 6.1720 6.1980 %.000 5.000
Ar"itrage #ule of hum"% &f the difference in interest rates is greater than the forward premium/discount, or expected change in the spot rate for U&A, invest in the higher interest yielding currency! &f the difference in interest rates is less than the forward premium 'or expected change in the spot rate(, invest in the lower yielding currency! i##erence in interest rates ;ikr i> ?orar' 'iscount on t!e krone CA pro#it potential
2.000 1.678 0.%22
,hi% tell% ?eii ?Mi 5en%en that he %houl borro oll ar% an inve%t in the higher 0ieling currenc0 the !ani%h kroner& for C"A profit+
U.S. dollar interest rate (&'onth) %.000
SA
5:000:000.00 Spot ;kr=> 6.1720 kr %0:860:000.00
D
D
1.0075
D
D
D
B 90 'a+s B
D
D
1.0125
D
D
5:0%7:500.00 5:041:26%.%1 %:76%.%1 @ @ @ ?orar'90 ;kr=> 6.1980 @ @ @ kr %1:245:750.00
5.000 $anish roner interest (&'onth)
?eii ?Mi 5en%en generate% a covere intere%t arbitrage (C"A) profit becau%e %he i% able to generate an even higher intere%t return in !ani%h kroner than %he Ggive% upG b0 %elling the procee% forar at the forar rate+
Problem 7.9 Copen!a)en Co$ere' ;-> Part a ?eii ?Mi 5en%en i% no evaluating the arbitrage profit potential in t he %a#e #arket after intere%t rate% change+ (Note that an0ti#e the ifference in intere%t rate% oe% not exactl0 e@ual the forar pre#iu#& it #u%t be po%%ible to #ake C"A profit one a0 or another+) Assumptions Arbitra)e #un's a$ailable Spot e(c!an)e rate ;kr=> %mont! #orar' rate ;kr=> 3S 'ollar %mont! interest rate anis! kroner %mont! interest rate
Value 5:000:000 6.1720 6.1980 4.000 5.000
kr ui$alent kr %0:860:000
a> a>
Ar"itrage #ule of hum"% &f the difference in interest rates is greater than the forward premium/discount, or expected change in the spot rate for U&A, invest in the higher interest yielding currency! &f the difference in interest rates is less than the forward premium 'or expected change in the spot rate(, invest in the lower yielding currency! i##erence in interest rates ;ikr i> ?orar' 'iscount on t!e krone CA pro#it potential
1.000 1.678 0.678
,hi% tell% ?eii that %he %houl borro !ani%h kroner an inve%t in the >'4LB intere%t rate currenc0& the ollar& gaining on the re=exchange of ollar% for kroner at the en of the perio+
U.S. dollar interest rate (&'onth) 4.000
5:000:000.00 @ @ @ @ @ Spot ;kr=> 6.1720 @ @ @ kr %0:860:000.00
SA
D
D
1.0100
D
D
B 90 'a+s B
D
D
1.0125
D
5.000 $anish roner interest (&'onth)
D
5:050:000.00 ?90 ;kr=> 6.1980 kr %1:299:900.00 kr %1:245:750.00 kr 54:150.00 D
a) ?eii ?Mi 5en%en generate% a covere intere%t arbitrage profit of kr-:&*- becau%e& although +S+ ollar i ntere%t rate% are loer& the +S+ ollar i% %elling forar at a pre#iu# again%t the !ani%h krone+
Problem 7.10 Copen!a)en Co$ere' ;-> Part b ?eii ?Mi 5en%en i% no evaluating the arbitrage profit potential in t he %a#e #arket after intere%t rate% change+ (Note that an0ti#e the ifference in intere%t rate% oe% not exactl0 e@ual the forar pre#iu#& it #u%t be po%%ible to #ake C"A profit one a0 or another+) Assumptions Arbitra)e #un's a$ailable Spot e(c!an)e rate ;kr=> %mont! #orar' rate ;kr=> 3S 'ollar %mont! interest rate anis! kroner %mont! interest rate
Value 5:000:000 6.1720 6.1980 %.000 6.000
kr ui$alent kr %0:860:000
b> b>
Ar"itrage #ule of hum"% &f the difference in interest rates is greater than the forward premium/discount, or expected change in the spot rate for U&A, invest in the higher interest yielding currency! &f the difference in interest rates is less than the forward premium 'or expected change in the spot rate(, invest in the lower yielding currency! i##erence in interest rates ;ikr i> ?orar' 'iscount on t!e krone CA pro#it potential
%.000 1.678 1.%22
,hi% tell% ?eii ?Mi 5en%en that %he %houl borro S ollar% an inve%t in the ?"?LB intere%t rate currenc0& the kroner& gaining on the re=exchange of kroner for ollar% at the en of the perio+
U.S. dollar interest rate (&'onth) %.000
SA 5:000:000 Spot ;kr=> 6.1720 kr %0:860:000.00
D
D
1.0075
D
D
B 90 'a+s B
D
D
1.0150
D
D
D 5:0%7:500.00 5:05%:710.87 16:210.87 @ @ @ ?90 ;kr=> 6.1980 @ @ @ kr %1:%22:900.00
6.000 $anish roner interest (&'onth)
b) "f the !ani%h kroner intere%t rate increa%e% to 1+<& hile the +S+ ollar intere%t rate %ta0% at 6+< an %pot an forar rate% re#ain the %a#e& ?eii ?Mi 5en%en;% C"A profit i% $*1&*+2.+
Problem 7.11 Casper Ean'sten CA Ca%per >an%ten i% a foreign exchange traer for a bank in Ne York+ ?e ha% $* #illion (or it% Si%% franc e@uivalent) for a %hort ter# #one0 #arket inve%t#ent an oner% if he %houl inve%t in +S+ ollar% for three #onth%& or #ake a covere intere%t arbitrage inve%t#ent in the Si%% franc+ ?e face% the folloing @uote%O Assumptions Arbitra)e #un's a$ailable Spot e(c!an)e rate ;S?r.=> %mont! #orar' rate ;S?r.=> 3.S. 'ollar %mont! interest rate Siss #ranc%mont! interest rate
Value 1:000:000 1.2810 1.2740 4.800 %.200
S?r. ui$alent S?r. 1:281:000
Ar"itrage #ule of hum"% &f the difference in interest rates is greater than the forward premium/discount, or expected change in the spot rate for U&A, invest in the higher interest yielding currency! &f the difference in interest rates is less than the forward premium 'or expected change in the spot rate(, invest in the lower yielding currency! i##erence in interest rates ; i S?r. i > ?orar' premium on t!e Siss #ranc CA pro#it potential
1.600 2.198 0.598
,hi% tell% Ca%per >an%ten he %houl borro +S+ ollar% an inve%t in the >'4LB 0ieling currenc0& the Si%% franc& in orer to earn covere intere%t arbitrage (C"A) profit%+
U.S. dollar interest rate (&'onth) 4.800
SA
1:000:000.00 Spot ;S?r.=> 1.2810 S?r. 1:281:000.00
D
D
1.0120
D
D
D
B 90 'a+s B
D
D
1.0080
D
D
1:012:000.00 1:01%:5%8.46 1:5%8.46 @ @ @ ?orar'90 ;S?r.=> 1.2740 @ @ @ S?r. 1:291:248.00
%.200 Swiss "ranc interest rate (&'onth)
a) Ca%per >an%ten #ake% a net profit& a covere intere%t arbitrage profit& of $*&-62+:1 on each #illion he inve%t% in the Si%% franc #arket (b0 going aroun the box)+ ?e %houl therefore take avantage of it an perfor# covere intere%t arbitrage+ b) A%%u#ing a $* #illion inve%t#ent for the 9=a0 perio& the annual rate of return on thi% near ri%k=le%% inve%t#ent i%O
0.62
Problem 7.12 Casper Ean'sten 3A Ca%per >an%ten& u%ing the %a#e value% an a%%u#ption% a% in the previou% @ue%tion& no ecie% to %eek the full :+2< return available in S ollar% b0 not covering hi% forar ollar receipt% == an uncovere intere%t arbitrage ("A) tran%action+ A%%e%% thi% eci%ion+ Assumptions Arbitra)e #un's a$ailable Spot e(c!an)e rate ;S?r.=> %mont! #orar' rate ;S?r.=> (pecte' spot rate in 90 'a+s ;S?r.=> 3.S. 'ollar %mont! interest rate Siss #ranc%mont! interest rate
Value 1:000:000 1.2810 1.2740 1.2700 4.800 %.200
S?r. ui$alent S?r. 1:281:000
Since Ca%per i% in the S #arket (%tarting point)& if he ere to unertake uncovere intere%t arbitrage he oul be fir%t exchange ollar% for Si%% franc%& inve%ting the Si%% franc% for 9 a0%& an then exchanging the Si%% franc procee% (principle an intere%t) back into S ollar% at hatever the %pot rate of exchange i% at that ti#e+ "n thi% ca%e Ca%per ill have to == at lea%t in hi% #in == #ake %o#e a%%u#ption a% to hat the exchange rate ill be at the en of the 9 a0 perio+
SA
1:000:000 Spot ;S?r=> 1.2810 S?r. 1:281:000
D
U.S. dollar interest rate (&'onth) 4.800
D
D
1.0120
D
D
1:012:000.00 1:012:029.16 29.16 @ @ @ (pecte' Spot ;S?r=> 1.2759 @ @
D
S?r. 1:291:248
B 90 'a+s B
D
D
1.0080
D
%.200 Swiss "ranc interest rate (&'onth)
"f Ca%per a%%u#e the %pot rate at the en of 9 a0% ere the %a#e a% the current %pot rate (SIr*+2*/$)& the "A tran%action oul not #ake #uch %en%e+ ,he loer Si%% franc intere%t rate oul 0iel final ollar procee% of onl0 $*&2&& a full $:& le%% than %i#pl0 inve%ting in the S (%traight acro%% the top of the box)+ Ior an "A tran%action to re%ult in higher ollar procee% at the en of t he 9 a0 perio& the ening %pot rate of exchange oul have to be SI*+.-9/$ or le%% (a %tronger an %tronger Si%% franc re%ulting in #ore an #ore S ollar% hen exchange)+ Shoul Ca%per o it3 4ell& epen% on hi% bank;% policie% on uncovere tran%action%& an hi% belief% on the future %pot exchange rate+ 7ut& given that he i% inve%te in a foreign currenc0 ith a loer intere%t rate& not a higher one& %o he i% placing all of hi% ;bet%; on the exchange rate& it i% not a %peculation for the eak of heart+
Problem 7.1% Casper Ean'sten %0 'a+s later 'ne #onth after the event% e%cribe in the previou% to @ue%tion%& Ca%per >an%ten once again ha% $* #illion (or it% Si%% franc e@uivalent) to inve%t for three #onth%+ ?e no face% the folloing rate%+ Shoul he again ener into a covere intere%t arbitrage (C"A) inve%t#ent3 Assumptions Arbitra)e #un's a$ailable Spot e(c!an)e rate ;S?r.=> %mont! #orar' rate ;S?r.=> 3.S. 'ollar %mont! interest rate Siss #ranc%mont! interest rate
Value 1:000:000 1.%%92 1.%286 4.750 %.625
S?r. ui$alent S?r. 1:%%9:200
Ar"itrage #ule of hum"% &f the difference in interest rates is greater than the forward premium/discount, or expected change in the spot rate for U&A, invest in the higher interest yielding currency! &f the difference in interest rates is less than the forward premium 'or expected change in the spot rate(, invest in the lower yielding currency! i##erence in interest rates ; i S?r. i > ?orar' premium on t!e Siss #rance CA pro#it
1.125 %.191 2.066
,hi% tell% Ca%per >an%ten he %houl borro +S+ ollar% an inve%t in the loer 0ieling currenc0& the Si%% franc& an then %ell the Si%% franc principal an intere%t forar three #onth% locking in a C"A profit+
U.S. dollar interest rate (&'onth) 4.750
SA 1:000:000 Spot ;S?r.=> 1.%%92 S?r. 1:%%9:200.00
D
D
1.011875
D
D
D
B 90 'a+s B
D
D
1.0090625
D
D
1:011:875.00 1:017:11%.1% 5:2%8.1% @ @ @ ?90 ;S?r.=> 1.%286 @ @ @ S?r. 1:%51:%%6.50
%.625 Swiss "ranc interest rate (&'onth)
Ye%& Ca%per %houl unertake the covere intere%t arbitrage tran%action& a% i t oul 0iel a ri%k=le%% profit (exchange rate ri%k i% eli#inate ith the forar contract& but counterpart0 ri%k %till exi%t% i f one of hi% counterpartie% faile to actuall0 #ake goo on their contractual co##it#ent% to eliver the forar or pa0 the intere%t) of $-&62+*6 on each $* #illion inve%te+
Problem 7.14 Pulau Penan) slan' esort ,here%a Nunn i% planning a 6=a0 vacation on Pulau Penang& Fala0%ia& one 0ear fro# no+ ,he pre%ent charge for a luxur0 %uite plu% #eal% in Fala0%ian ringgit (BF) i% BF*&:-/a0+ ,he Fala0%ian ringgit pre%entl0 trae% at BF6+*6-/$+ She figure% out the ollar co%t toa0 for a 6=a0 %ta0 oul be $*&+ ,he hotel infor#e her that an0 increa%e in it% roo# charge% ill be li#i te to an0 increa%e in the Fala0%ian co%t of living+ Fala0%ian inflation i% expecte to be +.-< per annu#& hile +S+ inflation i% expecte to be onl0 *+-<+
a+ ?o #an0 ollar% #ight ,here%a expect to nee one 0ear hence to pa0 for her 6=a0 vacation3 b+ 70 hat percent ha% the ollar co%t gone up3 4h03 Assumptions Charge for %uite plu% #eal% in Fala0%ian ringgit (BF) Spot exchange rate (BF/$) S$ co%t toa0 for a 6 a0 %ta0
Fala0%ian ringgit inflation rate expecte to be +S+ ollar inflation rate expecte to be
Value 1:045.00 %.1%50 10:000.00 2.750 1.250
a. "o man+ 'ollars mi)!t +ou e(pecte to nee' one +ear !ence #or +our %0'a+ $acation,
Spot exchange rate (ringgit per S$) Fala0%ian ringgit inflation rate expecte to be +S+ ollar inflation rate expecte to be
%.1%50 2.750 1.250
Spot (expecte in * 0ear) Spot x ( * Q BF inflation) / ( * Q S inflation) (pecte' spot rate one +ear #rom no base' on PPP ;F=> "otel c!ar)es e(pecte' to be pai' one +ear #rom no #or a %0'a+ sta+ ;F>
S ollar% neee on the ba%i% of the%e to expectation%O
%.181444 %2:212.1% 10:125.00
b. -+ !at percent !as t!e 'ollar cost )one up, &!+,
Ne ollar co%t 'riginal ollar co%t Percent c!an)e in 3S cost
10:125.00 10:000.00 1.250
,he ollar co%t ha% ri%en b0 the S oll ar inflation rate+ ,hi% i% a re%ult of ,here%a;% e%ti#ation of the future %uite co%t% an the exchange rate changing in proportion to inflation (relative purcha%ing poer parit0)+
