In your own words, analyze Purchasing Power Parity and the relationship to exchange rates. Your response should be at least 200 words in length. All sources used, including the textbook, must be referenced; paraphrased and quoted material must have accompanying citations.
Moffett, M. H., Stonehill, A. I., & Eiteman, D. K. (2012). Fundamentals of multinational finance. (IV ed., pp.174-179). New York: Pearson.
In-text citation
(Moffett, Stonehill & Eiteman, 2012)
No Wiki, no dictionary.com, please cite all work.
174 PA trT 2 Foreign Exchange Theory and Markets
Prices and Exchange Rates
If identical products or services can be sold in two different
markets’ and no restrictions exis
t
on ihe sale or transportation costs of moving the product.between
markets’ the product’s
fri”” st outO be the same in both markets. This is called
the latv of one price
‘
A primary principle of competitive markets is that prices will
equaiize across markets if
frictions or costs of -ouing the products or services
between markets do not exist’ If the two
markets are in two differeit “ountri”q
the product’s price may be stated in different currency
terms, but the price of the product should still be the
same’ comparing prices would require
;;tt;
“onu”rrion
from one currency to the other’ For example’
P$xS:PY
where the price of the product in U.S. dollars (P$), multiplied
by the spot exchange rate
(S, yen per U.S. dotUij, iquuf, the price of ttre pro6uct in Japanese
yen (PY). Conversely, if
the prices of the two pt”Ar”,t were stated in local currencies,
and markets were efficient at
competing away a hig;;; frice in one market relative to the other,
the exchange rate could be
deduced from the relative local product prices:
s:q:o$
Purchasing Power Parity and the !-aw of One Price
If the law of one price were true for all goods and services ,the
purchasing power parjry (PPP]
exchange rate could t” rouno from any inJividual set of prices. By comparing
the prices ol
identical products denominated in difierent currencies,
one could determine the “real” or
ppP exchange rate that should exist if *urt”tt were efficient’ This is the
absolute version oi
the theory of purchasing power parity. Absolute
PPP states that the spot exchange rate is
determined Oy ttre retatiie prices of ti-ilar baskets of goods’
The.,Big Mu” tnJ”*,,,u, it hu, ueen ctriistenedv’irne
Eco,nomist (see trxhibit 7’1) and
calculated regularly ,1n”” rgse , is a prime “”u*pr.
of ihe law of one price’ Assuming that
the
Big Mac is indeed identical in all iountries listed’
it serves as one form of comparison oi
whether currencies are currently trading at market
rates which are close to the exchange rate
implied by Big Macs in local currencies’
For example, using Exhibit 7.1, in china a Big Mac
costs yuan 13’2 (local currency)’ whiie
in the Unitea states iie same Big Mac costs $3.73′ The actual
spot exchange rate was yuan
6.7gl$ at this time. Th” pri”” ,r u 6ig vtu” in china in u.S.
dollar terms was therefore
_ Yuan 13.2 = $1.95- Yuan 6.78/$
This is the value in column 2 0f Exhibit 7.1 for
china’ The Economisl then calculates the
imptied purchasing pr*,’ po’i’y r(tje.of::c!nng’ uing,-th.” u:l”ul
price of the Big Mac
in
China (yuan 13.2) o.r”, it ”
pricl of theBig lutu””i., thefJnited State: in U’S’ dollars
($3’73):
Price of Big Mac in China in Yuan –
VrylE’Z : Yuan 3.54l$
Ptt.”
“f
Btg N{* tt the U’S’ in $ $3’73
Thisisthevalueincolumn4ofExhibitT.l.forChina.Inprinciple,thisiswhattheBig
Mac Index is saying the exchange rate betwe”rr
tn” yuan and tire dollar should be according
to the theorY
.
Price of Big Mac in China in Yuan
Yuan/$ spot rate
CHAPTER 7 lnternational Parity Conditions 175
xist
,ct’s
ts if
two
rncy
;uire
rate
ely, if
:nt at
rld be
(PPP)
‘ices of
eal” or
‘sion of
rate is
‘.1) and
ftat the
rison ot
nge rate
y),while
ras yuan
rlates the
g Mac in
s ($3.73):
lt the Big
according
Selected Rates from the Big Mac lndex
(1) (21
Big Mac Aciual Dollar (3)
Price in Local Exchange Rate Big Mac
9g-gtt!ry_ atrg 9qlry!191t– QCrJe!,c-y-
— -9n-.J9ly-L-= –
,?J!991!-Pe!19I9- –
.i. / .)
3.48
4.A1
1.95
4.91
4.33u
3.A7
2,34
6.1S
2.17
(5)
(4) Under/over
lmplied PPP Valuation against
of the Dollar Dollar
United States
$ J./\t
Britain | 2.29
canada c$ 4’17
China Yuan 13.2
Denmark DK 28.5
0
Euro area € 3.38
Japan Y 320 ”
Russia Rouble 71 0
6.50
70.o
1.04
6.78
5.81
t.to
B7.2
30.4
1.O5
JZ.O
1,63*
1.12
3.54
7.64
LI0u
B5.B
1
9.0
1.74
18.8
-7%
7%
-48%
JZ”/a
16%
– 210
-37o/o
66o/o
-42o/o
Switzerland SFr
Thailand Baht
s
t
*These
exchange rates are stated in US$ per unit of local currency, $/l and $/€’
**percentage
under/over valuation against the dollar is calculated as (lnrplied-Actual)(Actual), except
for the Britain and Euro area calculations’ which are
(ActLial – lmplied)/{lmplied)
Source: Data drawn from “The Big Mac lndex”‘ The Economist, July 22′ 2O1O’
Now comparing this implied PPP rate of exchange, yuan 3.54l$, with the actual market
rate of exchange atihat time, yuan 6.781$.,the degree to which the yuan is either undervalued
(-%) or overvalued (+%) versus the u.S. dollar is calculated as follows:
Implied Rate – Actual Rate _
Actual Rate
In this case, the Big Mac Index indicates fhat the Chinese yuan is undervalued by 48o/” versus
the U.S. dollar as indicated in the far right-hand column for China in Exhibit 7 .1. The Econo-
mist isalso quick to note that althoughihis indicates a sizable undervaluation of the managed
value of the Chinese yuan versus the dollar, the theory of purchasing power parity is sup-
posed to indicate wheie the value of currencies should go over the long-term, and not neces-
sarily its value todaY.
it is important to understand why the Big Mac may be a good candidate for the applica-
tion of the law of one price and *”a*ut”-“nt of under or overvaluation. First, the product
itself is nearly identicai in each and every market. This is the result of product consistency,
process **.”il”nr”, and McDonald’s brand image and pride-. Second, and just as important’
ihe product is a result of predominantly local materials and input costs. This means that
its
price in each country is reiresentative of domestic costs and prices and not imported ones-
which would be influencei by exchange rates themselves. But as The Economjsr points out’
the Big Mac Index is not Perfec
t.
The index was never intended to be a precise pred.ictor of currency movements, simply a
take-away guide to whether currencies are at their “correct” long-run level’ Curiously,
how-
ever, burgirnomics has an impressive record in predicting exchange rates: currencies that
show up as overvalued often tend to weaken in later years. Bttt you must always remember
Yuan 3.54l$ – Yuan 6.78/$
Yuan 6.78/$
= -48″/”
176 PA F1 T 2 Foreign Exchange
Theory and Markets
theBigMac,slimitations’BurgersconnotsensiblybetradedQcrossbordersandpricesare’a.i,,’,La
bv diff,’:;;;”i”;;;; ;”;i;X:;*f:f::l:!l:;!’;’:;::!”::,:,’#,:;2s.2006
Alessextfemeformofthisprinciplewouldbetharinrelativelvefficientmarketsthe
price of a basket ot good,v/ouldbe
ttr.e sum’e in each market. Replacing
the price of a sin-
gle product with a p.i””” *i”* allows th” P;;;*”hange
rate betiveen lwo countries to be
stated as
PIY
s :;p
where pIY and PI$ are price indices
expressed in local culrency for Japan
and the United
Stares, respectively “;
H;#,;;;.i;;;il uurr.”, of goods cost Y1,000 in
Japan and $10
in the United States, the PP? exchange
rate would be
i?f : Yloo/$
Just in case you are starting to
believe thi:’PPf-1:]ust about numbers’
Global Finance in
prorrirT.l ,”*i”d’ you of the human side of the equatton’
Ftelative Flirchasing F*wer Fariiy .^ ,^r^-.^.{ o }rir rxre nhserve wl
IftheassumptionsoftheabsoluteversionofPPPtheoryarerelaxedabit’weobservewhatts
tcfmed relative purchasing power parity.R”i;i”;
ppp rrorat that PPP is not particularly
help-
ful in determining wtrat tf,e spot iate
is aa”V, u”iift”t the relative change in prices between
But it was this very basic market economy
which
pr”.iJ”nt Kim Jong-il and the governing regime wished^to
7.1
The lmmis€raticn of the f{orth Korean
puopf**fhe “Flevaluation” of the North
Korean Won
The principles o{ purchasing
power are not iust a-theoretical
principle, they can also caiture the
problems’ poverty’ and
;;; ; a peopte’ The devaluation of the North Korean
won
tXpfnO in November 2009
was one such case’
The North Korean government has
been trying to stop
tne growtl^, and activity in the street
markets of its country for
decades, For many years the street
markets have been the
[“”
“pp”nr”ity
for most of the Korean people to
earn a liv-
;;;. d;;;; Lommunist state’s stewardship’ the
qualitv or
life for its 24 million people has continued
to deteriorate’
Between1990and2O0B’thecountry’sinfant-mortalityrate
had increased 30%, and iife expectancy
had fallen by three
vears. The United Nations estimated
that one in three children
ffi; il;#’oinul .utt”*d malnutrition’ Although most of
the working population worked officially
{or the government’
;;;;;,i”jerpaid (or in manv cases not paid)’ that
thev
often bribed their bosses to allow
them to leave work early to
i,y a ,”rup” out a living in the street markets of
the under-
ground economY’
.i;il ;. on November 30′ 2009′ the Kdrean
government
madeasurpriseannouncementtoitspeople:anew’more
valuable Korean won would replace
the old one’ “You have
,”,il-ih” end of the day to exchange
your old won for new
won.” All old 1,000 won notes would
be replaced with 10
*ln norlu, knocking off two zeros from the officially
recog-
nized valug of the currency This
meant that everYone holding
“‘O
*””, in”‘t cash and savings’ would now officially,be
worth
1/100th of what it was prevLusly.
Exchange was limited to
i*,ooo oto *on. People who had worked
and saved for
decades to accumulate what was
roughly $200 or $300 in
“.”i”g” “””,Ce
o{ North Korea were wiped out;
their total life
ilvi;[l were essentially worthless’ By ofiicialty denouncing
i*'”n*””**u, the North Korean people would be
lorced to
;;;fu; their holdings for new won’ The government
would
indeed undermine the underground
economy’
.
The results were dev-astating’ After
daYs of street
protests, the government raised the 100’000
ceiling to
15O,OOO By {ate January 2010′ inflation
was rising so rapidly
d; G Jong-il apologized to the people for the revaluation’s
*p-“”i
“”
af-r”ir lives The government administrator
who had
led the revaluation was arlsted’ and
in February 2010′ exe-
cuted “for his treason'”
t.
CHAPTEF 7 lnternational Parity Conditions 1 -1-l
two countries over a period of time determines the change in the exchange rate over that
period. More specifi cally, if the spot exchange rote between two countries starts in equilibrium,
any change in the differential rate of inflation between them tends to be offiet over the long run
by an equal but opposite change in the spot exchange rate.
Exhibit 7.2 shows a general case of relative PPP The vertical axis shows the percentage
change in the spot exchange rate for foreign currency, and the horizontal axis shows the percent-
age difference in expected rates of inflation (foreign relative to home country).The diagonal par-
ity line shows the equilibrium position between a change in the exchange rate and relative
inflation rates. For instance, point P represents an equilibrium point where inflation in the foreign
country Japan, is 47o lower than in the home country, the United States. Therefore, relative PPP
would predict that the yen would appreciate by 4% per annum with respect to the U.S. dollar.
The main justification for purchasing power parity is that if a country experiences infla-
tion rates higher than those of its main trading partners, and its exchange rate does not
change, its exports of goods and services become less competitive with comparable products
produced elsewhere. Imports from abroad become more price-competitive with higher-
priced domestic products. These price changes lead to a deficit on current account in the bal-
ance of payments unless offset by capital and financial flows.
firnpiri*al Tests of P*rchasing Power Farity
Extensive testing of both the absoiute and relative versions of purchasing power parity
and the law of one price has been done.1 These tests have, for the most part, not proved
PPP to be accurate in predicting future exchange rates. Goods and services do not in
Relative Purchasing Power Parity {PPP)
Percentage change in the sPot
exchange rate for foreign
currency
Percentage difference
in expected rates of
inflation (foreign
relative to home
country)
1See, for example, Kenneth Rogoff, “The Purchasing Power Parity Puzzle,” Jottntal of Economic Literature,Volume 34,
Number2,June 1996,pp.647-668;and Bary K. Goodwin,Thomas Greenes,and Michael K.Wohlgenant,”Testing the
Law of One Price When Tiade Thkes Time,” Journal of International Money and Finutce,March1990,pp.2140.
IS
,-
n
r78 PA R T 2 Foreign Exchange Theory and Markets
reality move at zero cost between countries, and in fact many services are not “tradable”-
for example, haircuts. Many goods and services are not of the same quality across countries,
reflecting differences in the tastes and resources of the countries of their manufacture
and consumption.
Two general conclusions can be made from these tests: 1) PPP holds up well over the very
long run but poorly for shorter time periods and 2) the theory holds better for countries with
relatively high rates of inflation and underdeveloped capital markets.
Exehange ffiate lridiees: Real and ruominaI
Because any single country trades with numerous partners, we need to track and evaluate its
individual currency value against all other currency values in order to determine relative pur-
chasing power. The objective is to discover whether its exchange rate is “overvalued” or
“undervalued” in terms of PPP. One of the primary methods of dealing with this problem is
the caiculation of exchange rate indices. These indices are formed by trade-weighting the
brlateral exchange rates between the home country and its trading partners.
T}ae nominal effective exchange rste index uses actual exchange rates to create an index,
on a weighted average basis, of the value of the subject currency over time. It does not really
indicate anything about the “true value” of the currency, or anything related to PPP. The
nominal index simply calculates how the currency value relates to some arbitrariiy chosen
base period, but it is used in the formation of the real effective exchange rate index. The real
effective exchange rate index indicates how the weighted average purchasing power of the
currency has changed relative to some arbitrarily selected base period. Exhibit 7.3 piots the
real effective exchange rate indexes for the United States and Japan over the past22years.
IMF’s Real Effective Exchange Rate lndexes for the United States, Japan,
and the Euro Area
2005
=
100
140
130
I ll)
.*\o{o*.”8.*\.f^.ot^.{**s.”*to
Source: lnternatianal Ftnancial Statislics, lMF, annual, CPI-weighted real effective exchange rates, series RECZF.
United States
CHAPTER,; lnternational ParityConditions 1′.79
The reai effective exchange rate index for the U.S. dollar, Ef, is found by multipiying
the
nominal effective “..;;;;;;;.
i;1”;, rh by the ratio of U.S. dollar costs, C$, over foreign
currency costs, CFC, both in index form:
El: El, t s
If changes in exchange rates just offset differential inflation rates-if purchasing power
parity holdJ-all the reaf effective exchange rate indices would stay at 100′ If an exchange
rate strengthened more than was justified by differential inflation, its
index would rise above
100. If the real effective exchange rate index is above 100, the currency would be
considered
..overvalued” from a competitiie perspective. An index value below 100 would suggest an
“undervalued” currencY’
Exhibit 7.3 shows that the real effective exchange rate of the dollar, yen, and
euro
have changed over the past three decades. The doilar’s index value was
substantially
above 100 in the il80s (overvalued), but has remained below 100 (undervalued) :11:t,th”
Iate 1980s (ir did rise stigtrtty aboue’i00 briefly in 1995-1996 and again
in 2001-2002)’ The
Japanese yen’s real effeitive rate has remained above 100 for nearly the
entire 1980 to
ZObe perloa (overvalued). The euro, whose value has been back-calculated
for the years
priorio its introduction in l-999, has been largely below 100 and undervalued in its real
lifetime.
Apart from measuring deviations from PPP, a country’s real effective exchange
late 1s an
imporiant tool for *unug-“*”nt when predicting upward or downward pressure
on a coun-
try”s balance of paymentJ and exchange rate, as well as an indicator of
the desirability to pro-
duce for export from that country. CtJUot Fiinance in Practice 7’2 shows
deviations from PPP
in the twentieth centurY.
Exchange Hate Fass-Through
Incomplete exchange rate pass-through is one reason that a country’s real effective
exchange rate index can deviate for lengthy periods from its- PPP-equilibrium
level of
.l-00′
The degree to which the prices of importei and exported goods change as
a result of
exchan[e rate changes is teimed pa ss-tirough. Although PPP implies
that a]lexch?\g:,:u'”
changes are passed-through by equivalent changes in prices to trading
partners, empirical
research in the 1980s que”stioned this long-held assumption’ For example,
sizable current
account deficits of the United States in the 1980s and f99Os did not respond to
changes in
the value of the dollar’
To illustrate e*”harrge rate pass-through, assume that BMW..produces an
automobile in
Germany and pays all production expenses in euros’ When the firm
exports the auto to the
united States, the price of the BMW in the u.S. market should simply be
the euro value con-
verted to dollars at the spot exchange rate:
P$”r,”:PfirvrwxS
rvhere p$*, is the BMW price in dollars, Pfr* is the BMW price in euros, and S is the num-
ber of dollars per euro. Ii the euro appreciated 107o versus the U’S’ dollar, the new spot
exchange rate should result in the price of the BMW in the united states
rising a propor-
tional 10%. If the price in doliars increases by the same pelcentage change
as the exchange
,ur”, th” pass-throughof exchange rate changes is complete
(or 100%)’
However, if the price in dollirs rises by IJss than the percentage
change in exchange rates
(as is often the case in international trade), the pass-ihrough is
partial, as illustrated in
Ci’iAPTE h / lnternational ParityConditions
Exchange Rate Pass-Through
pass-through is the measure of response of rmporled and exported product prices to exchange rate
changes, Aisume that the price in dollars and euros of a BMW automobile produced in Germany and sold in
the United States at the spot exchange rate is
PBviv: PFuw x ($/€) : €35’000 x $1,000/€ = $35’000
lf ihe euro were io appreciate 200/o versus the U.S. dollar, from $1.0000/€ to $1 ,2000/€, the price of the
BMW in the U.S. market should theoretically be $42,000. But if the price of the BMW in the U.S. does noi
rise by 20%-for example, it rises on{y to $4O,0OO*then the degree of pass-through is partial;
PLr*, $4o.ooo
“ffi
-;ffi = 1.1429,ora14.2eo/o increase
The degree of passthrough is measured by the proporlion of the exchange rate change reflected in dollar
prices. in this example, ihe dollar price of the BMW rose only 14 29o/o, while the euro appreciated 20%
against the U.S. dollar. The degree of passthrough is partial; 14.29% + 2O.OOVo, or approximately 0.71
Onty Zt y” of the exchange rate change was passed-through to the U.S. dollar price. The remaining 29olo of
the exchange rate change has been absorbed by BMW.
change in quantity of the good demanded as a result of the
own price:
Price elasticity of demand :
“o
=
where Q2 is quantity demanded and P is product price. If the absolute value of ep is less than
1.0,
then the good is relatively “inelastic.” If it is greater than 1.0, it is a relatively “elastic” good.
^A.Gi,rarrp,unrtr.J,,ilra!ir-ralefLvglp.lricrJrclefiJia,,uFanglgJJtal.thq,fl,tle.+$ty-4pnrsA”0
is relatively unresponsive to price changes, may often demonstrate a high degree of pass-
through. This is because a higher dollar price in the United States market would have little
noticeable effect on the quantity of the product demanded by consumers. Dollar revenue
would increase, but euro revenue would remain the same. However, products that are rela-
tively price-elastic would respond in the opposite way. If the2O”/” euro appreciation resulted
in20% higher dollar priceg U.S. consumers would decrease the number of BMWs purchased.
If the price elasticity of demand for BMWs in the United States were greater than one, total
dollar sales revenue of BMWs would decline.
lnteres€ Rates and Exchaslge Rates
We have already seen how prices of goods in different countries should be reiated through
exchange rates. We now consider how interest rates are linked to exchange rates.
The Fisher Effect
The Fisher effect, named after economist Irving Fisher, states that nominal interest rates in
each country are equal to the required real rate of return plus compensation for expected
inflation. More formally, this is derived from (1 + r)(1 + n)-1.:
i:r*r*rr
where I is the nominal rate of interest, r is the real rate of interest, and rr is the expected rate
of inflation over the period of time for which funds are to be lent. The final compound term,
181
percentage change in the good’s
“/o LQa
“/. LP
182 F A E T 2 Foreign Exchange
Theory and Markets
rz, is frequently clropped fronr “:Tl1″ji:tn
due to its relatively nrinor value’
The Fishei
.it”.t ri .n reduces to (approxinlate
lorm):
i=rl r
TheFishereffectappliedtotheUnitedStatesandJapanwouldbeasfoliows:
j$: r$ + n.$; lY – rY + trv
where the superscripts $ anct
Y pertain to the respective
nominal (l)’ reai r’ and expected
infla-
tion (n) componenrs-of financial
inrtrr-“‘ll}#;;;;;;;^; iJll”tt and ven’
respectivelr”
we need to forecast ;;;;;;;;;i” “t
i’n”r*;, ;;;;; inflation has been’ Predicting
the
future can be difficult’
Empiricat tests r-ising ex-postnational
inflation rates have shorvn
that the Fisher effect
usuaily exists for short-maturity
governm””i ,”t*iii”s such as Tieasury
bills and notes’ com-
oarisons based on t”;s;;;i;ies suffet
f;;;;;;;”reased financial rist< inherent
in rluc-
iuarions or ti,. *orr,’i? “”i;;;;;l.,;
to19r’;;’;”;; maturitv -comparisons
ol pri’a’te sectoi
securjties are influenced
by unequa| cre-{lwlrtniness
of the issuers’ A1i the tests
are inconclu-
sive to the extent tt ur r”.”nt
past rates oi ;nnutio” are not a
correct measure of future
exPected inflation’
T i’:* !iri*r’ll;rtl*r:el! F:ish*r
ti{?e*t
Therelationshipbetweenthepercentag:cl].angeinthespotexchanger.ateovel’tim:1:r-djhe]l
dilferenriat bcrrveen cornparable
inT.r:r, :i,-.t-;
arii”l”lt national”capital mat’kets
is known
as the inrcrnationctl efirtr, ifrn “Fisher-op-Jtjl “‘
it is often t”t-“;’ states that the spot
t
exchange rare shoutd:’#gJi;;r “qrurr*ount
but in the opposit” di'”‘tiott to
the differ- I
ence in interesl ‘ut”‘
o”l’Gn two countries’ More formally’
tt’
Sr-Sz:l$_iy
S2
where r$and
jy are rrre:”,p:”ll]’:,:1:’,1ilT$::’L:?:’j”1ffi’*;t^?’;:Til’?:j::,:!1il:
‘
indirect quotes (an indirect
quote on ttts u’
;;’t”d rsr “‘g llr-:#iJ[“,,#;i.ti;li*jllJLi”t*.i'”‘i””
rorm com’lronrv used in ,
industry’The prectse lollrturd(rvrr ( .!
5r -Sz:i’-‘,.
52 1+i’
JustificationfortheinternationalFishereffectisthatinvestolsmustberervardedor
oenalizedtooflsetthe-expectedchangei”‘”-.t’.”g”,u,”,.po’.*ample.ifadollar-based
investor buys a t’-yeu, y”,’unno
earills-|v.
.**..i1*.’ead of a l.-vear dollar bond earnlns
67o inrerest, the investo’r
musr be expec,t”g;;;;;-i” ^nqttt]i::
vis-d-vis the clollar by at
least
;:;;;;;;^,0:”,i1?yi'”‘*:X5’#i:n’f;:tfi lry*:g*tg**3;f ;l*
ing in dollars lf the vert atl;;;;;n. Hor.,”-“.’. ihe internalior
*’3rrro earn a bonus of 17o
higher t”*:::)^:l,T;’iii”?tt*””ii” *rt”tr’er his bond is in do1-
ri+r**;*:i****l;j*:r*:;1;nt””;*iFiil:;;’;;;;re’ir111i1″*”v
Empirical ,”rrr’l*Ji-rr-e supporr
,” ,ri” r*r”tlonship po”uiu'”0 by
the international
Fisher effect” ^r,n”rril “”rria”ruUi”
,ftort-run deviations ott”” A -ore
slrious criticism has
been posed, nt*”ti1′”#'”””^’ “”01″‘
th;;”;”‘; Ji'” “ti’t””””
oi u tnt”ign exchange risk
oremium for most .uil, currencies.
Aft””‘p”?-‘fation in u**'”4 interJst
arbitrage (on
pages 1g7-1aS; cr”ot”, distortions
t” ;'”#”*
“;””tk”it
Thus’ the expected change
in
exchange ,ut”, *rgii.LJri”ntrv
u” *”*-irt”t ih” diff”t”tt”e in interest
rates’
C li A t) I E i’l I Foreign Currency Derivatives and Swaps
Long Positions. If Amber McClain expected the peso to rise in value versus the doilar in the
near term, she could take a long position, by buying a March future on the Mexican peso,
Buying a March future means that Amber is locking in the price at which she must buy Mex-
ican pesos at the future’s maturity date. Amber’s futures contract at maturity would have the
following value:
Value at maturity (Long position) : Notional principal X (Spot – Futures)
Again using the March settle price on Mexican peso futures in Exhibit s.1, $.10958/MXN, if
the spot exchange rate at maturity is $.1100/MXN,Amber has indeed guessed right.The value
of her position on settlement is then
Value : MXN500,000 x ($.11000iMXN – $.10958/MXN) : $ZtO
In this case. Amber makes a profit in a matter of months of $210 on the single futures con_
tract. We couid say that’Amber buys at $.10958 and sells at $.11000 per peso.’,
But what happens if Amber’s expectation about the future value of the Mexican peso
proves wrong? For example, if the Mexican government announces that the rate of inflation
in Mexico has suddenly risen dramatically, and the peso falls to $.0g000lMXN by the March
maturity date, the value of Amber’s futures contract on settlement is
Value : MXN500,000 x ($.0S000/MXN – $.10958/MXN) : ($14,790)
In this case, Amber McClain suffers a speculative loss.
Futures contracts could obviously be used in combinations to form a variety of more
complex positions. When we are combining contracts, however, valuation is fairly straightfor-
ward and additive in character.
Foreigr: *unreney F*tures vsrsu$ Fsrward eontraets
Foreign currency futures contracts differ from forward contracts in a number of important
ways. Individuals find futures contracts useful for speculation because they usually do not
‘nave access’totorward conuacIS.Tor’oustnesses,lr.Ilurcs uurl[racLS are utrel Lurririlsrc&’urcA-
ficient and burdensome because the futures position is marked to market on a daily basis
over the life of the contract. Aithough this does not require the business to pay or receive
cash dail;’, it does result in more frequent margin calls from its financial service providers
than the business typically wants.
ilae s”s”* s: cy *g:ti *n: s
A foreign ctrrrency option is a contract that gives the option purchaser (the buyer) the right, but
not the obligation, to buy or seli a given amount of foreign exchange at a fixed price per unit for
a specified time period (until the maturity date). The most important phrase in this definition is
“but not the obligation”; this means that the owner of an option possesses a valuable choice.
In many ways buying an option is like buying a ticket to a benefit concert. The buyer has
the right to attend the concert, but does not have to. The buyer of the concert ticket risks noth-
ing more than what she pays for the ticket. Similarly, the buyer of an option cannot lose more
than what he pays for the option. If the buyer of the ticket decides later not to attend the con-
cert-priot to the day of the concert, the ticket can be sold to someone else who wishes to go.
S There are two basic types of options, cqlls and puts. A cali is an option to buy foreign cur-
rency, and a put is an option to sell foreign currency.
* The buyer of an option is termed the holcler,while the seller of an option is referred to as
the wriler or gr0ntor.
,fT.
-,’i! \r.**’
,-l\’\*, ( I
i I \*-r
Everr- op:ion has three iiifierent price eienre nts: i, .ii- r,-.trr::i ari _ciiiA-a grri..srirrluttr FrrrLL LlLrtlllla:. i; i.ir. r_irli::,: ili _11r_ing I]ri:.,. ,_.;
exchange rate at rvhich the foreign currencv can L.re purchased {cailI or sold (pur}: I r :r-:E LildrrFtr rd”Ltr aL wlliclt Lfie loretgn cUfrencv Can be purchased {cail I or Sold (pgf }: : I
prentittm, the cost, price, or value of the option itself; and 3) the unrierlyins or aciuai
exchange rate in the market
An Antericon option grves the buyer the right to exercise the option at any time betu’e;,
the date of u’riting and the expiration or maturity date. A Europectn optiort can be exelci>.,
onlY on its expiration date, not before. Nevertheless, American and
-European
options j,:
priced aimost the same because the option holder wouid normally sell the optio,r itielf beic,.
maturity. The option would then still have some “time value” ibou” its ,,intrinsic value ‘
exercised (explained later in this chapter).
S The premittnt or option price is the cost of the option, usually paid in advance by the bu…,:
to the seller. In the over-the-counter morket (options offerecl by banks), premiums a::
quoted as a percentage of the transaction amount. Premiums on exchange-traded optitr::
are quoted as a domestic currency amount per unit of foreign currency.
S An option rvhose exercise price is the same as the spot price of the underlying currenc\- r:
said to be at-the-money (ATM).An option that would be profitable, excluding the cosr i,.
the premium, if exercised immediately is said to be in-the-money (ITM). An option rb”.
rn’ould not be profitable, again excluding the cost of the premium, if exercised immediate,.,
is referred to as out-of-the-money (OTM).
f,*r*!gr: *urr*n*y *pti*n* fl#*rke€s
In the past three decades the use of foreign currency options as a hedging tooi and for specr-
lative purposes has blossomed into a major foreign exchange activity. A number of banks i-
ihe Urriied States ard othrei capi’ral rirarke-Lr olter flexibLe ioie’.gl cirirercy optiora oir +ri?r,:-
actions of $1 million or more. The bank market, or over-the-counter market as it is calie;.
offers custom-tailored options on all major trading currencies for any period up to one yeai
and in some cases, two to three years.
In December 1982,the Philadelphia Stock Exchange introduced trading in standarciize:
foreign clirrency option contracts in the United States. The Chicago Mercantile Exchans:
and other exchanges in the United States and abroad have foliowed suit. Exchange-trade;
contracts are particularly appealing to speculators and individuals who do not normall=.
have access to the over-the-counter market. Banks also trade on the exchanges because it i.
one of several ways they can offset the risk of options they have transacted with clients or
other banks.
Increased use of foreign currency options is a reflection of the explosive growth in the
use of other kinds of options and the resultant improvements in option pricing models. The
originai option pricing model developed by Black and Scholes in1973 has been commercial-
ized since then by numerous firms offering software programs and even built-in routines for
handheld calculators. Several commercial programs are available for option writers and
traders to utilize.
Options on the Over-the-Counter Market. Over-the-counter (OTC) options are most frequentlr
written by banks for U.S. dollars against British pounds sterling, Swiss francs, Japanese yen.
Canadian dollars, and most recentiy, the euro.
The main advantage of over-the-counter options is that they are tailored to the specific
needs of the firm. Financial institutions are wiiling to write or buy options that vary by amount
(notional principal), strike price, and maturit,v. Although the over-the-counter markets were
relatively illiquid in the early years, the market has grown to such proportions that liquidity is
now quite good. On the other hand, the buyer must assess the writing bank’s ability to fulfill
CHAPTEiI S Foreign Currency Derivatives and Swaps
the option contract’ Termed counterpariy risk, the financiai risk associated with the counter-,r.atlw’is;1p.irucc.arirg*’stur ,ir,inLrrn*tirrri.,rrror,{“rs as a ,rr..rrt ,i tne lncreaslng use oI llnan_cial contracts like options.and- swaps by MNE management. nxcnunge-traded options aremore-the territory of individuats and rinancial instituti”ons themselves than of business firms.If an investor wishes to purchase an option in the over-the-counter rnarket, theinvestor will normally place a call to the currency option desk of a major money centerbank’ specify the currencies, maturity, strike rate(s), and ask for an intlication-a bid-offer
[Tie; ffji,l-
wili normallv rake a few minutes’to a few hours ro price the option and
options on organized.Exchanges. options on the physical (underiying) currency are tradedon a number of organized exchanges woriclwide, irrcluaing tir” pr,itua”tphia Stock Exchange(PHLX) and the Chicago Mercaniile Exchange.
Exchange-traded options are settled through a clearinghouse, so that buyers do not dealdirectl,v wili sellers The cleanaghouse is the counferpart)’ to et’cry. option contract a’rl ifguarantees fulfillment.,clearinghouse obligations ur” in t*n the obligation of all membersof the exchange, including a large numbei of banks. In the case of the philadelphia StockExchange, clearinghouse sen’ices are provicled by the options Ciearing Corporation (ocC).
eurreney fiptien euatatlcns and prlees
Typical quotes in the wall street Journal for options on Swiss francs are shown in Exhibit g.2.The Journal’s quotes refer to transactions completed on the philaclelphia stock Fxchange onthe previous day’ Quotations usually are availatie for more combinations of strike prices andexpiration dates than were actualiy tradecl and thus reported in the newspaper. Currencyoption strike prices and premiums on the u.S. dollar are typicaity iuoted as direct quotationson the U.s. dollar and indirect quotations on rhe foreign ,u.r”n.y iglSF, $/y, etc.).Exhibit 8’2 illustrates the three different prices that iharacteruiany foreign curency option.The three prices that characterize an’Augusi58.5 call option” qrr;ghhghtea in Exhibit g.2) are rhefollowing:
1. spot Rate. In Exhibit 8.2, “option and Underlying,,means that 5g.51 cents, or $0.5g51,was the spot dollar price of one Swiss franc at the ilose of trading on the preceding day.
Sw\ss Franc Optron euotatrons (U.S. centslsF\
Calls-Last Puts-Last
Option and Underlying Strike Price
58.51
58,51
58.51
58.51
58.51
58.51
5B.5.1
58.51
58,51
56.O
57,0
57.5
58.0
58.5
59.0
59.5
60.0
r, iJ
0.75
o.71
0.30
u. t3
0.66
0.40
0.31
*_!:1_\”_L_
2.16 0.o4
0.06
– 1.74 0.10
0.17
1.05 1 .28 0.27
4.22 1.16
0.30
0.38 1.27
0.55
0,89 1,81
– 0.50 0.99
1 21 0.90 1 36
– z.Jz
– 2.32 2.62 3.30
Each option : 62’500 swiss francs The August, september, and December listings are the option maturities or expiration dates.
PA RT 2 Foreign Exchange Theory and Markets
2. Exereise Frice. Theexercise price,or “Strike price”listed inExhibit S.2,meanstheprice
per franc that must be paid if the option is exercised. The August caii option on francs of
58.5 means $0.5850/SF Exhibit 8.2 lists nine different strike prices, ranging from
$0.5600/SF to $0.6000/SF, although more were available on that date than are listed here.
3. Premium. The premium is the cost or price of the option. The price of the August 58.5 call
option on Swiss francs was 0.50 U.S. cents per franc, or $0.0050/SF.There was no trading of
the September and December 58.5 call on that day. The premium is the market value of
the option, and therefore the terms premium, cost, price, and value are al1 interchangeable
when referling to an option.
The August 58.5 cali option premium is 0.50 cents per franc, and in this case, the
August 58.5 put’s premium is also 0.50 cents per franc. Since one option contract on the
Philadelphia Stock Exchange consists of 62,500 francs, the total cost of one option contract
for the catl (or put in this case) is SF62,500 x $0.0050/SF : $312.50.
Suyer sf * **ii
Options differ from all other types of financial instruments in the patterns of risk they pro-
duce. The option owner, the holder, has the choice of exercising the option or allowing it to
expire unused. The owner will exercise it only when exercising is profitable, which means
oniy rvhen the option is in the money. In the case of a call option, as the spot price of the
underlying currency moves up, the holder has the possibility of unlimited profit. On the down
side, however, the holder can abandon the option and walk away with a loss never greater
than the premium paid.
Hans Schmidt is a currency speculator in Zurich, Switzerland. The position of Hans as a
buyer of a cail is illustrated in Exhibit 8.3. Assume he purchases the August call option on
ffi Profit and Loss for the Buyer of a call option
Profit
(U S. cents/SF)
“At the Money”
Strike Price
“Out ol the Money” “ln the $Jloney”
+1.00
+
0.50
0
0.50
-1 00
Unlimited Profit
1,-.
,l!’;
ii:j
.Ei.
.E
j;T
.;l
ti:,
.*
‘i-,t
il,:
…e
ll:l
,lt;.]
u:
.:,
Ji
.+
Spot Price
(U S. cents/SF)
9.0
Break-
59.5
even Price
Lo.s.9
The buyer of a cail option on SF, with a strike price of 58.5 centsiSF, has a limited loss
of 0.50 cents/SF at spot rates less than 58.5 (“out of the rnoney”), and an unlirnited profil
potential at spot rates above 58.5 cents/SF (“in ihe monev”).
CHAPT ER S Foreign Currency Derivatives and Swaps 211
Swiss francs described previously, the one with a strike price of 5g.5 ($0.5g50/SF), and a pre-
mium of $0.005/SF. The vertical axis measures profit oi los for the option buyer at each of
several different spot prices for the franc up to ihe time of maturity.
At all spot rates below the strike price of 58.5, Hans would choose not to exercise his
option. This is obvious because at a spot rate of 58.0 for example, he would prefer to buy a
Swiss franc for $.580 on the spot market rather than exercising tris option to Uuy a franc at
$0’585′ If the spot rate remains below 58.0 until August when the option expired, Hans would
not exercise the option. His total loss would be limited to only what he piia tor the option,
the $0.005/SF purchase price. At any lower price for the franc, hir lort *outO similarly be iim-
ited to the original $0.005/SF cost.
Alternatively, at all spot rates above the strike price of 58.5, Hans would exercise the
option, paying only the strike price for each Swiss franc. For example, if the spot rate were
59.5 cents per franc at maturity, he would exercise his call option, buying Swiss francs for
$0.585 each instead of purchasing them on the spot market at $0.595 each. He could sell the
Swiss francs immediately in the spot market for gO.595 each, pocketing a gross profit of
$0.010/Sn or a net profit of $0.005/SF after deducting the original cost of the option of
$0.005/SF. Hans’ profit, if the spot rate is greater than the strike price, with strike price $0.585,
a premium of $0.005, and a spot rate of $0.595, is
Profit : Spot Rate – (Strike Price * Premium): $0.s95rsF * ($0.s8srsF + $0.00slsF): $0.00s/sF
More likely, Hans would realize the profit through executing an offsetting contract on
the options exchange rather than taking delivery of the currency. Because the dollar price of
a franc could rise to an infinite level (off the upper right-hand side of Exhibit 8.3), maximum
profit is unlimited. The buyer of a call option thus possesses an attractive combination of out-
comes; limited loss and unlimited profit potential.
Note that break-even price of $0.590/SF is the price at which Hans neither gains nor loses
on exercising the option. The premium cost of $0.005, combined with the cost of exercising
Lrr&opndntrr$r$.3S,is’crd’ct?i’dqridildtriS^ptrdueTdi’Saterii#gtdj?r’dftririili}Gp’6ih6i”
ket at $0.590. Note that he will still exercisi the call oprion at tie break-even price. This is
because by exercising.it he at least recoups the premium paid for the option. At any spot
price above the exercise price but below the briak-even price, the gross profit
“urn”d
on
exercising the option and selling the underlying currency .ou”r, part ftut not utt; of the pre-mium cost.
Writer of a Call
The position of the writer (seiler) of the same call option is illustrated in Exhibit g.4. If theoption expires when the spot price of the underlying currency is below ttre exercise frlceof 58’5, the option holder does not exercise. What the holdei loses, the writer gains. The
w11er keeps as profit the entire premium paid of $0.005/sF. Above ttre exeilse price
of 58.5, the writer of the call must deliver the underiying currency for $0.5g5/SF at a time
when the value of the franc is above $0.585. If the wrieiwrote the option ,,naked,’, that is,without owning the currency, that writer wili now have to buy the currency at spot andtake the loss’ The amount of such a loss is unlimited and increases as the price of theunderlying currency rises. Once again, what the holder gains, the writer losls, and vice
versa’ Even if the writer already owns the currency, the writer will experience an opportu-
nity loss, surrendering against the option the same currency that could have been sold for
more in the open market.
