PRÉSENTATION DU MARCHÉ OBLIGATAIRE
description
Transcript of PRÉSENTATION DU MARCHÉ OBLIGATAIRE
-
PRSENTATION DU MARCH OBLIGATAIRE
-
Exemple de description dune obligation
-
Les caractristiques dune mission obligataireLa valeur nominale : cest la valeur faciale dune obligation -
Encours de lmission : nombre dobligations mises multipli par la valeur nominale -
Pour notre OAT 5% 25/04/2012nominal de 1 euroEncours 16.809 Mds deuro
-
Les caractristiques dune mission obligataireLe prix dmission : il peut tre diffrent du pairGnralement, lobligation est price de sorte que son prix dmission soit lgrement en dessous du pair Le prix de remboursement : cest la valeur laquelle sera rembours le titre obligataire Gnralement au pair, Le prix de march : cest la valeur sur la base de laquelle les acheteurs et les vendeurs schangent librement le titre sur le march secondaire,
-
Les caractristiques dune mission obligataireLa date de jouissance ou date de valeur: cest la date partir de laquelle les intrts commencent courir
La date de maturit, cest la date laquelle : lobligation est retire du march par lmetteur le capital emprunt est compltement rembours
-
Les caractristiques dune mission obligataireLe coupon
frquence - en Europe en gnral annuel
taux fixe taux variable
diffrents indices possibles : TEC, inflation, euribor nouvelles variabilit en fonction du rating - ex: emprunt France Telecom
-
Les emprunts de rfrence dits benchmarksLes conditions ncessaires : une bonne qualit de rating une politique dmission et une communication financire transparente une taille minimum et une bonne liquidit une bonne diffusion des missions sur toute la courbe des taux
Lexemple du Trsor franais : BTF, BTAN, OAT Les SVT, le march terme
Le cas des swaps
-
La dette de lEtat Les titresLes obligations assimilables du Trsor (OAT) sont le support de l'endettement long terme de l'tat. La maturit de ces titres est comprise entre sept et trente ans. La plupart des OAT est taux fixe et remboursable in fine. Mais le Trsor met aussi des obligations taux variable (OAT TEC 10 indexes sur le taux de l'chance constante 10 ans) et des obligations indexes sur l'inflation (OATi, OATei).
Les bons du Trsor taux fixe et intrt annuel (BTAN) reprsentent l'endettement moyen terme de l'tat. Leur maturit l'mission est de deux ou cinq ans.
Les bons du Trsor taux fixe et intrts prcompts (BTF) sont l'instrument de gestion de trsorerie de l'tat. Ils servent couvrir les fluctuations infra-annuelles de le trsorerie de l'Etat, qui dcoulent pour l'essentiel du dcalage entre le rythme d'encaissement celui des paiements, et de l'chancier d'amortissement de la dette. La maturit des BTF l'mission est de moins d'un an.
-
Courbe de tauxUne courbe des taux permet de reprsenter la fonction suivie par les taux d'intrts pour diffrentes chances.
Pour construire cette courbe, on part du principe que les taux ont la mme priodicit de rglement d'intrts (dtachement de coupons) et utilisent la mme convention de calcul.
Ces rendements sont matrialiss par l'ordonne de la courbe, les abscisses reprsentant la dure de l'investissement.
Les coupons des obligations ne permettent pas d'avoir une belle relation maturit/taux. On va crer des instruments zro coupons
-
Courbe des taux au 01/08/2007
-
Courbe des taux et cycle conomiqueLa courbe des taux sinverse avant chacune des cinq dernires rcessions aux US (spread 5 ans/3 mois)
-
Les missions corporate
-
Les ratings
-
PRICING DES OBLIGATIONS
-
Taux de rendement actuarielUne obligation taux fixe dlivre des flux des dates futures.
Le prix est obtenu par actualisation de ses flux futurs, au taux actuariel
Le taux de rendement actuariel maturit de lobligation de prix P dlivrant les flux fi aux dates i = 1,..., N est le taux t qui vrifie lquation
-
Taux de rendement actuarielLe taux de rendement actuariel contient tous les taux ZCIl permet de calculer lui seul le prix dune obligation
Ex. Soit une obligation de maturit 5 ans, coupon 2.79%, taux de rendement actuariel 2.90%Calculer son prix
-
Taux de rendement actuarielExemple: Obligation 5 ans, mise en 2006 chance 2011, de coupon 2.79%, mise 99.50% et rembourse au pair.
-
Calcul du taux actuarielConnaissant le prix dune obligation, on en dduit son taux t.
Directement, sur une calculatrice (HP12C), Excel, Bloomberg
Ex :P = 98.50, le coupon est de 2.79%, N = 5 ans, et le prix de remboursement 100.
Remarque : en choisissant t = 2.79%, P = 100!
-
Calcul du taux actuarielCalculons P avec t = 2.70% et t = 3.20%P2.70% =3.20% > t > 2.70%P3.20% = < 98.50 <
RemarqueLa fonction qui lie le prix au taux de rendement est une fonction dcroissante
Quand le prix le taux
Quand le prix le taux
-
Pricing avec le taux actuarielPar ttonnement nous arrivons au rsultat t = 3.12%
Le taux actuariel permet de trouver le prix dune obligation classiqueLe prix dune obligation classique est associe un seul taux actuariel.Si on a une donne, on en dduit lautre.
-
Taux de rendement actuarielLe prix de 98,5 est la somme des valeurs prsentes des flux futurs au taux (unique) de 3.12%. 3.12%
PV(coupon1) : 2.79/1.0312 = 2.711 an 2.79PV(coupon2) : 2.79/1.03122 = 2.622 ans 2.79PV(coupon3) : 2.79/1.03123 = 2.553 ans 2.79PV(coupon4) : 2.79/1.03124 = 2.474 ans 2.79PV(coupon5) : 2.79/1.03125 = 2.395 ans 2.79PV(principal) : 100/1.03125 = 85.765 ans 100.0098.50
-
Taux de rendement actuarielSi les coupons ont t rinvestis au taux de 3.12%, alors:
1re anne 2me anne 3me anne 4me anne 5me anne 3.15 + 3.06 + 2.97 + 2.88 + 102.79 = 114.85Lopration a effectivement permis de gnrer un taux de rendement t sur la priode tel que
Et si le taux de rinvestissement diffre ?
-
Pricing par les taux actuarielsTout se passe comme si, tous les taux, actuariels et zro coupon taient gaux 3.12%Investir dans une obligation au taux actuariel t Cest considrer que la courbe des taux est plate Que tous les taux valent tEt vaudront t jusqu la maturit de lobligation
-
Pricing par les taux actuariels
-
Pricing par les taux actuariels
-
Prix dune obligationLe gain daccumulation reprsente la convergence du prix de lobligation vers le pair dans lhypothse dune stabilit des taux dintrt
Exemple:
Obligation 2 ans coupon 2% rendement actuariel 10%Prix en to: 102/(1,10) + 2/(1,10) = 86,11Prix en t+1 102/(1,10) = 92,72
-
Comment passe le temps ?Que se passe-t-il si le prochain coupon ne se dtache pas dans un an plein et si la maturit nest plus un nombre entier danne?
Il faut pouvoir saccorder sur la manire de calculer le temps qui passe
Chaque march a ses conventions
-
Effet du temps qui passeAveca = fraction danne entre la date de jouissance et le prochain paiement de coupon= nombre de jours jusquau prochain coupon/nombre de jours entre le dernier et le prochain couponn = nombre dannes pleines jusqu la maturit
-
Calcul actuariel exactAvec Ci = coupon pay la date ir = taux de rendement observ dans le marcha = fraction de priode entre date de jouissance et prochain couponn = nombre dannes pleines jusqu maturit
-
Coupon CouruEntre deux dates de paiement de coupon le prix de lobligation augmente
Le jour de la tombe du coupon, lobligation perd la valeur du coupon
-
Coupon couruLeffet du coupon qui court rend difficile le suivi du march car il est sans lien avec lvolution du march
En retirant le coupon couru du prix brut on obtient le prix pied de coupon - cest ce prix qui est cot sur les marchs
coupon couru = acc * coupon plein
avec acc = fraction de priode depuis le paiement du dernier coupon
Prix brut = prix pied de coupon + coupon couru dirty clean cot
-
Le taux actuariel et ses limitesLe taux actuariel permet de comparer diffrentes obligations en supposant que la courbe de taux est plate
Il suppose en effet que les coupons reus par linvestisseur sont rinvestis au mme taux que le taux actuariel de lobligation (appel taux de rendement ou taux interne)
Le taux actuariel valorise les mme flux dargent diffremment quand ils sont issus dobligation diffrentes
-
COUVERTURE DES OBLIGATIONS CLASSIQUESCouverture en Duration
-
Duration de MacaulayLa Duration de Macaulay reprsente le nombre moyen dannes, pondres par la valeur prsente des Cash Flows quelles gnrent, pour rentabiliser le prix initial P dune obligation
D = Duration fi = cash flow de la priode i t = taux actuarielP = prix initialN = maturit (en annes) i = priode laquelle le cash flow est pay
-
Proprits de la DurationLa Duration dune obligation zro-coupon = sa maturit
A maturit et taux de rendement fixs, la Duration dune obligation est une fonction dcroissante du coupon
A taux de coupon et taux de rendement fixs, la Duration dune obligation est une fonction croissante de sa maturit
La hausse du prix dune obligation est suprieure la baisse du prix de cette obligation, en cas de variation quivalente de taux
La Duration dune obligation est une fonction dcroissante du taux de rendement
-
Duration dite Macaulay
-
Duration dite Macaulay
-
Proprit de la durationEssayons de raisonner laide du diagramme du point dquilibre:
A votre avis que se passe-t-il si le coupon de lobligation augmente.. La duration augmente ou baisse?
Et si la maturit de lobligation augmente ?
-
Proprits de la DurationValeur du portefeuille anne aprs anne selon trois scnarii dvolution des taux
-
Proprits de la DurationValeur du portefeuille anne aprs anne selon 3 scnari dvolution des taux
-
Sensibilit, duration modifie ou modified durationCest la sensibilit de la valeur dun titre au taux dintrt :
Soit:
-
Utilisation de la sensibilit ou modified durationPour une petite variation de r on pourra calculer la variation de VCette mesure S de la sensibilit est relative
-
Variation, PVBP, DV01, $ DurationLa price value of a basis point est une autre manire dexprimer la sensibilit
Elle donne lcart de prix pour une obligation donne d une variation de son taux de rendement de 1 point de base
PVPB = S * V * 0.01%
Cette mesure de la sensibilit est absolue
-
Proprits de la sensibilit et de la duration en fonction des tauxSensibilit et duration varient en sens inverse avec les taux de rendement: pour une variation de taux donn, le prix dune obligation est dautant plus volatile que le taux de dpart est petit
Pour les titres in fine sensibilit et duration diminuent quand le coupon augmente
-
Utilisation et limites de la sensibilit et de la durationLa sensibilit dun portefeuille est gal la moyenne pondre de la sensibilit des titres qui le composent Hypothse = shift parallle de la courbe des taux ----> tous les dr sont gaux
La duration dun portefeuille est la moyenne pondre des durations des composantes
Hypothse = tous ces taux sont gaux ---> courbe plate
-
Utilisation de la sensibilit
-
Utilisation de la sensibilitLe 12/03/2003, vous avez en portefeuille 10 mio de lOAT 7.25 4/06Votre analyste crdit vous convainc que le titres France Telecoms sont sous-cts. Vous dcidez de vendre vos OAT pour acheter des titres France tel.Voici les informations dont vous disposez.
Combien de titres France Tel 2006 devez vous acheter pour garder la mme exposition au risque de taux?
Feuil1
PriodeTaux proportionnel annuelTaux quivalent annuel
Semestre3% * 2 = 6%[(1.03)2 - 1] * 100 = 6.09%
Trimestre1.5% * 4 = 6%[(1.015)4 - 1] * 100 = 6.14%
Mois0.5% * 12 = 6%[(1.005)12 - 1] * 100 = 6.17%
Clean PriceDirty PriceSensibilitPVBP
OAT 7.25 25/04/2010113.87120.2462.6973.243
FRTEL 6.25 11/2010105.50108.31253.083.336
Future102.003.80
Feuil2
Feuil3
-
Variation de la sensibilit en fonction de la variation des taux
-
Limites de la sensibilitLa sensibilit ou modified duration nous permet de calculer et prvoir la variation du prix dune obligation seulement pour une petite variation de taux donne car:
La relation entre dV et dr nest pas linaire, elle est convexeLa sensibilit change quand les taux changent
Lhypothse implicite qui sous-tend certaines des utilisations de la sensibilit posent problme. (Mouvement parallle des taux ..).
-
COUVERTURE DES OBLIGATIONS CLASSIQUESCouverture en convexit
-
Notion de convexitPour une meilleure estimation de la variation du prix dune obligation on a besoin de mieux apprhender la drive seconde de V
La convexit est le montant de curvature de la relation prix/taux.. la drive seconde
-
Calcul de la convexitLa convexit est la drive seconde de V
Donc
Terme correctif supplmentaire faisant intervenir C -> meilleure apprciation de leffet des variations de taux
-
Calcul de la convexitOn drive de ce qui prcde :
On peut donc calculer la convexit de chaque titre
-
Importance de la convexit dans la comparaison des obligations
-
Utilisation de la convexitLa convexit est positive pour les dtenteurs de bonds:
quand les taux baissent, plus lobligation est convexe plus la hausse des prix de lobligation ira de plus en plus vite
quand les taux montent, plus lobligation a une forte convexit plus lentement baissera son prix
-
Utilisation de la convexitExemple :
Toute chose gale par ailleurs, quelle obligation allez vous acheter si vous pensez que les marchs vont tre trs volatils?
Feuil1
PriodeTaux proportionnel annuelTaux quivalent annuel
Semestre3% * 2 = 6%[(1.03)2 - 1] * 100 = 6.09%
Trimestre1.5% * 4 = 6%[(1.015)4 - 1] * 100 = 6.14%
Mois0.5% * 12 = 6%[(1.005)12 - 1] * 100 = 6.17%
Clean PriceDirty PriceSensibilitPVBPConvexit
OAT 7.25 25/04/2010113.87120.2462.6973.2430.1057
FRTEL 6.25 11/2010105.50108.31253.083.3380.1310
Future102.003.80
Feuil2
Feuil3
-
Utilisation de la convexitSi lon considre un titre trs convexe, il sera cot au dessus de son prix thorique :
les taux ayant autant de chance de varier la hausse qu la baisse,
le prix du march sera la moyenne des prix pour la variation [-dr, +dr] attendue.
-
Cotation des titres convexes
-
Cotation des titres convexes
-
Utilisation de la convexitSi on anticipe un grand dcalage de la courbe de taux alors la convexit possde de la valeur.
Une personne nanticipant aucun changement de taux ne payera pas de surplus pour la convexit du titre considr.
-
Comparatif des convexits d'un zro-coupon et d'une obligation classique
-
Convexit des zro-couponsUn arbitrage sensibilit constante dans lequel un investisseur remplace lOAT de maturit 30 ans par du STRIP 30 ANS gnre un gain en capital en cas de forte volatilit des taux.
La combinaison de STRIP 30 ans et de cash est plus convexe, sensibilit quivalente que le 30 ans couponn.
-
La convexit Proprits de la Convexit
la convexit dune obligation est une fonction dcroissante du taux de coupon.
la convexit dune obligation est une fonction croissante de sa maturit.
la convexit dune obligation est une fonction dcroissante du taux de rendement.
-
Arbitrages de convexit1an plus tard
-
Arbitrages de convexit
-
ConvexitUtilisation de la convexit pour couvrir le risque de taux:
Il faut construire un portefeuille o la duration et la convexit sont nulles. Or, il est pratiquement impossible de trouver un seul instrument pour couvrir ces deux paramtres.
Nous avons donc besoin, pour couvrir notre portefeuille P de deux actifs de couverture, C1 et C2 en quantit Q1 et Q2
-
GESTION DE LA COURBE DES TAUX
-
La dformation de la courbeLa courbe des taux subit trois mouvements essentiels de dformation :
- La translation (75-80%) La rotation (aplatissement ou pentification 20-25%) La courbure (0-5%) Les autres dformations sont en gnral ngligeables
Ces rsultats peuvent tre reproduits laide doutils danalyse des donnes (Analyse en Composantes Principales)
Pour se prmunir contre les dformations de la courbe des taux comme la rotation (aplatissement ou repentification) ou la courbure (concave ou convexe), on peut utiliser la mthode du cash flow matching.
Une couverture ajuste en permanence en duration et convexit permet de se prmunir contre les deux premiers facteurs, ce qui est gnralement satisfaisant. Une couverture immunisant contre le risque de variation de courbure peut tre calibre partir dune modlisation de la courbe.
-
Corrlations France 1995 1998La corrlation diminue avec lcart de maturit.Le segment court terme [1 mois -6 mois] et le segment long terme [5 ans -10 ans] sont trs corrls.
-
Volatilit des tauxLa volatilit est gnralement une fonction dcroissante de la maturit des taux
-
Les paris sur la courbe des tauxLes paris sur la courbe des taux sont de 4 natures :
Translation
Absence de mouvements
Courbure
Rotation
-
Mouvement parallle
-
Mouvement de pivotLa courbe des taux nest pas fige.
-
Mouvement de torsion
-
La gestion de courbeTranslation- les stratgies simples- les stratgies de roll-over
Labsence de mouvement - Les stratgies riding the yield curve.
La repentification, laplatissement ou la courbure Les butterfliesLes stratgies en duration nulle
-
Rotation ou TwistAutour dun axe
-
Rotation
-
Courbure : Butterfly Shifts
-
Butterfly shift
-
Pricing & Gestion obligataireExercice
Anticipation dune hausse du 5 ans et une baisse du 2 ans et 10 ans.
Soit 3 obligations de coupon 5% et nominal de 1.
Construction dun butterfly de sensibilit nulle et de dcaissement nul.Le 2 ans et le 10 ans passent de 5% 4% et le 5 ans de 5% 6%. Quel est le gain de la stratgie ?
III) Gestion obligataire : Stratgies de gestion
-
Pricing & Gestion obligataireSystme deux quations :
Soit et
Donc, il faut vendre 1000 obligations de 5 ans et acheter 422 de 10 ans et 578 de 2 ans.
Gain :
-
Pricing & Gestion obligataireIl existe 2 grandes catgories de butterfly dfinies par la seconde contrainte :
Premire contrainte :
Sensibilit bullet = Sensibilit barbell
Seconde contrainte :
Cash neutre.Risque gale entre les deux ailes du barbell .
-
Objectifs et contraintesNous grons un portefeuille de 100mPlacement au taux sans risque 2%La Duration du portefeuille peut varier de 2 8 ansNous pouvons acheter des obligations zro-coupon sur les maturits 2, 5 et 10 ansPas de position short possible
-
4 scnariosVoici 4 paris possibles Timing : trs court terme (une semaine)
-
3 obligationsVoici 3 obligations zro coupon, et leur prix en cas de ralisation des scnarios
-
4 scnarios & 3 obligationsLe profil de gain/perte selon le scnario est la suivante (pour 100m investis)
-
Choix du portefeuille optimalSi nous parions sur une hausse des taux, quelle est la meilleure stratgie?La Duration minimale est de 2 donc on ne peut pas investir la totalit au taux sans risque (Duration = 0)Si nous avions pari sur une baisse parallle des taux, cest la zro-coupon 10 ans qui aurait le mieux performSi nous parions sur un positive butterfly, quelle est la meilleure tratgie?Lachat de lobligation zro coupon 5 ansSi nous parions sur une repentification, quelle est la meilleure stratgie? lachat dun zro-coupon 2 ans est la meilleure stratgieUn flattening aurait bnfici lobligation de 10 ans
-
Roll over : scnario dans 1 anObjectif : Je dois placer 10m sur 5 ans au meilleur tauxScnario = hausse des taux de 2% dans 1 anOn peut mettre en place une stratgie de Roll-overPlacement 3% pendant 1 anAchat dans un an dune obligation de 4 ans 6%
On a 3% la 1re anneet 6% les 4 suivantesA comparer avec 4.5% pendant 5 ans
T = 0TranslationT=11 an3%5%4 ans4%6%5 ans4.5%6.5%
-
Stratgie de Roll-overAchat dune obligations zro coupon de 5 ansT=5 10m(1+4.5%)5 12.461.819
Achat de 2 obligations successivesT=1 10.300.000, rinvestissement 6% pour 4 ansT=5 10.300.000(1+6%)4 13.003.513
Pour un investissement de dure j, le Roll-over consiste parier sur une hausse de taux la date i
-
Absence de mouvementObjectif : Investissement sur 1 an de 10m au meilleur tauxScnario : Courbe des taux ascendante et inchange
Nous pouvons acheter un titre de maturit plus longue, et le revendre dans 1 an. ride the yield curve
On profite du rendement plus lev des taux longs
-
Absence de mouvementConsidrons la courbe zro-coupon suivante et 3 obligations zro coupon. Calculons la valeur de ces obligations la date T=0, et un an plus tard (en T=1), la courbe des taux restant inchange
Quand on nanticipe aucun mouvement, lorsque la courbe est ascendante, on achte lobligation la plus longue et on la revend lhorizon initial de notre placement
T=0Prix T=0Prix T=1Rendement1 ans3%97.081003%2 ans4%92.4697.085%3 ans5%86.3892.467.04%
-
Absence de mouvementAttention il faut prvoir le Downside riskA chaque scnario, le gestionnaire doit prvoir lventualit de sa non-ralisation
Ex. Dans un an, le taux du an et/ou du 2 ans varie(nt).Calculons notre point mort
Point mort = Point auquel nos 3 stratgies sont quivalentes.= Elles rapportent toutes 3%
-
Absence de mouvementCherchons t1/1, le taux du 1 an dans un an qui donnera un rendement de 3% notre investissement sur lobligation zro-coupon 2 ans.
Nous en dduisons P1/1 = 95.23 => t1/1 = (100/95.23) -1= 5%
Cherchons t2/1, le taux du 2 an dans un an qui donnera un rendement de 3% notre investissement sur lobligation zro-coupon 3 ans.
Nous en dduisons P2/1 = 88.97 => t2/1 = (100/88.97)1/2 -1= 6%
Si t1/1 = 5% ou t2/1 = 6%, alors investir 1 an ou 2 ou 3 ans et revendre ces investissements au bout dun an sont quivalents.
-
Gestion de la courbe des tauxBullet:
Barbell :
Ladder:
-
BulletLes portefeuilles sont soit des Bulletlinvestissement est concentr sur une partie prcise de la courbeConstruire un tel portefeuille est rpond un pari sur la baisse du taux spot correspondant
-
BarbellsSoit des BarbellsLes investissements sont concentrs sur 2 maturitsConstruire un tel portefeuille correspond un pari sur lvolution de taux de 2 zones de la courbe
-
LadderSoit des LadderLinvestissement est quilibr sur chaque maturitChaque anne, lobligation rembourse est rinvestie sur une nouvelle obligation de maturit maximale. Correspond une absence de stratgieOffre un bon niveau de convexit duration quivalente
-
LeverageDans certains cas, les stratgies peuvent tre mises en place pour un montant suprieur au montant de lactif grer. (Trader, Hedge funds)Le leverage magnifie le rendement de la stratgieEffet de levierSi la stratgie est gagnante, elle le sera encore plusSi la stratgie est perdante, elle le sera encore plusRemarque On peut obtenir le mme rsultat par le biais des produits drivs (Futures et options)
-
Leverage : Total returnExemple : Achat de 10m dune obligation 10 ans, coupon 5% dont 5m emprunts, et revente dans 1 an. P0= 100% , t0 = 5%Taux sans risque = 2%. Emprunt de 5m sur le march montaire pendant 1 anUn an aprs, le taux du 9 ans est 4%Remboursement -(5m+2%x5m)= -5.100.000 dans 1 anJe touche le coupon sur 10m : 500.000Valeur de lobligation aprs un an
-
Placement 6 mois T bond 8% 30 ans
-
Vente dcouvertAfin de profiter de la survaluation momentane dun titre, on le vend dcouvert.On utilise alors le RepoOn emprunte le titre moyennant une rmunration proche du taux sans risque (Rf - marge)Reprenons lexemple prcdentMarge Repo = 0.20% On emprunte lobligation pour 10m nominal pendant 1 an, et la vendons dcouvert 100% (10m)Au bout dun an, le taux du 9 ans est 6%
-
Vente dcouvertP1 =
Taux de rendement ???Investissement = 0 t = 0 t = 1
Au bout dun an, nous payons -500.000 de couponNous avons plac 10m dans un Repo et recevons de lemprunteur (10m+1.80%x10m) = +10.180.000Calcul du gain 10.180.000 9.820.000 = +360.000
+10m Vente dcouvert-10m Achat du repo+10.180.000 Repo-9.820.000 Rachat +Coupon
-
OAT TEC 10OATiZERO COUPONS
-
LOAT TEC 10Avantages de lindice :rfrence de taux internationalecouverture possible :taux de marchinstruments liquides (OAT de rfrence)maturit constante
2 OAT actuellement sur le march :OAT TEC10 25 Octobre 2006OAT TEC10 25 Janvir 2009L'encours des OAT TEC tait de 21,74 milliards d'euros le 31 mars 2002 rpartis comme suit : OAT TEC 10 octobre 2006 : 11,89 Md EUR OAT TEC 10 janvier 2009 : 9,85 Md EUR
-
Taux de march et taux calculsLindice TEC 10 (1)Taux Echance Constante de 10 ans :Taux actuariel moyen dune OAT notionnelle de maturit 10 ans obtenu par interpolation linaire entre les taux de rendement des deux OAT les plus liquides encadrant lchance 10 ans.
Ces deux taux de rendement tant chacun dtermins comme un Libor.
Rfrence demprunt dEtat.
(mis pour la premire fois le 9/04/1996)
-
Taux de march et taux calculsLindice TEC 10 (2)Mthode de calcul :Critres des deux OAT de rfrence les plus liquides encadrant lchance 10 ans :OAT taux fixe amortissable in fineencours rgl > 20 MdFmaturit = 25/1, 25/4, 25/7 ou 25/10Cotations retenues pour chacune des deux OAT :prix spot = pied de coupon avec 2 dcimales valeur J+3cots 10 h par tous les SVTlimination des prix extrmes (4 + hauts et 4 + bas)moyenne arithmtique simple des prix milieuCalcul des deux taux de rendements actuariels
-
Taux de march et taux calculsLindice TEC 10 (3)Mthode de calcul (suite) :Interpolation linaire simpleentre les 2 taux de rendementspour une maturit exacte de 10 ans (sans tenir compte des jours fris)arrondi la 2 dcimale par dfautCalcul quotidien par le Comit de Normalisation ObligatairePublication :Par le Trsor 12 h tous les jours
-
Taux de march et taux calculsLindice TEC 10 (4)Cest le premier taux de march de rfrence long terme en FranceCalqu sur le CMT U.S. et le REX allemandDestin remplacer le TME (Taux Moyen des Emprunts dEtat) qui a 3 dfauts :taux calcul a posteriori ( partir des THE (Taux hebdomadaire des Emprunts dEtat)) et non fix ex antecalcul partir des cours de Bourse (liquidit contestable)maturit relle volutive et imprvisible : modifie par toute nouvelle mission plus de 7 ans
-
Taux de march et taux calculsLindice TEC 10 (4)Avantages :rfrence de taux internationalecouverture sans risque possible :taux de marchinstruments liquides (OAT de rfrence)maturit constanterfrence officielle possible pour les produits taux rvisable et maturit constante :constant maturity floater (ex : OAT TEC 10)constant maturity swap...
-
Les obligations indexes sur linflation : Un produit compltement nouveauLes obligations indexes constituent une catgorie dactifs compltement nouvelle, il nexiste :ni instrument de pricing,ni instrument de couverture,seule couverture : autres instruments indexs sur linflation.
Objectif du Trsor:conomie de la prime de risque sur linflation,diversification des instruments de financement,diversification et largissement de la base dinvestisseur,crer un benchmark en euro sur cette rfrence.
-
La structure mixte : une solution simpleCalcul des flux en pourcentage comme pour une obligation taux fixe classique : lobligation paie tous les semestres un taux fixe correspondant au taux rel qui a t dtermin lors de la premire adjudication, le principal est rembours lchance avec le dernier coupon.
Prise en compte de lindexation : tous les flux calculs ci-dessus, coupons et principal sappliquent un nominal major du coefficient dindexation leur date de paiement, pour une date donne, le coefficient dinflation est obtenu en divisant la valeur de lindice cette date, par la valeur de lindice la date dmission, indice galement appel indice de base. Indice date nCoefficient dindexation date n = _____________________ Indice date dmission
-
Priodicit des couponsPour lOATi un coupon annuel a t prfr :
simplicit, conomie de back office, standard des OAT taux fixe, facilite les comparaisons actuarielles. priodicit idale pour la liquidit des strips.
-
Formation du prixLobligation indexe est une obligation taux fixe dans un monde en euros constants.
-
CotationOn peut coter une obligation indexe en prix en pourcentage ou en taux rel, la relation entre les deux tant analogue celle entre les prix des obligations taux fixe et leur taux nominal.
-
Courbe dinflation anticipeA partir du rendement des OAT taux fixe de 1 10 ans, on peut construire une courbe des taux terme, le 1 an dans 1 an, le 1 an dans 2 ans ... le 1 an dans 9 ans.Si on soustrait de cette courbe des taux terme le taux rel que lon suppose constant, par exemple 3,25%, on obtient une courbe des anticipations terme dinflation.
-
Inflation point mortPour lvaluation des obligations indexes, le march utilise une notion plus simple qui est celle de linflation point-mort, dfinie ainsi :
Linterprtation de cette formule est immdiate:
si linflation ralise est infrieure au point mort dinflation lachat,
le titre index est moins performant que les obligations non indexes.
si linflation ralise est suprieure au point mort dinflation lachat,
le titre index est plus performant que les obligations non indexes
-
Performance relative de lOATi 10 ans, vs OAT10 ans et Euribor
-
Critre dinvestissementUn investisseur final ne raisonnera pas en terme de sensibilit linflation :
linstrument est justement cens le couvrir contre linflation.
il peut confronter linflation point-mort ses anticipations dinflation, ce qui lui permettra de dcider son niveau de couverture contre linflation, cest--dire la part dobligations indexes dans son portefeuille.
-
Inflation point mort
Chart1
369581.32915215261.8099714632
369591.35153758931.8101501555
369621.34429591061.7944788481
369631.36774021351.8197006908
369641.34149954661.8329597301
369651.33913758591.8516315673
369661.2969773781.8441363045
369691.32446035631.8558973975
369701.3311369951.8529542554
369711.29275840981.8176266768
369721.27508809321.777205496
369731.28177992411.7769483548
369761.30373545541.8016484445
369771.32622971131.8223700934
369781.32607885371.8252207823
369791.37935758231.8805195983
369801.36436633511.8744503032
369831.38094034381.9142009747
369841.36768901781.8916861742
369851.39741952251.9372894607
369861.40580982631.9363220514
369871.3561275111.9003618709
369901.36766699151.9219772408
369911.41097823221.9395589989
369921.45273650541.9536931644
369931.47646916311.9357193417
369941.4762947011.9356853195
369971.4762947011.9356853195
369981.46223284231.9639224427
369991.45482868621.9962101186
370001.51217692772.0578768725
370011.47179359421.9985194042
370041.44550754081.9811408061
370051.46676501251.974179366
370061.46667829081.9713165206
370071.4345732911.9308705215
370081.498972361.9795652062
370111.57305381052.0290297958
370121.57305381052.0290297958
370131.56102882112.0125474332
370141.52849016821.9984201795
370151.52017535771.9804413566
370181.52038232311.9803856485
370191.5011806451.9691996724
370201.49945117181.9822211997
370211.52566418172.0349925082
370221.63346999892.1294367407
370251.67247600682.1804544242
370261.68515862952.169906027
370271.67889973192.1728986624
370281.69685280892.1608408332
370291.68217674742.1220761331
370321.66251180282.09062231
370331.69139915162.1116227854
370341.7208117022.1668013431
370351.74470458342.2075725679
370361.74536901532.2245271622
370391.74549853342.2245401985
370401.68876550222.1798154167
370411.67945684162.1620263708
370421.68783715492.1636243142
370431.58169002522.0952563692
370461.5773562122.1077314308
370471.53865744372.0586830501
370481.57482463762.1203030782
370491.60365196532.1261634734
370501.60781278982.0912093965
370531.60703218952.1000305548
370541.69711565172.1745977147
370551.7247145922.1974950641
370561.66475013352.1642712499
370571.66702453212.1709466484
370601.62205011342.155966561
370611.6364950642.168011921
370621.61115755442.1587401966
370631.58213886192.1252004837
370641.56779688992.1101725901
370671.57497456892.1182039755
370681.58197021962.1172771101
370691.57340421062.1001996903
370701.61992106532.1158674631
370711.61677399662.1156166111
370741.58827816722.1070504466
370751.57995039452.0651201869
370761.5307251092.0231035429
370771.52862928892.0334748821
370781.50871422751.995272775
370811.53800082231.9998586761
370821.51174433982.0029790722
370831.48193291231.9870342927
370841.46416967961.957495717
370851.46728104471.9596965668
370881.43546061441.9361822894
370891.43209204971.9173265861
370901.41525755311.9146105113
370911.40385650341.8827058742
370921.37854240041.8574781255
370951.3747759511.8711835024
370961.38255073681.89393036
370971.39056632881.9133804365
370981.35976027481.8710596272
370991.34307420231.8618922668
371021.35761106981.8687594149
371031.32871557891.8407871782
371041.37056020441.9048970783
371051.38066972431.8998460766
371061.34312161171.8778448432
371091.34613063381.8807807602
371101.34562361991.8701223917
371111.35898466721.8954405131
371121.3257384871.8532818698
371131.31600850651.8365653506
371161.31935906971.8277005886
371171.34580521031.8625792771
371181.3823779371.8922558443
371191.36066715341.8778793013
371201.33850104621.8769290276
371231.36114815971.9014781474
371241.38308246021.9226384049
371251.38834155861.9408153357
371261.3848068761.9294591593
371271.39696978151.9391332501
371301.39705514481.9391078739
371311.32995826191.8872828904
371321.31724990271.8796528415
371331.2994786581.8946583283
371341.31300127461.9395120643
371371.30930628361.9331879441
371381.39474393862.007161724
371391.36108611131.9567163796
371401.33084990411.9525450211
371411.31014577061.9413030207
371441.36077311531.98699092
371451.31806286551.9373094138
371461.35676494222.1054401355
371471.33531820942.0916902058
371481.32049721112.1265213114
371511.33938774262.0905737577
371521.33023636512.113635727
371531.32348663462.1375289656
371541.34471507772.1206873929
371551.36800097662.1669746668
371581.38189952872.1181991757
371591.32436221792.0604054105
371601.3084248562.0039198702
371611.27619401281.9790830597
371621.30687378852.0219809597
371651.30017328151.9957721248
371661.24997947971.9492727957
371671.24713707441.9700748036
371681.25566862031.9659956903
371691.25829735361.9617014937
371721.23990673111.9599411086
371731.23882477641.9412962196
371741.20949628511.8900610841
371751.22953156251.8960742932
371761.23245402621.8889767453
371791.21660534681.8551549066
371801.23343911241.8694583154
371811.23772164841.8598259066
371821.24577891051.8569347893
371831.26956487091.8944157922
371861.2418358611.8628870447
371871.23101070991.8407332685
371881.17188661491.7516982378
371891.13328652081.7361880458
371901.13423360111.7137735275
1.6394475041.10446759141.6797333934
1.58187626241.04221905041.652495385
1.57479654291.05054855961.5967505719
1.460089850.96159343511.4325149077
1.52631767611.02882523191.5335271672
1.49113527940.98802701531.5672405403
1.51017743011.01783532841.5986059875
1.46098874810.99271915991.5772827581
1.51452875611.03647917931.5954522823
1.53428064381.05291867451.6074780949
1.52406924241.04086366321.6035775623
1.59992598241.11994400561.6721018895
1.63929771251.13629959741.6803406947
1.70283693551.22186641061.7325543178
1.71950253611.23309357711.7457824647
1.67721484951.20010189951.7151435521
1.70389585991.22687625911.7356330189
1.7496457111.27314050561.7699605691
1.74920149711.27998567341.8050751623
1.71920189091.26967177811.796391579
1.68735995671.24781358391.7820860947
1.76215302671.31969087481.8412385981
1.70705974221.25261900381.8164297543
1.67151394631.22789731061.7762951337
1.63719165161.2013142261.7585504516
1.59157792321.11613813451.6887120687
1.58736048611.1604665961.6812734762
1.7394575461.31645251961.8055729607
1.7318449081.31584552711.7464559683
1.80444100521.38712403281.8437098812
1.80519697931.36974926131.84398037
1.74917543421.31224847891.793811507
1.70342579991.24706492171.7426816575
1.77950475891.32305333841.7419752601
1.75825067181.31922216111.7638188887
1.80123924751.38269359631.827702689
1.76357956151.33310450751.808956392
1.73678046741.31772491.8160246596
1.75916879241.33407304121.8246140587
1.79069385981.38604657621.8761839059
1.81010679991.40520783891.8871884667
1.80999433541.40520783891.8871884667
1.80999433541.40491065321.8871818658
1.8255576051.42928566141.8995833312
1.88107815491.46735889431.9329117118
1.88102522661.46748920481.9329008828
1.88102522661.46748920481.9329008828
1.84809899581.4276501661.9022646576
1.81619115431.40241991281.8793950583
1.79589147951.388298661.8341893005
1.68314776261.27151867651.7218640444
1.69512534071.27918659211.7455530988
1.72016838571.30313794991.7139277352
1.68612790971.28149749821.7108289183
1.64682369941.25484859851.6783034875
1.60835870921.21952520691.636292303
1.65734658541.27395908421.6801116472
1.71837853591.31252049981.7441100484
1.71575330151.30839191561.7482190859
1.7189610171.31305487441.759432365
1.70584515021.30073477451.7409145593
1.79397199871.3828740441.7936286122
1.78650243391.38110351381.7848094206
1.85503480481.46372122981.8278688177
1.9009430011.50685284771.8471646779
1.84692479371.46843449431.7924268917
1.83198992211.45650095691.7756857838
1.81082841651.43950967881.7598159763
1.78437630011.42193120411.7294718608
1.79784880061.42398065311.7482927827
1.77943441461.38940618461.7585066104
1.7712767481.38152461221.7657137274
1.81214487891.40273666691.7803344297
1.86241606441.46616722471.8521235108
1.82932858531.4336157941.8461267231
1.84192547941.44304210381.8650129888
1.86385178271.46412872031.8826348595
1.85716608151.47639898241.8611300966
1.83043579241.44511873851.8202568112
1.78227678441.40111895791.7946354297
1.78802929781.40568702131.8096811114
1.81993857891.43912787871.8445690716
1.79265357421.40412211231.846373435
1.85090829241.4691220441.9027666159
1.78740105691.38635499861.8359954171
1.84087523631.44994906931.9222303038
1.85959482091.47878454011.895668496
1.86488548931.4855571651.8888239555
1.85170503651.47104712921.8672455492
1.89863077751.51186420661.8904405417
1.89679947431.50786982661.8849709627
1.94348077291.5637409591.9464200661
1.98551547731.60519768322.0095465892
1.96484290281.61057427741.9803541794
1.96488692311.60981723881.9711223934
1.94512370441.59642357951.9636565334
1.97503917271.63412954852.0023555584
1.97910865251.6260783832.0054224327
1.96841004651.61619251751.9921614365
1.97011688661.62447565611.9696578655
1.93914783451.5901729841.944299626
1.948035091.59474757521.9518286687
1.98993385691.63711663091.9933318832
1.9911957671.64221098231.9881424459
2.00956480211.66637943371.9953682574
2.03723561771.69381527832.0251311506
2.0243112821.68369108562.0181130611
2.02137592881.67894396492.0170740827
2.03499684511.69059340752.0389946742
2.03499684511.69059340752.0389946742
2.04696114021.69059340752.0389946742
2.05871286491.70393171772.0810636106
2.07461575551.708112662.099823665
2.05380977291.68455816652.0698514482
2.07071813961.69850245482.084154387
2.10939396451.72746338422.1294823839
2.11833778971.73906309442.1194790331
2.12234310911.74537646492.1241726882
2.09658930471.72230881352.1044135836
2.10708172791.73792023022.1055046349
2.07820108961.69751842982.0827699732
2.1125331551.76673981082.1229347018
2.16271875711.78630338212.1703208535
2.17609789061.79978433552.1708576713
2.17298652881.80291226162.1651517236
2.15259399541.78185441632.1480988531
2.17237278911.79141568082.1631244041
2.13136684741.75383886962.109034811
2.0985890251.70928801022.0903412578
2.07567096851.68750848032.0587928796
2.10607619841.71450156422.0842329817
2.09074700151.70455185972.063604829
2.09974122261.71416076582.071604801
2.13894687681.76436240552.1045178759
2.05615395791.68473915062.0259361288
2.05604817741.68471710332.0258857995
2.06779197821.69243542112.0439122143
2.11882692211.74525800842.0862920075
2.1370352281.76537956272.0986423493
2.14383841611.7759693972.1007379144
2.16432101651.80333018882.1203913915
2.1989393381.83813650312.139560828
2.19553558421.83445605292.1310382966
2.19529020821.82983429882.1288020222
2.22472645161.85449288142.1503961142
2.16945438081.8009404272.1227264232
2.14770744711.77444877112.1026535182
2.14249971391.76418753542.1102334371
2.11662152751.73488826562.0665728659
2.16125354741.77730573212.1029755245
2.16858043351.78558706692.1065529694
2.14476984741.76598755792.0825570611
2.13181393211.75446322012.0837127123
2.11425897281.74346716932.0839785778
2.13483048421.76173453182.099542084
2.129747811.75792862982.0993875438
2.1050119941.72837613832.0786244798
2.08473463971.70381969392.067975468
2.06841880621.68831279862.0669066829
2.09396885861.70673603312.1065653525
2.06684402781.67347514032.0797238507
2.08338770541.69575501082.0927526893
2.03303316831.64830515142.041529812
2.01769025481.61751341252.0539946269
1.9520707331.54769139071.9908021912
1.9774520471.57099050761.9988818168
1.95968674181.55966228041.9761051627
1.95339492061.56202298561.9580562572
1.99126016341.59851310951.9843150527
1.9606636511.57315278571.9467032411
1.92788698991.53805681351.9015458773
1.98203961441.58709399231.9648818306
1.94912732971.55113331411.9121526898
1.94320005461.54628819911.9261676854
1.96886652451.56084676421.9743398051
1.99950981831.5746030072.0256778608
1.96845575021.55018431791.9983665362
1.96698586681.55191807541.9845035918
1.97901532291.56795072171.9977386481
1.9811594631.56919321381.9968159566
1.97201969711.56305398161.9959084137
1.96464162121.55069660771.9896713938
1.90237191881.48903100341.9327299517
1.88086035421.46597664511.9023027227
1.88462693791.4791292131.9105861212
1.87108243871.46233361691.9023090781
1.89527770531.48321453071.9394643235
1.91537189811.51388878971.9841207476
1.90892132561.50442071121.9779698962
1.86578988811.45712211891.9481866087
1.8547086661.44300839711.928691501
1.86506614551.44257475371.9135022282
1.80247599031.41999261321.9132170655
1.84743401911.41769371631.9147669891
1.84677767741.39876798661.9369780286
1.8737691521.42926644021.9950375083
1.86567306761.43118540071.990146759
1.84601936861.40425304431.955181238
1.82306944241.37934932641.9132585805
1.85082963161.36423717351.9046074698
1.7511426011.27085962491.8253097392
1.7834794161.30590908861.8522530408
1.76212187011.2696864851.825555916
1.7659848731.2971853481.8504264098
1.75708569431.29291472861.8227855849
1.74428094641.28537444461.8055021214
1.7237843771.26597809821.7953064082
1.69678427041.2502406311.7588058174
1.7896898691.36167867151.8209981949
1.77321056161.36189752561.8101982225
1.8010663151.38035301761.843338726
1.77782686331.3457706011.8269594438
1.81584762811.38397504411.8640304558
1.86082268991.41617484511.8962220066
1.8294615181.3722322161.8629341055
1.83690248491.38001939721.8706891278
1.83693252951.37243543851.8782848105
1.78859815911.32031771831.8278348573
1.82350819161.34963826841.8776253985
1.83908034551.36157019141.9090969739
1.80363506271.3335431151.889197413
1.76745460391.30736300961.8581954597
1.78540422211.33975213161.8842207289
1.78770803311.3238570051.9078855138
1.79415142711.35593760571.9298571293
1.79703057681.37878212161.9123372385
1.84843048281.43027831441.9691792958
1.87184666041.4550601011.9787198401
1.86695608551.43122922341.9698929099
1.86107715171.42852345841.9827168376
1.85811206281.42695259441.9895633809
1.85174390121.40954360661.9854134716
1.8457460031.39828945761.9858357335
1.80815727161.35304693311.9522290923
1.80281292161.35303350161.9306264012
1.77433247631.31195549781.9133857097
1.76942420071.30197501681.8950329178
1.78492548231.32678157371.9235548618
1.80093578091.35691244291.9400342724
1.78957432191.33882502461.9316119562
1.74754226051.27127993581.9159826885
1.75903716451.30527114611.8991163857
1.77502174651.32264407091.9049079244
1.77235360771.31187779091.9218449582
1.75618879961.3140836441.8900552219
1.73390615561.2919477691.8784758599
1.73585638161.29329783051.8646493907
1.71093573991.27095963321.8641810909
1.71748448251.28896224731.8604000083
1.73920682671.30372149441.8789492218
1.75755111021.31614423211.9005651642
1.78749575741.36136067081.9180707325
1.79958414291.3868618171.9413553391
1.77625408981.36324287681.9279921597
1.78911284991.37006751221.9354482246
1.78831467191.36239245971.9404823475
1.78295051141.36322322341.9198268183
1.77333372071.34219660761.9045047502
1.78924490661.35356758241.9336549695
1.77794157561.34039615131.9259964275
1.74733827841.30115841531.9109643659
1.72431691091.24502918981.8919912501
1.76995305011.280268181.9186185732
1.73327843161.25214611111.9046444136
1.76413240981.25482420561.9188302629
1.75327111761.25958958331.9163754758
1.77116833891.28481415031.9307047021
1.77862042071.29103518951.9355847902
1.74884649921.26947570371.9038998798
1.71653259421.20962353231.8827559412
1.69469901051.20288620031.8899367215
1.69526734131.21257421191.9013195406
1.70441355341.21997867161.9084611209
1.72415274161.24279164891.9309971937
1.73231406611.25032300441.9264135466
1.72940959571.2471236121.9149372828
1.70864358281.23904406791.9023511936
1.69881049491.2241946491.8990662972
1.76633410151.27598900811.942770685
1.76402000691.27988658091.9423104612
1.77965533021.2978827151.9407845222
1.74842901761.25728603791.8996041363
1.77747469331.29364276711.9242692293
1.76981448611.30876250881.9281888924
1.75026211011.28625922331.9123895575
1.76476908641.29727836551.928933986
1.75456298731.2846282711.927454788
1.76162029761.30326243251.9362297895
1.75083560071.29882472051.9262500091
1.73806626271.27060669111.915153162
1.73794969911.2484077521.9283630692
1.73586242371.24124740221.929178109
1.7321882381.23894852051.9260591323
1.71807739471.23411639391.9088866347
1.73243965821.24601928411.927603148
1.76138279911.27107961881.9575503746
1.75471883551.24637842181.9564907132
1.7536984421.25530799131.9586814072
1.77512948151.27414594071.9842617899
1.79352518731.29291298681.9991406453
1.78846865311.28870975751.9894362367
1.78837805941.28879044661.9894357643
1.78837805941.28879044661.9894357643
1.78837805941.28879044661.9894357643
1.76205904411.26088208841.9753079962
1.78383936591.2635337751.9959858231
1.78369662591.26392696691.9959771607
1.78369662591.26392696691.9959771607
1.82805531681.31884495432.0370554215
1.84027946541.33450583532.0554777736
1.82224151841.32424023232.0546458286
1.80865770251.31982356332.0404600031
1.796808821.31152448072.0253693656
1.84303733791.36621516152.0699519508
1.85673598471.36792336512.0742889331
1.86548284541.38551775542.088822943
1.86665698451.41979413242.0776430643
1.88180964251.45982709382.0940147806
1.87670212651.45918823382.1057516425
1.8574258311.44162107362.1151545369
1.86257418131.45161388232.1210163803
1.83553106071.43717536542.0865026205
1.82652079181.42989985342.0700205299
1.82465281381.42834745912.0406731107
1.79817862071.40343469542.0190355837
1.77995301321.38734807871.9835700962
1.79476561961.38112879071.9908507418
1.81163086621.39790565692.0010716894
1.84230734271.4197414462.0546060269
1.84943377851.43346903882.0588776895
1.86108035311.44626662132.0754160486
1.88526629721.48044503422.0944416707
1.94554444191.57073750382.1434373684
1.94413384831.57746498452.1470261702
1.92435302671.54753319142.1391430058
1.9404572621.582788242.1638289689
1.93666756551.60095379242.1409198821
1.94848579461.61954752592.1632926693
1.95294549581.61590182492.1760811877
1.95366054741.63289873682.1575444101
1.94578747111.6271420422.1308172174
1.93699860461.62161693452.1033948385
1.91017367411.59616481542.0904496025
1.90385574081.61110627752.1227264067
1.9288387421.63292135872.1370263234
1.92784121951.6452459462.1526082545
1.94834482111.64554600372.190827835
1.92688294661.61142741122.1570645578
1.92042614441.61381979152.1661275137
1.91373220841.59360028272.173889395
1.9026157971.58992721782.164715255
1.91488408941.62348645042.1824831144
1.92075539181.64746366342.1672667148
1.91746576651.66023049162.1820765766
1.91544943241.68582635352.1638916698
1.91089384681.68539395952.1611263213
1.92259336881.704241172.1624255927
1.91168609361.70324658252.1459111981
1.90629865031.71249202992.1299055683
1.91100900131.78791777482.1254806003
1.88585778951.80289147812.0968517589
1.88622748671.7705287332.082879447
1.92171730311.82448975522.10865196
1.91546971431.7988255712.1148560496
1.90861895941.7999775032.107668435
1.90967617321.79101890322.11379155
1.90691321481.77899412582.1232826912
1.91438092581.78307331192.1390779241
1.91564289511.77485014062.156755036
1.92175533951.79251760772.1558361562
1.91903037581.78790021142.1747916769
1.93446535831.80192163282.1899581709
1.92143429861.80217335292.15147501
1.92552932191.79518429512.1392445275
1.91976703321.77946477612.124605938
1.92102733871.78109382062.0941956108
1.92762087991.7714593812.0761570964
1.88761982551.75436325242.0714405573
1.87243830791.70295281522.0715840066
1.88395147061.73971751062.0703042057
1.88335120781.73549089842.0503189492
1.85882613941.71780361232.0456961164
1.8488012861.70516729152.026076832
1.84258147431.68861513232.0312200112
1.84258147431.68861513232.0312200112
1.84258147431.68861513232.0312200112
1.84772825611.68083728972.0518467628
1.83118605151.64669446642.0348186321
1.81099445491.61074576212.0057831045
1.81998916931.61386115832.0240542048
1.83486696871.62879885322.0362741588
1.82003407271.60983657572.0253186421
1.81067975331.59709373312.0203189296
1.81067975331.59709373312.0203189296
1.8135281461.59870556562.0340551184
1.80575629121.59321055052.0202635335
1.82136499231.60436204452.0248699164
1.78367027441.55208106912.0160774344
1.77606619531.54656514522.032266268
1.7175131161.48967730091.9708764536
1.69855730951.4737556551.9629836424
1.67848812061.4205725161.9462628514
1.68417904691.4156159981.9301523091
1.68332736631.43105405351.9306090743
1.67099551181.41628753241.934050882
1.67023985831.39589479071.9195737139
1.68117052641.40800383041.9343515047
1.70191927621.41407976531.9615808607
1.69843885531.39584442061.9643748031
1.67811349311.35968663031.9358515173
1.67030615971.33356708471.9115020566
1.62359542051.33205720451.9219300566
1.64641893541.31671180851.9412817279
1.66286670861.31484123371.9568668854
1.68911217511.33267089491.9765328032
1.70418672511.34302044282.0054132428
1.68934263261.31928382751.9875619898
1.68889608621.36720175941.9811860944
1.67228498371.33861347691.9725735544
1.68242479331.35896371381.9802917256
1.67606110851.35102845551.9757068442
1.66140285161.35203255211.9823199358
1.65170344651.34940047961.9745526126
1.64418075571.35472866391.9746586446
1.62212784611.32535622331.9259888147
1.60749760121.33863359641.8963763608
1.60769874321.33972131071.9081174572
1.63747706131.35804966381.9135414438
1.65175823071.37014028861.9323466781
1.67458654141.40461021181.9448480616
1.67127793681.40692783211.9356474679
1.65437372621.38875964111.9098125356
1.64993316261.38980477331.8999670425
1.69527652121.45920682311.9337841512
1.71035170761.46642594571.9366342427
1.71414688911.46934453621.9229494296
1.71590047591.45850385371.9871978338
1.72187139621.46681751382.0016174838
1.7306958251.48111724752.0336173798
1.75346805321.49140145662.0603507347
1.76348540891.50626811782.0721174354
1.76173500091.49377837812.0624347875
1.743953911.4628982762.0426427604
1.75133578911.46741337392.0612825533
1.78522489761.51622267962.0964593342
1.79170214031.527093432.1142933337
1.84055254861.57300917562.1374005972
1.85276937241.59127988412.1169245557
1.86118692871.58922326742.1019210027
1.85999231671.58579313442.1151311017
1.89070643281.62602255232.1252173484
1.87966500921.62122240612.1031173469
1.85888680661.59578275682.0738131314
1.89160800231.62556370272.1065167936
1.86294611111.59416648122.0895394892
1.90692116441.63749767482.1407721096
1.89196371551.63813791642.151887785
1.88326552541.64069730492.1390401322
1.89104108741.68337487672.132796102
1.89637268851.70675927542.1315762623
1.90395966531.68464073942.1258652536
1.90740830881.68181665692.1453285188
1.89196244581.66917292112.1256825435
1.868554141.64304295152.1165396527
1.86722066111.6298152372.1293252369
1.869319011.64711776022.1309335518
1.88138330161.66750208212.1357854305
1.90394827051.69351962642.1556641534
1.92099536891.74207036932.1678933081
1.91191663731.73019154832.1444433801
1.91429382051.72154480122.1485509632
1.9199501551.7411713382.1493286701
1.92226119421.73743401472.1640061647
1.91767347431.73902349792.172642914
1.91804793051.74424135912.1809422646
1.91126414421.70227140222.1887839509
1.90848375651.7281854222.1831004674
1.91071785471.72108578922.1918648478
1.90954009611.72983075622.192140566
1.91441317261.73975029052.2000600001
1.91060426581.73354971442.1878285732
1.9171346131.76081720372.1869580754
1.93017115481.77797963532.198584621
1.9434273821.78188023312.2185784271
1.94825086521.76504168572.2361806758
1.938520921.73825365732.2350623394
1.94984105421.7547527842.2484209617
1.94678036031.75836343022.2379450157
1.95286041321.7818084132.2455385144
1.94527576161.76576110522.2654441647
1.94868955581.76071160382.2533651714
1.94098258391.75475264012.2558344173
1.93489044731.74123948842.2522201261
1.92615067161.74731305482.2408354548
1.92639907321.76183327122.2456807235
1.92544923021.75494589542.2484556705
1.92862819911.76663885962.2506250025
1.92314686661.75683838642.2509549277
1.92287028921.74084299582.2429122315
1.92060447421.75443475192.2415308273
1.93168781581.75846294352.2467244851
1.9437925981.78834114712.2763940181
1.93496648821.79593710782.2587469265
1.93715113291.80570714222.2571802989
1.96952819171.85113561072.2572332725
1.96459040431.84242941162.2486501348
1.99239829711.84780090352.2519198096
2.01305681381.87733158362.2826609019
2.02507483041.90206114062.2856803223
2.08133238571.9687075422.3544406158
2.11364365322.00412904342.3781815711
2.12101991952.0007654882.3791761247
2.13685649782.03165566062.4015352479
2.10713595762.00739640462.3726803749
2.11663989072.03033642832.3728241314
2.11174612442.02028728152.3624375941
2.08664603981.97970717492.3636802887
2.0811736731.95644821952.3655497714
2.10098076241.98479136512.3754254355
2.0919071651.98123212752.3761804933
2.10347292741.99352976882.3706630573
2.11736639282.00763573762.3804399857
2.14107851392.01961616742.4027680617
2.18273183512.05345577642.435447268
2.17105310032.0423815852.4266566405
2.18750342052.05252648642.4411802857
2.18717351372.05534749662.4487153489
2.18540112972.05000747172.4534894727
2.19738451712.05213323282.4620971819
2.19161132842.04907797512.4607921628
2.1861918692.04076333232.4642310415
2.18477729182.04610216622.4871805167
2.19458001212.04264349452.4886805076
2.1722048112.02394885052.4743196521
2.14400754432.00003398872.4537228242
2.12295100011.97151127322.4361802625
2.12110326431.96452391412.4362149267
2.13084011131.98168751762.4469073266
2.13332366651.98477829612.4431803346
2.11424162861.950138952.4189105715
2.11411416821.9622545222.4025406449
2.11993438551.97044483462.4061802624
2.12718398881.98632233592.3971806836
2.14896212992.01861281552.407823969
2.16894055082.02951243992.4234680284
2.17767800572.03694296162.4306802871
2.1915233462.04473990652.443344057
2.19066609052.03585059982.445469705
2.19044478732.03581564042.4446806249
2.15781962842.01051007052.4117941849
2.16387411552.01469301482.4247908435
2.16204893592.01131332152.421691839
2.15260381181.9916997852.4114955854
2.14868446291.99042764942.4084884401
2.10908830481.92737625322.3875843447
2.08189879181.90940796392.3761920178
2.07254492491.90063659112.3571050732
2.06994127231.90779139022.3587881652
2.06211195741.90224428132.350384104
2.06693122571.91083001242.3452945768
2.07152635121.91957641982.3448873662
2.0622485371.91287761382.3361920667
2.0623609531.91324849562.3362159253
2.0623609531.91324849562.3362159253
2.0623609531.91324849562.3362159253
2.07948556051.9333010472.3521920086
2.11577684471.9679612912.4051921407
2.11590531051.96835970362.4052694869
2.11590531051.96835970362.4052694869
2.11414395951.9696896172.4028424632
2.12358791051.97786434462.409706291
2.10212102671.94971240072.3998561488
2.07663076111.92485406362.3936919015
2.07351140231.92769935422.4003789021
2.05885992841.89033125032.3972529356
2.04403636761.87642802782.3810068977
2.03764037561.85687825182.3548158797
2.02441706211.83877253712.3373096973
2.0268168471.83848559842.3329754805
2.03535317221.83864266852.3455964544
2.03741358751.83900462522.3621918402
2.03931858711.83817246392.3751917112
2.06797485231.85782004232.3918057583
2.08920527731.87532568962.4195750047
2.09846268521.8854592792.4365870329
2.10288414791.889973142.4263013114
2.07667296111.86684401992.3923847589
2.07080923321.85627071382.3858033299
2.09372100151.887370742.3938991191
2.10348403991.89151842532.4064315923
2.09101470111.88247629512.4158955042
2.0875503671.87569707622.4282998579
2.06860990781.86091189112.4114901955
2.06716615851.85747328982.423391902
2.05504361241.85120762032.4268889631
2.03889633291.83810043092.4159952462
2.04299091071.83944698312.4100934626
2.05924709461.84764923872.4233633896
2.07874684951.87853505612.4415837928
2.08128814551.87445746842.4292893565
2.08462068541.8780984182.4371921264
2.06976400371.85064357572.4306917889
2.06901119831.84763440372.4457743138
2.07347606591.84886415282.4444930018
2.07400101961.8509001712.43679219
2.07910416771.85269960782.4389929895
2.07001863061.83950624762.431997289
2.06271422141.80421132022.4370056004
2.0728914811.82146352062.4403889794
2.06837971011.81100371622.4400781645
2.05890750971.80105168082.4094971372
2.06463877791.8192540522.4124953856
2.07863129391.83499933752.4176921253
2.08062884211.83508744082.434890448
2.07157184851.81964194182.4335227721
2.07129978191.81871489682.4432025234
2.06806436531.82068176282.4426117734
2.07555086121.83106563842.4390225428
2.08144691681.83789523122.4526124677
2.08426355281.8644829562.4613937692
2.08080345851.86052495262.466022665
2.09033861131.87190455962.4820224905
2.08780974491.88600413242.4984267034
2.09304053451.90354250262.5017036241
2.09318755221.92309717852.5070665038
2.09007379951.92415562312.505522739
2.09168264551.92904623142.5025227503
2.09844452141.9327502042.5134716114
2.09773215011.94878329792.5130225121
2.1117059321.96383683172.5186120875
2.11969902821.96489696972.5117136122
2.11311481651.95849440532.4830734016
2.12509382941.9642725582.4851446751
2.1325037561.97922391862.4860225204
2.17207578312.0326410552.476850821
2.15152786062.01242903862.4592326183
2.13588357792.00066241052.4563126029
2.12639517291.98816705322.4547302219
2.09912419481.97370708242.438813797
2.09912419481.97370708242.438813797
2.09912419481.97370708242.438813797
2.10955637942.0158858192.4363045256
2.14408729642.06369567172.4690225887
2.16137704572.08880833832.4899083747
2.13008505182.03910003092.474455125
2.11913598152.02583431082.4778056994
2.12653833992.04065476092.4828003332
2.12875917862.03983240322.4665226665
2.12708773032.03342800542.4642979145
2.1386312852.04223384022.4757495468
2.12752115682.01961442442.4627513222
2.13022721131.9910048652.4597936043
2.13076864611.98047327722.4620225903
2.14113779861.99251696932.4770223972
2.14190671172.00931897752.4818354027
2.14305900482.0088425392.4885683166
2.14608654072.01608462762.4855225223
2.15037066122.0199012932.4875223836
2.17228901872.04192071532.5020227522
2.19398395792.05732872432.5074988677
2.1795781112.04725709272.4887766351
2.18448626872.06255236692.4945228271
2.21730439552.10382198782.5255224851
2.24903294082.12294922152.5390223973
2.2515095252.11547204652.5390243284
2.24232109352.10264013362.5387765134
2.23113132722.09160479952.5320225003
2.24136881622.0998514772.5410224718
2.25825684892.11674529082.5505304536
2.25793544732.12281863962.5457702419
2.26325042362.12457434392.5397666261
2.27125936192.11911150172.5407682722
2.28348387882.13181452832.5450267916
2.27738911492.12044293672.5522750203
2.29594687192.14887178692.5610065142
2.34650705362.21474852872.5810058963
2.35964884522.22484684912.5960397056
2.3819185992.24665356122.6080228394
2.38742435752.25159151112.6060226367
2.36142064792.21176920622.5891843098
2.34495676692.19881422472.5769197261
2.32506300482.17707108072.5654196815
2.27577140292.11887480842.5345980162
2.28935547912.13306909012.5424194895
2.30182855252.1584432122.5521020997
2.30157027172.15595516872.5484195041
2.30797599162.17127727752.5655690572
2.30014819172.17921803122.557098335
2.29749597632.19470107072.5632397392
2.2825811952.18285957052.5495957604
2.25406089262.15739381132.5254197856
2.24236445392.1448728392.5155983334
2.23782671352.1327677382.5032396834
2.22744289772.10614453262.4979348867
2.22727987792.09195782642.5012443591
2.24380057732.10261694362.5093244819
2.24580622662.09768279422.5100568237
2.25727814592.09668705632.5200962337
2.26172958412.10097363892.5267418218
2.26894575552.09357111292.5389195697
2.27073974052.11748320232.5447480422
2.2708096232.11729074772.5447630229
2.25681161082.09609806932.5277375728
2.24197983762.0955465032.5174196185
2.24211033032.09383098912.5182485607
2.2343022252.06829720292.5140810156
2.25362950422.09819699342.5240942705
2.23917347582.0877067892.5110699174
2.24142560222.08837034142.5140699448
2.23673887562.0808003592.517251163
2.21913021542.06468111442.5097500181
2.21041165482.04905735792.4912485555
2.21332377782.0525127892.4754196067
2.21088161432.04420422552.4702436847
2.1975750212.02773583652.453742979
2.22995767372.0526479362.4665612638
2.23850131872.07090094562.4691008052
2.22757428472.05947168072.4580502568
2.20733485042.04537855092.4449196701
2.19588320172.02166694542.4422166626
2.18846456312.00884054912.4262689479
2.18880889932.01505660572.4235933333
2.18373019212.0130861432.4227461856
2.18098979952.00764221862.4189195703
2.17328492282.01000354052.4142570462
2.16682558982.00975300782.4164195703
2.14590255061.99042646142.408757413
2.15163396251.99058358942.4137529384
2.16229348971.99734181062.4199195703
2.16718171522.00509081862.4359195703
2.17003840182.00989052782.4319195703
2.15866376261.99588346052.4274195703
2.14929166751.97657235322.4139195703
2.16127231841.98455404152.4322520724
2.19043301472.01527472562.4630856578
2.20480216212.02856211552.4640925017
2.20900562592.03579843642.4670919451
2.1900620782.01881429422.4569195703
2.17407886312.00040162972.4329195703
2.15928289741.9896026122.4159195703
2.15858337481.99345776632.4094195703
2.14797355541.97280734072.4012544956
2.14447810241.96905320242.3899195703
2.1603482881.98550113292.3984195703
2.18333966132.02646842492.4050572317
2.19256894862.03985720062.4079195703
2.17830280362.03019617812.3933911233
2.16248031922.00673261522.3995708226
2.16410446322.0082121742.4051206758
2.15121509762.00073428652.3965992244
2.15399786492.00368912322.3940708226
2.1760418122.00650574482.3974708226
2.1687571652.00479087112.3920708226
2.16999793222.0086325672.3862217627
2.15979909841.99285010312.3705708226
2.16709723782.01019192912.3710708226
2.17612827292.02545931872.3675708226
2.16246417792.01557527992.3570708226
2.15676564022.00758696062.3605708226
2.16953691222.02050967942.3635708226
2.16785816022.02034862722.3649056514
2.1870460792.04538130792.3690708226
2.20428034322.06878114722.384243604
2.22522032672.08361137972.3957428157
2.2405468122.08946727612.4190708226
2.2148170152.06541304962.3975708226
2.21149140972.05863811792.3965708226
2.21351887592.04985502122.4025708226
2.21249437982.03971213972.4120708226
2.20825140812.03695080392.4215708226
2.1997927862.03046060382.4090708226
2.17803634082.01197917332.3635708226
2.17493251682.01060709862.3700708226
2.18314619482.03570800362.3709043945
2.19179718862.04051000652.3675708226
2.18510431342.03938407212.3745708226
2.18654364282.02957261922.3735708226
2.17132501882.0246323642.3704058787
2.16661639892.02915905642.3580708226
2.17681207382.04660628892.3720708226
2.18174414542.06292570042.3772337062
2.20355956372.10060459172.3855708226
2.20493070542.10135482082.3799052226
2.21460876052.09918610592.3943990843
2.23020484712.1118236032.407241178
2.23191494762.10952794622.4070708226
2.21394246772.09043282952.3865708226
2.23039353632.11068319272.3938956917
2.22471759132.11258212682.3840708226
2.21966538582.09772093362.3835708226
2.24439441012.12151681882.3855708226
2.2613673242.12266248392.3815708226
2.25109884072.10289643792.3680708226
2.24061475782.08362604082.3710708226
2.22262016312.07019013392.3497364794
2.20693144312.06817143552.3270708226
2.20962478672.06370327282.3230708226
2.23607907912.08365764672.3512373651
2.23896654952.09139163922.3496561704
2.23263780842.07089796912.3413249027
2.23346743342.06495000672.3465708226
2.21373541082.03419871942.3455708226
2.20851624482.0250047732.3380708226
2.20967888042.02439756292.3397346671
2.20256499882.0290110432.3255708226
2.20334024352.02779338762.3320708226
2.21474311912.03134517472.3372376723
2.22038776972.02361837582.3455708226
2.23351313042.04454383532.3590460643
2.20494276342.01324966852.3509074166
2.21514450612.02134134452.3452322101
2.20406848892.00997971292.3286503721
2.20613136252.0018381062.3217340306
2.20084214252.00036728322.3030727415
2.21260205952.02045780362.3022396615
2.21131698862.02345387652.2950767658
2.21222924642.02512943682.3040709889
2.207487222.02523942252.2975116371
2.20731899762.04696177382.304514848
2.22420343362.06140929352.3260319201
2.20810826692.03661100072.3196811878
2.21760088622.04600442592.3307882852
2.20345446662.03861786682.3375242199
2.24963106752.0929264352.3748970588
2.20278063892.0376637252.3514450097
2.22688270162.05502953372.3768573306
2.28638059172.12879953952.4293130386
2.2193075832.04102190642.3695493676
2.21701165362.03330484132.3748426434
2.21703984552.03381389832.3749260571
2.22005316642.0461489882.3761613733
2.22775047872.06198400892.3855304757
2.23681753422.06515579592.3960317738
2.21813811642.04912642412.3818447022
2.20548260162.0345390792.3697242682
2.19431977412.0276548622.3642262812
2.18373267812.02007469432.3380872998
2.16123713511.99289348372.3164058699
2.16931232772.00436744392.3411682839
2.17325668462.01196266082.3342871314
2.17019510352.00946629892.3257882055
2.17595589872.01964574372.3137733014
2.16796779022.01892226832.3015660341
2.17090848992.00947943542.3041498177
2.17981989112.01842485462.3183407044
2.18661729632.02848124222.3142588745
2.17137329612.02035146362.2892767874
2.17216395452.01287658212.2891557749
2.17671607812.01874498242.3010284062
2.15463935332.00079967382.3095325252
2.14992245251.99686113462.3030948116
2.12461756181.97810770892.2861646201
2.13034534031.98242101482.2799058622
2.15288327011.97561680342.3066558366
2.14087017591.95717121622.2892939033
2.12862087331.94606695812.2827957451
2.1254887781.93986244572.2746557257
2.11663191761.96380007062.2580675271
2.10768784321.95775974012.2638913583
2.10979164331.97347403762.2827944232
2.12342686011.98202714752.3097826948
2.13401230351.99971022642.3035934718
2.12579631422.00132000752.2979265089
2.10838490621.97874518962.2963047786
2.10939491271.98721347722.3081928471
2.09827769491.96391046872.2892586399
2.07197889181.9227517312.2868031129
2.05442719291.90152889612.2943181523
2.05131086671.88197060172.2893078226
2.02873325551.86661086492.2583546042
2.02755009391.86414284062.2623575926
2.05705610271.89694155452.2907324756
2.09001384791.92713550312.3025199217
2.06890262821.91163330882.2961558419
2.06363222781.93591552412.2749572573
2.06597213751.94666111112.2780069992
2.10138676231.98237855962.2893268381
2.1497013532.03661140332.2902250478
2.14524152992.03890539232.2873143545
2.10691586692.01137345772.2603617998
2.12036003772.0249628852.2639941619
2.13562882672.05836005842.2688288042
2.13371880212.0903749822.2503263589
2.14093114522.08847197292.2472523142
2.1545430852.12010562592.2651760662
2.15428402542.11534882712.2600190853
2.18636778932.14157076132.2800212331
2.21197152222.15629486432.3048372884
2.19599573012.13013469372.2980973222
2.19599573012.13013469372.2980973222
2.19599573012.13013469372.2980973222
2.19635318642.13003872032.3008341153
2.18273841452.11287678622.3020204901
2.19556740162.14194377482.3029203132
2.21220591042.15822938272.3120524224
2.21327488052.17035232892.3135286534
2.20508511312.16572215632.3198773117
2.18695733692.14289425762.3185265492
2.17530643132.13600137332.309822153
2.16171487642.11187593682.3017993992
2.16036573742.1132351022.2805563754
2.16325663272.1340544862.2824735576
2.15666894262.15885893332.2867227015
2.13959536742.13470466582.2716517696
2.13169659792.12163998942.2549773859
2.11605466582.11433684662.2313501071
2.12503657342.11502673082.2259636683
2.12732764922.10980539222.2213425889
2.11836149352.10331872.2295597644
2.11179581522.08742849552.2355116519
2.11034848622.06716220572.2288550065
2.10837434882.05604604342.2285461922
2.09298232692.03426364762.2186617426
2.07240761122.01323689792.2133395917
2.06442083292.00435331512.220275428
2.07744611532.01526602672.2321318753
2.04575355111.97061510022.2038975411
2.04161257181.96055454392.2047973143
2.0421626851.96472732752.2045667586
2.05909912731.98136950472.2067139902
2.05740496391.9769848062.1999519014
2.05296026261.973790652.1867200467
2.0418139441.94638123512.1746069769
2.04478626521.95161744872.1733311876
2.0361488651.92667791532.1647548103
2.0306880461.92537602892.1677269354
2.0219758121.91869311652.1639175838
2.01328015481.91452230092.1563309374
2.00650935531.8900613632.1375627757
2.00923730621.91030327462.1438838341
2.01025731491.92159767642.1432514003
2.00466887841.91045424222.1588319435
2.00659080381.90631111422.1712520964
2.00217332971.89793186072.1566298304
1.9655546961.85147094872.1200898938
1.95965010381.86205788252.1225478723
1.97961280521.88464104082.1397578677
1.9250584931.82529400842.0941321225
1.93799546731.85177041292.1047464334
1.9324715021.83136430512.1122366864
1.95045191141.86742972352.1085350316
1.95557513481.86524485622.1135883221
1.9644505781.85463106182.1329247123
1.94434721171.81958955362.0998564502
1.94782537041.82490144982.1014554535
1.94214732781.81674478552.1109839262
1.91731960231.78965334262.0766249842
1.92422051111.78881652012.0693178234
1.94673614861.81151162542.0842781273
1.94217780861.79233515632.0872530859
1.9395523531.7973202292.0841485117
1.94266822891.81027806252.0895475447
1.92902306321.7938622822.0807563772
1.94483320831.82584493242.0896812429
1.92952561261.8128524962.0725595427
1.92038464191.81066344252.0531894131
1.95288052631.85058121922.0762525882
1.93929074931.82361727362.0776031434
1.95435372811.83933002682.0933178059
1.93421721851.81637925912.086490293
1.92704999321.80703443782.0812990925
1.95361006561.83730729522.1026895941
1.96686944831.85560043642.1097305064
1.94405013461.83029235542.0898421753
1.94085831031.84043880582.0931821139
1.95216804681.84583645542.10424097
1.9556368331.86753660232.0944204878
1.97110820551.8713795272.1031310674
1.9757034491.8534639262.1145612429
1.96701845681.83524937662.1060090728
1.96661401211.83764630382.1046804553
1.98274458891.84861861062.1189665295
1.98153059541.84135384982.1174807952
1.97863758471.83719527282.1244379993
1.97154058671.83751459112.1234024505
1.97750677261.84942184482.1255918434
1.98973152231.83875096452.1526580502
1.98321662861.83151873232.1484881468
1.99026452641.84693321192.1562746275
2.01481892211.88130075192.1758319897
2.02813677871.89701055222.1900925487
2.03035547461.9145516472.194740443
2.02536608481.92323687352.1863426276
2.02473949551.92515413152.1798288737
2.04168111041.95179448292.1839798395
2.03837005241.95402301332.1828630187
2.03886594621.95465325112.1764911225
2.03328858251.95775361372.1833820121
2.02998436531.96191128332.1862744283
2.00119582941.92367042752.1543082706
1.97620069791.8958643772.1364634948
1.98275091851.90801410342.1317035583
1.97932762511.91087721472.1244306856
1.96998158751.89220749182.113629438
1.97309981381.90268052462.1259069499
1.995611051.92189911632.1497313258
1.99694840561.93277938882.1527443876
2.00089162561.9432963772.1555693526
2.02327712661.92546065942.1598998806
2.02504373621.92268816842.1556431322
2.03482463031.93430400542.1595937274
2.0414275271.94421158662.1589823971
2.04811063481.95882000962.1644804707
2.04022576551.94620572122.1554365465
2.05054290031.9639520482.1629860318
2.05677142021.96760617242.1660408702
2.07181711971.98955146492.172581645
2.07700655762.0028595522.1806604758
2.0743256552.00761108142.1707165044
2.07076523742.02271727182.1573307308
2.08122796662.03079918872.1596309787
2.09202444842.07998804122.1691577593
2.07239607462.07412567492.151503439
2.07601581332.06455932642.1438755119
2.09450150052.07272070362.153503898
2.0772609282.04597850152.136927696
2.09421687942.05130585582.1559815169
2.0835664672.04901615592.1519856283
2.0769623172.0522368442.1441796078
2.09294067332.06198786352.152512251
2.09879444862.07433293392.1781708315
2.11338117352.0915724332.1763063754
2.12500568672.10607993832.1821716398
2.13316557112.12459236932.1860716157
2.13050697712.12262054432.1971887246
2.14082533212.12960907522.2172267322
2.14017876572.13706848772.2233145741
2.13441088132.11668300552.2086564099
2.11466541252.10234213512.1980313166
2.11118958462.11332390732.2042126702
2.11391839032.1218703732.2061266122
2.11417833152.11481044882.2107201441
2.12009831662.10820363352.2018685006
2.13327995152.10352719852.2107145448
2.14431368032.0932164732.2244521069
2.14370845582.08955694922.2258128934
2.1430726632.08159334442.2264114758
2.12916218492.06540869052.2190323765
2.1262126142.06221566662.2188696029
2.09191940912.01249523812.1942365262
2.08007656031.99959963162.1913401878
2.11764807172.03649677922.2004021444
2.1229838332.03222609882.2074446767
2.11063211671.99863694912.1968377438
2.11885532292.01491176732.2094362406
2.14687775072.04044898852.2294815299
2.13775364152.01014025432.2226528355
2.15409244382.02555705612.2295622796
2.16570437532.02994242722.2335376924
2.16186311112.01903611922.2230972389
2.13857652272.01827345352.2144982746
2.1237770362.01606239292.2053896546
2.09443558631.99481081022.1843984563
2.08790903671.96209096292.191221292
2.07866657271.97221144182.1817544858
2.07947344431.96712035812.1816719898
2.05884539861.94742622732.1698306715
2.04431836421.92238276912.152654527
2.0483417591.94373067592.1650528672
2.04984047291.93893720462.1648726029
2.02169858561.90768505182.1553002523
2.02400850031.90410022452.1507913571
2.03257712011.91176297872.1527209621
2.02051160211.9054471492.1461238803
2.0306456651.91491012632.1506801432
2.04179529731.93415584542.1592186334
2.04805764041.92628336632.1690756249
2.06026190231.92609076072.1692174447
2.06514334091.91976724122.1739074319
2.06699512511.91591365752.161831372
2.07190279531.92833278592.1713733599
2.07461499021.9448688572.1756938571
2.07019485341.91639716882.1724797792
2.06048787181.91867065082.1748342276
2.05882731791.91715126672.1782121196
2.04894499571.91139931862.1774487856
2.04594766171.90429318982.17942126
2.03374189361.88779203872.171264205
2.02656731811.88181101852.1691545101
2.00970901051.86758219372.1593961919
2.01966549691.87451125352.1591661071
2.01489755061.86377596992.1589171498
2.01960253991.86426906342.162407453
2.01998124911.86401644422.1716013957
1.97961635971.83388932192.1354991434
1.97961635971.83388932192.1354991434
2.00304867741.85195784732.1721892122
2.00478184641.85430175432.1739124435
2.03072378771.87721286632.2030714271
2.02773757941.87509539772.2145041447
2.03860205121.89114083712.218666587
2.03876775381.88747208732.233377604
2.04830756751.88500442432.2432352028
2.05053295461.87848237192.2286330254
2.0412168311.87648881082.2056091466
2.0524815651.89955849972.1991038252
2.07509002841.91422270662.221181601
2.07751073251.91849062192.226274883
2.06091370131.90100021832.2134543478
2.0637704021.89627185112.2019468567
2.05497393771.88338164012.1988183502
2.06156877491.88451131362.1961093956
2.07897643171.90035636332.200018713
2.08163826161.89445575952.2028866189
2.10004868831.92034566382.2237160833
2.10034423971.93429074542.2291020365
2.08650004011.92570953862.2224495961
2.09334125521.93392579632.2398456164
2.10566575261.94509043992.2452329736
2.0855147241.94458522612.2312517765
2.09425645481.97086726262.2333097889
2.11728898712.0029888842.2643449262
2.13076950922.01575012622.2803626363
2.12421253642.01592327272.2650863088
2.11015363842.00526803132.2552884447
2.11926675732.0157816492.2474762686
2.12060219192.00783160652.2491929548
2.09745777441.98501685732.2413342521
2.07918146841.95549074992.2335721674
2.07860015841.93823166582.2392990628
2.0768587811.93547655912.2436276103
2.0732885351.93223174662.2550104277
2.06995722811.93264598162.2640732157
2.06249363241.94326964112.2488544773
2.03966200281.94599866582.2291866602
2.05483879561.94583500182.2235449319
2.06174280471.99567821152.228684643
2.07453135452.00746949362.2391148949
2.05200186041.9809872392.2371176729
2.07235124642.00125910892.2494314518
2.07635774292.01285726812.2573182915
2.07000665022.0083638562.251984475
2.08484665622.02228197792.2696768803
2.1019361482.03573461582.2726523773
2.11350296932.04353524362.2714992814
2.11707025512.05218298632.2715337094
2.11820504242.06849761842.2731922929
2.11446704852.07718888452.2829818465
2.09968623692.05999914712.2778101411
2.10651334742.06840196192.2776019324
2.11327386662.06819055132.2740296638
2.1090456382.07382103192.2597901095
2.12415732992.07655613342.2692298758
2.13332779012.0796549152.2649502921
2.13964663522.07224869852.263463895
2.13291853482.07283498262.2534209376
2.11724552072.05503746622.238739892
2.12767751412.06929023422.239033104
2.13856961992.06693485362.2412113941
2.14845623312.0678550012.238369743
2.1566932342.07974363432.241578471
2.17440525142.08671601152.2425580907
2.18271682992.11397939872.2450357206
2.18495854652.11350724252.2476757495
2.16501974992.11244002612.2387939074
2.18091566122.12098408562.2463265202
2.17805036282.10960853882.2431641034
2.16205250322.12076971512.2345019737
2.17202144292.12025344872.2471258076
2.16630469492.12134489122.2381807004
2.16558856132.13361748792.2354959307
2.16481117532.13960420572.2388242814
2.17186357812.14468762462.2418049207
2.16985940072.09754518882.240461113
2.16985940072.09754518882.240461113
2.16985940072.09754518882.240461113
2.16641381762.09841392942.2417525994
2.17812298712.10996684242.2499454914
2.17376680372.11398246522.2464912174
2.17398387472.099593942.2496001635
2.17800033822.10611895852.2509598345
2.19808792542.12606181712.2527258919
2.21728720422.14554779892.2560561667
2.23152890652.14073122132.2631669596
2.23707377532.15933612322.2733894155
2.23707377532.15933612322.2733894155
2.26009178222.17706570922.2871080033
2.2681153542.17971764732.3081338664
2.2705984012.17505394112.3079177383
2.24882205242.16032170252.3041716607
2.24873367062.16300884542.3046876684
2.23938123452.15835146682.3051650021
2.2454688492.16339885322.3113625159
2.25982317112.17446331722.3246259574
2.28423345762.18749381492.3349633773
2.27171270852.17634483382.3369326628
2.26568741162.16721181582.3333377716
2.25227709962.14852319542.3195016372
2.24818998622.1445023952.3224049935
2.24295236272.13824441612.3117782503
2.21391674042.10816828372.2752121344
2.2148590822.1138299182.2727576344
2.2154635122.11031465842.265722992
2.20021879062.09894021472.2582281091
2.19721696582.09524170192.2566015523
2.18674974152.08962572182.2452776389
2.19958838982.09592080662.2519067476
2.21354021782.10822158312.2745596296
2.22089598952.12010794262.2836633078
2.22601202452.12210503792.285641707
2.22044308692.10624346772.2828277417
2.23062177732.10974712722.2925258861
2.2119869662.08015702552.2850554469
2.1909220782.05135223022.2784067655
2.18951094622.0397581722.2781493291
2.19403580912.04355938632.2772832683
2.17606326032.04129530142.2715917459
2.17596244022.04752491012.278809499
2.17784618842.04422814122.2846554248
2.18278943152.05903402772.2930591488
2.17747791352.06427107252.2936959195
2.1773733262.07555482912.2948828803
2.16316881372.05453154562.292213397
2.16781956842.05232425462.2940848229
2.16719861032.04775869222.3006069323
2.16863285132.0601581942.3111599811
2.17561828132.07039972552.310929514
2.1799024932.08596530762.3153726327
2.18909376652.09605727722.3246930909
2.20067775232.11368274642.3480939941
2.20851552932.11618442822.354722155
2.20771964472.1061735472.3539421485
2.20826218742.1015664372.3548621766
2.21047155042.11441768952.3565754036
2.2120946952.12431881092.355598177
2.21259541222.12491583372.3560455096
2.20789881122.12608532912.3523797949
2.20353384222.11911240152.3506070385
2.18461328142.07498931022.3322441552
2.19177452232.07558471472.329901308
2.1941308692.07226393962.3309585062
2.18573238072.06835201692.3269439508
2.17029970852.05308712892.3174233831
2.16311700522.03596959942.3137288212
2.16472799252.02079548732.314499783
2.15170931092.00707194982.3077699494
2.15174591552.00408814132.30711718