{"id":6292,"date":"2023-04-10T16:33:31","date_gmt":"2023-04-10T14:33:31","guid":{"rendered":"https:\/\/dobretrejdy.com\/?p=6292"},"modified":"2024-08-18T16:47:40","modified_gmt":"2024-08-18T14:47:40","slug":"dluhopisy-viii","status":"publish","type":"post","link":"https:\/\/dobretrejdy.com\/?p=6292","title":{"rendered":"Dluhopisy – VIII."},"content":{"rendered":"

\u00a0 \u00a0Lep\u0161\u00ed okam\u017eik pro naps\u00e1n\u00ed tohoto \u010dl\u00e1nku jsem si ani nemohl p\u0159\u00e1t. Lehk\u00e9 n\u00e1znaky bankovn\u00ed krize vypl\u00fdvaj\u00edc\u00ed z podivn\u00e9 likvidity speci\u00e1ln\u00edch bankovn\u00edch dom\u016f opep\u0159en\u00e9 koment\u00e1\u0159i jejich v\u00edce \u010di m\u00e9n\u011b schopn\u00fdch p\u0159edstavitel\u016f p\u0159in\u00e1\u0161ej\u00ed na p\u0159elomu m\u011bs\u00edce b\u0159ezna a dubna 2023 skv\u011bl\u00fd r\u00e1mec pro t\u00e9ma tohoto \u010dl\u00e1nku. Jakou roli v t\u00e9to \u0161lamastyce sehr\u00e1ly z\u00e1kladn\u00ed vlastnosti dluhopis\u016f bude p\u0159edm\u011btem n\u00e1sleduj\u00edc\u00edch \u0159\u00e1dk\u016f.<\/span><\/p>\n

\n

\u00a0\u00a0 Rostouc\u00ed \u00farovn\u011b \u00farokov\u00fdch sazeb znamenaj\u00ed pro dluhov\u00e9 cenn\u00e9 pap\u00edry s pevn\u00fdm v\u00fdnosem pokles jejich ceny a naopak, poklesy hodnot \u00farokov\u00fdch sazeb na trz\u00edch znamenaj\u00ed pro tyto cenn\u00e9 pap\u00edry r\u016fst jejich aktu\u00e1ln\u00edch cen. Ob\u011b tyto z\u00e1vislosti ji\u017e byly v dosavadn\u00edch \u010dl\u00e1nc\u00edch o dluhopisech pops\u00e1ny s nazna\u010den\u00edm, co by mohlo tyto z\u00e1vislosti vysv\u011btlovat. Pokud jsem tedy dr\u017eitelem dluhopisu, bude m\u011b p\u0159edev\u0161\u00edm zaj\u00edmat, jak takovou skute\u010dnost kvantifikovat, jak ur\u010dit m\u00edru z\u00e1vislosti pohybu \u00farokov\u00fdch sazeb na cen\u011b dr\u017een\u00e9ho dluhopisu a p\u0159\u00edpadn\u011b, jak\u00e9 n\u00e1stroje k tomu mohu vyu\u017e\u00edt. Z\u00e1kladn\u00ed pochopen\u00ed t\u011bchto \u201em\u011b\u0159\u00edc\u00edch n\u00e1stroj\u016f\u201c pak m\u016f\u017ee b\u00fdt dobr\u00fdm z\u00e1kladem pro jejich spr\u00e1vnou interpretaci a m\u016f\u017ee tak\u00e9 spoluvytv\u00e1\u0159et rozhodnut\u00ed, kdy do t\u011bchto dluhov\u00fdch cenn\u00fdch pap\u00edr\u016f vstoupit a jak\u00e9 si k tomu vybrat.<\/span><\/p>\n

\u00a0\u00a0 V\u00a0p\u0159edchoz\u00edch \u010dl\u00e1nc\u00edch jsem popisoval mou konkr\u00e9tn\u00ed investici, kterou m\u00e1m na sv\u00e9m obchodn\u00edm \u00fa\u010dtu, a to investici do p\u011btilet\u00e9ho dluhopisu Ford s\u00a0kup\u00f3nem 6.625% p.a. a se splatnost\u00ed 15.2.2028, vyu\u017eiji tak pro uk\u00e1zku z\u00e1vislosti ceny a v\u00fdnosu dluhopisu op\u011bt tento konkr\u00e9tn\u00ed dluhopis. Mohu pozorovat, na obr\u00e1zku n\u00ed\u017ee, jeho aktu\u00e1ln\u00ed cenov\u00e9 parametry.<\/span><\/p>\n

\"\"<\/p>\n

\u00a0\u00a0 Aktu\u00e1ln\u011b bych byl schopen nakoupit tento dluhopis za cenu 1.024,73 USD<\/strong>. Nyn\u00ed u\u017e v\u00edm, \u017ee investice do tohoto dluhopisu by p\u0159edstavovala v\u00fdnos do splatnosti 5.838%<\/strong> p.a., tento v\u00fdpo\u010det jsem popisoval v \u010dl\u00e1nku Dluhopisy \u2013 V.<\/a><\/strong><\/span>, kdy\u017e p\u0159i jeho v\u00fdpo\u010dtu jsem vych\u00e1zel z\u00a0excelovsk\u00e9 tabulky, kterou jsem si pro tento \u00fa\u010del vytvo\u0159il. Tento v\u00fdpo\u010det je na obr\u00e1zku n\u00ed\u017ee.<\/span><\/p>\n

\"\" \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/p>\n

\u00a0\u00a0 Pro p\u0159ipomenut\u00ed, co vlastn\u011b na obr\u00e1zku mohu vypozorovat, upozorn\u00edm na z\u00e1kladn\u00ed momenty tohoto v\u00fdpo\u010dtu. Aktu\u00e1ln\u00ed cena 1.024,70 USD (1)<\/span><\/strong> mus\u00ed b\u00fdt zat\u00ed\u017eena \u010d\u00e1stkou -9.0174 USD (2)<\/span><\/strong>, kter\u00e1 p\u0159edstavuje \u00faroky, kter\u00e9 mi nepat\u0159\u00ed a budou mi sra\u017eeny v\u00a0p\u0159\u00edpad\u011b, \u017ee bych opravdu tento dluhopis nyn\u00ed nakoupil a p\u0159edstavuj\u00ed nab\u011bhl\u00e9 \u00faroky z\u00a0kup\u00f3nu za dobu od jeho posledn\u00ed v\u00fdplaty dne 15.2.2023 (3)<\/strong> <\/span>do dne, kdy si jej po\u0159\u00edd\u00edm. Mus\u00edm tak svou investici upravit na pat\u0159i\u010dnou cenu ve v\u00fd\u0161i -1.033,717 USD (4)<\/span><\/strong>, kter\u00e1 je sou\u010dtem po\u0159izovac\u00ed ceny a tohoto \u201em\u011b nen\u00e1le\u017eej\u00edc\u00edho\u201c \u00faroku. Mohu pak pozorovat, \u017ee m\u011b v budoucnu \u010dek\u00e1 deset pen\u011b\u017en\u00edch tok\u016f (5)<\/span><\/strong>, kup\u00f3nov\u00fdch v\u00fdplat, kdy posledn\u00ed kup\u00f3nov\u00e1 platba je doprov\u00e1zena spl\u00e1tkou Face Value dluhopisu. Excel mi vypo\u010d\u00edt\u00e1 v\u00fdnos do splatnosti<\/strong> (YTM) ve v\u00fd\u0161i 5.838% p.a. (6)<\/span><\/strong>. Mohu pak p\u0159istoupit k jednoduch\u00e9mu modelov\u00e1n\u00ed<\/strong> a pomoc\u00ed diskontov\u00e1n\u00ed budouc\u00edch cash flow z dluhopisu podle mnou zadan\u00e9ho po\u017eadovan\u00e9ho v\u00fdnosu (7)<\/strong><\/span> cht\u00edt zjistit, jak\u00e1 by byla jeho aktu\u00e1ln\u00ed cena. Konkr\u00e9tn\u011b, pokud bych po\u017eadovat v\u00fdnos do splatnosti ve v\u00fd\u0161i 6% p.a., musel bych b\u00fdt schopen nakoupit dluhopis za \u010d\u00e1stku 1.026,66 USD (8)<\/strong><\/span>, tedy musel bych jej po\u0159\u00eddit zhruba o \u0161est dolar\u016f levn\u011bji ne\u017e nyn\u00ed. U tohoto modelov\u00e1n\u00ed nyn\u00ed z\u016fstanu.<\/span><\/p>\n

\u00a0\u00a0 Nab\u00edzenou mo\u017enost modelovat<\/strong> a n\u00e1sledn\u011b prozkoumat v\u00fdvoj ceny dluhopisu v z\u00e1vislosti na po\u017eadovan\u00e9m v\u00fdnosu jsem vyu\u017eil pro zji\u0161t\u011bn\u00ed tohoto chov\u00e1n\u00ed na \u0161k\u00e1le po\u017eadovan\u00e9ho v\u00fdnosu v rozmez\u00ed od -3% p.a.<\/strong> a\u017e po +50% p.a.<\/strong> a v\u00fdsledek takov\u00e9ho zkoum\u00e1n\u00ed jsem si nechal zobrazit graficky, n\u00ed\u017ee je v\u00fdsledek:<\/span><\/p>\n

\"\"<\/p>\n

\u00a0\u00a0 Pravd\u011bpodobn\u011b v\u00a0ka\u017ed\u00e9 publikaci nebo obecn\u00e9m \u010dl\u00e1nku o dluhopisech budete moci spat\u0159it takto podobn\u011b vykreslenou z\u00e1vislost ceny dluhopisu na jeho v\u00fdnosu. Co bude pro tuto chv\u00edli st\u011b\u017eejn\u00ed, je pozn\u00e1n\u00ed z\u00e1kladn\u00ed charakteristiky t\u00e9to k\u0159ivky, a to konstatov\u00e1n\u00ed, \u017ee jej\u00ed tvar je konvexn\u00ed<\/strong>. \u00a0Nen\u00ed to tedy \u017e\u00e1dn\u00e1 line\u00e1rn\u00ed z\u00e1vislost, nicm\u00e9n\u011b vykreslen\u00fd tvar napov\u00edd\u00e1, \u017ee s r\u016fstem po\u017eadovan\u00e9ho v\u00fdnosu dluhopisu (zleva doprava) kles\u00e1 jeho cena a naopak. Mohu pak nyn\u00ed na t\u00e9to k\u0159ivce vyzna\u010dit alespo\u0148 dva \u201ekritick\u00e9 body\u201c<\/strong>, kter\u00e9 by m\u011b mohly v tuto chv\u00edli zaj\u00edmat.<\/span><\/p>\n

\u00a0\u00a0 1\/ Hodnot\u011b 0% v\u00fdnosu<\/strong> odpov\u00edd\u00e1 cena<\/strong> dluhopisu ve v\u00fd\u0161i 1.331,25 USD<\/strong>. Co to znamen\u00e1? V\u00fdpo\u010det v\u00fdnosu do splatnosti (\u010dl\u00e1nek Dluhopisy \u2013 V.<\/a><\/strong><\/span>) vych\u00e1z\u00ed z\u00a0\u00favahy, \u017ee po\u0159\u00edzen\u00ed kup\u00f3nov\u00e9ho dluhopisu za ur\u010ditou cenu (v m\u00e9m p\u0159\u00edpad\u011b 1033,717 USD) s\u00a0ur\u010dit\u00fdm kup\u00f3nem (v m\u00e9m p\u0159\u00edpad\u011b 6.625% p.a.) bude p\u0159edstavovat ur\u010dit\u00fd vypo\u010d\u00edtan\u00fd v\u00fdnos do splatnosti (v m\u00e9m p\u0159\u00edpad\u011b 5.838% p.a.) za spln\u011bn\u00ed p\u0159edpokladu, \u017ee v\u0161echny kup\u00f3nov\u00e9 platby budu v\u00a0budoucnosti reinvestovat pr\u00e1v\u011b s vypo\u010d\u00edtanou \u00farokovou sazbu 5.828% p.a., potom mohu s\u00a0takto vypo\u010d\u00edtan\u00fdm v\u00fdnosem opravdu po\u010d\u00edtat (neberu v\u00a0\u00favahu p\u0159ed\u010dasn\u00e9 svol\u00e1v\u00e1n\u00ed emise \u2013 Call). Pokud bych se ov\u0161em rozhodl, \u017ee tento p\u011btilet\u00fd dluhopis Ford 6.625% nakoup\u00edm a \u017e\u00e1dn\u00e9 reinvestice kup\u00f3n\u016f prov\u00e1d\u011bt nebudu<\/strong>, nesm\u00edm jej koupit za cenu vy\u0161\u0161\u00ed<\/strong> ne\u017e je cena 1.331,25 USD<\/strong>, proto\u017ee pr\u00e1v\u011b tato cena p\u0159edstavuje sou\u010det v\u0161ech budouc\u00edch plateb kup\u00f3n\u016f a splacen\u00ed Face Value tak, abych obdr\u017eel alespo\u0148 p\u016fvodn\u00ed investici ve v\u00fd\u0161i 1331,25 USD zp\u011bt. Konkr\u00e9tn\u011b: -1.331,25 USD po\u0159izovac\u00ed cena dluhopisu + (10*kup\u00f3n ve v\u00fd\u0161i 33.125 USD) + (1.000 USD Face Value u maturity) = -1.331,25 + 331,25 USD + 1.000 USD = 0. \u00a0\u00a0<\/span><\/p>\n

\u00a0 \u00a02\/ Hodnot\u011b 6.625% v\u00fdnosu<\/strong> odpov\u00edd\u00e1 cena dluhopisu ve v\u00fd\u0161i 1.000,00 USD<\/strong>. Pokud se rovn\u00e1 po\u017eadovan\u00fd v\u00fdnos<\/strong> dluhopisu hodnot\u011b jeho kup\u00f3nu<\/strong> (6.625% p.a.), m\u011bla by b\u00fdt jeho cena rovna hodnot\u011b Face Value<\/strong>. Tento v\u00fdnos do splatnosti je tak hrani\u010dn\u00edm bodem, kde se l\u00e1me cena dluhopisu vzhledem ke sv\u00e9 Face Value, v\u00fdnosy vy\u0161\u0161\u00ed ne\u017e vyzna\u010den\u00fd kup\u00f3n znamenaj\u00ed cenu ni\u017e\u0161\u00ed ne\u017e je Face Value a naopak, v\u00fdnosy ni\u017e\u0161\u00ed ne\u017e vyzna\u010den\u00fd kup\u00f3n znamenaj\u00ed cenu vy\u0161\u0161\u00ed ne\u017e je Face Value.<\/span><\/p>\n

Stejn\u00fd dluhopis \u2013 jin\u00fd kup\u00f3n<\/span><\/strong><\/h2>\n

\u00a0\u00a0 Aktu\u00e1ln\u00ed \u00farokov\u00e9 sazby se m\u011bn\u00ed na trz\u00edch neust\u00e1le a stejn\u011b tak se prom\u00edtaj\u00ed do ceny dluhopis\u016f, jejich ceny odpov\u00eddaj\u00edc\u00edm zp\u016fsobem fluktuuj\u00ed a odr\u00e1\u017eej\u00ed tak jejich aktu\u00e1ln\u00ed v\u00fd\u0161i. P\u0159esto\u017ee se do ceny dluhopis\u016f prom\u00edtaj\u00ed dal\u0161\u00ed cenotvorn\u00e9 prvky, nap\u0159\u00edklad doba do splatnosti dluhopisu nebo kreditn\u00ed riziko popisovan\u00e9 v minul\u00e9m \u010dl\u00e1nku<\/a><\/strong><\/span>, je vliv \u00farokov\u00fdch sazeb na jejich cenu z\u00e1sadn\u00ed a zaslou\u017e\u00ed si v\u00edce m\u00e9 pozornosti. Mohu tak nyn\u00ed modelov\u00e1n\u00ed roz\u0161\u00ed\u0159it na pozorov\u00e1n\u00ed, jak by vypadalo p\u016fsoben\u00ed t\u00e9to zm\u011bny \u00farokov\u00fdch na cenu dluhopisu v\u00a0p\u0159\u00edpad\u011b, \u017ee budu srovn\u00e1vat dluhopisy se stejnou dobou splatnosti<\/strong> a stejn\u00fdm aktu\u00e1ln\u00edm v\u00fdnosem<\/strong>, pouze se budou li\u0161it velikost\u00ed vyzna\u010den\u00e9ho kup\u00f3nu<\/strong>. Konkr\u00e9tn\u011b srovn\u00e1m m\u016fj nakoupen\u00fd p\u011btilet\u00fd dluhopis Ford s kup\u00f3nem 6.625% s fiktivn\u00edm dluhopisem Ford se stejnou dobou do splatnosti, tento by m\u011bl v\u0161ak kup\u00f3n pouze 2.00 % p.a. Na obr\u00e1zku n\u00ed\u017ee srovn\u00e1n\u00ed obou k\u0159ivek \u2013 p\u016fvodn\u00edho dluhopisu s kup\u00f3nem 6.625% a dluhopisu s ni\u017e\u0161\u00edm kup\u00f3nem.<\/span><\/p>\n

\u00a0 \"\"<\/span><\/p>\n

\u00a0\u00a0 P\u011btilet\u00fd dluhopis<\/strong> s\u00a0kup\u00f3nem 6.625%<\/strong> (modr\u00e1 k\u0159ivka) s\u00a0aktu\u00e1ln\u00edm v\u00fdnosem 5.838%<\/strong> by dnes st\u00e1l 1.033,717 USD<\/strong> (s p\u0159ipo\u010d\u00edtan\u00fdmi n\u00e1klady na \u00farok, kter\u00fd mi nepat\u0159\u00ed), stejn\u00fd p\u011btilet\u00fd dluhopis<\/strong> se stejn\u00fdm po\u017eadovan\u00fdm v\u00fdnosem 5.838%<\/strong> ov\u0161em s\u00a0kup\u00f3nem pouze 2% p.a.<\/strong> by pak musel st\u00e1t mnohem m\u00e9n\u011b a proto\u017ee po\u017eadovan\u00fd v\u00fdnos je vy\u0161\u0161\u00ed ne\u017e jeho kup\u00f3n, mus\u00ed jeho cena b\u00fdt siln\u011b pod Face Value. Aktu\u00e1ln\u011b bych jej po\u0159\u00eddil za 832.90 USD<\/strong>. V\u00a0proveden\u00e9 simulaci pak bude k\u0159ivka mapuj\u00edc\u00ed zm\u011bnu ceny s\u00a0ohledem na v\u00fdnos (\u010derven\u00e1 k\u0159ivka) na ni\u017e\u0161\u00edch \u00farovn\u00edch, bude v\u0161ak m\u00edt m\u00edrn\u011b jin\u00fd sklon. Na obr\u00e1zku jsem vyzna\u010dil pohyb \u00farokov\u00fdch sazeb z\u00a0hladiny 4% na 10%. Mohu pak pozorovat, \u017ee oba dluhopisy ztrat\u00ed na sv\u00e9 cen\u011b, ka\u017ed\u00fd ale jinak. Dluhopis s\u00a0vy\u0161\u0161\u00edm kup\u00f3nem<\/strong> 6.625% p.a. ztrat\u00ed z\u00a0ceny 1117.90 hodnotu 248.20 USD a jeho cena bude o -22% ni\u017e\u0161\u00ed<\/strong> a bude na \u00farovni 869.70 USD. Dluhopis s\u00a0ni\u017e\u0161\u00edm kup\u00f3nem<\/strong> 2% p.a. spadne z\u00a0ceny 910,17 USD p\u0159ipadaj\u00edc\u00ed na 4% p.a. v\u00fdnos na \u00farove\u0148 691.13 USD p\u0159edstavuj\u00edc\u00ed v\u00fdnos 10% p.a., tento pokles o -219.04 USD ale p\u0159edstavuje -24%<\/strong>. Mohu nyn\u00ed konstatovat (popsat dal\u0161\u00ed vypozorovanou vlastnost), \u017ee stejn\u00e9 dluhopisy se stejnou splatnost\u00ed a aktu\u00e1ln\u00edm v\u00fdnosem nebudou reagovat na zm\u011bnu \u00farokov\u00fdch sazeb stejn\u011b, n\u00e1chyln\u011bj\u0161\u00ed na zm\u011bnu ceny budou dluhopisy s\u00a0ni\u017e\u0161\u00edm kup\u00f3nem. \u010cek\u00e1m zv\u00fd\u0161en\u00ed \u00farokov\u00fdch sazeb<\/strong> a chci nakoupit dluhopisy, pokud budu cht\u00edt vyb\u00edrat mezi dluhopisy se stejnou splatnost\u00ed, m\u011bl bych se zam\u011b\u0159it na ty s\u00a0vy\u0161\u0161\u00edm kup\u00f3nem<\/strong>, jejich cenov\u00fd pokles v\u00a0souvislost\u00ed se zv\u00fd\u0161en\u00ed \u00farokov\u00fdch sazeb nebude tak siln\u00fd, jako u stejn\u00e9ho typu dluhopisu s\u00a0ni\u017e\u0161\u00edm kup\u00f3nem. O\u010dek\u00e1v\u00e1n\u00ed sn\u00ed\u017een\u00ed \u00farokov\u00fdch sazeb by m\u011blo doprov\u00e1zet opa\u010dn\u00e9 rozhodnut\u00ed.<\/span><\/p>\n

Stejn\u00fd dluhopis \u2013 jin\u00e1 splatnost<\/strong><\/span><\/h2>\n

\u00a0\u00a0 Rozhodov\u00e1n\u00ed o po\u0159\u00edzen\u00ed dluhopisu v\u00a0souvislost\u00ed s\u00a0o\u010dek\u00e1v\u00e1n\u00edm pohybu \u00farokov\u00fdch sazeb aplikovan\u00e9 na dluhopisy se stejnou kvalitou, stejnou dobou do splatnosti a stejn\u00fdm aktu\u00e1ln\u00edm v\u00fdnosem ale s\u00a0p\u0159ihl\u00e9dnut\u00edm k\u00a0jin\u00e9 v\u00fd\u0161ce kup\u00f3nu mohu obohatit o dal\u0161\u00ed rozhodovac\u00ed proces. Mohu srovnat p\u016fvodn\u011b nakoupen\u00fd p\u011btilet\u00fd dluhopis Ford s\u00a0kup\u00f3nem 6.625% s\u00a0fiktivn\u00edm dluhopisem se stejn\u00fdm kup\u00f3nem, ov\u0161em se splatnost\u00ed deset let, tedy dvojn\u00e1sobnou d\u00e9lkou do maturity<\/strong>. Na obr\u00e1zku n\u00ed\u017ee graficky zn\u00e1zorn\u011bn\u00e1 z\u00e1vislost ceny dluhopisu na zm\u011bn\u011b v\u00fdnosu.<\/span><\/p>\n

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\u00a0\u00a0 Na prvn\u00ed pohled je jist\u00e9, \u017ee mezi k\u0159ivkami zn\u00e1zor\u0148uj\u00edc\u00ed citlivost ceny dluhopisu na zm\u011bnu v\u00fdnosu m\u00e1 strm\u011bj\u0161\u00ed charakter k\u0159ivka identicky kvalitn\u00edho dluhopisu<\/strong> se stejn\u00fdm kup\u00f3nem a aktu\u00e1ln\u00edm v\u00fdnosem li\u0161\u00edc\u00edm se pouze d\u00e9lkou splatnosti<\/strong> (zelen\u00e1 k\u0159ivka). Mohu pak prov\u00e9st obdobnou simulaci pohybu \u00farok\u016f z hladiny 4% p.a. na \u00farove\u0148 10% p.a. a pozorovat, jak se zm\u011bn\u00ed ceny t\u011bchto dluhopis\u016f. P\u016fvodn\u00ed p\u011btilet\u00fd dluhopi<\/strong>s Ford s kup\u00f3nem 6.625% ztrat\u00ed p\u0159i takov\u00e9m pohybu \u00farokov\u00fdch sazeb -22%<\/strong> sv\u00e9 ceny, to se oproti simulaci v\u00fd\u0161e v odstavci nezm\u011bnilo. Identick\u00fd dluhopis, ov\u0161em s dvojn\u00e1sobnou dobou do splatnosti, v\u0161ak ztrat\u00ed ze sv\u00e9 ceny 1214.61 USD vypo\u010d\u00edtan\u00e9 pro v\u00fdnos na \u00farovni 4% p.a. \u010d\u00e1stku -424.91 USD, proto\u017ee cena tohoto desetilet\u00e9ho dluhopisu<\/strong> p\u0159i v\u00fdnosu 10% p.a. bude pouze 789.70 USD, tento pokles ceny pak p\u0159edstavuje zna\u010dn\u00fdch -35%<\/strong>. Mohu tak definovat dal\u0161\u00ed obecn\u00e9 pravidlo pro rozhodov\u00e1n\u00ed o n\u00e1kupu dluhopisu spojen\u00e9 s o\u010dek\u00e1v\u00e1n\u00edm pohybu \u00farokov\u00fdch sazeb na trz\u00edch. O\u010dek\u00e1v\u00e1m-li dal\u0161\u00ed r\u016fst \u00farokov\u00fdch sazeb<\/strong> a vyb\u00edr\u00e1m mezi stejn\u011b kvalitn\u00edmi dluhopisy se stejn\u00fdm kup\u00f3nem, u dluhopisu s\u00a0del\u0161\u00ed dobou splatnosti<\/strong> mohu o\u010dek\u00e1vat jeho v\u00fdznamn\u011bj\u0161\u00ed sn\u00ed\u017een\u00ed ceny<\/strong> ne\u017e u stejn\u011b kvalitn\u00edch dluhopis\u016f s\u00a0krat\u0161\u00ed dobou do splatnosti, obdobn\u011b samoz\u0159ejm\u011b opa\u010dn\u00e1 \u00favaha s o\u010dek\u00e1v\u00e1n\u00edm pokles\u016f \u00farokov\u00fdch sazeb. \u00a0<\/span><\/p>\n

\n

Durace<\/strong><\/span><\/h1>\n

\u00a0 Pozn\u00e1n\u00ed, \u017ee cena dluhopisu je funkc\u00ed jeho v\u00fdnosu, umo\u017e\u0148uje \u201ezmatematizov\u00e1n\u00ed\u201c t\u00e9to z\u00e1kladn\u00ed poznan\u00e9 z\u00e1vislosti. Pokud jsem mohl na tomto webu na spoust\u011b m\u00edst zkoumat, jak se m\u011bn\u00ed cena op\u010dn\u00edho kontraktu v z\u00e1vislosti na cen\u011b podkladu pomoc\u00ed \u0159eck\u00e9ho p\u00edsmene Delta, mohl bych se pokusit zjistit, jak\u00fdm zp\u016fsobem je matematicky pops\u00e1no toto z\u00e1kladn\u00ed chov\u00e1n\u00ed zm\u011bny jeho ceny v z\u00e1vislosti na zm\u011bn\u011b \u00farokov\u00fdch sazeb u dluhopisu. V \u010dl\u00e1nku Delta Neutral \u2013 VI.<\/a><\/strong><\/span> jsem v \u00favodu matematick\u00e9 \u00favahy o zm\u011bn\u011b ceny opce v z\u00e1vislosti na zm\u011bn\u011b ceny podkladu definoval tento pohyb jako prvn\u00ed derivaci cenov\u00e9 funkce t\u00e9to vlastnosti zm\u011bny ceny op\u010dn\u00edho kontraktu. Pokud jsem tedy schopen nal\u00e9zt takovou funkci popisuj\u00edc\u00ed vztah z\u00e1vislosti zm\u011bny ceny na zm\u011bn\u011b argumentu \u2013 \u00farokov\u00e9 sazby, mus\u00ed existovat matematick\u00e9 vyj\u00e1d\u0159en\u00ed, jak tento vztah zachytit. V\u00fd\u0161e uveden\u00e9 obr\u00e1zky, kter\u00e9 zachycovaly nejz\u00e1kladn\u011bj\u0161\u00ed simulace vztahu ceny a v\u00fdnosu nejsou ni\u010d\u00edm jin\u00fdm ne\u017e zobrazov\u00e1n\u00edm cenov\u00fdch funkc\u00ed nejr\u016fzn\u011bji definovan\u00fdch dluhopis\u016f v z\u00e1vislosti na zm\u011bn\u00e1ch \u00farokov\u00fdch sazeb, tedy aktu\u00e1ln\u00edho v\u00fdnosu odv\u00edjej\u00edc\u00edho se od aktu\u00e1ln\u00ed \u00farokov\u00e9 sazby na dluhopisov\u00fdch trz\u00edch, ka\u017ed\u00e1 modelovan\u00e1 zm\u011bna v\u00fdnosu p\u0159inesla jinou cenu ka\u017ed\u00e9ho konkr\u00e9tn\u00edho dluhopisu, kterou zachycovaly jednotliv\u00e9 k\u0159ivky zobrazen\u00e9 v grafech. Bylo na obr\u00e1zc\u00edch patrn\u00e9, \u017ee ka\u017ed\u00e1 z k\u0159ivek funkce ceny v z\u00e1vislosti na v\u00fdnosech m\u00e1 jinou \u201estrmost\u201c podle zadan\u00fdch vlastnost\u00ed dluhopis\u016f, tuto strmost pak lze matematicky m\u011b\u0159it. Zji\u0161t\u011bn\u00ed vlastnosti \u00fahlu, kter\u00fd sv\u00edraj\u00ed te\u010dny k t\u011bmto k\u0159ivk\u00e1m v ka\u017ed\u00e9m konkr\u00e9tn\u00edm bod\u011b, kter\u00fd pot\u0159ebuji, je pr\u00e1v\u011b kl\u00ed\u010dem k hled\u00e1n\u00ed odpov\u011bdi, jak velik\u00e1 je z\u00e1vislost ceny dluhopisu na pohybu \u00farokov\u00fdch sazeb. Na obr\u00e1zku n\u00ed\u017ee je patrn\u00e9, jak je to my\u0161leno:<\/span><\/p>\n

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\u00a0\u00a0 Zjevn\u011b vy\u0161\u0161\u00ed strmost<\/strong> a tak\u00e9 \u00fahel A sv\u00edr\u00e1 te\u010dna k cenov\u00e9 k\u0159ivce a osa \u201ex\u201c pro dluhopis Ford 6.625% se splatnost\u00ed 10 let pro v\u00fdnos 1% p.a.<\/strong> ne\u017e je strmost<\/strong> a \u00fahel B te\u010dny pro v\u00fdnos p\u0159edstavuj\u00edc\u00ed 13% p.a.<\/strong>, je pak jasn\u00e9, \u017ee v oblastech s vy\u0161\u0161\u00ed strmost\u00ed se budou ceny dluhopisu v z\u00e1vislosti na v\u00fdnosu m\u011bnit dramati\u010dt\u011bji ne\u017e v oblastech s ni\u017e\u0161\u00ed strmost\u00ed a toto um\u00ed matematika zachytit. K vyhodnocen\u00ed strmosti (jej\u00edho \u00fahlu) mus\u00edme zn\u00e1t tvar cenov\u00e9 funkce se kterou nakl\u00e1d\u00e1me, a pokud ji tedy budeme zn\u00e1t, bude n\u00e1m sta\u010dit m\u00edt pov\u011bdom\u00ed o derivov\u00e1n\u00ed a m\u00e1me vyhr\u00e1no :c). \u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0\u00a0 Cenovou funkci pro v\u00fdpo\u010det aktu\u00e1ln\u00ed ceny kup\u00f3nov\u00e9ho dluhopisu zn\u00e1me z p\u0159ede\u0161l\u00fdch \u010dl\u00e1nk\u016f, je uvedena na obr\u00e1zku n\u00ed\u017ee:\u00a0<\/span><\/p>\n

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\u00a0\u00a0 Aktu\u00e1ln\u00ed cena dluhopisu SH<\/em><\/span> je sou\u010dtem v\u0161ech budouc\u00edch pen\u011b\u017en\u00edch tok\u016f, kter\u00e9 mi po\u0159\u00edzen\u00fd dluhopis p\u0159inese diskontovan\u00fdch p\u0159\u00edslu\u0161n\u00fdm \u00farokov\u00fdm v\u00fdnosem \u00farok<\/em><\/span>. Ka\u017ed\u00e1 budouc\u00ed kup\u00f3nov\u00e1 v\u00fdplata C<\/em><\/span> a z\u00e1v\u011bre\u010dn\u00e1 spl\u00e1tka Face Value FV<\/em><\/span> vstupuje do tohoto sou\u010dtu s p\u0159edpokladem jej\u00edho reinvestov\u00e1n\u00ed za p\u0159\u00edslu\u0161nou \u00farokovou sazbu \u00farok<\/em><\/span>, hodnota n<\/em> <\/span>\u2013 je po\u010det period, kter\u00e9 tyto budouc\u00ed pen\u011b\u017en\u00ed toky p\u0159inesou. Derivov\u00e1n\u00edm t\u00e9to cenov\u00e9 funkce mohu zjistit, jak se zm\u011bn\u00ed cena dluhopisu s p\u0159ihl\u00e9dnut\u00edm ke zm\u011bn\u011b jeho v\u00fdnosu:\u00a0\u00a0<\/span><\/p>\n

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\u00a0\u00a0 Zkoum\u00e1n\u00edm t\u00e9to prvn\u00ed derivace funkce ceny dluhopisu je mo\u017en\u00e9 posuzovat vliv v\u00fdnosu \u2013 \u00farokov\u00e9 sazby na jeho cenu, tedy zkoumat vlastnosti t\u00e9to derivace cenov\u00e9 funkce podle aktu\u00e1ln\u00edho v\u00fdnosu \u2013 hodnoty \u00farok<\/em><\/span> v derivovan\u00e9 rovnici. Kanadsk\u00fd ekonom a matematik Frederic Macaulay, aby mohl posoudit tuto derivaci podle aktu\u00e1ln\u00ed ceny dluhopisu SH, provedl v t\u00e9to derivovan\u00e9 rovnici \u00fapravu vyd\u011bl\u00edm obou stran rovnice pr\u00e1v\u011b sou\u010dasnou hodnotou SH<\/em><\/span> dluhopisu a nav\u00edc v rovnici na prav\u00e9 stran\u011b vytkl v\u00fdraz 1\/(1 + \u00farok<\/em>) p\u0159ed z\u00e1vorku. Rovnice po \u00faprav\u011b pak vypadala takto:\u00a0<\/span>\u00a0 \u00a0\"\"<\/span><\/p>\n

\u00a0 \u00a0Z derivovan\u00e9 rovnice je zaj\u00edmav\u00e1 jej\u00ed \u010d\u00e1st na prav\u00e9 stran\u011b rovnice ozna\u010dena n\u00ed\u017ee:<\/span><\/p>\n

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\u00a0 \u00a0\u010cinitel – zlomek na prav\u00e9 stran\u011b rovnice <\/strong>(\u010derven\u00fd r\u00e1me\u010dek), kde d\u011blitelem je sou\u010dasn\u00e1 hodnota dluhopisu, se naz\u00fdv\u00e1 Macaulayova Durace<\/strong>, potom „\u010dist\u011bji“ zobrazeno:<\/span><\/p>\n

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\u00a0\u00a0 Macaulayova Durace<\/strong> p\u0159edstavuje v\u00e1\u017een\u00fd pr\u016fm\u011br splatnosti v\u0161ech budouc\u00edch pen\u011b\u017en\u00edch tok\u016f z po\u0159\u00edzen\u00e9ho dluhopisu, kde vahami jsou pr\u00e1v\u011b tyto pen\u011b\u017en\u00ed toky. Mohu toti\u017e ze zlomku vypozorovat, \u017ee se jedn\u00e1 o sou\u010det v\u0161ech diskontovan\u00fdch plateb kup\u00f3n\u016f a z\u00e1v\u011bre\u010dn\u00e9 v\u00fdplaty Face Value, co\u017e ji\u017e b\u011b\u017en\u011b d\u011bl\u00e1m ve sv\u00e9m excelu ke zji\u0161t\u011bn\u00ed v\u00fdnosu do splatnosti, pouze je ka\u017ed\u00fd tento tok obda\u0159en vyn\u00e1soben\u00edm \u201epo\u0159ad\u00edm\u201c, kdy tento pen\u011b\u017en\u00ed tok nastane (v \u010ditateli 1C, 2C\u2026nC, nFV). Z tohoto pohledu, p\u0159esto\u017ee to zn\u00ed dost nepochopiteln\u011b a nep\u0159edstaviteln\u011b, Macaulayovu Duraci lze velmi jednodu\u0161e vypo\u010d\u00edtat a vyu\u017e\u00edt ke zji\u0161t\u011bn\u00ed toho, co jsem od sv\u00e9ho teoretizov\u00e1n\u00ed vlastn\u011b pot\u0159eboval, tedy zjistit, jak\u00fdm zp\u016fsobem se mi zm\u011bn\u00ed cena dluhopisu, pokud se zm\u011bn\u00ed \u00farokov\u00e1 sazba o n\u011bjakou p\u0159edem danou hodnotu, nap\u0159\u00edklad o +\/-1%. Stejn\u011b jako u \u0159eck\u00e9ho p\u00edsmene Delta, kter\u00e1 postihovala vyj\u00e1d\u0159en\u00ed zm\u011bny ceny op\u010dn\u00edho kontraktu, pokud se zm\u011bn\u00ed cena podkladu o +\/- 1.00 USD, bude m\u011b to sam\u00e9 zaj\u00edmat u dluhopis\u016f. Dosad\u00edm<\/strong> tedy v\u00fdraz Macaulayova Durace<\/strong> do p\u016fvodn\u00ed derivovan\u00e9 rovnice:<\/strong>\u00a0\u00a0<\/span><\/p>\n

\u00a0 \"\" <\/span><\/p>\n

\u00a0\u00a0V\u00fdsledn\u00e1 rovnice pak vlastn\u011b znamen\u00e1 vyd\u011blen\u00ed Macaulayovy Durace<\/strong> pr\u00e1v\u011b aktu\u00e1ln\u00edm v\u00fdnosem<\/strong>\u00a0a takto upraven\u00e9 Macaulayov\u011b Duraci se \u0159\u00edk\u00e1 Modifikovan\u00e1 Durace<\/strong>, matematicky tedy po \u00faprav\u011b, aby to bylo z\u0159eteln\u011bj\u0161\u00ed:<\/span><\/p>\n

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\u00a0\u00a0 Pom\u011b\u0159en\u00edm Macaulayovy Durace<\/strong> s\u00a0aktu\u00e1ln\u00ed \u00farokovou sazbou<\/strong> obdr\u017e\u00edm p\u0159esn\u011b to, co pro sv\u00e9 pot\u0159eby pot\u0159ebuji, normalizaci pohybu ceny dluhopisu k n\u011bjak\u00e9 hodnot\u011b v\u00fdnosu, tedy v\u00fdpo\u010det zm\u011bny ceny dluhopisu<\/strong>, pokud se zm\u011bn\u00ed<\/strong> \u00farokov\u00e9 sazby o +\/-1% bod<\/strong>. Z nast\u00edn\u011bn\u00e9ho postupu, by\u0165 se m\u016f\u017ee zd\u00e1t komplikovan\u00fd a slo\u017eit\u00fd, mohu ob\u011b durace pro jak\u00fdkoliv dluhopis velmi jednodu\u0161e vypo\u010d\u00edtat, co\u017e tak\u00e9 ud\u011bl\u00e1m pro sv\u016fj dluhopis Ford s kup\u00f3nem 6.625% a se splatnost\u00ed za p\u011bt let a pokus\u00edm se sv\u016fj v\u00fdpo\u010det interpretovat.<\/span><\/p>\n

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\u00a0\u00a0 Pokud bych dnes nakoupil p\u011btilet\u00fd dluhopis Ford za 1.024,70 USD (1)<\/span>,<\/strong> kter\u00fd vypl\u00e1c\u00ed pololetn\u011b (2)<\/span><\/strong> kup\u00f3n ve v\u00fd\u0161i 6.625% p.a.<\/strong> z\u00a0Face Value (3)<\/span><\/strong>, potom by cel\u00e1 investice p\u0159edstavovala \u010d\u00e1stku 1.033,717 USD (4)<\/span><\/strong>, proto\u017ee bych musel z\u00a0prvn\u00edho kup\u00f3nu odevzdat jeho \u010d\u00e1st p\u0159edch\u00e1zej\u00edc\u00edmu dr\u017eiteli. Deset pen\u011b\u017en\u00edch budouc\u00edch tok\u016f (5)<\/span><\/strong> by p\u0159edstavovalo p\u0159i dan\u00fdch po\u0159izovac\u00edch podm\u00ednk\u00e1ch v\u00fdnos do splatnosti<\/strong> ve v\u00fd\u0161i 5.838% p.a. (6)<\/span><\/strong>. V\u00a0\u010d\u00e1sti v\u00fdpo\u010dtu \u201eModelov\u00e1n\u00ed\u201c<\/strong><\/em> p\u0159i zad\u00e1n\u00ed stejn\u00e9ho v\u00fdnosu ve v\u00fd\u0161i 5.838% p.a. (7)<\/span><\/strong> mohu pozorovat v\u0161echny budouc\u00ed toky diskontovan\u00e9<\/strong> k\u00a0dne\u0161n\u00edmu dni pr\u00e1v\u011b podle t\u00e9to \u00farokov\u00e9 sazby (8)<\/strong><\/span> a jejich sou\u010det (9)<\/span><\/strong> mi mus\u00ed d\u00e1t (pro kontrolu spr\u00e1vn\u00e9ho diskontov\u00e1n\u00ed) p\u0159esn\u011b sou\u010det p\u0159edstavuj\u00edc\u00ed aktu\u00e1ln\u00ed po\u0159izovac\u00ed cenu (4)<\/strong><\/span>. Ve sloupci \u201eDurace\u201c<\/em> (10)<\/span><\/strong> mohu vypozorovat, \u017ee jsem diskontovan\u00e9<\/strong> pen\u011b\u017en\u00ed toky ze sloupce „Modelov\u00e1n\u00ed“<\/em> vyn\u00e1sobil vahami<\/strong> jejich po\u0159ad\u00ed (11),<\/strong><\/span> tedy nap\u0159\u00edklad pro t\u0159et\u00ed pen\u011b\u017en\u00ed diskontovan\u00fd kup\u00f3n ve v\u00fd\u0161i 30.386 USD jsem tuto hodnotu vyn\u00e1sobil trojkou. Takto \u201ezv\u00e1\u017een\u00e9\u201c pen\u011b\u017en\u00ed toky jsem se\u010detl<\/strong> a vyd\u011blil<\/strong> skute\u010dnou po\u0159izovac\u00ed cenou<\/strong> zkouman\u00e9ho dluhopisu<\/strong> v bu\u0148ce C17 (12)<\/strong><\/span>, t\u00edm jsem vypo\u010d\u00edtal hodnotu Macaulayovy Durace<\/strong>, proto\u017ee je ale kup\u00f3n vypl\u00e1cen 2x za rok, vyd\u011blil jsem tuto duraci ve vzorci dv\u011bma (hodnotou z bu\u0148ky C11). Pr\u016fm\u011brn\u00e1 v\u00e1\u017een\u00e1 doba splatnosti v\u0161ech pen\u011b\u017en\u00edch tok\u016f je pro m\u016fj dluhopis 4.35 let<\/strong>. To je sice hezk\u00e9, ale j\u00e1 jsem je\u0161t\u011b hodnotu Macaulayovy Durace vyd\u011blil aktu\u00e1ln\u00edm v\u00fdnosem<\/strong> ve v\u00fd\u0161i 5.838% (13)<\/span><\/strong>, abych se dobral hodnoty Modifikovan\u00e9 Durace<\/strong> ve v\u00fd\u0161i 4.110%<\/strong>. To je jednoduch\u00fd konec m\u00e9, na prvn\u00ed pohled slo\u017eit\u011b popisovan\u00e9 pr\u00e1ce. Co mohu pro toto \u010d\u00edslo konstatovat?<\/span><\/p>\n

\u00a0\u00a0 Pokud se zvednou \u00farokov\u00e9 sazby na trz\u00edch o +1% p.a.,<\/strong> poklesne hodnota m\u00e9ho p\u011btilet\u00e9ho dluhopisu Ford s\u00a0kup\u00f3nem 6.625% o -4.110%<\/strong>, tedy o v\u00edce ne\u017e \u010dty\u0159icet dolar\u016f. Pokud by \u00farokov\u00e9 sazby m\u011bly o -1% klesnout, mohl bych p\u0159ihl\u00ed\u017eet r\u016fstu ceny m\u00e9ho dluhopisu o p\u0159ibli\u017en\u011b stejnou \u010d\u00e1stku.<\/span><\/p>\n

\n

Nen\u00ed to tak slo\u017eit\u00e9…<\/strong><\/span><\/h2>\n

\u00a0\u00a0 P\u0159esto\u017ee je v\u00fdpo\u010det durace velmi jednoduch\u00fd pomoc\u00ed excelu, kde m\u00e1me vypo\u010d\u00edt\u00e1n nap\u0159\u00edklad v\u00fdnos do splatnosti s p\u0159edp\u0159ipraven\u00fdmi diskontovan\u00fdmi budouc\u00edmi cash-flow, je velmi komfortn\u00edm zji\u0161t\u011bn\u00edm, \u017ee obchodn\u00ed platformy \u00fadaje o duraci nab\u00edzej\u00ed pro ka\u017ed\u00fd kvalitn\u011bj\u0161\u00ed dluhopis. Mohu pak z m\u00e9 platformy TWS od Interactive Bokers prozkoumat uv\u00e1d\u011bnou duraci pro m\u016fj p\u011btilet\u00fd dluhopis Ford. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/span>\u00a0 \"\"<\/span><\/p>\n

\u00a0\u00a0 Mohu vypozorovat, \u017ee m\u00e1 obchodn\u00ed platforma ukazuje v\u00fdnos do splatnosti (YTM) ve v\u00fd\u0161i 5.921% (nam\u00edsto mnou vypo\u010d\u00edtan\u00fdch 5.838%), tedy o pouhou desetinku vy\u0161\u0161\u00ed (1)<\/strong><\/span>, hodnota Durace<\/strong> je pak v\u00a0m\u00e9 platform\u011b na \u00farovni 4.21%<\/strong>, nam\u00edsto mnou vypo\u010d\u00edtan\u00fdch 4.11%, tedy o stejnou desetinku vy\u0161\u0161\u00ed (2)<\/span><\/strong>. Mohu spokojen\u011b konstatovat, \u017ee na v\u00fdpo\u010det Durace se mohu pln\u011b spolehnout a nemus\u00edm pro jej\u00ed stanoven\u00ed pou\u017e\u00edvat \u017e\u00e1dn\u00e9 vlastn\u00ed pom\u016fcky a hled\u00e1n\u00ed jej\u00ed aktu\u00e1ln\u00ed v\u00fd\u0161e v\u00fdrazn\u011b komplikovat. \u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0\u00a0 Pokud jsem v\u00fd\u0161e v\u00a0\u010dl\u00e1nku ukazoval modelov\u00e1n\u00ed r\u016fzn\u00fdch vlastnost\u00ed stejn\u00fdch dluhopis\u016f, mohu pak toto modelov\u00e1n\u00ed prom\u00edtnout tak\u00e9 do hodnoty durace. Pokud budu tedy uva\u017eovat o po\u0159\u00edzen\u00ed dluhopis\u016f<\/strong> se stejnou kvalitou a stejnou dobou do splatnosti<\/strong>, dluhopisy s\u00a0ni\u017e\u0161\u00edm kup\u00f3nem<\/strong> budou citliv\u011bj\u0161\u00ed na zm\u011bnu \u00farokov\u00e9 sazby a budou m\u00edt tak\u00e9 vy\u0161\u0161\u00ed (modifikovanou) duraci<\/strong>, toto bych pak mohl demonstrovat na obr\u00e1zku n\u00ed\u017ee:<\/span><\/p>\n

\"\"<\/p>\n

\u00a0\u00a0 T\u0159i dluhopisy se splatnost\u00ed v\u00a0\u00fanoru 2028 maj\u00ed ka\u017ed\u00fd jinou v\u00fd\u0161i kup\u00f3nu, s\u00a0klesaj\u00edc\u00ed v\u00fd\u0161i kup\u00f3n\u016f se ale zvy\u0161uje senzitivita na pohyb \u00farokov\u00fdch sazeb, proto s\u00a0klesaj\u00edc\u00edm kup\u00f3nem durace roste.<\/span><\/p>\n

\u00a0\u00a0\u00a0 Obdobn\u011b jsem v\u00fd\u0161e ukazoval, \u017ee pokud maj\u00ed dluhopisy<\/strong> p\u0159ibli\u017en\u011b stejnou kvalitu a stejn\u00fd kup\u00f3n<\/strong>, potom jsou na zm\u011bnu hladiny \u00farokov\u00fdch sazeb citliv\u011bj\u0161\u00ed dluhopisy s del\u0161\u00ed dobou do splatnosti <\/strong>a tyto dlouhodob\u00e9 dluhopisy maj\u00ed tak\u00e9 vy\u0161\u0161\u00ed duraci.<\/span><\/p>\n

\"\"<\/p>\n

\u00a0\u00a0\u00a0 Na obr\u00e1zku jsou dva americk\u00e9 vl\u00e1dn\u00ed dluhopisy s p\u0159ibli\u017en\u011b stejn\u00fdm kup\u00f3nem (6.125% a 6.25%) ov\u0161em jeden m\u00e1 splatnost v listopadu 2027 a druh\u00fd v kv\u011btnu 2030. Durace dluhopisu s del\u0161\u00ed dobou splatnosti je na hodnot\u011b 5.86%, dluhopis s krat\u0161\u00ed dobou splatnosti m\u00e1 duraci 4.03%, rozd\u00edl +\/-1.03% v duraci ale p\u0159edstavuje t\u00e9m\u011b\u0159 o \u010dtvrtinu vy\u0161\u0161\u00ed riziko pohybu ceny dluhopisu s del\u0161\u00ed dobou splatnosti oproti dluhopisu s krat\u0161\u00ed dobou splatnosti v p\u0159\u00edpad\u011b zv\u00fd\u0161en\u00ed \u00farovn\u011b \u00farokov\u00e9 sazby o +1%.<\/span><\/p>\n

\n

\u00a0 Aktu\u00e1ln\u011b k duraci :c)<\/strong><\/span><\/h2>\n

\u00a0 \u00a0Vr\u00e1t\u00edm se k pozn\u00e1mce z \u00favodn\u00edho odstavce tohoto \u010dl\u00e1nku, kdy jsem podotkl, \u017ee je opravdu vhodn\u00e1 doba pro t\u00e9ma tohoto \u010dl\u00e1nku z pohledu aktu\u00e1ln\u00edho d\u011bn\u00ed na trz\u00edch, zejm\u00e9na v bankovn\u00edm sektoru. Jak si mohu ve sv\u011btle v\u00fd\u0161e napsan\u00fdch \u0159\u00e1dk\u016f vysv\u011btlit nyn\u011bj\u0161\u00ed pot\u00ed\u017ee n\u011bkter\u00fdch americk\u00fdch bankovn\u00edch dom\u016f, kter\u00e9 utrp\u011bly v\u00fdznamn\u00e9 ztr\u00e1ty z cenn\u00fdch pap\u00edr\u016f s fixn\u00edm v\u00fdnosem souvisej\u00edc\u00ed s probl\u00e9my jejich likvidity? Nemohu si nev\u0161imnout, \u017ee p\u0159ed rokem (do roku 2021) nenab\u00edzely nap\u0159\u00edklad t\u0159icetilet\u00e9 americk\u00e9 vl\u00e1dn\u00ed dluhopisy nijak v\u00fdznamn\u00e9 v\u00fdnosy, tyto se pohybovaly okolo 2% p.a.<\/span><\/p>\n

\"\"<\/p>\n

\u00a0\u00a0 V atmosf\u00e9\u0159e n\u00edzk\u00fdch v\u00fdnos\u016f jsem jako fiktivn\u00ed bank\u00e9\u0159 spravuj\u00edc\u00ed pen\u011b\u017en\u00ed prost\u0159edky z vklad\u016f sv\u00fdch klient\u016f nucen tyto vklady n\u011bjak\u00fdm bezpe\u010dn\u00fdm zp\u016fsobem zhodnocovat, proto se jev\u00ed nakoupen\u00ed bezrizikov\u00fdch americk\u00fdch vl\u00e1dn\u00edch dluhopis\u016f se splatnost\u00ed t\u0159icet let jako vhodn\u00e1 investice. Trhy t\u011bchto cenn\u00fdch pap\u00edr\u016f jsou dostate\u010dn\u011b likvidn\u00ed, mohu tak kdykoliv tyto vl\u00e1dn\u00ed bondy p\u0159etavit zp\u011bt na hotov\u00e9 pen\u00edze, pokud bych tyto hotov\u00e9 pen\u00edze pot\u0159eboval. Mohu tak\u00e9 prozkoumat, jakou maj\u00ed tyto dluhopisy duraci, abych zjistil, co se m\u016f\u017ee st\u00e1t, pokud by centr\u00e1ln\u00ed banka za\u010dala p\u0159i ekonomick\u00fdch probl\u00e9mech navy\u0161ovat \u00farokov\u00e9 sazby. Na obr\u00e1zku n\u00ed\u017ee je pro p\u0159\u00edklad jeden z takov\u00fdch dluhopis\u016f vyobrazen. \u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0 \"\"<\/span><\/p>\n

\u00a0\u00a0\u00a0 T\u0159icetilet\u00fd<\/strong> americk\u00fd vl\u00e1dn\u00ed dluhopis<\/strong> se splatnost\u00ed v\u00a0listopadu 2050<\/strong> m\u00e1 modifikovanou duraci z\u00e1vratn\u00fdch 20.71%<\/strong>. Zv\u00fd\u0161en\u00ed \u00farokov\u00e9 sazby o +1% bod bude znamenat ztr\u00e1tu ceny t\u011bchto dluhopis\u016f o jednu p\u011btinu, a to je velmi z\u00e1sadn\u00ed zji\u0161t\u011bn\u00ed. Jak v\u00edme, ke zvy\u0161ov\u00e1n\u00ed \u00farokov\u00fdch sazeb nakonec do\u0161lo a v leto\u0161n\u00edm roce (2023) dokonce zcela z\u00e1sadn\u00edm tempem, kter\u00e9 je tak\u00e9 zn\u00e1zorn\u011bno na obr\u00e1zku s v\u00fdvojem v\u00fdnosu t\u0159icetilet\u00e9ho dluhopisu v\u00fd\u0161e. Dluhopisov\u00e1 portfolia s vysokou durac\u00ed, tedy zejm\u00e9na takov\u00e1, kter\u00e1 obsahuj\u00ed dluhopisy s dlouhou dobou splatnosti, za\u010d\u00ednaj\u00ed v takov\u00e9m p\u0159\u00edpad\u011b ztr\u00e1cet na sv\u00e9 hodnot\u011b a \u201evypaluj\u00ed\u201c tak d\u00edry do rozvah \u00fastav\u016f, kter\u00e9 je po\u0159\u00eddily. Nakonec tuto ji\u017e tak v\u00e1\u017enou situaci zkomplikuj\u00ed vkladatel\u00e9, kte\u0159\u00ed na soci\u00e1ln\u00edch s\u00edt\u00edch zji\u0161\u0165uj\u00ed, \u017ee jejich vklady u n\u011bkter\u00fdch bankovn\u00edch instituc\u00ed mohou b\u00fdt v ohro\u017een\u00ed a je jim doporu\u010deno, aby sv\u00e9 pen\u00edze vybrali. Run na banku je tady. Nam\u00edsto toho, aby mana\u017ee\u0159i bankovn\u00edch dluhopisov\u00fdch portfoli\u00ed se stoick\u00fdm klidem vy\u010dkali sn\u00ed\u017een\u00ed \u00farokov\u00fdch sazeb a n\u00e1vratu ceny jejich dluhopis\u016f na \u00farovn\u011b, kde byly p\u0159ed z\u00e1sahy FEDu, musej\u00ed tyto organizace vypl\u00e1cet vklady klient\u016fm, kte\u0159\u00ed si pro n\u011b v roz\u010dilen\u00ed p\u0159ib\u011bhli. Ve snaze nal\u00e9zt pro tyto masov\u00e9 v\u00fdb\u011bry pot\u0159ebnou likviditu, musej\u00ed vyprod\u00e1vat tato dluhopisov\u00e1 portfolia, t\u00edm ale jen stvrzuj\u00ed ztr\u00e1ty, kter\u00e9 na nich utrp\u011bly, bankovn\u00ed apokalypsa u t\u011bch z nich, kter\u00e9 s takov\u00fdmi pohyby na \u00farokov\u00fdch sazb\u00e1ch nepo\u010d\u00edtali, je dokon\u00e1na. Na sv\u00e9 si pak p\u0159ijdou nejr\u016fzn\u011bj\u0161\u00ed analytici a odborn\u00edci, kte\u0159\u00ed budou sp\u00edlat bankovn\u00edm mana\u017eer\u016fm, \u017ee se na takovou situaci nep\u0159ipravili, kdy\u017e investovali zejm\u00e9na do dluhopis\u016f s vysokou durac\u00ed. Co na to \u0159\u00edct? Nikdy nem\u016f\u017eu v\u011bd\u011bt, co se stane za t\u00fdden, nato\u017e za deset let, co bych pak m\u011bl d\u011blat nyn\u00ed? Nakupovat dluhopisy s vysokou durac\u00ed, proto\u017ee je jist\u00e9, \u017ee \u00farokov\u00e9 sazby klesnou a j\u00e1 inkasuji profit z r\u016fstu jejich ceny?<\/span><\/p>\n

\n

\u00a0 \u00a0Je u\u017eite\u010dn\u00e9 m\u00edt pov\u011bdom\u00ed, co se m\u016f\u017ee st\u00e1t, kdy\u017e se \u00farokov\u00e9 sazby daj\u00ed do pohybu, pokud jsem tedy dluhopisov\u00fd obchodn\u00edk. Nemus\u00edm ale prov\u00e1d\u011bt slo\u017eit\u00e9 v\u00fdpo\u010dty, sta\u010d\u00ed m\u00edt pov\u011bdom\u00ed o jednoduch\u00fdch ukazatel\u00edch a n\u00e1stroj\u00edch, kter\u00e9 mi d\u00e1 k dispozici m\u00e1 obchodn\u00ed platforma sou\u010dasn\u011b s jejich spr\u00e1vnou interpretac\u00ed. Mohu pak odhadovat, co se s m\u00fdmi dluhopisy stane, pokud se zm\u011bn\u00ed n\u00e1lada na trz\u00edch \u00farokov\u00fdch sazeb, tedy jak postihne m\u00e9 dluhopisov\u00e9 portfolio risk zm\u011bny \u00farokov\u00fdch sazeb popisovan\u00fd v minul\u00e9m \u010dl\u00e1nku.<\/span><\/p>\n

\u00a0\u00a0 Excel s\u00a0v\u00fdpo\u010dtem durac\u00ed je mo\u017en\u00e9 st\u00e1hnou v\u00a0Diskuzn\u00edm f\u00f3ru ve vl\u00e1kn\u011b k\u00a0tomuto \u010dl\u00e1nku<\/a><\/strong><\/span>, stejn\u011b tak zde m\u016f\u017eete p\u0159id\u00e1vat sv\u00e9 koment\u00e1\u0159e :c)<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0Lep\u0161\u00ed okam\u017eik pro naps\u00e1n\u00ed tohoto \u010dl\u00e1nku jsem si ani nemohl p\u0159\u00e1t. Lehk\u00e9 n\u00e1znaky bankovn\u00ed krize vypl\u00fdvaj\u00edc\u00ed z podivn\u00e9 likvidity speci\u00e1ln\u00edch bankovn\u00edch dom\u016f opep\u0159en\u00e9 koment\u00e1\u0159i jejich v\u00edce \u010di m\u00e9n\u011b schopn\u00fdch p\u0159edstavitel\u016f p\u0159in\u00e1\u0161ej\u00ed na p\u0159elomu m\u011bs\u00edce b\u0159ezna a dubna 2023 skv\u011bl\u00fd r\u00e1mec pro t\u00e9ma tohoto \u010dl\u00e1nku. Jakou roli v t\u00e9to \u0161lamastyce Continue Reading<\/i><\/a><\/p>\n","protected":false},"author":1,"featured_media":6315,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[60],"tags":[61],"class_list":["post-6292","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dluhopisy","tag-dluhopisy"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8zd8A-1Du","jetpack-related-posts":[{"id":6987,"url":"https:\/\/dobretrejdy.com\/?p=6987","url_meta":{"origin":6292,"position":0},"title":"Dluhopisy \u2013 XVI. \u00a0\u00a0\u00a0\u00a0\u00a0","author":"dobretrejdy :c)","date":"10.3.2024","format":false,"excerpt":"\u00a0 \u00a0V posledn\u00edm \u010dl\u00e1nku dluhopisov\u00e9 minis\u00e9rie Dluhopisy \u2013 XV. jsem popsal jednoduch\u00fd obchod s n\u00e1kupem dluhopisu a jeho zaji\u0161t\u011bn\u00ed pomoc\u00ed odpov\u00eddaj\u00edc\u00edho dluhopisov\u00e9ho futures. 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