Universidad Nacional de La Plaa Sépimas Jornadas de Economía Monearia e Inernacional La Plaa, 9 y 0 de mayo de 2002 The Term Srucure of Counry Risk and Valuaion in Emerging Markes Cruces, Juan José (Universidad de San Andrés), Buscaglia, Marcos (IAE School of Managemen and Business, Universidad Ausral) and Alonso, Joaquín (Mercado Abiero)
The Term Srucure of Counry Risk and Valuaion in Emerging Markes Juan José Cruces Marcos Buscaglia Joaquín Alonso Firs draf: January 2002 Absrac Mos praciioners add he counry risk o he discoun rae when valuing projecs in Emerging Markes. In addiion o he problems already poined ou in he lieraure, in his paper we claim ha such pracice leads o a pro-cyclical bias in he valuaion of long-erm projecs. The mismach beween he duraion of he projec and he duraion of he mos widely used measure of counry risk, J.P. Morgan s EMBI, leads o an overvaluaion of long-erm projecs in good imes (upward sloping defaul risk) and o an undervaluaion of hem when shor-erm defaul risk is high (he conrary is rue wih respec o shor-erm projecs.) Using sovereign bond daa from five Emerging Markes, we esimae a simple model ha capures mos of he variaion of defaul probabiliies a differen horizons for a given counry a one poin in ime. This model can be used o solve he misesimaion problem. JEL classificaion codes: G5, G3 Keywords: Emerging Economies, Cos of Capial, Defaul Risk Universidad de San Andrés, Vicoria, Province of Buenos Aires, Argenina. E-mail address: cruces@udesa.edu.ar IAE School of Managemen and Business, Universidad Ausral, Pilar, Province of Buenos Aires, Argenina. Tel.: 54-2322-48069. E-mail address: mbuscaglia@iae.edu.ar. Corresponding auhor. Mercado Abiero, S.A., Buenos Aires, Argenina. E-mail address: joaquin@masa.com.ar.
I. Inroducion Projecs in emerging markes are generally perceived as riskier han oherwise similar projecs in developed counries. These addiional risks include currency inconveribiliy, civil unres, insiuional insabiliy, expropriaion, and widespread corrupion. Emerging markes (henceforh EM) are also more volaile han developed economies: heir business cycles are more inense, and inflaion and currency risks are higher. Several problems have resriced he use among praciioners of he Capial Asse Pricing Model (CAPM) or is inernaional version, he ICAPM 2, o calculae he cos of capial of projecs in EM. Firs, here is no complee agreemen abou he degree of inegraion of EM capial markes o he world marke (see Errunza and Losq, 985, and Bekaer e al., 200). Secondly, local reurns are non-normal, show significan firs-order auocorrelaion (Bekaer e al., 998), and here are problems of liquidiy and infrequen rading. Finally, as correlaions beween local reurns and inernaional reurns are so low (see Harvey, 995), he cos of capial ha emerges from he use of hese models appears as oo low. These problems have lead praciioners o accoun for he addiional risks by making ad hoc adjusmens o he CAPM. Godfrey and Espinosa (996), for insance, propose o calculae he cos of capial in EM by using E[R i ]= ( R f US + Credi Spread ) + σ i * 0.60 * ( US E[Rm ] R US f ) () σ US where credi spread is he spread beween he yield of a U.S. Dollar-denominaed EM sovereign bond and he yield of a comparable U.S. bond, and he erm preceding he las parenhesis is an adjused bea, ha is equivalen o 60% of he raio of he volailiy of he domesic marke o ha of he U.S. marke. 3 Neumeyer and Perri (200) find ha oupu in Argenina, Brazil, Korea, Mexico and Philippines is a leas wice as volaile as i is in Canada. 2 See Adler and Dumas (983). 3 The 60% adjusmen is due o he finding ha 40% of he volailiies of domesic markes are explained by variaions in credi qualiy. 2
Alhough here are differen versions of his model (see Pereiro and Galli, 2000, Abuaf and Chu, 994, and Harvey, 2000), all of hem add he counry risk o he U.S. risk free rae in order o define he EM s analog of he U.S. risk free rae. There are few sysemaic surveys of cos of capial esimaion pracices in EM, bu hose available show ha varians of his model are he mos widely used among praciioners. Pereiro and Galli (2000) show ha he vas majoriy of argenine corporaions (including financial and non-financial firms) add he counry risk o he US risk free rae. Keck e al. (998) find similar resuls in a survey of Chicago School of Business graduaes. Several objecions have been raised in he lieraure o he addiion of he counry risk o he discoun rae. Firs, he model lacks any sound heoreical foundaion (Harvey, 2000). Second, in mos versions of his model counry risk is double couned, since par of he variabiliy in marke reurns is correlaed wih counry risk (Esrada, 2000). The 60% adjusmen of Godfrey and Espinosa does no solve he problem, as i is compleely ad-hoc. Third, for inernaionally diversified invesors par of he counry risk is diversifiable, and hence i should no be included in he discoun rae. Fourh, alhough his model gives a unique discoun rae for all projecs, he addiional risks inheren o EM do no have a uniform impac on all firms and projecs (Harvey, 2000). Someimes he counry risk is high because he marke expecs a sharp devaluaion ha would deeriorae he public secor s financial posiion. A devaluaion, however, would benefi some secors (e.g., exporers), and damage ohers (e.g., imporers). 4 In his simple paper, we discuss anoher problem ha he addiion of counry risk in he discoun rae as in equaion () has; namely, ha i implicily assumes ha he defaul-risk erm srucure is fla, leading o a pro-cyclical valuaion of long erm projecs in EM. The counry risk measures mos widely used are he ones given by J.P. Morgan s EMBI and EMBI+. Table I shows ha here is a grea cross-counry variabiliy in he average duraion of he EMBI Global as of Augus 2000. For example, an invesor considering wheher o locae an oherwise similar facory in Poland or in Hungary would be using for 4 Some propose o make addiional adjusmens o he discoun rae o reflec his. These adjusmens, however, also lack any sound foundaion. 3
Poland a counry spread corresponding o a duraion of 6 years, whereas in Hungary he would be using a spread associaed wih a duraion of 2.3 years. Using hese defaul-risk measures in he discoun rae o value long-erm projecs would bear no addiional problem o he ones menioned above if he defaul-risk erm srucure were fla. Bu, in fac, his is no he case. In good imes, when capial is flowing o EM, risk spreads are low a he shor end of he curve, bu hey are upward sloping. In many insances, moreover, he defaul-risk erm srucure is downward sloping. This usually happens when he marke expecs a defaul in he shor erm. The mismach beween he duraion of he projec and he duraion of he EMBI leads o an overvaluaion of long-erm projecs in good imes and o an undervaluaion of hem when defaul risk is high (he conrary is rue wih respec o shor erm projecs.) Figure I.A. illusraes his poin. While in Augus 200 Mexico and Russia had similar spreads on bonds wih shor duraions, Russia s risk was much higher a longer horizons. A mechanical applicaion of equaion () would ignore hese daa, which are readily available from bond markes, and would have led o an undervaluaion of oherwise similar long-erm projecs in Mexico relaive o Russia. Using sovereign bond daa from five Emerging Markes, in his paper we esimae a simple model ha capures mos of he variaion of defaul probabiliies a differen horizons for a given counry a one poin in ime. This model can be used o solve he miss-esimaion problem. The paper proceeds as follows. In Secion II we explain he model we use o esimae he defaul-risk erm srucure in EM sovereign deb markes and discuss he effecs ha a nonfla defaul-risk erm srucure has on he valuaion of projecs. In Secion III we describe he daa used o esimae he model. In Secion IV we presen he esimaion resuls. Secion V concludes. II. The Model Consider a perpeuiy ha promises o pay a coupon of $ c every period (a period represens one year for simpliciy). Le i be he expeced annual rae of reurn on his bond from 4
period zero up o period, γ he recovery value condiional on defaul, p he period- probabiliy of paymen condiional on previous full paymen, and P he probabiliy of paymen -periods from now. Given ha each coupon paymen has cross-defaul provisions wih every successive coupon, P measures he cumulaive probabiliy of no defaul from incepion up o period. Then, we can express he bond s curren value, Bo, as B 0 = = P c + P ( + i ) ( p ) γ (2) where he numeraor gives he expeced receips from he bond in period. For simpliciy, we assume ha he recovery value once here is a defaul on a sovereign bond is zero (i.e., γ = 0 ). This assumpion does no change he main resuls of his paper and avoids unnecessary complicaions in he esimaion. We also posulae ha 5 P p = αp β if = if 2 (3) so we can express B 0 P c = ( + i ) + = ( + 2 β αp c i ) (4) Noe ha his specificaion implies ha no necessarily p = p 2 = p 3 In his paper, we use daa from U.S. Dollar-denominaed EM bonds o esimae equaion (3) and illusrae how differen implied values of α and β change he value of invesmen projecs relaive o ha assessed by he sandard pracice. 5 See Merrick (999) and Yawiz (977) for alernaive specificaions. 5
II.. Implicaions on Valuaion in EM Consider he case of a firm locaed in an EM whose mos likely oucome is ha i will produce a dividend of $ d (consan) per period forever. The sandard valuaion pracice in EM is o discoun he mos likely oucome (cenral scenario) a a consan discoun rae r ô. ô sands for he duraion of he bond porfolio used o measure he discoun rae as in equaion (). In his case, he value of he firm in our example can be calculaed as d d V ˆ = = ( + r ) (5) = r τ τ We call Vˆ miscalculaed value, for reasons ha will become apparen below. Tradiional finance heory suggess, however, ha we should discoun he expeced free cash flows by heir respecive expeced reurns. Using equaion (3), he rue value, V, of he firm in our example would be pd = + ( ) P d V (6) + f = ( + f ) 2 where f is he expeced reurn of invesing in his firm, and he numeraor gives he expeced dividend each period. In equaion (6), f does no include he counry risk and we can easily assume ha i is consan, bu every erm in is numeraor is lower han he corresponding one in equaion (5) due o he downward risks borne by projecs in EM (see Esrada, 2000). If per-period defaul probabiliies were consan (i.e., could express V as P p = ), hen we V c d p + f p = (6b) where he subscrip c is added o sress ha a consan probabiliy of defaul is assumed. I is easy o show ha he r ha makes V ˆ =Vc, r c, is given by 6
r c + f p p = (7) Suppose now ha he defaul-risk erm srucure is as in equaion (3) 6. In his case he value of he firm, V v,, is 2β d α P V v = p + β (6c) + f + f P where he subscrip v indicaes ha defaul risk per period varies wih duraion. Again, for any value of á and â here is a value of r, r v, ha makes V ˆ =Vv. I is given by + f r v = (7b) 2β αp p + β + f P Tha is, when he defaul-risk erm srucure is non-fla, he mismach beween he duraion of he projec and he duraion of he bond porfolio used o measure he discoun rae as in equaion () inroduces a mispricing error, m, given by rc for τ = V r v v m = = V rτ forτ 2 rv (8) In Appendix I we show for = α = τ ha if > ( β <) β, hen r r r < r ). 7 v > c ( v c 6 Noe ha we are using he informaion given by counry risk in order o assess he probabiliy of receiving he mos likely dividend. The usual criicisms o his pracice have been oulined in Secion. Here we only wan o poin ou he problems originaed by implicily assuming a fla defaul-risk erm srucure. See Robichek and Myers (966) and Chen (967) for an old debae abou he effecs on discoun raes of alernaive assumpions abou he resoluion of uncerainy over ime. 7
III. The Daa We colleced effecive annual ask yields and duraions of non-guaraneed U.S. Dollardenominaed EM sovereign bonds (ypically called global bonds ). Daa are from Bloomberg for he las rading day of each monh since Sepember 995 unil December 200. Also included are comparable U.S. Treasury yields, which are aken as he risk free rae. The sample was narrowed o hose emerging counries which had daa for more han one bond a any poin hroughou he sample: Argenina, Brazil, Colombia, Ecuador, Mexico, Poland, Russia, Thailand, Turkey, and Venezuela. Since we focus on yields spaced oneyear appar saring one year from he beginning of each period, we furher narrowed he sample o counries whose shorer raded bond had a duraion greaer han 365 days. This resriced our sample o Argenina, Colombia, Mexico, Russia and Turkey. Appendix I liss he characerisics of all he included bonds. 8 Because he aim of his paper is o illusrae he effec of differen yield curve shapes on valuaion, we resriced our aenion o hree monhs ha seemed represenaive: April 997, January 2000 and Augus 200. Figure I repors he yield curves for he sample considered, which were consruced by linear inerpolaion of he available daa. Neverheless, plos of all he yield curves available are posed a hp://www.udesa.edu.ar/cruces/coc/yield_curves.pdf. We focused on effecive yields a inervals of one year up o where he available daa permied. From he no arbirage condiion beween -year and and +-year spo yield we 7 From he no arbirage condiion and our model of probabiliy of paymen [equaion (3)] we can deduce, for τ 2, ha r τ τ β α P τ β P + f =. α 8 The only bond ha is parially guaraneed is Russia-99, which had debenures as collaeral. If he bond were sripped, he non-guaraneed par of he bond should have a greaer duraion and a higher yield, so he April 997 Russian yield curve would have had an even greaer downward slope han ha repored in Figure I.C. 8
compued he forward one-year yield saring a ime for each counry (see Table II). For a bond ha carries no sysemaic risk, and assuming ha recovery condiional on defaul is zero [i.e. γ = 0 in (2)], he probabiliy of full paymen for period resuls from, ( r, ) = + i p, + (9) where r -, is he one-year risky forward rae saring in year - and i is he comparable risk free rae. When = boh raes are spo raes and p is he probabiliy of full paymen, while for >, boh raes are forward raes and p is he probabiliy of full paymen condiional on full paymen up o ime -. Table I repors, for each counry, p, he cumulaive probabiliy of full paymen ha would resul from assuming α = β =, o and including ime implici in bond prices, P. P, and he probabiliy of full paymen from ime zero up Table II shows ha while on some occasions P P, i is ofen he case ha hey differ subsanially. As an example of our poin, Figure I.A repors ha Argenina has a negaively sloping yield curve. This ranslaes in a cummulaive probabiliy of full paymen up o year 0 implici in bond prices of 0.3 (Table II.A), which is much higher han wha would resul from compounding for en years he firs period probabiliy of full paymen (0.6). The converse is rue for Colombia, which has a seep yield curve in Augus 200. IV. Esimaion Resuls and heir Implicaions on Valuaion in EM IV.. Esimaion Resuls Wih hese daa in hand, we esimaed he empirical analog of equaion (3), β P = α P + e = 2,..., T (0) separaely for each counry and for each ime period, by non-linear leas squares. The raionale behind separae esimaion is ha he yield curves in Figure I change dramaically across ime and counries so ha he efficiency gain resuling from join esimaion of he parameers would come a he expense of assuming a model wih consan parameers ha 9
is clearly inadequae. This shorcoming could be avoided by he use of condiioning informaion so ha alpha and bea depend on lagged insrumens. While ha is an ineresing approach ha we propose o explore in fuure research, i would lead us ino yield curve modelling, an issue beyond he scope of his paper. Table III repors he resuls of esimaing (0), and shows ha i provides a good fi o he sequence of defaul probabiliies implici in bond prices. All parameer signs agree wih he inuiion ha when sovereign spreads are upward sloping β s are greaer han one, and conversely when hey are decreasing. I is noeworhy ha all parameer esimaes are saisically significanly differen from one --he mainained hypohesis in he sandard pracice refleced in equaion (5). Since β is he parameer ha affecs he cummulaive probabiliy of full paymen as ime passes, i is he one ha changes he mos as he economic environmen changes: from a minimum of abou 0.5 as counries approach defaul (Argenina in Augus 200 and Russia in April 997) o abou 5 when he yield curve seeps up. IV.2. Implicaions for Valuaion in Emerging Markes Table IV repors he main findings of his paper. For a range of parameer values ha are consisen wih he empirical esimaes of alpha, bea, P, and for values of i ha are consisen wih real reurns on long-erm bonds, we show r v from (7b), he mispricing raio for τ = as in (8), V / V ˆ, and he duraion of a consan free cash flow projec. The op and boom panels only differ by he value of he risk-free rae (i). For 95 percen probabiliy of full paymen during he firs year, he shor-erm risky rae is 9 percen when i is 4 percen and i jumps o 2 when i equals 6. When β is less han one, he shor-erm sovereign spread is much higher han is long-erm counerpar and he rue value of a long-erm projec can be up o 54 percen higher han he value esimaed using a one-year discoun rae and assuming a fla yield curve. On he conrary, when β is larger han one, he real value can be only one-hird of he miscalculaed value. For a given β, higher values of α raise he rue value relaive o is esimaed one since higher α s raise expeced dividends. 0
Naurally, when he yield curve seeps up, he consan discoun rae ha would make he value of he projec from (5) equal o ha of (6) is much higher han he shor erm rae. V. Conclusions and Furher Research Several problems have resriced praciioners from using he CAPM in order o esimae discoun raes in Emerging Markes, and have led hem o accoun for he addiional risks of EM by adding he counry risk o he discoun rae. In his paper we claim ha such pracice does no make an efficien use of he informaion given by sovereign deb markes. In paricular, i does no accoun for he fac ha he defaul-risk erm srucure is non-fla, being upward sloping in good imes, and downward sloping when he shor-erm defaul risk is high. The mismach beween he duraion of he projec and he duraion of he mos widely used measures of counry risk, J.P. Morgan s EMBI, leads o an overvaluaion of long-erm projecs in good imes and o an undervaluaion of hem when defaul risk is high (he conrary is rue wih respec o shor erm projecs.) In his paper, using daa from five EM, we esimae a simple model of he erm srucure of defaul-risk and derive is implicaions on valuaion. We find ha by implicily assuming ha he erm srucure of defaul risk is fla, mispricing errors in he range of plus or minus 50 percen can be made for reasonable parameer values. This mispricing can be avoided by using daa ha are readily available from bond markes. To enrich he analysis, fuure research should be direced o he inclusion of recovery values and he use of condiioning informaion in a model of defaul-risk erm srucure.
Figure I. Yields on U.S. Dollar-Denominaed Sovereign Bonds Yield (% poins) 30 25 20 5 0 5 0 Figure I.A. Augus 200 Turkey 2 3 4 5 6 7 8 9 Duraion Argenina USA Russia Colombia Mexico Yield (% poins) 4 2 0 8 6 4 Figure I.B. January 2000 Argenina Colombia USA Mexico 2 3 4 5 6 7 8 9 Duraion Yield (% poins) 2 0 8 6 4 Figure I.C. April 997 Russia Argenina Colombia USA 2 3 4 5 6 7 8 Duraion
Table I: Average Duraion of Counry Componens of JP Morgan's EMBI Global Index Counry Duraion Algeria 3.05 Argenina 4.3 Brazil 4.94 Bulgaria 4.59 Chile 6.20 China 4.56 Colombia 5.40 Coe d'ivore 6.20 Croaia 3.80 Ecuador 5.90 Hungary 2.33 Lebanon 2.30 Malaysia 4.93 Mexico 4.93 Morocco 3.24 Nigeria.92 Panama 6.56 Peru 7.02 Philippines 7.4 Poland 6.0 Russia 5.78 Souh Africa 6.53 Souh Korea 3.79 Thailand 4.98 Turkey 5.95 Ukraine 2.59 Venezuela 4.5 Mean 4.77 Sandard Deviaion.52 Source: J.P. Morgan (2000)
Table II.A: Sovereign Raes and Implied Defaul Probabiliies - Augus 200 USA Argenina Colombia Mexico Forward Forward p P P Forward p P P Forward p P P 3.33 24.00 0.83 0.83 0.83 6.3 0.97 0.97 0.97 5.06 0.98 0.98 0.98 2 4.0 28.56 0.8 0.69 0.67 8.03 0.96 0.95 0.94 6.5 0.98 0.97 0.96 3 4.52 2.65 0.86 0.58 0.58 9.25 0.96 0.92 0.90 7.96 0.97 0.95 0.93 4 5.40 2.64 0.87 0.48 0.50 0.34 0.96 0.90 0.86 9.00 0.97 0.94 0.90 5 5.52 7.5 0.90 0.40 0.45.0 0.95 0.88 0.8 0.36 0.96 0.92 0.86 6 5.29 3.45.00 0.34 0.45 7.08 0.90 0.85 0.73 0.37 0.95 0.9 0.82 7 6.22 6.68 0.9 0.28 0.4 6.97 0.9 0.83 0.67 0.86 0.96 0.89 0.79 8 5.64 7.97 0.90 0.23 0.37 8.90 0.89 0.8 0.59.59 0.95 0.88 0.74 9 6.34 7.76 0.90 0.9 0.33.... 9.64 0.97 0.86 0.72 0 6.65 7.54 0.9 0.6 0.30........ Russia Forward p P Turkey P Forward p P 6.99 0.97 0.97 0.97 0.04 0.94 0.94 0.94 2.57 0.93 0.93 0.90 3.7 0.92 0.88 0.86 3 2.59 0.93 0.90 0.84 4.68 0.9 0.83 0.78 4 3.3 0.93 0.87 0.78 6. 0.9 0.78 0.7 5 3.59 0.93 0.84 0.72 6.8 0.90 0.73 0.64 6 4.58 0.92 0.8 0.66 5.74 0.9 0.69 0.58 7 5.46 0.92 0.78 0.6 5.0 0.92 0.64 0.54 8........ 9........ 0........ P Noe: Based on closing prices from end of Augus 200of dollar-denominaed sovereign bonds, aken from Bloomberg. The raes for he firs year are spo raes while for subsequen years hey are forward one year raes implied by he linearly inerpolaed yield curves of each counry assuming ha recovery value condiional on defaul is zero and ha EM bonds carry no sysemaic risk. Given cross-defaul provisions, he cummulaive probabiliy ha paymens in year will be honored in full and on ime is he produc of he probabiliy ha all paymens be made in like manner up o and including year. For Argenina in =6 in Table II.A is forward rae was lower han he risk free rae --we assumed ha his was due o measuremen error and declared p6=.
Table II.B: Sovereign Raes and Implied Defaul Probabiliies - January 2000 USA Argenina Colombia Mexico Forward Forward p P P Forward p P P Forward p P P 6.44 0.04 0.97 0.97 0.97 7.30 0.99 0.99 0.99 7.38 0.99 0.99 0.99 2 7.02.40 0.96 0.94 0.93 0.97 0.96 0.98 0.96 8.95 0.98 0.98 0.97 3 6.86 2.75 0.95 0.9 0.88 3.4 0.94 0.98 0.90 0.46 0.97 0.97 0.94 4 6.93 5.56 0.93 0.88 0.82 3.0 0.95 0.97 0.85.95 0.96 0.97 0.90 5 7.40 6.07 0.93 0.85 0.75 4.75 0.94 0.96 0.80.30 0.97 0.96 0.87 6 6.40 4.29 0.93 0.82 0.70 3.33 0.94 0.95 0.75.87 0.95 0.95 0.83 7 7.0 2.48 0.95 0.79 0.67.....27 0.96 0.94 0.79 8 6.58 6.70 0.999 0.77 0.67.....59 0.96 0.93 0.76 9 7.48........ 8.9 0.99 0.92 0.75
Table II.C: Sovereign Raes and Implied Defaul Probabiliies - April 997 USA Argenina Colombia Russia Forward Forward p P P Forward p P P Forward p P P 5.99 7.92 0.98 0.98 0.98 6.43 0.996 0.996 0.996.9 0.95 0.95 0.95 2 6.8 8.46 0.99 0.97 0.97 8.52 0.98 0.99 0.98 0.20 0.97 0.9 0.92 3 6.76 8.48 0.98 0.95 0.95 8.39 0.99 0.99 0.97 9.2 0.98 0.87 0.90 4 7.0 0.28 0.97 0.93 0.92 8.84 0.98 0.98 0.95.... 5 6.84.28 0.96 0.9 0.89 9.24 0.98 0.98 0.93.... 6 7.0 3.05 0.95 0.90 0.84 9. 0.98 0.98 0.9.... 7 7.5 4.7 0.94 0.88 0.79........ 8 7.78 5.28 0.94 0.87 0.74........
Table III: Esimaes of Alpa and Bea for Differen Samples β P = α P + e = 2,..., T Augus 200 T α β R 2 Argenina 0 0.78 0.53 0.972 (0.026) (0.034) Colombia 8.2 2.7 0.960 (0.037) (0.26) Mexico 9.05 2.53 0.995 (0.007) (0.07) Russia 7.05 2.2 0.990 (0.006) (0.04) Turkey 7.03.5 0.9900 (0.006) (0.02) January 2000 T α β R 2 Argenina 8.047.87 0.974 (0.023) (0.4) Colombia 6.08 7.55 0.999 (0.004) (0.3) Mexico 9.06 4.55 0.994 (0.007) (0.4) April 997 T α β R 2 Argenina 8.08 2.46 0.958 (0.02) (0.23) Colombia 6.09 4.52 0.995 (0.003) (0.8) Russia 3 0.97 0.47... Minimum 0.78 0.47 Maximum.2 7.55 Esimaed by non-linear leas squares. Approximae Sd. Errors in parenheses. Since only wo observaions of P are available for Russia in April 997, we logged he model and solved for he wo unknowns. No saisics are involved in ha paricular case.
Table IV: Raio of Correcly o Miscalculaed Value for Differen Parameer Specificaions Assumpions: i = 4% P = 0.95 r = 9% α Row β Conen 0.5 0.8.0.5 2.5 4.0 7.0 0.8 r v V =V ha 8% 0% 2% 5% 22% 3% 50% V /V ha.5 0.92 0.82 0.63 0.44 0.30 0.9 Dur. Proj. 3. 0.7 9.6 7.7 5.6 4.2 3.0.0 r v V =V ha 7% 8% 9% 2% 8% 27% 44% V /V ha.4.3.00 0.77 0.53 0.35 0.22 Dur. Proj. 5.9 3.0.6 9. 6.6 4.7 3.3. r v V =V ha 6% 8% 9% % 7% 25% 4% V /V ha.54.24.09 0.84 0.57 0.38 0.23 Dur. Proj. 7.3 4. 2.5 9.9 7.0 5.0 3.4 Assumpions: i = 6% P = 0.95 r = 2% α Row β Conen 0.5 0.8.0.5 2.5 4.0 7.0 0.8 r v V =V ha % 3% 4% 7% 24% 34% 52% V /V ha.08 0.9 0.82 0.66 0.48 0.34 0.22 Dur. Proj. 0.3 8.8 8. 6.7 5. 3.9 2.9.0 r v V =V ha 9% 0% 2% 4% 20% 29% 46% V /V ha.32..00 0.80 0.57 0.40 0.25 Dur. Proj. 2.4 0.6 9.6 7.9 5.9 4.4 3.2. r v V =V ha 8% 0% % 3% 9% 27% 44% V /V ha.44.2.09 0.87 0.62 0.43 0.27 Dur. Proj. 3.5.4 0.4 8.5 6.3 4.7 3.3
Appendix I Le = α = τ for simpliciy. We wan o show ha if > ( β <) Assume, by conradicion, ha β > bu r. This would imply ha v r c β, hen r > r r < r ). v c ( v c r v r c p + f + = 2 P + β f p + f + = 2 P + f For every, he erm beween parenhesis on he lef hand side is bigger han he β corresponding erm on he righ hand side if and only if P P, which is a conradicion.
Appendix II: Characerisics of he Bonds Used Argenina Colombia Coupon Mauriy Code ISIN Coupon Mauriy Code ISIN 8.25% 5-Oc-97 (Arg-97) XS004007964 7.25% -May-98 (Col-98) USP2874AE62 0.95% -Nov-99 (Arg-99) US0404AJ99 8% 4-Jun-0 (Col-0) US9532NAA46 9.25% 23-Feb-0 (Arg-0) US0404AK62 7.5% -Mar-02 (Col-02) US9532NAE67 8.375% 20-Dec-03 (Arg-03) US0404AH34 7.25% 5-Feb-03 (Col-03) US95325AH80 % 4-Dec-05 (Arg-05) US0404BA7 0.875% 9-Mar-04 (Col-04) US95325AP07 % 9-Oc-06 (Arg-06) US0404AN02 7.625% 5-Feb-07 (Col-07) US95325AK0.75% 7-Apr-09 (Arg-09) US0404BE93 8.625% -Apr-08 (Col-08) US95325AM75.375% 5-Mar-0 (Arg-0) US0404FC9 9.75% 23-Apr-09 (Col-09) US95325AR62.75% 5-Jun-5 (Arg-5) US0404GA27.75% 25-Feb-20 (Col-20) US95325AU9.375% 30-Jan-7 (Arg-7) US0404AR6 2.25% 25-Feb-9 (Arg-9) US0404BC38 2% -Feb-20 (Arg-20) US0404FB9 Coupon Mauriy Code ISIN 9.75% 9-Sep-27 (Arg-27) US0404AV28 9.75% 6-Feb-0 (Mex-0) US593048AV35 0.25% 2-Jul-30 (Arg-30) US0404GB00 8.5% 5-Sep-02 (Mex-02) US593048AQ40 2.25% 9-Jun-8 (Arg-8) US0404GG96 9.75% 6-Apr-05 (Mex-05) US9086QAB4 2% 9-Jun-3 (Arg-3) US0404GH79 9.875% 5-Jan-07 (Mex-07) US593048BB6 0% 5-Mar-02 (LETE 90) ARARGE03334 8.625% 2-Mar-08 (Mex-08) US593048BF75 0.375% 7-Feb-09 (Mex-09) US593048BG58 Turkey 9.875% -Feb-0 (Mex-0) US9086QAD07 Coupon Mauriy Code ISIN.375% 5-Sep-6 (Mex-6) US593048BA88 8.75% 5-Oc-98 (Tur-98) XS006054642.5% 5-May-26 (Mex-26) US593048AX90 9.00% 5-Jun-99 (Tur-99) US90023AC4 0% 23-May-02 (Tur-02) XS0076567774 8.875% 2-May-03 (Tur-03) XS008699630 Coupon Mauriy Code ISIN.875% 5-Nov-04 (Tur-04) US90023AK66 3% 4-May-99 (Rus-99) RU000446067 9.875% 23-Feb-05 (Tur-05) XS008474954 9.25% 27-Nov-0 (Rus-0) XS007496623 0% 9-Sep-07 (Tur-07) XS008040389.75% 0-Jun-03 (Rus-03) USX74344CZ79 2.375% 5-Jun-09 (Tur-09) US90023AJ93 8.75% 24-Jul-05 (Rus-05) XS0089372063.75% 5-Jun-0 (Tur-0) US90047AB5 8.25% 3-Mar-0 (Rus-0) XS04295560.875% 5-Jan-30 (Tur-30) US90023AL40 % 24-Jul-8 (Rus-8) XS0089375249 5% 3-Mar-30 (Rus-30) XS04288789 * ISIN is he Inernaional Securiies Idenificaion Number. Mexico Russia
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