Problem 7.1 Traveling Down Under +erry +erry Lamoreaux has homes in &oth Sy%ney, Australia Australia an% Phoenix, Ariona# e tra.els &eteen the to cities at least tice a year# 'ecause 'ecause of his fre0uent trips he ants to &uy some ne, high 0uality luggage# e1s %one his research an% has %eci%e% to go ith a 'riggs 2 iley &ran% three piece luggage set# set# +here are retail stores in &oth Phoenix an% Sy%ney# Sy%ney# +err +erry y as a finance ma4or an% ants to use purchasing poer parity to %etermine if he is paying the same price no matter here he ma5es his purchase# a# 6f the price of the 3-piece luggage set in Phoenix is $!" an% the price of the same 3-piece set in Sy%ney is $3", using purchasing poer parity, is the price of the luggage truly e0ual if the th e spot rate is A$#"/$7 &# 6f the price of the luggage luggage remains the same in Phoenix one year from from no, %etermine hat the price of the luggage shoul% shoul% &e in Sy%ney in one year1s year1s time if PPP hol%s true# +he US inflation rate is #!* an% the Australian inflation rate is 3#3*# Assumptions Price of 3-Piece Luggage set in US$ Price of 3-Piece Luggage set in A$ Spot exchange rate, (A$/$) US inflation for year (per annum) Australian inflation for year (per annum)
Value 850.00 90.00 1.09!1 1.15" .1"
a. #s t$e spot rate a%%urate given bot$ luggage pri%es&
Price of 3-Piece Luggage set in US$ Price of 3-Piece Luggage set in A$ Spot rate as %etermine% &y PPP Spot rate = Price in A$ / Price in US$
!"#"" 3"#"" 1.09!1
b. '$at s$ould be t$e pri%e o( t$e luggage set in A) in 1 *ear i( PPP $olds&
'eginning spot rate (A$/$) Australian inflation US inflation PPP exchange rate Price of 3-Piece Luggage set in US$ PPP exchange rate Price of 3-piece luggage set in Sy%ney (A$)
#" 3#3* #!* 1.1155
!"#"" #!! 9!8.19
However, However, purchasing power parity is not always an accurate accurate predictor predictor of exchange exchange rate movements, particularly particularly in the short term
Problem 7.+ Pulau Penang #sland ,esort +heresa >unn is planning a 3"-%ay .acation on Pulau Penang, :alaysia, one year from no# +he present charge for a luxury suite plus meals in :alaysian ringgit (:) is :,"!/%ay# +he :alaysian ringgit presently tra%es at :3#3!"/$# She figures out the %ollar cost to%ay for a 3"-%ay stay oul% &e $","""# +he hotel informe% her that any increase in its room charges ill &e limi te% to any increase in the :alaysian cost of li.ing# :alaysian inflation is expecte% to &e @#!* per annum, hile U#S# inflation is expecte% to &e only #@!*#
a# o many %ollars might +heresa expect to nee% one year hence to pay for her 3"-%ay .acation7 &# 'y hat percent ill the %ollar cost ha.e gone up7 8hy7 8hy7 Assumptions 9harge for suite plus meals in :alaysian ringgit (:) Spot exchange rate (:/$) US$ cost to%ay for a 3" %ay stay
:alaysian ringgit inflation rate expecte% to &e U#S# %ollar inflation rate expecte% to &e
Value 1-0!5.00 .150 )10-000.00 +.750" 1.+50"
a. ow man* dollars mig$t *ou e/pe%t to need one *ear $en%e (or *our 0da* va%ation& va%atio n&
Spot exchange rate (ringgit per US$) :alaysian ringgit inflation rate expecte% to &e U#S# %ollar inflation rate expecte% to &e
.150 +.750" 1.+50"
Spot (expecte% (expecte% in year) year) ; Spot x ( < : inflation) / ( < US inflation) /pe%ted spot rate one *ear (rom now based on PPP 2,34) ote otell %$ar %$arge gess e/pe e/pe%t %ted ed to be paid paid one one *ear *ear (rom (rom now now (or (or a 0d 0da* a* sta* sta* 2,3 2,3
US %ollars nee%e% on the &asis of these t hese to expectations=
.181!!! +-+ +-+1+ 1+.1 .1 )10-1+5.00
b. 6* w$at per%ent $as t$e dollar %ost gone up& '$*&
>e %ollar cost ?riginal %ollar cost Per%ent %$ange in U) %ost
)10-1+5.00 )10-000.00 1.+50"
+he %ollar cost has risen &y the US %oll ar inflation rate# +his is a result of +heresa1s estimation of the future suite costs an% the exchange rate changing in proportion to inflation (relati.e purchasing poer parity)#
Problem 7. tarbu%s in roatia Star&uc5s opene% its first store in Cagre&, 9roatia in ?cto&er @""# +he price of a tall .anilla latte in Cagre& is @!#"5n# 6n >e Dor5 9ity, the price of a tall .anilla latte is $@#F!# +he exchange rate &eteen 9roatian 5unas (5n) an% U#S# %ollars is 5n!#F@/$# Accor%ing to purchasing poer parity, is the 9roatian 5una o.er.alue% or un%er.alue%7 Assumptions Spot exchange rate (Bn/$) Price of .anilla latte in Cagre& (5n) Price of .anilla latte in >D9 ($)
Actual price of 9roatian latte in USE 6mplie% PPP of 9roatian latte in USE Percentage o.er.aluation (positi.e) or un%er.aluation (negati.e)
Value 5.:+88 +5.70 +.:5
!.57 9.70 11+.!08"
Problem 7.! ;apanese4United tates Parit* onditions Eere5 +osh is attempting to %etermine hether US/Gapanese financial con%itions are at parity# +he current spot rate is a flat ¥89#""/$, hile the 3F"-%ay forar% rate is ¥84.90/$# Horecast inflation is #""* for Gapan, an% !#""* for the US# +he 3F"-%ay euro-yen %eposit rate is #""*, an% the 3F"-%ay euro-%ollar %eposit rate is #!""*# a# Eiagram an% calculate hether international parity con%itions hol% &eteen Gapan an% the Unite% States# &# Hin% the forecaste% change in the Gapanese yen/U#S# %ollar (I/$) exchange rate one year from no# Assumptions Horecast annual rate of inflation for Gapan Horecast annual rate of inflation for Unite% States ?ne-year interest rate for Gapan ?ne-year interest rate for Unite% States Spot exchange rate (I/$) ?ne-year forar% exchange rate (I/$)
Value 1.100" 5.900" !.700" 9.500" 89.00 8!.90
a. Appro/imate
spot e/%$ange rate
J
J
!.8" 2;apanese *en at a premium
J
J
K K K K K International Fisher Effect (C) K K K K
K K K Interest rate parity (D)
!.8" 2Dollar e/pe%ted to weaen
J
Di((eren%e in nominal interest rates !.8" 2$ig$er in United tates
J
Purchasing power parity (A) K K K K
!.8" 2U $ig$er t$an ;apan
K K J
J
Fisher effect (B)
As is alays the case ith parity con%itions, the future spot rate is implicitly forecast to &e e0ual to the forar% rate, the implie% rate from the international Hisher effect, an% the rate im plie% &y purchasing poer parity# Accor%ing to Daie1s calculations, the mar5ets are in%ee% in e0uili&rium -- parity#
b. Spot exchange rate (I/$) ?ne-year forar% exchange rate (I/$) Horecaste% change in exchange rates
#"" #" !.8"
!"urrent Spot #ate %orward &xchange #ate' / !%orward &xchange #ate'
Problem 7.5 risis at t$e eart o( arnaval +he Argentine peso as fixe% through a currency &oar% at Ps#""/$ throughout th e "s# 6n Ganuary @""@ the Argentine peso as floate%# ?n Ganuary @, @""3 it as tra%ing at Ps3#@"/$# Euring that one year perio% Argentina1s inflation rate as @"* on an annualie% &asis# 6nflation in the Unite% States %uring that same perio% as @#@* annualie%# a# 8hat shoul% ha.e &een the exchange rate in Ganuary @""3 if PPP hel%7 &# 'y hat percentage as the Argentine peso un%er.alue% on an annualie% &asis7 c# 8hat ere the pro&a&le causes of un%er.aluation7 Assumptions Spot exchange rate, fixe% peg, early Ganuary @""@ (Ps/$) Spot exchange rate, Ganuary @, @""3 (Ps/$) US inflation for year (per annum) Argentine inflation for year (per annum)
Value 1.0000 .+000 +.+0" +0.00"
a. '$at s$ould $ave been t$e e/%$ange rate in ;anuar* +00 i( PPP $eld&
'eginning spot rate (Ps/$) Argentine inflation US inflation PPP exchange rate
1.00 +0.00" +.+0" 1.17
b. 6* w$at per%entage was t$e Argentine peso undervalued on an annuali=ed basis&
Actual exchange rate (Ps/$) PPP exchange rate (Ps/$) Percentage o.er.aluation (positi.e) or un%er.aluation (negati.e)
%. '$at were t$e probable %auses o( undervaluation&
+he rapi% %ecline in the .alue of the Argentine peso as a result of not only inflation, &ut also a se.ere crisis in the &alance of payments (see 9hapter )#
.+0 1.17 :.07"
Problem 7.: orolla /ports and PassT$roug$ Assume that the export price of a +oyota 9orolla from ?sa5a, Gapan is I@,!","""# +he exchange rate is I#F"/$# +he forecast rate of inflation in the Unite% States is @#@* per year an% is "#"* per year in Gapan# Use this %ata to anser the folloing 0uestions on exchange rate pass-through# a# 8hat as the export price for the 9orolla at the &eginning of the year expresse% in U#S# %ollars7 &# Assuming purchasing poer parity hol%s, hat shoul% the exchange rate &e at the en% of the year7 c# Assuming ""* pass-through of exchange rate, hat ill &e the %ollar price of a 9orolla at the en% of the year7 %# Assuming !* pass-through, hat ill &e the %ollar price of a 9orolla at the en% of the year7 teps 6nitial spot exchange rate (I/$) 6nitial price of a +oyota 9orolla (I) xpecte% US %ollar inflation rate for t he coming year xpecte% Gapanese yen inflation rate for the coming year Eesire% rate of pass through &y +oyota a. '$at was t$e e/port pri%e (or t$e orolla at t$e beginning o( t$e *ear& Dear-&eginning price of a 9orolla (I) Spot exchange rate (I/$) Dear-&eginning price of a 9orolla ($) b. '$at is t$e e/pe%ted spot rate at t$e end o( t$e *ear assuming PPP& 6nitial spot rate (I/$) xpecte% US$ inflation xpecte% Gapanese yen inflation xpecte% spot rate at en% of year assuming PPP (I/$) %. Assuming %omplete pass t$roug$- w$at will t$e pri%e be in U) in one *ear& Price of 9orolla at &eginning of year (I) Gapanese yen inflation o.er the year Price of 9orolla at en% of year (I) xpecte% spot rate one year from no assuming PPP (I/$) Price of 9orolla at en% of year in ($) d. Assuming partial pass t$roug$- w$at will t$e pri%e be in U) in one *ear& Price of 9orolla at en% of year (I) Amount of expecte% exchange rate change, in percent (from PPP) Proportion of exchange rate change passe% through &y +oyota Proportional percentage change ffecti.e exchange rate use% &y +oyota to price in US$ for en% of year Price of +oyota at en% of year ($)
Value 87.:0 +-150-000 .!00" 0.000" 75.000"
)
+-150-000 87.:0 +!-5!.8
87.:0 .!0" 0.00" 8!.7+
)
+-150-000 0.000" +-150-000 8!.7+ +5-77.85
)
+-150-000 .!00" 75.000" +.550" 85.!++ +5-1:9.+!
Problem 7.7 Taes$i >amada #A ;apan +a5eshi Bama%a, a foreign exchange tra%er at 9re%it Suisse (+o5yo), is exploring co.ere% interest ar&itrage possi&ilities# e ants to in.est $!,""",""" or its yen e0ui.alent, in a co.ere% interest ar&itrage &eteen U#S# %ollars an% Gapanese yen# e face% the folloing exchange rate an% interest rate 0uotes# Assumptions Arbitrage (unds available pot rate 24) 180da* (orward rate 24) 180da* U.. dollar interest rate 180da* ;apanese *en interest rate
Value )5-000-000 118.:0 117.80 !.800" .!00"
?en @uivalent 59-000-000
Ar(itrage #ule of )hum(* +f the difference in interest rates is greater than the forward premium/discount, or expected change in the spot rate for U+A, invest in t he higher interest yielding currency +f the difference in interest rates is less than the forward premium !or expected change in the spot rate', invest in the lower yielding currency
Di((eren%e in interest rates 2 i i )
1.!00" 1.58" 0.0!+"
+his tells +a5eshi Bama%a that he shoul% &orro yen an% in.est in the higher yiel%ing currency, the U#S# %ollar, to loc5-in a co.ere% interest ar&itrage (96A) profit#
U! dollar interest rate ("#$ days) !.800" )
5-000-000
M
B B B B B pot 24) 118.:0 B B B 59-000-000.00 ;apanese *en TA,T
M
1.0+!0
M
M
)
C C C C C
180 da*s
M
M
1.0170
M
.!00" %apanese yen interest rate ("#$ days)
5-1+0-000
M
:0-1:-000 :0-081-000 55-000 ED
+a5eshi Bama%a generates a 96A profit &y in.esting in t he higher interest rate currency, the %ollar, an% simultaneously selling the %ollar procee%s forar% into yen at a forar% premium hich %oes not completely negate the interest %ifferential#
Problem 7.8 Taes$i >amada U#A ;apan +a5eshi Bama%a, 9re%it Suisse (+o5yo), o&ser.es that the I/$ spot rate has &een hol%ing stea%y, an% &oth %ollar an% yen interest rates ha.e remaine% relati.ely fixe% o.er the past ee5# +a5eshi on%ers if he shoul% try an unco.ere% interest ar&itrage (U6A) an% there&y sa.e t he cost of forar% co.er# :any of +a5eshi1s research associates -- an% their computer mo%els -- are pre%icting the spot rate to remain close to I#""/$ for the coming " %ays# Using the same %ata as in the pre.ious pro&lem, analye the U6A potential# Assumptions Arbitrage (unds available pot rate 24) 180da* (orward rate 24) /pe%ted spot rate in 180 da*s 2 4) 180da* U.. dollar interest rate 180da* ;apanese *en interest rate
Value )5-000-000 118.:0 117.80 118.00 !.800" .!00"
?en @uivalent 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
Di((eren%e in interest rates 2 i i ) /pe%ted gain 2loss on t$e spot rate U#A pro(it potential
1.!00" 1.017" 0.8"
+his tells +a5eshi Bama%a that he shoul% &orro yen an% in.est in the higher yiel%ing currency, the U#S# %ollar, to potentially gain on an unco.ere% &asis (U6A)#
U! dollar interest rate ("#$ days) !.800" )5-000-000 B
M
B B B B pot 24) 118.:0 B
M
1.0+!0
M
M
)5-1+0-000 C C C C /pe%ted pot ,ate in 180 da*s 24) 118.00 C
180 da*s
B B 59-000-000.00 ;apanese *en TA,T
C
M
M
1.0170
M
.!00" %apanese yen interest rate ("#$ days)
M
:0!-1:0-000 :0-081-000 1-079-000 ED
a) +a5eshi Bama%a generates an unco.ere% interest ar&itrage (U6A) profit of I,",""" if his expectations a&out the future spot rate, the one in effect in " %ays, pro.e correct# &) +he ris5 +a5eshi is ta5ing is that the actual spot rate at the en% of the perio% can theoretically &e anything, &etter or orse for his speculati.e position# e in fact has .ery little Niggle room,N as they say# A small mo.ement ill cost him a lot of money# 6f the spot rate en%s up any stronger than a&out #/$ (a smaller num&er), he ill lose money# (Oerify &y inputting I#"/$ in the expecte% spot r ate cell un%er assumptions#)
Problem 7.9 open$agen overed 2A ei%i i Gensen, a foreign exchange tra%er at G#P# :organ 9hase, can in.est $! million, or the foreign currency e0ui.alent of the &an51s short term fun%s, in a co.ere% interest ar&itrage ith Eenmar5# Using the folloing 0uotes can ei%i ma5e co.ere% interest ar&itrage (96A) profit7 Assumptions Arbitrage (unds available pot e/%$ange rate 2r4) mont$ (orward rate 2r4) U dollar mont$ interest rate Danis$ roner mont$ interest rate
Value )5-000-000 :.17+0 :.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, inves t in the higher interest yielding currency +f the difference in interest rates is le ss than the forward premium !or expected change in the spot rate', invest in the lower yi elding currency
Di((eren%e in interest rates 2ir i)
+.000" 1.:78" 0.++"
+his tells ei%i i Gensen that he shoul% &orro %ollars an% in.est in the higher yiel%ing currency the Eanish 5roner, for 96A profit#
U! dollar interest rate (&'onth) .000"
TA,T )
5-000-000.00 C C C C C pot 2r4) :.17+0 C C C r 0-8:0-000.00
M
M
1.0075
M
ED
M
90 da*s
M
M
1.01+5
M
M
)
5-07-500.00 5-0!1-+:.1 ) -7:.1 B B B
5.000" Danish roner interest (&'onth)
ei%i i Gensen generates a co.ere% interest ar&itrage (96A) profit &ecause she is a&le to generate an e.en higher interest return in Eanish 5roner than she Ngi.es upN &y selling the procee%s forar% at the forar% rate#
Problem 7.10 open$agen overed 26 Part a ei%i i Gensen is no e.aluating the ar&itrage profit potential in the same mar5et after interest rates change# (>ote that anytime the %ifference in interest rates %oes not exactly e0ual the forar% premium, it must &e possi&le to ma5e 96A profit one ay or another#) Assumptions Arbitrage (unds available pot e/%$ange rate 2r4) mont$ (orward rate 2r4) U dollar mont$ interest rate Danis$ roner mont$ interest rate
Value )5-000-000 :.17+0 :.1980 !.000" 5.000"
r @uivalent r 0-8:0-000
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, inves t in the higher interest yielding currency +f the difference in interest rates is le ss than the forward premium !or expected change in the spot rate', invest in the lower yi elding currency
Di((eren%e in interest rates 2ir i)
1.000" 1.:78" 0.:78"
+his tells ei%i that she shoul% &orro Eanish 5roner an% in.est in the L?8 interest rate currency, the %ollar, gaining on the re-exchange of %ollars for 5roner at the en% of the perio%#
U! dollar interest rate (&'onth) !.000" )
5-000-000.00 B B B B B pot 2r4) :.17+0 B B B r 0-8:0-000.00
M
M
1.0100
M
M
90 da*s
M
M
1.01+5
M
M
)
5-050-000.00 C C C C C <90 2r4) :.1980 C C r 1-+99-900.00 r 1-+!5-750.00 r 5!-150.00
5.000" TA,T
Danish roner interest (&'onth)
ED
a) ei%i i Gensen generates a co.ere% interest ar&itrage profit of 5r!,!" &ecause, although U#S# %ollar interest rates are loer, the U#S# %ollar is selling forar% at a premium against the Eanish 5rone#
Problem 7.11 open$agen overed 26 Part b ei%i i Gensen is no e.aluating the ar&itrage profit potential in the same mar5et after int erest rates change# (>ote that anytime the %ifference in interest rates %oes not exactly e0ual the forar% premium, it must &e possi&le to ma5e 96A profit one ay or another#) Assumptions Arbitrage (unds available pot e/%$ange rate 2r4) mont$ (orward rate 2r4) U dollar mont$ interest rate Danis$ roner mont$ interest rate
Value )5-000-000 :.17+0 :.1980 .000" :.000"
r @uivalent r 0-8:0-000
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 t he 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
Di((eren%e in interest rates 2ir i)
.000" 1.:78" 1.++"
+his tells ei%i i Gensen that she shoul% &orro US %ollars an% in.est in the 6Q interest rate currency, the 5roner, gaining on the re-exchange of 5roner for %ollars at the en% of the perio%#
U! dollar interest rate (&'onth) .000" TA,T )5-000-000 C C C C C pot 2r4) :.17+0 C C C r 0-8:0-000.00
M
M
1.0075
M
M
90 da*s
M
M
1.0150
M
M
) ) )
ED 5-07-500.00 5-05-710.87 1:-+10.87 B B B <90 2r4) :.1980 B B B r 1-++-900.00
:.000" Danish roner interest (&'onth)
&) 6f the Eanish 5roner interest rate increases to F#""*, hile the U#S# %ollar interest rate stays at 3#""* an% spot an% forar% rates remain the same, ei%i i Gensen1s 96A profit is $F,@"##
Problem 7.1+ asper Fandsten #A 9asper Lan%sten is a foreign exchange tra%er f or a &an5 in >e Dor5# e has $ million (or its Siss franc e0ui.alent) for a short term money mar5et in.estment an% on%ers if he shoul% in.est in U#S# %ollars f or three months, or ma5e a co.ere% interest ar&itrage in.estment in the Siss f ranc# e faces the folloing 0uotes=
Assumptions Arbitrage (unds available pot e/%$ange rate 2
Value )1-000-000 1.+810 1.+7!0 !.800" .+00"
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
Di((eren%e in interest rates 2 i
1.:00" +.198" 0.598"
+his tells 9asper Lan%sten he s houl% &orro U#S# %ollars an% in.est in the L?8 yiel%ing currency, the Siss franc, in or%er to earn co.ere% interest ar&itrage (96A) profits#
U! dollar interest rate (&'onth) !.800"
TA,T )
1-000-000.00 C C C C C pot 2
M
M
1.01+0
M
ED
M
90 da*s
M
M
1.0080
M
M
)
1-01+-000.00 1-01-58.!: ) 1-58.!: B B B
.+00" !wiss franc interest rate (&'onth)
a) 9asper Lan%sten ma5es a net profit, a co.ere% interest ar&itrage profit, of $,!3#F on each million he in.ests in the Siss franc mar5et (&y going aroun% the &ox)# e shoul% therefore ta5e a%.antage of it an% perform co.ere% interest ar&itrage# &) Assuming a $ million in.estment for the "-%ay perio%, the annual rate of return on this near ris5less in.estment is=
0.:+"
Problem 7.1 asper Fandsten U#A 9asper Lan%sten, using the same .alues an% assumptions as in the pre.ious 0uestion, no %eci%es to see5 the full #""* return a.aila&le in US %ollars &y not co.ering his forar% %ollar receipts -- an unco.ere% interest ar&itrage (U6A) transaction# Assess this %ecision#
Assumptions Arbitrage (unds available pot e/%$ange rate 2
Value )1-000-000 1.+810 1.+7!0 1.+700 !.800" .+00"
Since 9asper is in the US mar5et (starting point), if he ere to un%erta5e unco.ere% interest ar&itrage he oul% first exchange %ollars for Siss francs, in.esting the Siss francs for " %ays, an% then exchanging the Siss franc procee%s (principle an% interest) &ac5 into US %ollars at hate.er the spot rate of exchange is at that time# 6n this case 9asper ill ha.e to -- at least in his min% -- ma5e some assumption as to hat the exchange rate ill &e at the en% of the " %ay perio%#
TA,T
)
1-000-000 C C C C pot 2
ED
U! dollar interest rate (&'onth) !.800"
M
M
1.01+0
M
M
1-01+-000.00 1-01+-0+9.1: +9.1: B B B /pe%ted pot 2
M
90 da*s
M
M
1.0080
M
) ) )
.+00" !wiss franc interest rate (&'onth)
6f 9asper assume% the spot rate at the en% of " %ays ere the same as the current spot rate (SHr#@"/$), the U6A transaction oul% not ma5e much sense# +he loer Siss franc interest rate oul% yiel% final %ollar procee%s of only $,"",""", a full $,""" less than s imply in.esting in the US (straight across the top of the &ox)# Hor an U6A transaction to result in higher %ollar procee%s at the en% of the " %ay perio%, the en%ing spot rate of exchange oul% ha.e to &e SH#@!/$ or less (a stronger an% stronger Siss franc resulting in more an% more US %ollars hen exchange%)# Shoul% 9asper %o it7 8ell, %epen%s on his &an51s policies on unco.ere% transactions, an% his &eliefs on the f uture spot exchange rate# 'ut, gi.en that he is in.este% in a foreign currency ith a loer interest rate, not a higher one, so he is placing all of his 1&ets1 on the exchange rate, it is not a speculation for the ea5 of heart#
Problem 7.1! asper Fandsten T$irt* Da*s Fater ?ne month after the e.ents %escri&e% in the pre.ious to 0uestions, 9asper Lan%sten once again has $ million (or its Siss franc e0ui.alent) to in.est for three months# e no faces the folloing rates# Shoul% he again enter into a co.ere% interest ar&itrage (96A) in.estment7 Assumptions Arbitrage (unds available pot e/%$ange rate 2
Value )1-000-000 1.9+ 1.+8: !.750" .:+5"
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 i n the higher interest yielding currency +f the difference in interest rates is l ess than the forward premium !or expected change in the spot rate', invest in the lower yielding currency
Di((eren%e in interest rates 2 i
1.1+5" .191" +.0::"
+his tells 9asper Lan%sten he shoul% &orro U#S# %ollars an% in.est in the loer yiel%ing currency, the Siss franc, an% then sell the Siss franc principal an% interest forar% three months, loc5ing in a 96A profit#
U! dollar interest rate (&'onth) !.750"
TA,T )1-000-000 C C C C C pot 2
M
M
1.011875
M
ED
M
90 da*s
M
M
1.0090:+5
M
M
)
1-011-875.00 1-017-11.1 ) 5-+8.1 B B B <90 2
.:+5" !wiss franc interest rate (&'onth)
Des, 9asper shoul% un%erta5e the co.ere% int erest ar&itrage transaction, as it oul% yiel% a ris5less profit (exchange rate ris5 is eliminate% ith the forar% contract, &ut counterparty ris5 still exists if one of his counterparties faile% to actually ma5e goo% on their contractual commitments to %eli.er the forar% or pay the interest) of $!,@3#3 on each $ million in.este%#
Problem 7.15 tatoil o( Eorwa*Gs Arbitrage Statoil, the national oil company of >oray, is a large, sophisticate%, an% acti.e participant in &oth the currency an% petrochemical mar5ets# Although it is a >oregian company, &ecause it operates ithin the glo&al oil mar5et, it consi%ers the U#S# %ollar as its functional currency, not the >oregian 5rone# Ari Barlsen is a currency tra%er for Statoil, an% has imme%iate use of $3 million (or the >oregian 5rone e0ui.alent)# e is face% ith the folloing mar5et rates, an% on%ers hether he can ma5e some ar&itrage profits in the coming " %ays# Assumptions Arbitrage (unds available pot e/%$ange rate 2Eo4) mont$ (orward rate 2Eo4) U.. dollar mont$ interest rate Eorwegian rone mont$ interest rate
Value )-000-000 :.01+ :.018: 5.000" !.!50"
>rone @uivalent 18-09-:00
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
Di((eren%e in interest rates 2 i Eo i )
0.550" 0.85" 0.+85"
+his tells Ari Barlsen he shoul% &orro U#S# %ollars an% in.est in the loer yiel%ing currency, the >oregian 5rone, selling the %ollars forar% " %ays, an% therefore earn co.ere% interest ar&itrage (96A) profits#
*orwegian rone interest rate (&'onth) !.!50"
18-09-:00.00 B B B B B pot 2Eo4) :.01+ B
)
B B -000-000.00 6orrow U)
M
M
1.0111+50
M
M
M
1.01+50000
M
18-+9!-891.0 C
C C C C
90 da*s
M
M
) ) )
C -09-710.+5 -07-500.00 +-+10.+5
5.000" TA,T
U! dollar interest rate (&'onth)
ED
Ari Barlsen can ma5e $@,@"#@! for Statoil on each $3 million he in.ests in this co.ere% interest ar&itrage (96A) transaction# >ote that this is a .ery slim rate of return on an in.estment of such a large amount# Annuali=ed rate o( returnH
0.+9!7"
Problem 7.1: eparated b* t$e Atlanti% Separate% &y more than 3,""" nautical miles an% fi.e time ones, money an% foreign exchange mar5ets in &oth Lon%on an% >e Dor5 are .ery efficient# +he folloing information has &een collecte% from the respecti.e areas= Assumptions Spot exchange rate ($/R) ?ne-year +reasury &ill rate xpecte% inflation rate
Fondon 1.+:! .900" Un5non
Eew ?or 1.+:! !.500" 1.+50"
a# 8hat %o the financial mar5ets suggest for inflation in urope next year7 &# stimate to%ay1s one-year forar% exchange rate &eteen the %ollar an% the euro#
a. '$at do t$e (inan%ial marets suggest (or in(lation in urope ne/t *ear&
Accor%ing to the Hisher effect, real interest rates shoul% &e the same in &oth urope an% the US# Since the nominal rate ; (
10.900" & 10.+10"
T$e e/pe%ted rate o( in(lation in urope is t$enH
I
0.::9"
b. stimate toda*Gs one*ear (orward e/%$ange rate between t$e dollar and t$e euro.
Spot exchange rate ($/R) US %ollar one-year +reasury &ill rate uropean euro one-year +reasury &ill rate Jne *ear (orward rate 2)4K
1.+:! !.500" .900" 1.!1
10!.500" 101.+50" 10.+10" .+10"
Problem 7.17 $amoni/ $ateau ,entals Dou are planning a s5i .acation to :t# 'lanc in 9hamonix, Hrance, one year from no# Dou are negotiating o.er the rental of a chateau# +he chateau1s oner ishes to preser.e his real income against &oth inflation an% exchange rate changes, an% so the present ee5ly rent of R,"" (9hristmas season) ill &e a%4uste% upar%s or %onar%s for any change in the Hrench cost of li.ing &eteen no an% then# Dou are &asing your &u%geting on purchasing poer parity (PPP)# Hrench inflation is expecte% to a.erage 3#!* for the coming year, hile U#S# %ollar inflation i s expecte% to &e @#!*# +he current spot rate is $#3F@"/R# 8hat s houl% you &u%get as the U#S# %ollar cost of the one ee5 rental7 Assumptions Spot exchange rate ($/R) xpecte% US inflation for coming year xpecte% Hrench inflation for coming year 9urrent chateau nominal ee5ly rent (R)
Value )1.:+0 +.500" .500" K 9-800.00
Value
Pur%$asing power parit* e/%$ange rate (ore%ast 2)4K
1.!88
Spot (one year) ; Spot x ( < US$ inflation ) / ( < Hrench inflation ) Eominal mont$l* rent- in euros- one *ear (rom now
10-1!.00
ent no x ( < inflation Hrance ) ost o( rent one *ear (rom now in U dollars
)
1-:81.+9
ent one year from no / PPP forecaste% spot rate >ote= stu%ents may in0uire as to hether the euro, a currency for a multitu%e of countries hich may actually ha.e su&stantial %ifferencies in inflation locally, really ill react to inflationary pressures an% %ifferentials as PPP oul% pre%ict# A goo% 0uestion#
Problem 7.18 ast Asiati% ompan* T$ailand +he ast Asiatic 9ompany (A9), a Eanish company ith su&si%iaries all o.er Asia, has &een fun%ing its 'ang5o5 su&si%iary primarily ith U#S# %ollar %e&t, &ecause of the cost an% a.aila&ility of %ollar capital, as oppose% to ith +hai &aht-%enominate% (') %e&t# +he treasurer of A9-+hailan% is consi%ering a one-year &an5 loan for $@!","""# +he current spot rate is '3@#"F/$, an% the %ollar-&ase% interest is F#!* for the one year perio%# ?ne year loans are @#""* interest in &aht# a# Assuming expecte% inflation rates of #3* an% #@!* in +hailan% an% the Unite% States, repecti.ely, for the coming year, accor%ing to purchasing po er parity, hat oul% the effecti.e cost of fun%s &e in +hai &aht terms7
&# 6f A91s foreign exchange a%.isers &elie.e strongly that the +hai go.ernment ants to push the .alue of the &aht %on against the %ollar &y !* o.er the coming year (to promote its export competiti.eness in %ollar mar5ets), hat might the effecti.e cost of fun%s en% up &eing in &aht terms7 c# 6f A9 coul% &orro +hai &aht at 3* per annum, oul% this &e cheaper than either part (a) or part (&) a&o.e7
Assumptions urrent spot rate- T$ai ba$t4) /pe%ted T$ai in(lation /pe%ted dollar in(lation Foan prin%ipal in U.. dollars T$ai ba$t interest rate- 1*ear loan U dollar interest rate- 1*ear loan
Value +.0: !.00" 1.+50" )+50-000 1+.000" :.750"
Hirst, it is necessary to forecast the future spot exchange rate for the &aht/$# PPP (ore%ast o( T$ai ba$t4)
.0+58
Eifferent expectations of the future spot exchange rate, either PP P for part a), or an expecte% %e.aluation for part &), allo the isolation of exactly ho many +hai &aht oul% &e re0uire% to repay the %ollar loan#
U! dollar borrowing rate (one year) :.750" )
+50-000
M
M
1.0:750
M
M
C C C C C pot 26a$t4) +.0:00 C C C 8-015-000.00 T$ai ba$t
)
+::-875 C
:0 da*s
1+.000" T$ai ba$t borrowing rate 2one *ear Iplied cost + (,epaid-Initial proceeds) ' "
C C C C /pe%ted pot 26a$t4) .0+58 C C 8-81-7:0.8 6a$t needed to repa* U.. dollar loan
9.9::"
a) Assuming a purchasing poer parity forecast of the future spot rate, '33#"@!/$, it ill ta5e ,3,F" &aht to repay the U#S# %ollar loan# +he implie% cost of fun%s, in &aht terms, is #FF*# &) Assuming a future spot rate for the &aht that is !* ea5er than the current spot rate ('3@#"F/$ ÷ ( - #"!), or '33#/$), the implie% cost is @#3F*# (+his is foun% &y plugging in this ne forecast spot rate in the expecte% spot rate cell on the right-han% si%e of the &ox#) urrent +.0:00 P%t $g 5.00" Eew spot L old spot ÷ 2 1 .05
Problem 7.19 3altese
+he current spot exchange rate is "#3 :altese lira (:L) per U#S# %ollar# :altese inflation is expecte% to &e a&out #!* for the coming year, hile U#S# inflation, on the heels of a %ou&le-%ip recession, is expecte% to come in at only #!*# 6f the in.estor &ases .alue in the U#S# %ollar, oul% he &e &etter off recei.ing :altese lira in one year -assuming purchasing poer parity, or recei.ing a guarantee% %ollar payment assuming a gol% price of $@" per ounce7
'eig$t o( (al%on- in pounds Total number o( oun%es in weig$t Pri%e o( gold- )4oun%e
) )
3ar%$ +00 !8 7:8 !!0.00 7-9+0.00
) )
3ar%$ +00! !8 7:8 !+0.00 ++-5:0.00
+he purchasing poer parity forecast of the :altese lira/%ollar exchange rate= urrent spot rate- 3altese lira4) /pe%ted 3altese in(lation /pe%ted dollar in(lation PPP (ore%ast o( 3altese lira4)
0.900 8.500" 1.500" 0.!1:9
6f the in.estor &ases his gross sales procee%s in U#S# %ollars, the guarantee% %ollar payment at $@"/ounce yiel%s a larger amount ($3@@,!F") than accepting :altese lira, assuming PPP ($3F,F)#
urrent Value ) 7-9+0 C
#nvestor ,e%eives in 3ar%$ +00! Assuming PPP ) 1:-11: B
C C C C pot 23F4) 0.900 C C
B B B B /pe%ted pot 23F4) 0.!1:9 B B
C 11-788.80 3altese lira
:0 da*s
B 11-788.80
Problem 7.+0 3ala*sian ,is 9layton :oore is the manager of an international money mar5et fun% manage% out of Lon%on# Unli5e many money fun%s that guarantee their in.estors a near ris5-free in.estment ith .aria&le interest earnings, 9layton :oore1s fun% is a .ery aggressi.e fun% that searches out relati.ely high interest earnings aroun% the glo&e, &ut at some ris5# +he fun% is poun%-%enominate%# 9layton is currently e.aluating a rather interesting opportunity in :alaysia# Since the Asian 9risis of , the :alaysian go.ernment enforce% a num&er of currency an% capital restrictions to protect an% preser.e the .alue of the :alaysian ringgit# +he ringgit as fixe% to the U#S# %ollar at :3#"/$ for se.en years# 6n @""!, the :alaysian go.ernment alloe% the currency to float against se.eral ma4or currencies# +he current spot rate to%ay is :3#3!/$# Local currency time %eposits of "-%ay maturities are earning #""* per annum# +he Lon%on eurocurrency mar5et for poun%s is yiel%ing #@""* per annum on similar "-%ay maturities# +he current spot rate on the 'ritish poun% is $#!@"/, an% the "-%ay forar% rate is $#!!F/#
Assumptions Principal in.estment, 'ritish poun%s Spot exchange rate ($/) "-%ay forar% rate ($/) :alaysian ringgit "-%ay yiel% Spot exchange rate, :alaysian ringgit/$
) )
Values M1-000-000.00 1.58+0 1.55:1 8.900" .18!
+he initial poun% in.estment implicitly passes through the %ollar into :alaysian ringgit# +he ringgit is fixe% against the %ollar, hence the en%ing :alaysian ringgit/$ rate is the same as the current spot rate# +he poun%, hoe.er, is not fixe% to either the %ollar or ringgit# 9layton :oore can purchase a forar% against the %ollar, alloing him to co.er the %ollar/poun% exchange rate#
,eturn + (Proceeds-Initial in.estent) ' "
#nitial #nvestment M1-000-000.00 C C C C pot 2)4M 1.58+0 C C C ) 1-58+-000 C C C C pot 23)4) .18! C C C !-9:!-9!8.80 3ala*sian ringgit
British pounds .ersus U! dollars 180 da*s
U.. dollar values
/alaysian ringgit .ersus U! dollars 180 da*s
M
M
1.0!!5
M
M
:.188" #nvestment Pro%eeds M1-0:1-88!.8! B B B B
8.900" 3ala*sian ringgit deposit rate 2180 da*s
6f 9layton :oore in.ests in the :alaysian ringgit %eposit, an% accepts the unco.ere% ris5 associate% ith the :/$ exchange rate (manage% &y the go.ernment), an% sells the %ollar procee%s forar%, he shoul% expect a return of F#* on his "-%ay poun% in.estment# +his is &etter than the #@""* he can earn in the euro-poun% mar5et#
6nterestingly, if 9layton chose to >?+ sell the %ollars forar%, an% accepte% the unco.ere% ris5 of the $/ exchange rate as ell, he may or may not %o &etter than F#*# Hor example, if the spot rate remaine% unchange% at $#!@"/, 9layton1s return oul% only &e #!"*# +his %emonstrates that much of the a%%e% return 9layton is earning is arising from the forar% rate itself, an% not purely from the nominal interest %ifferentials#
Problem 7.+1 T$e 6eer tandard 6n the &conomist reporte% the creation of an in%ex, or stan%ar%, for the e.aluation of African currency .alues using the local prices of &eer# 'eer as chosen as the pro%uct for comparison &ecause :cEonal%1s ha% not peneterate% the African continent &eyon% South Africa, an% &eer met most of the same pro%uct an% mar5et characteristics re0uire% for the construction of a proper currency in%ex# 6n.estec, a South African in.estment &an5ing firm, has replicate% the process of creating a measure of purchasing poer parity (PPP) li5e that of the 'ig :ac 6n%ex of the &conomist, for Africa#
+he in%ex compares the cost of a 3! milliliter &ottle of clear lager &eer across su&-Sahara Africa# As a measure of PPP the &eer nee%s to &e relati.ely homogeneous in 0uality across countries, nee%s to possess su&stantial elements of local manufacturing, inputs, %istri&ution, an% ser.ice, in or%er to actually pro.i%e a measure of relati.e purchasing poer# +he &eers are first price% in local currency (purchase% in the ta.erns of the local man, an% not in the high price% tourist centers), then con.erte% to South African ran%# +he prices of the &eers in ran% are then compare% to form one measure of hether the local currencies are un%er.alue% (-*) or o.er.alue% (<*) .ersus the South African ran%# Use the %ata in the exhi&it an% complete the calculation of hether the in%i.i%ual currencies are un%er- or o.er-.alue%#
ountr* out$ A(ri%a 6otswana N$ana >en*a 3alawi 3auritius Eamibia Oambia Oimbabwe
6eer astle astle tar Tuser arlsberg P$oeni/ 'ind$oe astle astle
Eame o( lo%al %urren%* ,and Pula edi $illing >wa%$a ,upee E) >wa%$a O)
6eer Pri%es #n lo%al %urren%* +.0 +.+0 1-+00.00 !1.+5 18.50 15.00 +.50 1-+00.00 9.00
>otes= # 'eer price in South African ran% ; Price in local currency / spot rate on 3/!/# @# 6mplie% PPP exchange rate ; Price in local currency / @#3"# 3# Un%er- or o.er-.alue% to ran% ; 6mplie% PPP rate / spot rate on 3/!/#
#n rand ---+.9! .17 !.0+ +.:: .7+ +.50 .5+ 1.!:
#mplied PPP rate ---0.9: 5+1.7! 17.9 8.0! :.5+ 1.09 5+1.7! .91
pot rate 2415499 ---0.75 79.10 10.+7 :.9: !.0 1.00 !0.:8 :.15
Under or overvalued to rand 2" ---+7.9" 7.:" 7!.:" 15.:" :1.8" 8.7" 5.1" :.!"
