of the dollar implies an appreciation of other currencies, a reverse relationship .... invested in the foreign bond, financed by borrowing at the interest rate R in.
Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized Public Disclosure Authorized
(
Policy, Planning, and Re.eirch
WORKING
I
PAPERS
Debtand Intemational Finance
Intemationa! Economics Department TheWorldBank January1989 WPS150
Improving the Currency Composition of External Debt: Applications in Indonesiaand Turkey Ken Kroner and Stijn Claessens
The debt service ratio of manydevelopingcountriesshot up whenthedollarfell. Thepapershowshowdevelopingcountries can alter the currency compositionof their extemal debt to minimize their vulnerability to fluctuations in international exchangerates.
Tle Policy. Planting, nd Researh Cmnplea distributes PPR Wo*ring Pap=esto dissnte the findings of wok in progress and to enouege the exchange of ideu anong Bank staff and all others interested in developmem issues. These papes carry the nsmes of the authoesm reflect only their views, and should be used and dted accordingly.The findings. intespretatims, and conclusions are the authoie own. They should not be attnbuted tothe World Bank, its Board of Dircton, its management, or any of its manbercountries.
Plc,Planning, and Researc
DebtandIntemallonalFinance
Changes in exchange rates affect both the structure and level of a country's external debt. Much of Lndonesia's debt was denominated in yen, for example, so the depreciation of the dollar since 1985 has increased the level of Indonesia's debt and reduced the dollar-denominated portion of that debt. Indonesia's debt service increased from 10 percent in 1980 to 37 percent in 1986, largely because of the depreciation of the U.S. dollar and the fall in oil prices. Other countries had similar experie.ices. Developed countries can hedge against exchange rate and commodity price changes by purchasing currency futures or other hedging instruments, but most developing countries do not have access to futures markets. They can,
however, reduce their exposure by matching the currency composition K.their extemal debt with the currency composition of the cash flows with which they service their debL Using advanced econometric techniques, the authors analyze what the currency exposures might have been in Indonesia and Turkey - and suggest borrowing portfolios that might be effective in hedging these countries' terms of trade against exchange rate fluctuations. The results are promising for Indonesia, where the optimal currency portfolios might have resulted in a significant reduction in risk. The results are less satisfying for Turkey although they do indicate possible research directions.
This paper is a product of the Debt and Intemational Finance Division, Intemational Economics Department. Copies are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Leah Chavarria, room S7-033, extension 33730.
The PPR Working Paper Series disseminates the findings of work under way in the Banks Policy, Planning, and Research Complex. An objective of the series is to get these rmdings out quickly, even if presentations are less than fully polished. The findings, interpretations, and conclusions in these papers do not necessarily represent official policy of the Bank. Produced at the PPR Dissemination Center
Optimal Currency Composition of External Debt: Applications to Indonesia and Turkey Ken Kroner
by and Stijn Claessens*
Table I. II. III. IV. V. VI. VII.
of Contents
Introduction Issues The Model Data Estimation 1.The Arch Model 2.The Estimation Results The Optimal Portfolios Conclusion
1 4 11 15 20 20 22 26 34
Appendix 1 Appendix 2 Appendix 3 Bibliography
35 37 44 46
*University of Arizona and the World Bank respectively. We would like to thank Rob Engle, Amer Bhattacharya, Jeff Balkind, Sweder van of the Canadian Econometrics Wijnbergen, Bela Balassa and participants Study group conference in Bariff, Canada during October 1988 for comments, though we of course accept full responsibility for any errors ourselves.
I. Introduction Over the last decade, Indonesia anedTurkey have been affected by large changes in cross-currencyexchangerates and in commodityprices. For ezample,the debt service ratio for Indonesiavose from 10% in 1980 to 37Z in 1986, largelyas a result of the depreciationof the US dollar and the fall in oil prices.
(About one-half of Indonesia'sexports are petroleum.) The
exchange rate changes have affected the structureas well as the level of Indonesia'sdebt. Much of Indonesia'sborrowinghas been denominatedin the Japanese yen, so the large depreciationof the dollar since 1985 has both increased the level of its debt as well as reduced the dollar-denominated portion of that debt.
Assuming exchange rates remain constant, this will
imply that the debt servicelevelwill continueto remain higher over the next couple of years than it would have been had exchangesrates remainedat their 1985 level. In general,whetherwe are dealing with Indonesia,Turkey, or any other developing country, cross-currencyexchange rate fluctuations and commodity price changeshave affectedboth the structureand the level of the country'
s external obligations debt.
Developed by purchasing
countriesare able to hedge againstexchange rate changes
currency
futures
or other
hedging
instruments
on organized
or
over-the-countermarkets. Most developingcountries,however, do not have access to these markets,due to institutionalconstraints,credit constraints and other reasons. An alternativehedging instrumentwhich can be used to reduce exchange risk exposure and is available to all countries, is the currency composition of external debt.
Indonesia and Turkey could have
minimizedtheir exposuresby matchingin some fashionthe currencycomposition of their debt with the currencycompositionof those cash flows with which
- 2-
they are able to service their debt. Even though a perfectmatch might have been difficult to achieve for Turkey and Indonesia,as they might have been constrained in choosing and altering the currency compositionof their new borrowings,such as those due to foreigngovernments,and might not have been able to use market techniques,such as currencyswaps, to change the currency compositionof their existingdebt, marginalchanges could still have led to pome tangiblebenefits. Ex-post,one is able to determinewhat their optimal portfolioswould have been, but this does not necessarilyhelp in coming up with policy rules on how they can minimizetheir exposureto exchangerisks in the future. The purpose of this paper is to derive practical policy rules for developing countries in general on ways to use the currency compositionof their externaldebt to minimizethe exposureof their terms of trade (or other externalaccount variables,e.g., exports)to exchangerate fluctuations.The model is subsequentlyestimatedand appiiedto Indonesiaand Turkey. Section II presents a
discussion of a
number of alternative
approachesand related issues regardingcurrencymanagementof externaldebt. Section III presentsthe analyticalmodel, which is an abbreviatedversion of the model given in Claessens(1988),and SectionIV discussesthe data used in the paper.
The solution for the optimal portfoliosinvolves estimatinga
covariance matrix of exchange rates movements, which is changing through time.
An
econometric technique (called Autoregressive Conditional
Beteroskedasticity) which allows for this is described in Section V, along with some of the estimationresults. The actual portfoliosare presented in Section VI, and out of sample tests are conductedto see how effectivethese portfolios would be in hedging the terms of trade against exchange rate
- 3-
exposure. The results are very promisingfor Indonesiaand point out some further researchdirectionsfor Turkey. SectionVII concludes.
-4-
II. Issues Large changes in cross-currencyexchange rates and relative goods prices over the last decade have affectedmany developingcountries. Changes in cross-currencyexchangerates affect goods prices,as for instancehas been observed in the relationshipbetweenthe dollar exchangerate and the price of commoditiesbefore the most recentdepreciationof the dollar. Cross-currency exchange rate changes impact not only export prices but import prices as well.
Furthermore,Cross-currencyexchangerate changesaffect the relative
competitivenessof countrieswith which the developingcountrycompetes. As a result, many developingcountries'market shares and profit margins have been affected by movements in cross-currencyexchange rates.
In addition,
comodity price movements have had a substantialimpact on many developing countries because a large share of their export earnings have been derived frrm primary commodities. The increasedvolatilityof exchangerates and commodityprices (and interestrates) has thus led to increasedfluctuationsin the aggregateincome and welfare levels of many developingcountriesthrough their impact on their external accounts. It has highlightedthe importancefor many countriesof, first of all, developing a
conceptual framework for managing external
exposures,and secondly,for devisingpracticalpolicy rules. We will discuss in this section the concepts and principles that have been proposed for externalliabilitymanagement,and discuss their strengthsand weaknesses. Several options are open to a country that wants to reduce its exposureto externalfactors. First of all, the country can try to engage in real diversification throughthe sourcing,producinag and exportingof a mix of products which is close to optimal given the relationshipsbetween exchange
-5-
rates, interest rates,
good prices, and other external factors.
Of course,
the compositionof exports, and to a lesser extent of imports,can not be changed easily, but one can still expect some contributionin the long run. Secondly, a range of instrumentsis availableto private firms in developed financialmarkets to manage short-aermexposuresand some of these instruments could be used to manage a country'sexternalexposures. Transferof certain risks to market participantsmore able to absorb them or to transfer risks further could substantiallybenefit a country in terms of reducingrisks at reasonable costs. For example, well diversifiedfinancial institutionscan transforma floatinginterestliabilityinto a fixed interestliabilityat a below the opportunitycosts for the liability cost which can be substantially holder. Thirdly, the country has a potential financial hedging instrument against unanticipatedexchange rates movements in the form of the currency compositionof its existingexternal liabilities. In addition,the country can influence the currency composition of new external capital flows. Fourthly,the compositionof the externalliabilitiesof the country can also be a useful tool to manage the exposureto commodityprice movements to the extent that movementsin exchangerates and goods prices are correlatedand to the extent that the countryhas the flexibilityto influencethe composition. It is easy to tell, with the benefit of hindsight, what a good external liability policy is and what the optimal currency composition of external liabilities would have been.
Capital gains and losses due to
exch4nge rate movements could have been avoided by matching in the right fashion the currency compositionof external liabilitieswith the effective currency compositionof cash flows, i.e. non-interestcurrent account flows. However, such hindsight does not provide practical rules on how countries,
-6-
given their external debt situation,can hedge the economy against future exchangerate movements. One needs to look at the right risk-returntradeoffs and incorporatethe informationalconstraintsthat the nature of the problem suggests:hindsightdoes not help ex-ante. A number of often intuitivelyappealingrules have been proposedfor choosingthe csrLrency denominationof externalliabilitiesand new borrowings. The most favored strategies are to base the currency composition of a country's debt on the pattern of trade, on the currencydenominationof its ezport revenues or on the basis of the basket of currencieswith respect to which the exchangerate is managed. In the case of the pattern of trade rule, this would mean that a country would borrow in the currenciesaccordingto its trade pattern in the expectation that if the currency of an export market appreciates, the borrower'sterms of trade are likely to improveand thus partiallyoffsett the higher costs of servicingdebt in that currency,and vice versa for imports. This relies on the appreciationof a currency of an export market to be accompaniedby an increasein a country'sability to pay as its exports and terms of trade improve.
However, it is not clear a priori that an
appreciationof a currencyof an export market has to mean &n improvementin the country's terms of trade.
One contradictoryexample would be of two
different countriesexporting the same good to the same country.The crossexchangerate between the two exportingcountrieswould be more importantfor their relativecompetivenessand market shares in the importingcountry than the currencyof the importingcountryitself. Of course, if PurchasingPower Parity (PPP) would hold, it would not matter ir. what currency exports were denominatedand export shares would no be affected.For strong and conclusive
-7-
rejectionsof the PPP see Frenkel(1981)and Cumby and Obstfeld(1984). The rule to base the currency compositionof external debt on the currenciesof invoice or denominationof exports (or imports or both) could equally be critized. There is sufficientevidence that the relationship between the nominallydenominationand the real value of exports has at times been perverse. For example,the real price of commoditieshas in the past been inversely related to the real value of the dollar, even though most comodities are denominatedand traded in terms of dollars. This meant that when the dollar went down, commodityprices went up and a commodityproducing country's terms of trade improvedtoo. Such a relationshipwould imply that the dollar would not necessarilyhave been the optimal currencyto borrow as its value could have a perverse relationshipwith the country'sability to generate foreign exchangein the short run throughexports.As a depreciation of the dollar implies an appreciation of other currencies, a
reverse
relationshipmight exist between the value of other currenciesand commodity prices: when the dollar appreciates,comodity prices decline, but other currencies depreciate too, which might make non-dollar currencies good external liabilities. This shows that a currency compositionbased on a country's trade denominationpattern could still lead to large real risks. The currency basket rule could be equally critizedas being based on nominal concepts. In general,the nominal dimensionof trade flows is not necessarily crucial in the long run for the currencychoice of externaldebt. If one uses the nominal denomination of trade flows, the US dollar would be the predominant currency for most developing countries.
However, when one
realizesthat prices in world commodityand manufacturesmarketsdepend on the
- 8-
interaction betweenidemanders and suppliers across the whole world, one realizes that the ncminal currtencydenominationof a good or the nominal direction of trade do not have to reflect the real denominationof the price of a commodity or manufacture. In a world market for commodities ard manufacturessuppliersbecome more (or less) competitivedependingnot only on the changes in their own currencybut also on the changes in other suppliers currencies.
Similarly, demanders will consider goods more (or less)
attractive depending on the movements of the exchange rates of multiple suppliers.As a result, the changes in the price of a particulargr
-
i
commnodity as a result of exchangerates changes will cruciallydepend on the type of market structure(perfectcompetitive,oligopolistic,etc.). Demand and supply elasticitieswill play a crucial role in distributingthe effects of exchange rate in terms of (nominal)price and quantity changes over the differentmarket participants.A not perfectlycompetivemarket structurecan result in real effects of nominal exchange rate changes as the different suppliersand demandersare affecteddifferently.For a further analysis of this issue see, for instance,Dornbusch(1987). All of the rules mentionedso far can thus be critizedas not being explicitlyrelated to a specificgoal or objectiveand not being based on an explicit definitionand measurementof risk. It might then also be the case that these rules increaserather than decreasethe real costs of borrowings and the fluctuationsof these costs over time. A more integratedapproach would to base the currencycompositionchoice of externalliabilitieson some tradeoff of the level of real effectiv.costs of funds in a certain currency with the uncertainty of these costs, where the costs are related to, for instance,the abilityof the countryto generateforeignexchangeas reflected
-9-
in the short run by its level of exports. In this approach,the real costs and riskiness of borrowingin a particularcurrencywould depend not only on the nominal costs of borrowingsand its uncertaintybut also on whether the appreciationor depreciationof that particularcurrencyis associatedwith an increase or decrease in the ability of the country to generate foreign exchange and pay its external liabilities. Comonly used indicatorsof the ability to service externaldebt are the level of exports and the country's terms of trade. For exampl, if the country exportsonly one commodityand if the price of that particularcommodityis one to one related to a particular currency, say the Danish Krone, then borrowingin that currencywould be the lowest risk strategypossible. In this context,aiversification of risk could suggestthat a country should not only borrow in more than one currency,it could also suggestthat a country determinesthe~currencycompositionof externalliabilities,or other aspects of its externalliabilities,so as to reduce other forms of price risk (e.g., fluctuationsin export or import prices,or the terms of trade). As exchangerates (and interestrates) are very difficultto predict, it seems valid to use in the context of an optimal borrowing strategythe presumption that the objective of the country in choosing its currency compositionis not to "beat" the market. The market expectationsas a whole of the movements of cross-currencyexchangerates are related to the nominal interestdifferentialsbetweenditterentcurrencies. It can be expected that under perfect market conditionsex-ante deviations from uncovered interest rate parity are small and that expectedborrowingcosts will thus be similar in all currencies.
The currency composition choice will then becom^
predominantlya functionof the correlationof each of the currencieswith the
-
10
-
country'sability to pay externalliabilities. The countrywill minimizethe variabilityof its debt serviceobligationrelativeto its ability to pay and borrow a risk-minimizing hedge portfolio. The conclusionof this section is that a solid theoreticalframework is necessary and that only empirical work can clarify the optimal currency choice issue. We turn now to the theoreticalmodel.
I
-
11
-
III. The Modell Consider a world which consists of a small open economy (the home country) and N developed countries. Let each of the N developed countries have an exchangerate e(i), i=1,...,N,which followsthe diffusionprocess: de(i) e(i) -
(1)
V=e()dt+
Oe(i)dZe(i)'
Here e(i) is written in terms of the home countries'currencyper unit of the foreign currency (e.g., Turkish liras per US dollar) and dZe(i) is a Wiener process. So
(dZ)=0 and VAR(dZ)=dt. Thus, this differentialequation says
that the expected value of the depreciationof the i'th exchangerate during the time period dt is ve(i) and its
standarddeviationis oe(i)* We are thus
assumingthat the exchange rate depreciationsare approximatelynormal for 2 small intervalsdt, and that the exchangerates themselvesare lognormal.
Supposealso that the means and standarddeviationsve(i) and ae(i) are all allowed to depend on both time and a vectorof state variables(which will
I
be defined
later).
Ve(i) =
where S is a (SYl)
So
ve(i)(S,t)
and
°e(i)
=
e(i)(St)
vector of state variableswhich are assumed to follow Ito
processes. Thus we have N foreigncurrenciesin which the home country can invest its wealth and denominateits liabilities,which are assumed to follow the process 1. This section is a brief summary of a restrictedversion of the model presented in Claessens (1988). See his paper for the general model and a discussionof the model and its assumptions. 2. See Merton (1971) and Fischer(1975) for descriptionsof the propertiesof Wiener processesand stochasticdifferentialequations.
-
de(i) e(in
12 -
ve(i)(Spt)dt+
=
Ge(i)(S,t)dZe(i)
Suppose that each country in the "world" has one nominal riskless (instantaneous) bond. Let B (j)
be the price in the j'th currencyof country
j's riskless bond, and B be the price in the home currency of the home country'srisklessbond. The dynamicsfor B (j)
are given by
dB (j) R*(j)dt ,
=
(3)
j=l,...,N
where R (j)
is the instantaneous nominal rate of return on the j'th bond in
currency j.
Also, let R be the instantaneousnominal return on the safe
domesticbond. The interestrates R are assumedto be constant. Define the excess return of the j'th foreign bond for a domestic investor,dH(B*(j))/H(B(j)), as the return on one unit of domesticcurrency investedin the foreign bond, financedby borrowingat the interestrate R in the domesticcountry.,i.e. dH(B*(0)
(4)
B{B(Ij)) = R*(j)dt + =
de i) e(j)
-
(RW(m)+ Ve(j) - R)dt +
Rdt
,
Oe(j)dZe(j)
Notice that the foreign bonds are risk-freein their own countrybut exchange rate risks make them risky for investorsfrom our "home country",and that their excess returns are perfectly correlated with the changes in the correspondingexchangerate. Next, suppose there are K commoditiesconsumed in the home country, whose domesticcurrencyprices follow the differentialequation (5)
dP(i) P(i)
vp(i)dt +
Op(i)dZp(i)'
Again, vp(i) and ap(i) are allowed to be functionsof both time and a vector
- 13 -
of state variables. So the commodityprice changeshave a mean of vp(i)(S,t) and a standarddeviationof ap(i)(S,t)over short time intervalsdt.3 The first K elements in the (Sxl) vector of state variables are assumed to be the changes in the logarithmsof the conmnodity prices; the next N elements are assumed to be the changes in the logarithmsof the exchange rates$ and the remaining(S-K-N)elementsare assumed to be other unspecified exogenousvariables. Finally, we assume that the domestic investor maximizes a timeadditive von Neuman-Morgensternlifetime expected utility function which depends only
on
the
consumption of
the
K
commodities and
time,
i.e.St trU [c(z),...,ck(z)lezdzI where 6 is the intertemporalrate of time preferenceand ci is the consumptionrate of good i.
This assumption
completes the model, and allows us to solve for the optimal investment portfolio. Let b be the optimal holdingsof foreign bonds, let v be the (Nxl) vector of excess returns, let Vaa be the (NxN) covariancematrix of excess returns to the foreign bonds, and let Vas be the (NxS) matrix of covariances between the excess returnsand changes in the state variables. Notice that, because the excess returns are perfectly correlated with changes in the exchange rate changes, Vaa is the same as the covariancematrix of exchange rate depreciations,and Vas is the same as the matrix of covariancesbetween the exchangerate depreciationsand changesin the states variablestwhere the 3. We do not assume that the law of one price holds necessarilyexactly for all goods (nor that PurchasingPower Parity holds), i.e., P(i) # P (i,j)e(j) necessarilyfor all i and j, where P (i,j) is the price of the traded good i in terms of foreign currency j. Neither do we assume that changes in the terms of trade are perfectlycorrelatedwith the (weightedaverage of the) changes in the exchangerates.
-
14 -
first K state variables are the commodity prices.
It can be shown (see
Claessens, 1988; Stulz; 1981; or Breeden,1979) that the optimal holdingsof
forein bods
b
foreign bonds b =
1 -
-U
7
I Uj-~Vaa
-1
" -
-1
Vaa VasCs , where C = C(W,S,t) is the
w cc consumptionexpenditurefunctionof the investor,W is wealth, and subscripts refer to partial derivatives. Notice that this is a a linear combinationof (s+l) column vectors, each of which (when appropriatelyscaled) can be interpreted as a mutual fund portfolio. The first portfolio is a meanvarianceefficientportfolio(i.e.,a speculativeportfolio),given by Vaa lv, and the remainings portfoliosare hedging portfolios,given by the S columns of
Vaa-iVas
(6)
The weights in the linear combinationdepend on the parametersof the utility function (such as degree of risk aversionand the consumptionshares of the different goods) while the portfoliosthemselvesdo not. The weight on the U
speculative po-tfolio is C-w
U
c- where US- is just the inverse of the cc
cc
coefficient of risk aversion, and the weights on the hedging portfolios -C
are C-!.
For a country with a high degree of relative risk aversion, the
w
hedging mutual funds will clearlybe relativelymore importantin the overall optimal holding of foreignbonds than the speculativemutual fund. Assuming that most developing countries are relatively risk averse, and using the assumptionthat the expectedcosts of borrowingsin differentcurrenciesafter adjusting for exchangerate changesare all equal (i.e., v = O), we can focus on the hedging portfoliosfor the rest of this paper. The hedging portfoliosare the portfolioswhich provide the maximum
-
15
-
correlationwith the state variables8, and hence they can be used to hedge against unanticipatedchangesin the state variables. This is becauseafter a shock to a state variable,the hedgingportfolioleaves the investor'swealth "as near as possible" to what it was originallywas, where the "nearness" depends on the degree of correlation of that portfolio with the state variable. The model says that the optimalway to hedge the K commodityprices (and thun consumer'swelfare) against changes in the exchange rates is to borrow accordingto the first K elementsof the matrix Vaa IVas, because then a change in each currency leaves the investor's net welfare the least affected.
The borrowing shares would apply to the country's net foreign
liabilities,i.e.,gross debt minus foreignexchangereserves. In the next sectionof this paper we will assume that K is one, and that the first state variablewill be the differencebetween the logarithmof the export prices and the logarithm of the import prices, i.e. this state variableis the terms of trade. 4
IV. Data Weekly exchangerate data from April 1, 1977 to March 31, 1988 were collected (574 observations)for the JapaneseYen (JY), the Deutschemark(DM), the Swiss Franc (SWF), the AustrianSchiling(AUS), the Pound Sterling (PS), the French Franc (FF), the US Dollar (US), the IndonesianRupiah (INDO),and
4. The use of one price variable, terms of trade, instead of K can be justified if the utility function to be maximized exhibits constant consumptionshares. The covariancesof the terms of trade with the exchange rates can then be written as a functionof the covariancesof the individual prices with the exchange rates. I
- 16 -
5 the Turkish Lira (TUR).
From this data, the weekly exchangerates of the
developed countries' currencies were calculated in terms of number of IndonesianRupiahs and TurkishLiras per unit of foreigncurrency(e.g., Liras per Pound Sterling),giving two sets of seven exchangerates. For the first part of the sample period,both the Rupiah and the Lira were fixed with respect to the US Dollar. This would, of course,artificially affect our estimatesof the variancesand covariancesof the exchange rates, so
the sample size was truncated at April 30, 1980 for Indonesia (414
observations left) and at October 15, 1980 for Turkey (390 observations left).
Since that time, both currencieshave been under a managed float
exchangerate system. A few interestingfacts become obviouswhen one examinesthe plots of the exchange rates.
See Figures 1 and 2 for the plots of INDO/JY and
TUR/JY. The most strikingfeatureof these plots is the dramaticdepreciation of both the Rupiah and the Lira with respect to JY and with respect to the other currenciesas well. The Rupiah fell from 2.63 INDO/JYto 13.25 INDO/JY, and the Lira fell from 0.40 TUR/JY to 9.75 TUR/JY over our sample period. Another obvious feature is the two times that the Indonesian government devaluedthe Rupiah by large percentages- from 702 INDO/USto 970 INDO/USin March, 1983;and from 1134 INDO/USto 1643 INDO/USin September,1986. These two devaluations of the Rupiah would cause problems when estimating the covariancematrix of exchange rate changes, as the large MonetaryFund database 5. The source for INDO and TUR was the International TIBMER, and the source for the other rates was the IMF databaseFTFROR. The Indonesianand Turkish rates are "representative" rates - i.e., they come from markets within Indonesia and Turkey respectively. The other rates are all London Noon Spot Quotations. Wednesdayswere used wheneverpossible,but if a holiday fell on Wednesdaythen Thursday'squotationwas used.
INDONESIAN RUPIAH PER JAPANESE YEN
J3 I 13+
Figure
1
12 .M
11+
* ..
i
*.
10
a S*
9+
8
+
SEI
P
CTO9*IN**
U8
E82
JL3
F84
AU8
A8
EP5
DATE~~~~~~~~~~~~~~
~
~
~
NOTE: 246 OBSHIDDEN
~
~
~
~
~
~
~
~
~
~
~ ~ ~~~a.
AR6
OT8
A8
E8
TURKISH LIRA PER JAPANESE VEN
JY
Figure
10
2
.
9 .
I
*: 6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
7 * II
.5
.
I I+ *~~~~*
I
....
3 +** I N T*I
I
5
S..
H
OO
..
..
*.
5**S
I
*5SS
I
S. 505**@@
I4+
I
0e****e*
O*,5
NOE
254oe.H1DE
I-.
a
-
19
-
appreciationsof all currenciesat the same time would artificiallyincrease covariance estimates. A dummy variable is therefore used throughout the ensuing analysis to capture each of these two depreciations (one dummy variable for each depreciation). It is interestingto note that with these dumies
included, statistical tests (augmented Dickey-Fuller tests and
examination of the correlograms)reveal that the Rupiah-basedlog exchange rates all are random walks with drift. All the Turkish Lira based exchange rates, however, fail these tests, perhaps suggesting that the Turkish governmenthas some other, non-market-clearing motives in mind when it sets the value of the Lira. As mentioned in the previoussection, the analysis rocusses on the behavior of the countries'terms of trade in relationto the behaviorof the exchangerates. The unit value of exports(imports)are calculatedby dividing 6 the ezport (import)values by the export (import)volumes.
The terms of
trade are calculatedas the unit value of exportsdivided by the unit value of imports. The analysiswhich followsis based on the logarithmsof the exchange rates and the logarithmsof the terms of trade, multipliedby 100. This is in harmony with the literatureon exchange rates, and gives us the additional benefit of being able to interpretdifferencedlogs as percentagechanges. Recall that the theoreticalframeworkrequiresall the data to be differenced, so we will deal with percentage changes.
It should be noted that the
6. All the value data and the Indonesianexport volume data come from the InternationalFinancial Statistics. The source for the Indonesian import volume data is the IndikatorEkonomi,a publicationput out monthly by the Indonesian Bureau of Statistics,and the source for all the Turkish volume data is Aylik IstatistikBulteni,a publicationput out monthly by the Turkish Ministryof State.
-
20 -
percentagechanges from month to month in the terms of trade are quite high compared to the monthly exchange rate changes,which are much less volatile and usually fluctuate between +1OX. The correlationsbetween the exchange rate changes and the terms of trade changes are somewhatlow, suggestingthat the optimal portfoliowe derive might be a less
than perfecthedge against the
changes in the terms of trade.
V. Estimation
i)
The ARCH Model We are interestedin obtaininga portfolioof foreign assets which
has maximum correlationwith the changes in the terms of trade. This optimal hedging portfolio can be found by solvingequation(6), where Vas is now the vector of covariances between the changes in the terms of trade and the changes in the exchangerates. But notice that Vaa IVas is just a simple OLS regression of the changes in the state variable on changes in the exchange rates.
So one could calculate the optimal portfolio shares by running a
simple OLS regressionof the terms of trade changes on the exchange rate changes and using the parameterestimatesfor the slopes as shares. However, this procedure implicitlyassumes that the variancesand covariancesof the exchange rate changesare constantthrough time, an assumptionwhich has oeen proven false many times in the literature. It would seem appropriate,then, to use an estimationprocedurewhich allows the covariancematrix to change with time. Autoregressive Conditional Heteroskedasticity (ARCH) econometric technique developed by Engle (1982) to do just that.
is
an
In the
univariate version which he presents, the conditionalvariance of a time
- 21 -
series is allcwed to depend on lagged squared residualsin an autoregressive manner. This means that during periods in which there are large unexpected Ohocks to the variable its estimated variance will increase, and during periods of
relative stability its estimated variance will decrease.
Bollerslev (1986) generalizesthe ARCH model in much the same way that an Autoregressivemodel is generalizedto an Autoregressive Moving Average (ARMA) model. His model, called GeneralizedARCH, is the same as an ARMA model in squared residuals. So, just as the ARMA model allows the mean to cnange with time, the ARCH (and GeneralizedARCH) model allows the varianceto change with time. The generalizationof the univariateARCH models to multivariateARCH models involves allowing the whole covariancematrix to change with time, instead of allowing just the variance to change with time.
The first
multivariateARCH model presentedin the literaturewas the one presentedby Kraft and Engle (1982),which allows the elementsof the covariancematrix to be a function of all lagged squaresand cross productsof the residuals. So this generalizationis the same as 'the generalizationof a univariateARMA process to a vector ARMA process. This model is very general,and does not always give positive definite covariancematriceL, so Baba et.al. (1987) present a matrix.
model which imposes positive definitenbs on the covariance Bollerslev (1987) develops another multivariateARCH model which,
-anilemore restrictive,is simpler and much easier to estimate,while still allowing the covariancematrix to change with time. This model imposes the restriction that the correlationmatrix is constant through time while the covariancematrix changes. Because of the large number of equations in our model, we will be using the constantcorrelationsversion of the multivariate
-
22 -
ARCH model. See Appendix1 for a descriptionof the model.
2) The EstimationResults If Ht is the covariancematrix of exchangerate depreciationsand Yt is the exchangerate depreciation,then the model estimatedfor Indonesiais Yt - c 4 d1D 1 t + d 2 D2 t + et
Ht= VtCVt where yt, c, dl, d2, and et are all M7xO)vectors,Vt, C, and Ht are all (7x7) matrices (see Appendix 1), Dlt is a dummy variable for the first major depreciationin the rupiah and D2 t is a dummy variablefor the second major depreciation. Restrictionsare imposedwhich say that the effect of each of the two large depreciationswas the same on all seven exchangerates (in terms of percentages). This amounts to imposingthe restrictionsthat di= r1 i and d2
r2 i, where r, and r2 are scalars and i is a (7xM) vector of ones. The
model estimatedfor Turkey is the same as the model estimatedfor Indonesia, except without the dummy variables. These models are estimatedusing a program,graciouslysupplied by Tim Bollerslev, which uses maximum likelihoodestimation to estimate the values of the parameters in the model.
The correlationmatrix of weekly
exchange rate depreciationsfor the Indonesianmodel is given in Table I (t7 , and the correlationmatrix for Turkey is given in stats in parentheses)
Table 2. Notice that in both models the correlatior. of the US dollar with all other exchange rates is much lower than the correlationbetween any of the
7. It is interestingto note that without the dummy variables,all the correlationsincreaseddramatically. For example,the correlationsinvolving the US dollar increasedfrom about -.40 to +.80.
- 23 -
other exchange rates.
In the Indonesianmodel, the correlationsare even
negative. This is not surprisingin light of the fact that the dollar often moved in a directionopposite to other developedcountries'currenciesover the sample period covered. Notice also that the Europeancurrencies(DM,SWF, ASU, and PF) form a block with high correlations. In fact, DM and AUS are almost perfectlycorrelated,which leads one to questionhow much additional 8 informationis added by includingboth in the analysis.
Table 1 CorrelationMatrix for IndonesianBased ExchangeRate Depreciations JY 1.00 -
(22)
SWF .701 (27)
AUS .649 (21)
PS .460 (11)
FF .596 (15)
US -.477 (-10)
1.00 -
.919 (112)
.990 (949)
.649 (23)
.893 (91)
-.429 (-9)
1.00 _
.917 (114)
.627 (21)
.835 (51)
-.444 (-10)
1.00 -
.660
.901 (106)
-.422 (-9)
.660 (21)
-.335 (-6)
1.00 _
-.375 (-7)
DM .648
(24) 1.00 -
1.00
8. To keep the issues clear, the Austrianschilingis dropped in the ensuing analysis. This is done by simply deleting the row and column of the covariancematrix correspondingto AUS. It should be noted, however, that dropping AUS only causes a redistributionof the holdings of the European currenciesin our optimalportfolio,leavingthe portfolioweights of the nonEuropean currencies (JY, PS, US) almost unaffected. This supports the conjecturethat AUS is not adding much to the analysis.
- 24 -
See Appendix 2 for a presentationand a discussionof the other parametersin the model. A couple of observationswhich merit mention in the main text, however,are first that the parametersof the ARCH model are almost always significant,providing strong support for the hypothesis that the covariancematrix is changingwith time; and second that the constantsin the mean equationsare significant,capturingthe drift which is so obvious in the plots of the exchangerates.
- 25 -
Table 2 CorrelationMatrix for TurkishBased ExchangeRate Depreciations JY 1.00 _
DM .602 (17)
SWF .664 (21)
AUS .606 (17)
PS .446 (11)
PP .548 (15)
US .271 (6)
1.00
.895 (93)
.988 (754)
.612
(20)
.862 (73)
.082 (1.7)
1.00
.892 (94)
.593 (18)
.793 (41)
.056 (1.2)
1.00 -
.628 (21)
.871 (79)
.086 (1.8)
1.00
.627 (17)
.253 (5)
1.00 _
.101 (2)
-
-
-
1.00 The terms of trade data are only availablemonthly,which means that weekly covariances between exchange rate depreciationsand changes in the terms of trade cannot be calculated. Monthly covariancesmust then be used instead. A test is undertakento see whether or not these covariancesalso follow an ARCH process.- Under the null hypothesisthat there is no ARCH in the monthly covariancesbetweena currencies'exchangerate depreciationsand changes in the terms of trade, the test
statisticis distributedX21, with a
5Z criticalvalue of 3.84. See Table 3 for the computedtest statistics. As the test statisticsfor the Turkishdata are all less than 0.07, these values are all insignificantat any reasonable level of significance. We can
9. See Appendix 3 for a theoreticalderivation of the appropriate test statistic.
- 26 -
therefore be confident that the covariancesbetween terms of trade and the exchangerates are not changingwith time, and subsequentlythe unconditional covariancescan be used. The results for the Indonesiandata set is similar, though the test statisticfor the covariancebetween changes in the US dollar and the changes in the terms of trade is significant. Because all other test statisticsare highly insignificant, we will treat the US dollar covariances as though they are also constantthroughtime.
Table 3 LagrangeMultiplierStatisticsfor ARCH in the Covariances between the Changes in the Terms of Trade and CurrencyDepreciations Turkey Indonesia VI.
JY DM SWP PS 0.0003 0.002 0.0007 0.070 0.45 0.05 0.035 0.04
FF US 0.02 0.0007 0.0055 10.41
The Optimal Portfolios In order to calculate a nation's optimal currency compostion of
external debt over the next (say) three months, one must first obtain a forecastof the variance-covariance matrix of exchangerate depreciationsfor the next three months, then multiply the inverse of that by the forecasted covariance between exchange rate depreciationsand changes in the terms of trade. The forecastof the covariancebetweenthe exchangerate depreciations and the changes in the terms of trade are easy to derive - they are just the unconditionalcovariancesbecause they are not changingover time. The three month forecasts would be the monthly unconditionalcovariancemultiplied by three. The ARCH model can be used to forecastthe variancesand covariances of a series of exchange rate depreciationsin exactly the same way that an ARMA model can be used to forecast the mean of a series. So we can just
- 27 -
forecast the weekly covariancematrix for the next thirteen weeks, and use these forecasts to get a forecast of the three month covariancematrix. Tables 4a and 4b give the forecastedcovariancematrix for Indonesianbased currencies for the first quarter of 1988 and the unconditionalcovariance matrix over the sample period (Apr/80to Mar/88). Notice that they are quite different,and they suggest that the exchangerates in the first quarter of 1988 were expected to be relativelymore stable than over the previouseight years combined. Table 4a ForecastedCovarianceMatrix - Indonesia,1988.1 JY DM SWF PS 28.8 19.0 22.6 12.6 30.1 30.5 18.4 36.7 19.6 26.9
FF 17.2 26.7 27.5 18.5 29.6
US -1.3 -1.2 -1.4 -0.9 -1.0 .26
Table 4b UnconditionalCovarianceMatrix - Indonesia,1980.2 to 1987.4 JY DM SWF PS 36.7 20.8 26.1 17.0 33.0 32.8 19.6 39.3 22.0 31.0
FF 21.3 31.5 31.2 20.3 33.9
US -1.1 -.97 -1.1 -0.9 -0.9 .69
With this information,we are now able to calculate the optimal portfolioaccordingto equation(6). The result for the sharesfor Indonesia for the first quarterof 1988, when scaled to sum to one, is JY 0.031
DM 0.191
SWF -.005
PS 0.014
PF -0.139
US 0.907
The most striking feature of this portfolio is the heavy weight in the US
- 28 -
dollar and the lower weights in all other currencies. This might be as expected,though,because Indonesia'sexportsare largelymade up of petroleum and primary commodities,whose prices are evidentlymore related to the US dollar, and because Indonesiamanages its exchangerate with respectto the US dollar.
Borrowing a large fraction in US dollars provides then a hedge
against changes in terms of trade and export values. The optimal portfolio for Indonesiafor the first quarterof 1986 (i.e. based only on data up to the end of 1985, or the first 297 observations) was jy -0.005
DM 0.307
SWF PS -0.055 0.007
FF Us -0.154 0.900
This portfolio is not remarkablydifferentfrom their optimal portfolio for the first quarter of 1988, but it differssubstantially from their actual debt portfolioat the end of 1985. Indonesia'sdebt was actual outstandingin the followingproportions: JY 0.401
DM 0.106
SiP 0.062
PS 0.025
FF 0.038
US 0.369
It would seem, then, that the optimal portfolio could result in a large reduction in the variance of Indonesia's net position, as the optimal portfoliodiffers substantiallyfrom their actual portfolio. In order to calculatehow effective this portfolio strategy is in terms of dynamically hedging against changes in the terms of trade for Indonesia, we assume that the Indonesianauthorities followed the optimal strategy every quarter since the end of 1985. I.e., they estimatedthe ARCH model, forecasted the covariance matrix on exchange rate depreciations, estimated the unconditionalcovariancesof the exchange rate depreciations
-
29 -
with the changes in the terms of trade, and applied equation (6) to get the optimal hedging portfoliofor each quartersince the end of 1985. then
borrowed
the
resulting
portfolios, the
monthly
If they sequence
of (AlnT + BAlnPX)can be calculatedfor two years (1986 and 1987), where T = terms of trade, FX are the residuals from the exchange rate equations, and B are the portfolio weights.
The variance of this sequence can be
comparedwith the varianceof the sequencewhich resultswhen they use their 1985 portfolio throughoutthe two years, assuming borrowingat the absolute levels implied by the optimal portfolio strategies. Comparison of the variancesof the two portfoliosprovidesan indicationof how well the optimal strategiesare in hedging against changes in the terms of trade. Performing this exercise shows that the variance drops using the optimal strategy. Presumably,the movementin Indonesia'sborrowingportfolioaway from JY to US resultedin the increasedstability. The
optimal qua-terly portfolios which result from the above
analysis,are shown in Table 5. The portfoliosare scaled to sum to one. The relative shares of the currencieschange quite a bit from quarter to quarter. However, it is interestingto note that the effectivecurrencydistributionof the portfoliodoes not change that much throughtime once one accountsfor the high correlationbetween the Europeancurrencies. The sums of the shares of the European currencies(DM, SWF, PS and FF) are for each respectivequarter (from the first quarter of 1986 through the first quarter of 1988): lO.9Z, 13.8SZ,7.41, 18X, 34.4X,
19.7%, 25.81, 11.1 and 6.11. The combinedEuropean
share is somewhat more stable than the individual shares, potentially a reflectionof the high correlationamong the Europeancurrencies.In addition to the changes in shares,the unscaledportfoliosalso change. The sum of the
- 30 -
"nscaled portfolio weights ranges between about 5 and about 40, which suggests different absolute levels of borrowing.
Table 5 Optimal Portfolios - Indonesia period 1986.1 1986.2 1986.3 1986.4 1987.1 1987.2 1987.3 1987.4 1988.1
JY -0.005 -0.022 -0.001 -0.027 -0.009 0.006 -0.033 0.044 0.031
DM 0.307 0.320 0.164 0.384 0.801 0.462 0.703 0.323 0.191
SWF -0.055 -0.028 -0.012 0.019 0.026 0.015 -0.017 0.001 -0.005
PS 0.007 0.028 0.021 0.027 0.150 0.075 0.050 0.029 0.014
FF -0.154 -0.182 -0.100 -0.252 -0.632 -0.354 -0.479 -0.243 -0.139
US 0.900 0.884 0.928 0.849 0.665 0.797 0.777 0.847 0.907
A similar analysis can be conducted to find the portfolios that hedge against changes in export prices, export values, import prices or import values. These
portfolios are very similar to the ones above and achieve
equally remarkable reductions in variance. hedging
As expected, though, the import
portfolios are approximately the negative of
the export hedging
portfolios. The export hedging portfolios are approximately the same as the terms of trade portfolios.
The case for Turkey is analyzed similarly.
Applying the strategy
decribed above gives the optimal portfolio for the first quarter of 1988 as
JY 0.115
DM -0.086
SWF -1.842
PS 0.498
PF 2.511
US -0.197
This portfolio is much more diversified than Indonesia's optimal portfolio, which might not surprising because Turkey's trade is more diversified than Indonesia's and currency.
Turkey's exchange rate
policy
is
less
focussed on
one
Turkey's optimal portfolio involves investing large amounts in SWF,
- 31 -
DM and US (the negative portfolio shares) while borrowing JY, PS and FF.
The
investing can be done through the central bank's foreign exchange rserves, which could be financed by
the borrowings in the other currencies. Their
actual portfolio (row 1) and their optimal portfolio (row 2) for the first quarter of 1986 are:
JY 0.104 0.911
DM 0.183 -0.311
SWF 0.117 -0.893
PS 0.022 0.255
FF US 0.032 0.543 1.131 -0.093
This large discrepancy between their.actual debt portfolio and their optimal debt portfolio suggests that there is a lot of hedging that can be done by changing their debt portfolio. Unfortunately, this is not the case due to the large
changes
in
portfolio
shares from
period
strategies for each quarter are given in Table 6,
to
period.
The
optimal
from which one notices the
large changes in the optimal portfolio shares through time, unlike Indonesia where they were relatively stable.
Table 6 Optimal Portfolios - Turkey period 1986.1 1986.2 1986.3 1986.4 1987.1 1987.2 1987.3 1987.4 1988.1
JY 0.911 0.335 0.799 0.548 0.390 0.362 0.237 0.524 0.115
DM -0.311 -0.677 -0.479 -0.365 -0.363 -0.159 -0.123 -0.316 -0.086
SWF -0.893 -0.589 -0.833 -0.974 -1.022 -0.863 -1.234 -1.155 -1.842
PS 0.255 0.531 0.718 0.932 0.857 0.618 0.483 0.052 0.498
FF 1.131 1.265 1.019 0.867 1.086 1.190 1.783 1.728 2.511
US -0.093 0.135 -0.225 -0.007 0.052 -0.147 -0.146 -0.301 -0.197
The sum of the unscaled portfolio weights ranges between about 0.9 and 2, suggesting, similar to the results for Indonesia, different absolute levels of borrowing. However, the variability in the suggested absolute level
- 32 -
of borrowing is not as large for Turkey as it was for Indonesia.The sums of the shares of European currenciesare respectivelyfor the nine quarters: 18.2%, 53%, 42.62, 45.9%, 55.8%, 78.5%, 90.9%, 77.7% and 108X. The sums seems to suggest a relativelymore stable weight for the Europeancurrenciesas a whole compared to the individualEuropeancurrencyweights. Restrictingthe portfolio shares to be positive,i.e., not allowingany investingin foreign currencies,results for the nine quartersin the followingportfolios:
Table 7 Optimal Portfolios,Shares Positive- Turkey period 1986.2 1986.3 1986.4 1987.1 1987.2 1987.3 1987.4 1988.1
JY 0.075 0.338 0.117 0.000 0.020 0.000 0.037 0.000
DH 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
SWF 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
PS 0.337 0.462 0.677 0.582 0.436 0.228 0.251 0.124
FF 0.349 0.200 0.067 0.233 0.544 0.769 0.712 0.876
US 0.239 0.000 0.138 0.180 0.000 0.003 0.000 0.000
SUM 0.554 0.576 0.705 0.746 0.759 0.627 0.663 0.375
In general,restrictingthe weightsof the currenciesto be positive leads to less skewedand somewhatmore stable portfolios.In addition,the sum of the unscaled portfolioamounts, the right hand column in the table 7, i.s more stable.This indicatesthat the relativeamount to borrow each period to hedge against terms of trade movementsis more constantwhen the weights are restrictedto be positive.The sums of the shares of the Europeancurrencies for the eight quarters are respectively:0.656, 0.662, 0.744, 0.815, 0.980, 0.997, 0.963 and 1.00. This sum is more stable than the individualcurrency weights, the PS and the FP (and more stable than without restrictionson the portfolio shares). The relativelyhigh correlationbetween the PS and PF currenciesmakes these currencies in some sense "substitutes"in terms of
- 33 -
hedging against terms of trade movements.Small relativechanges from period to period in the correlationbetween the PS and PF exchange rates and the terms of trade movementscan then allow for large shifts within the European basket. The shifting shares within the Europeangroup need not be a reason for concern as long as Turkey sets its borrowingtargetswith respect to the groups of Europeancurrenciesas a whole. Overall the results for Turkey are not completelysatisfying,most likely due to weaker data. It seems unlikely that using better econometric techniques and imposing more restrictionswhile solving for the portfolio weights will lead to more satisfyingresults unless the data used for Turkey are improvedupon.
- 34 -
VII. Conclusion This paper outlines a theoreticalmodel of how to calculate the optimal debt portfolio for a nation which wants to hedge its terms of trade against exchange rate fluctuations.The paper applies the theoreticalanalyis to Indonesiaand Turkey. The portfoliowhich we derive for Indonesiais shown to be an effective hedge, reducing the variance of the costs of borrowing reletativetot Indonesiaterms of trade. So even though Indonesiamight only have limited access to organizedcurrencyfuturesand other hedging markets, they could still manage their external exposure effectively if they could structure their externaldebt optimally. Historicallythe optimal portfolios did not change much from one quarter to the next, so the quarterlyportfolio changes would mostly require fine-tuningtheir portfolio,which could make the borrowingstrategyall the more beneficialto implement. The results for Turkey are not completelysatisfying. Part of it might be due to the data for Turkey, which were less than perfect. But it also points out some directionsfor furtherresearch. One is to reperformthe analysis with some more currenciesincluded. The Turkey model, for example, should probably have as one of its borrowing currencies a
currency
representingthe Middle East - such as Saudia Arabia. Anotherdirectionwould be to use an instrumentalvariable technique to forecast currency changes against the Turkish Lira and to obtain the deviations from the expected exchange rate changes. This might enhance the analysis, especiallyas the Turkish exhange rates do not seem to followa random walk.
- 35 -
Appendix1
The multivariateARCH model used in this paper is the one first proposed by Bollerslev(1987). See his paper for a more detaileddiscussion of the model. Let Pt (the informationset) be the a-fieldgeneratedby past values of et, let yt be a (nxl) vector and let Ht be a (nxn) matrix. Then the multivariateARCH model is Yt|Rt-I
N(Xt.B' St)
Ht = VtcVt where C is a (nxn) correlationmatrix which is time-invariant,and Vt is a (nxn) diagonal matrix with the i'th diagonal element, hi,t
being the
standard deviation of the i'th variable, -whichis allowed to change with time. hitt
The variances are assumed to follow a univariateARCH process; i.e.
2 + bihi,t-i. This gives a covariance w wi * aiei",t1 matrix, Ht, with
constantcorrelationsbut time-changing variancesand covariances. Letting e be the parametersof the model and T be the number of observations,the likelihoodfunctionis
L (8)
-
2 log(2ar) -½ ~2Eh1(loglHtl* et'Htjlet)
which can be rewrittenas L (6)
-
TN 2 log(2w)- ½TloglCI -
h1
logIDtl
-
t 1 st'C7t
where st are the standardizedresidual'. This version of the likelihood function highlights one of this model's major advantages(and the reasonwe chose to use this model insteadof one of the other multivariateARCH models) - evaluationof the likelihood
I
-
36
-
functionrequiresinversionof only one (nxn)matrix insteadof T. Becausewe use
numeric methods to maximize the likelihood function and we have 50
parametersin the model with 400 observations, we reduce the number of matrix inversionsfrom 20,000 to 50 for each iteration. Given that we are estimating about 20 differentmodels with many iterationsFer model, the time and cost savings are enormous,while the results should not be qualitativelydifferent than with another model.
- 37 -
Appendix2
The full model estimatedwas Yt = c + et E(e
o Ht
e 1jFt_j)
et Ht
N(O,Hd) Vt'CVt
where Yt, c, and et are (71s) vectors,Ht and C are (7x7) matrices,and Vt is and a (7x7) diagonal matrix with diagonal elements (hjy,t,hDM,t,...,hUs,t) each hi,t a univariateCARCH(l,1)model. For example, hps,t a
2, aPsepS,t-l P
'US
bpShpS,t.l. The results for Indonesia are
presented in Table A2.1 and the results for Turkey are presented in Table A2.2.
Table A2.1 ARCH EstimationResults- Indonesia,Data throughMar/1988 parameter
PP
JY 0.327 (4.6)
DM 0.199 (2.6)
SWP 0.237 (2.9)
AUS 0.204 (2.7)
PS 0.091 (1.2)
0.104 (1.2)
US 0.029 (5.3)
t-stats
0.130 (3.5)
0.470 (2.1)
0.199 (1.5)
0.483 (2.1)
0.112 (2.1)
0.636 (1.9)
0.000 (1.5)
a t-stats
0.072 (5.7)
0.058 (2.4)
0.035 (1.6)
0.056 (2.2)
0.047 (2.9)
0.098 (4.4)
0.292 (5.8)
b t-stats
0.863 (30.7)
c t-stats W
0.734 0.892 (6.4) (16.0)
dummy variables
0.729 0.902 (6.2) (25.3)
depreciation#1 depreciation#2
0.623 0.739 (3.4) (23.4) 32.26 (163) 37.21 (531)
- 38 -
Table A2.2 ARCH EstimationResults - Turkey,Data throughMar/88 parae-ter c t-stats
JY DM 0.786 0.691 (9.9) (10.1)
SWF AUS 0.717 0.697 (9.2) (10.3)
PS 0.609 (7.2)
PP Us 0.609 0.676 (8.6) (10.8)
t-stats
0.166 (2.3)
0.326 (1.9)
0.032 (1.4)
0.265 (2.1)
0.071 (1.4)
0.732 (2.4)
0.673 (3.7)
a t-stats
0.095 (3.5)
0.016 (2.6)
0.046 (2.2)
0.044 (2.5)
0.025 (2.5)
0.116 (4.8)
0.234 (3.0)
b t-stats
0.823 (16.9)
0.797 0.943 (9.2) (32.6)
0.462 (2.4)
0.156 (0.9)
w
0.763 0.968 (7.0) (60.7)
The first observationon these results is that the ARCH parametersa and b are almost always highly significant,which suggeststhat the variances and covariancesare changivg through time and the ARCH estimationprocedure should give us better covarianceestimatesat any point in time than OLS. Another observationis that the constants in the mean equations are usually significantlypositive, capturing the upward trend in the exchange rates. Notice that for Turkey (for example)the constantsare around 0.70, which says that the average weekly depreciationof the Lira was about 0.70X.
For
Indonesia, the typical weekly depreciationwas smaller, but the two dummy variables capture two large depreciations(which probably make up for the smaller typical weekly depreciation). The first depreciationwas about 322 and the second was about 37%. From these results, a series of conditional variances can be constructedwhich allows
us to identifyperiodsof stabilityand instability
in each of the exchange rates. INDO/PS, TUR/SWF and
The conditional variances for INDO/US,
TUR/JY are
plotted in
Figures A2.1
to
A2.4
respectively. These are just a representativeaample of all of the possible plots; the conclusionsderived from these plots are similar to those which
I
- 39 -
would be derived from other plots. Some interestinginsightscan be gained from these plots. First, the variancesof the INDO/US series are much smaller than the other Indonesian-based series' variances(note the scale difference on the verticalaxis). This is expectedbecause the Rupiah is operatingon a dirty float with respect to the dollar. Notice also that uncertaintyin most exchange rates was at a peak in 1985; a time when uncertaintyin the dollar was relativelysmall. One possibleexplanationfor this is that this was when the dollar was falling. The market knew that the dollar was going to fall there was not much uncertaintythere - but there was a lot of uncertaintyin how the fall would be distributed. Into which currencywould the dollar be converted? This leads to increasedun..artainty in the other currencies.
INDONESIA:
H7
CONDITIONAL
VARIANCES OF US
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44 -
-
Appendix3
When testing for restrictionsin the ARCH models, the simplest test
is the LagrangeMultiplier(LM) test. This is a test which examineswhether the slope of the likelihoodfunctionevaluated at the parametersunder the null hypothesis,is zero. So the LM test requiresonly the uerivativesof the likelihood functionwith respect to all the parameters,evaluatedunder the null. If the null hypothesisis given by HO:O=eo then the LM test statistic, which is distributedX2 q where q is the number of restrictionsimposed by the null,
is
=L -4) where C
C 1 (6eLel
is the informationmatrix and L is the likelihoodfunction. Kroner (1987) shows that for ARCH models this test statisticalways
reduces to 3½( ='x
T. vtWt ljDt)(
=.
Dt'WitDt)1 ( 1=1 Dt'Witvt)
where Vt = vec(etet
Wt = Ht and
Qt' =
*
-Ht)
Ht
6vecHt
In this paper, we are interestedin testing whether or not the covariances between exchange rate depreciationsand terms of trade changes are varying with time.
This is done by setting up a bivariate seemingly unrelated
regressionsmodel, with the two variablesbeing the appropriateexchangerate tepreciationsand the changes in the terms of trade. We then test for ARCH in
- 45 -
the covariancesfrom this regression.,So if the model is
Ht= a + |
PClt-I 2t-I
then the null hypothesis for no ARCH in the covariancesis parameterse are
e-
1
This
lt-1 I
p=O, the
(vecd,p)and Qt is given by
0
4
P:
o
1 2t-I 2t-l
4xS
test statisticis distributedas a X2! under the null of no ARCH in the
covariances.
- 46 -
Bibliography Aylik IstatistikBulteni,Republicof Turkey,Ministryof State, Institute of Statistics;various issues. Baba, Y., R.L. Engle, D.F. Kraft, and K.F. Kroner,(1987),"Multivariate GeneralizedAutoregressiveConditionalHeteroskedasticity," UC San Diego manuscript. Bollerslev,T., (1986),"GeneralizedAutoregressiveConditional Journalof Econometrics,31, 307-327. Heteroskedasticity," Bollerslev,T., (1987),"Modellingthe Coherencein Short Run NominalExchange Rates: A MultivariateGeneralizedARCH Model,"Northwestern University manuscript. Breeden,D., (1979),"An Intertemporal Asset PricingModel with Stochastic Journalof Financial Consumptionand InvestmentOpportunities," Economics,7, 265-296. Claessen,iS., (1988),"The OptimalCurrency Composition of External Debt," Policy, Planning and Research Working Paper #14, Development Economics,World Bank. Cumby, R. and M. Obstfeld,(1984),"InternationalInterestand Price Level Linkages under Flexible Exchange Rates: A Review of Recent Evidence", in John P.O. Bilson and Richa'r C. Marston, editors, Exchange Rate Theory and Practice, Universityof Chicago Press, 1984 Diebold,F.X. and M. Nerlove,(1985),"ARCH Models of ExchangeRate Fluctuations,"Universityof Pensylvaniamanuscript. Diebold,F.X. and M. Nerlove,(1988),"The Dynamicsof ExchangeRate Volatility: A MultivariateLatent Factor ARCH Model," Journal of AppliedEconometrics,forthcoming. Dornbusch,R., (1987),"ExchangeRates and Prices,"AmericanEconomicReview, 77, pp. 93-106 Engle, R.F., (1982),"Autoregressive ConditionalHeteroskedasticity with," Estimatesof the Varianceof U.K. Inflation,"Econometrica,50, 987-1008. Fischer,S., (1975),"The Demand For Index Bonds,"Journal of Political Economy, 83, pp. 509-534 Frenkel,J. (1981),"FlexibleExchangeRates, Prices and the Role of 'News': Lessons from the 1970s",Journal of Political Economy 89, August 1981.
- 47
-
Gemmill,C., (1985),"OptimalHedgingon FuturesMarkets for CommodityExportingNations,"EuropeanEconomicReview,27, 243-261. IndikatorEkonomi,Biro Pusat Statistik,Jakarta,Indor.esia; various issues. InternationalFinancialStatistics,International MonetaryFund Publication; various issues. Kraft, D.F. and R.F. Engle, (1982),"Autoregressive Conditional Heteroskedasticity in MultipleTime Series Models,"UC San Diego DiscussionPaper #82-23. Kroner,K.F., (1987) "Estimatingand Testing for Factor ARCH," UC San Diego manuscript. Merton, R.C., (1971),"OptimalConsumptionand PortfolioRules in a Continuous-Time Model,"Journalof EconomicTheory, 3, pp. 373413. Stulz, R. (1981),"A Model of International Pricing,"Journalof Financial Economics,9, 383-406. Svensson,L.E.O., (1987),"OptimalForeignDebt Composition,' manuscript, World Bank, December1987.
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a
Contact
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