{"id":6122,"date":"2023-01-28T17:49:37","date_gmt":"2023-01-28T15:49:37","guid":{"rendered":"https:\/\/dobretrejdy.com\/?p=6122"},"modified":"2024-08-18T09:55:31","modified_gmt":"2024-08-18T07:55:31","slug":"dluhopisy-v","status":"publish","type":"post","link":"https:\/\/dobretrejdy.com\/?p=6122","title":{"rendered":"Dluhopisy – V."},"content":{"rendered":"

\u00a0\u00a0 Kupuji dluhopis. Prvn\u00ed v\u011bta z\u00a0minul\u00e9ho \u010dl\u00e1nku se tak opakuje, a proto\u017ee jsem si v\u00a0tomto p\u0159edch\u00e1zej\u00edc\u00edm \u010dl\u00e1nku<\/a><\/strong><\/span> ud\u011blal svou anal\u00fdzu z\u00e1kladn\u00edch vlastnost\u00ed dluhopisu, nyn\u00ed je m\u00e9 rozhodov\u00e1n\u00ed ji\u017e zam\u011b\u0159eno na vlastn\u00ed v\u00fdkon zam\u00fd\u0161len\u00e9 investice. Jak zm\u011b\u0159it investici do cenn\u00e9ho pap\u00edru s pevn\u00fdm v\u00fdnosem je opravdu v\u00fdzva a z nab\u00edzen\u00e9ho \u0159e\u0161en\u00ed pak vyplyne, pro\u010d jsem seri\u00e1l o dluhopisech za\u010dal dv\u011bma veskrze nudn\u00fdmi \u010dl\u00e1nky s \u00favahami o sou\u010dasn\u00e9 a budouc\u00ed hodnot\u011b pen\u011bz :c)<\/span><\/p>\n

\u00a0\u00a0 N\u00e1kup dluhopisu pro m\u011b p\u0159edstavuje investici, od kter\u00e9 samoz\u0159ejm\u011b \u010dek\u00e1m zhodnocen\u00ed s\u00a0p\u0159im\u011b\u0159en\u00fdm rizikem. Od vlo\u017een\u00e9 \u010d\u00e1stky do n\u00e1kupu dluhopisu mohu o\u010dek\u00e1vat dv\u011b z\u00e1kladn\u00ed verze chov\u00e1n\u00ed spojen\u00e9 s\u00a0jedn\u00edm (op\u011bt z\u00e1kladn\u00edm) p\u0159edpokladem, kter\u00e9 budou definovat m\u016fj celkov\u00fd v\u00fdnos, toto v\u0161e se pak odv\u00edj\u00ed od dvou z\u00e1kladn\u00edch typ\u016f dluhov\u00e9ho cenn\u00e9ho pap\u00edru, kter\u00fdmi se nyn\u00ed budu zab\u00fdvat. Dluhopis po\u0159\u00edd\u00edm za n\u011bjakou po\u0159izovac\u00ed cenu (Present Value) a u splatnosti (Maturity) obdr\u017e\u00edm jeho nomin\u00e1ln\u00ed hodnotu (Face Value), do splatnosti dluhopisu kas\u00edruji vyzna\u010den\u00e9 kup\u00f3ny vyj\u00e1d\u0159en\u00e9 procentn\u00ed sazbou p.a. z\u00a0Face Value, to je verze p\u0159edstavuj\u00edc\u00ed prvn\u00ed mo\u017enost, tedy po\u0159\u00edzen\u00ed<\/strong> klasick\u00e9ho dluhopisu s kup\u00f3nem<\/strong>. V\u00a0druh\u00e9 mo\u017enosti v\u00fdvoje celkov\u00e9ho v\u00fdnosu z\u00a0dr\u017eby dluhov\u00e9ho cenn\u00e9ho pap\u00edru po\u0159\u00edd\u00edm dluhopis za n\u011bjakou po\u0159izovac\u00ed cenu (Present Value) a u splatnosti (Maturity) obdr\u017e\u00edm jeho nomin\u00e1ln\u00ed hodnotu (Face Value), tyto dluhopisy<\/strong> jsou ale bez kup\u00f3nu<\/strong> (tzv. \u201ezero-coupon bonds\u201c, \u201ezerobonds\u201c \u010di \u201ezeroes\u201c). Vysloven\u00fd z\u00e1kladn\u00ed p\u0159edpoklad spo\u010d\u00edv\u00e1 v\u00a0p\u0159edstav\u011b, \u017ee kup\u00f3ny, kter\u00e9 obdr\u017e\u00edm p\u0159i investici do dluhopisu (prvn\u00ed verze) neutrat\u00edm, ale reinvestuji a sou\u010d\u00e1st\u00ed celkov\u00e9ho v\u00fdnosu je pak v\u00fdnos tak\u00e9 z\u00a0takto reinvestovan\u00fdch kup\u00f3n\u016f, zerobondy (druh\u00e1 verze) tento p\u0159edpoklad postr\u00e1daj\u00ed, proto\u017ee \u017e\u00e1dn\u00e9 kup\u00f3ny k\u00a0reinvestov\u00e1n\u00ed nenab\u00edzej\u00ed. Ostatn\u00ed typy dluhopis\u016f, nap\u0159\u00edklad s\u00a0plovouc\u00edm (variabiln\u00edm) kup\u00f3nem, infla\u010dn\u00ed dluhopisy apod. pak p\u0159i m\u011b\u0159en\u00ed v\u00fdnos\u016f budou vych\u00e1zet z\u00a0podobn\u00fdch p\u0159edpoklad\u016f, v\u00fdpo\u010dty budou ale t\u011bmto odli\u0161nostem pat\u0159i\u010dn\u011b a vhodn\u011b p\u0159izp\u016fsobeny.<\/span><\/p>\n

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\u00a0\u00a0 P\u0159edpoklad, vysloven\u00fd v p\u0159edchoz\u00edm odstavci, tedy reinvestice kup\u00f3n\u016f za dobu dr\u017een\u00ed dluhopisu, nemus\u00ed b\u00fdt napln\u011bn, nap\u0159\u00edklad z rozhodnut\u00ed, \u017ee tyto nashrom\u00e1\u017ed\u011bn\u00e9 kup\u00f3ny vyu\u017eiji pro jinou investici nebo je prost\u011b utrat\u00edm, nebudu tak po\u010d\u00edtat s jejich reinvestic\u00ed za aktu\u00e1ln\u00ed \u00farokovou sazbu. D\u00edky absenci tohoto pr\u016fb\u011b\u017en\u00e9ho v\u00fdnosu mohu na zm\u011b\u0159en\u00ed v\u00fdnosu aplikovat jednoduch\u00fd po\u010detn\u00ed postup.<\/span><\/p>\n

Current Yield (Aktu\u00e1ln\u00ed v\u00fdnos)<\/strong><\/span><\/h1>\n

\u00a0\u00a0 Absence reinvestov\u00e1n\u00ed p\u0159ijat\u00fdch kup\u00f3n\u016f zjednodu\u0161\u00ed pohled na m\u011b\u0159en\u00ed v\u00fdnosu dluhopisu do jednoduch\u00e9ho vzorce.<\/span><\/p>\n

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\u00a0\u00a0 Pom\u011br \u201ekolik mi to vynese ro\u010dn\u011b\u201c a \u201ekolik na to mus\u00edm vynalo\u017eit\u201c nen\u00ed zapot\u0159eb\u00ed n\u011bjak v\u00fdznamn\u011b komentovat. Pom\u011b\u0159\u00edm kup\u00f3nov\u00fd v\u00fdnos s nab\u00edzenou cenou za dluhopis. Mohu pak zcela konkr\u00e9tn\u011b zjistit v\u00fdnos dluhopisu od spole\u010dnosti MSFT podle obr\u00e1zku n\u00ed\u017ee:<\/span><\/p>\n

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\u00a0\u00a0 Aktu\u00e1ln\u011b mohu po\u0159\u00eddit tento dluhopis za cenu (Ask) 942.00 USD a ro\u010dn\u00ed kup\u00f3nov\u00fd v\u00fdnos (Coupon) p\u0159edstavuje 2.40% p.a., konkr\u00e9tn\u011b 24 USD ro\u010dn\u011b.<\/span><\/p>\n

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\u00a0\u00a0 Current Yield<\/strong> p\u0159edstavuje \u010d\u00e1stku 2,547% p.a.<\/strong> Mohu se spolehnout (jedn\u00e1 se \u201et\u0159\u00ed\u00e1\u010dkov\u00fd\u201c dluhopis), \u017ee tento v\u00fdnos budu schopen p\u0159ij\u00edmat na sv\u016fj \u00fa\u010det za dobu jeho \u017eivota vzhledem k jeho po\u0159izovac\u00ed cen\u011b. Je patrn\u00e9, \u017ee takto zm\u011b\u0159en\u00fd v\u00fdnos trp\u00ed z\u00e1kladn\u00ed vadou, tedy nezohled\u0148uje kapit\u00e1lov\u00fd v\u00fdnos\/ztr\u00e1tu z dluhopisov\u00e9 investice. Z obr\u00e1zku pozoruji, \u017ee Face Value dluhopisu je 1000 USD a j\u00e1 jej mohu po\u0159\u00eddit za 942.00 USD. P\u0159i dr\u017een\u00ed dluhopisu do maturity p\u0159id\u00e1m k v\u00fdnosu tak\u00e9 profit z rozd\u00edlu mezi po\u0159izovac\u00ed cenou dluhopisu a jeho Face Value, tento jsem toti\u017e po\u0159\u00eddil za diskont, tedy za m\u00e9n\u011b ne\u017e je Face Value. V m\u00e9m konkr\u00e9tn\u00edm p\u0159\u00edpad\u011b bych u maturity p\u0159i vypo\u0159\u00e1d\u00e1n\u00ed inkasoval nav\u00edc (-942.00 USD +1000.00 USD) \u010d\u00e1stku +58.00 USD za ka\u017ed\u00fd dr\u017een\u00fd dluhopis. Pokud bych naopak dluhopis po\u0159\u00eddil \u201es pr\u00e9miem\u201c, tedy za cenu vy\u0161\u0161\u00ed, ne\u017e je Face Value, tak vypo\u010d\u00edtan\u00fd Current Yield nezohled\u0148uje ztr\u00e1tu kapit\u00e1lu, kterou p\u0159edstavuje op\u011bt rozd\u00edl mezi po\u0159izovac\u00ed cenou a Face Value, takovou situaci mohu pozorovat nap\u0159\u00edklad na obr\u00e1zku n\u00ed\u017ee:<\/span><\/p>\n

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\u00a0\u00a0 Dluhopis spole\u010dnosti Ford nab\u00edz\u00ed kup\u00f3n 66,25 USD ro\u010dn\u011b a aktu\u00e1ln\u011b se nab\u00edz\u00ed za 1030.23 USD, potom:<\/span><\/p>\n

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

\u00a0\u00a0 Current Yield<\/strong> bude sice \u010dinit 6.43% p.a.<\/strong>, p\u0159i jeho splatnosti ale zcela jist\u011b utrp\u00edm ztr\u00e1tu -30.23 USD<\/strong> na ka\u017ed\u00e9m dr\u017een\u00e9m kusu, to je toti\u017e rozd\u00edl mezi jeho po\u0159izovac\u00ed cenou (-1030.23 USD) a Face Value (+1000.00 USD). P\u0159esto\u017ee v\u00fdpo\u010det Aktu\u00e1ln\u00edho v\u00fdnosu trp\u00ed vadou nezohledn\u011bn\u00ed kapit\u00e1lov\u00e9ho v\u00fdnosu\/ztr\u00e1ty z\u00a0dr\u017een\u00ed dluhov\u00e9ho cenn\u00e9ho pap\u00edru, m\u016f\u017ee b\u00fdt alespo\u0148 prvotn\u00edm z\u00e1kladn\u00edm vod\u00edtkem, jak se k\u00a0vyhodnocen\u00ed ve smyslu \u201ecena\/v\u00fdkon\u201c postavit.<\/span><\/p>\n

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\u00a0\u00a0 Kupuji dluhopis jako investici a takto s\u00a0n\u00ed budu cht\u00edt tak\u00e9 pracovat. Bude m\u011b tak zaj\u00edmat, jak mohu vyu\u017e\u00edt v\u0161ech pen\u011b\u017en\u00edch tok\u016f<\/strong>, kter\u00e9 z\u00a0po\u0159\u00edzen\u00ed dluhopisu vypl\u00fdvaj\u00ed. M\u011b\u0159en\u00ed v\u00fdnosu by pak m\u011blo tyto v\u0161echny budouc\u00ed pen\u011b\u017en\u00ed toky zahrnovat a v\u00fdsledkem m\u011b\u0159en\u00ed by pak m\u011blo b\u00fdt n\u011bjak\u00e9 ro\u010dn\u00ed procentn\u00ed ohodnocen\u00ed vlo\u017een\u00e9 investice. P\u0159esto\u017ee tedy pom\u00fd\u0161l\u00edm na nejnov\u011bj\u0161\u00ed model Ferrari, budu cht\u00edt se svou dluhopisovou investic\u00ed nalo\u017eit opravdu zodpov\u011bdn\u011b a vyu\u017e\u00edt v\u0161e co nab\u00edz\u00ed.<\/span><\/p>\n

\u00a0\u00a0 V\u00fdchoz\u00edm p\u0159edpokladem v\u00fdpo\u010dtu zji\u0161t\u011bn\u00ed ceny dluhopisu budou teoretick\u00e9 skute\u010dnosti popsan\u00e9 v\u00a0\u010dl\u00e1nku Dluhopisy \u2013 II.<\/a><\/strong><\/span>. Zjistit, jak\u00fd budu z\u00a0nakoupen\u00e9ho dluhopisu m\u00edt v\u00fdnos, mi umo\u017en\u00ed posouzen\u00ed jeho vlastnost\u00ed, kter\u00e9 mohu z\u00a0jeho popisu odvodit. Pohledem do obchodn\u00ed platformy zji\u0161\u0165uji, jak\u00e1 je jeho aktu\u00e1ln\u00ed cena, jak\u00e1 je jeho Face Value, jak\u00fd je kup\u00f3nov\u00fd v\u00fdnos a jak\u00e1 je frekvence jeho v\u00fdplaty, kdy je term\u00edn nejbli\u017e\u0161\u00ed kup\u00f3nov\u00e9 v\u00fdplaty a kdy je datum jeho posledn\u00ed v\u00fdplaty se splatnost\u00ed Face Value. Aktu\u00e1ln\u00ed cena dluhopisu, kterou vid\u00edm ve sv\u00e9 platform\u011b, je vyj\u00e1d\u0159en\u00edm p\u0159\u00e1n\u00ed prodejce dluhopisu, kter\u00fd do n\u011bj prom\u00edtnul o\u010dek\u00e1v\u00e1n\u00ed a stav dluhopisov\u00fdch trh\u016f v\u00a0kombinaci s\u00a0rizikem, kter\u00e9 dr\u017een\u00ed dan\u00e9ho dluhopisu p\u0159in\u00e1\u0161\u00ed spojen\u00e9 s\u00a0o\u010dek\u00e1van\u00fdm v\u00fdnosem tohoto cenn\u00e9ho pap\u00edru do jeho splatnosti. Nem\u00e1m pon\u011bt\u00ed o motivech prodejce a nechci se nyn\u00ed zab\u00fdvat rizikem z\u00a0dr\u017een\u00ed dluhopisu (o tomto v\u00a0dal\u0161\u00edm \u010dl\u00e1nku), bude m\u011b nyn\u00ed pouze zaj\u00edmat, jak\u00fd v\u00fdnos do splatnosti<\/strong> dluhopisu mohu o\u010dek\u00e1vat a jak jej mohu stanovit.<\/span><\/p>\n

\u00a0\u00a0 V\u0161echny poznan\u00e9 platby, kter\u00e9 m\u011b v souvislosti s dluhopisem \u010dekaj\u00ed v budoucnosti, mohu jejich diskontov\u00e1n\u00edm k dne\u0161n\u00edmu dni vt\u011blit do aktu\u00e1ln\u00ed ceny dluhopisu. Z\u00e1kladn\u00edm vzorcem pro zji\u0161t\u011bn\u00ed sou\u010dasn\u00e9 ceny cenn\u00e9ho pap\u00edru s pevn\u00fdm v\u00fdnosem je modifikovan\u00fd a upraven\u00fd vzorec z \u010dl\u00e1nku Dluhopisy \u2013 II.<\/a><\/strong><\/span> a mohl by vypadat takto:\u00a0<\/span><\/p>\n

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\u00a0\u00a0 Nen\u00ed t\u0159eba se takov\u00e9ho chuchvalce ob\u00e1vat. Vyjad\u0159uje v\u0161e, co mohu od dluhopisu \u010dekat. SH<\/em><\/span><\/strong> je sou\u010dasn\u00e1 hodnota dluhopisu<\/strong>, C<\/em><\/span><\/strong> je kup\u00f3nov\u00e1 v\u00fdplata<\/strong> za vyzna\u010denou periodu, FV<\/strong><\/em><\/span> je Face Value<\/strong> \u2013 \u010d\u00e1stka nomin\u00e1lu splatn\u00e1 k\u00a0Maturity Date (dni splatnosti) a \u00farok<\/em><\/strong><\/span> je sazba<\/strong>, kterou diskontuji<\/strong> v\u0161echny budouc\u00ed platby k\u00a0dne\u0161n\u00edmu dni<\/strong>. Ka\u017edou kup\u00f3novou v\u00fdplatu (jednu a\u017e do hodnoty n<\/span><\/em><\/strong> \u2013 podle toho, kolik jich je) diskontuji k dne\u0161n\u00edmu dni (zji\u0161\u0165uji, jejich aktu\u00e1ln\u00ed hodnotu) a nakonec diskontuji Face Value k dne\u0161n\u00edmu dni, abych sou\u010dtem t\u011bchto diskontovan\u00fdch hodnot zjistil sou\u010dasnou cenu dluhopisu. V modelov\u00e9m p\u0159\u00edpad\u011b dluhopisu se splatnost\u00ed za \u010dty\u0159i roky s Face Value 1000 USD, ro\u010dn\u00edm kup\u00f3nem 50 USD a p\u0159i \u00farokov\u00e9 sazb\u011b 4% p.a., mohu zjistit sou\u010dasnou hodnotu tohoto dluhopisu takto:<\/span><\/p>\n

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\u00a0 \u00a0Z v\u00fdpo\u010dtu mohu vypozorovat, \u017ee tento dluhopis by m\u011bl m\u00edt za zadan\u00fdch v\u00fdpo\u010detn\u00edch podm\u00ednek sou\u010dasnou hodnotu 1036.30 USD. Tento vzorec a postup v\u00fdpo\u010dtu pak budi\u017e z\u00e1kladn\u00edm stavebn\u00edm kamenem dal\u0161\u00ed \u00favahy o m\u011b\u0159en\u00ed v\u00fdkonu dluhopis\u016f\u00a0<\/span><\/p>\n

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Yield To Maturity (V\u00fdnos do splatnosti)<\/strong><\/span><\/h1>\n

\u00a0\u00a0 V\u00fdnos do splatnosti<\/strong> (Yield To Maturity – YTM) je pova\u017eov\u00e1n za nejb\u011b\u017en\u011bj\u0161\u00ed m\u011b\u0159\u00edtko v\u00fdnosu dluhopisu. Je vyj\u00e1d\u0159en procentn\u00ed sazbou za rok<\/strong> (% p.a.) a ukazuje s jakou m\u00edrou v\u00fdnosnosti mohu u dluhopisu po\u010d\u00edtat. Jak se k n\u00ed dobrat je z\u00e1kladn\u00ed premisou k pochopen\u00ed jej\u00ed interpretace a spolehlivosti. V p\u0159edchoz\u00edm odstavci jsem popsal z\u00e1kladn\u00ed teoretick\u00fd vzorec v\u00fdpo\u010dtu sou\u010dasn\u00e9 ceny dluhopisu p\u0159i zji\u0161t\u011bn\u00fdch p\u0159edpokladech – velikosti kup\u00f3nu, frekvenci kup\u00f3n\u016f, dob\u011b do splatnosti a \u00farokov\u00e9 sazb\u011b, z t\u011bchto poznan\u00fdch \u00fadaj\u016f pak vypo\u010d\u00edt\u00e1m sou\u010dasnou cenu dluhopisu. K \u010demu mi to ale je, kdy\u017e sou\u010dasnou cenu dluhopisu zn\u00e1m? Mohu se na ni pod\u00edvat do obchodn\u00ed platformy a nemus\u00edm ji slo\u017eit\u011b po\u010d\u00edtat! Proto si mus\u00edm polo\u017eit jinou ot\u00e1zku. Kde se vzala ta \u00farokov\u00e1 sazba<\/strong> v m\u00e9m v\u00fdpo\u010dtu, kter\u00e1 mi „to cel\u00e9“ diskontuje na sou\u010dasnou cenu<\/strong>? To je ta spr\u00e1vn\u00e1 ot\u00e1zka, pt\u00e1m se toti\u017e na \u00farokovou sazbu, kter\u00e1 mi ze v\u0161ech mo\u017en\u00fdch plateb, kter\u00e9 diskontuji, vytv\u00e1\u0159\u00ed sou\u010dasnou cenu dluhopisu, na kterou se d\u00edv\u00e1m. Tato popt\u00e1van\u00e1 a hledan\u00e1 \u00farokov\u00e1 sazba, kter\u00e1 mi „nadiskontuje“ budouc\u00ed platby do sou\u010dasn\u00fdch hodnot tvo\u0159\u00edc\u00edch aktu\u00e1ln\u00ed cenu dluhopisu je pr\u00e1v\u011b v\u00fdnos do splatnosti<\/strong>, tedy Yield To Maturity (YTM)<\/strong>.<\/span><\/p>\n

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\u00a0\u00a0 Pokud budu cht\u00edt dostat z v\u00fd\u0161e uveden\u00e9ho vzorce hodnotu \u00faroku (YTM) pomoc\u00ed v\u0161ech ostatn\u00edch poznan\u00fdch hodnot, \u010dek\u00e1 m\u011b nelehk\u00fd \u00fakol spojen\u00fd s iterac\u00ed, popsan\u00fd v \u010dl\u00e1nku Dluhopisy \u2013 II.<\/a><\/strong><\/span>, kter\u00fd v\u0161ak velmi jednodu\u0161e zvl\u00e1dnu pomoc\u00ed Exelu. P\u0159esto\u017ee mi Excel poskytuje velmi dobr\u00fd a elegantn\u00ed n\u00e1stroj na v\u00fdpo\u010det tohoto YTM, hled\u00e1m toti\u017e Vnit\u0159n\u00ed V\u00fdnosov\u00e9 Procento (funkce =IRR) s\u00e9rie budouc\u00edch cash flow, mus\u00edm sv\u00e9 hled\u00e1n\u00ed YTM konfrontovat s existenc\u00ed r\u016fzn\u00fdch typ\u016f dluhopis\u016f, vytvo\u0159it pro pochopen\u00ed YTM spr\u00e1vn\u00e9 p\u0159edpoklady, a nakonec zohlednit p\u0159i v\u00fdpo\u010dtu r\u016fzn\u00e9 technick\u00e9 detaily.<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 Zerobonds<\/strong><\/span><\/h1>\n

\u00a0\u00a0 Po\u0159\u00eddit dluhopis bez kup\u00f3nu<\/strong> nen\u00ed nic neobvykl\u00e9ho. Naopak, jedn\u00e1 se o velmi b\u011b\u017enou investici nap\u0159\u00edklad do Treasury Bills, kter\u00e9 nemaj\u00ed \u017e\u00e1dn\u00fd kup\u00f3n, ale prod\u00e1vaj\u00ed se s diskontem k Face Value. Neexistence kup\u00f3nu pak p\u0159in\u00e1\u0161\u00ed zna\u010dn\u00e9 zjednodu\u0161en\u00ed v\u00fdpo\u010dtu YTM. \u00a0<\/span><\/p>\n

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\u00a0\u00a0 Z cel\u00e9ho vzorce pro v\u00fdpo\u010det sou\u010dasn\u00e9 hodnoty SH<\/em><\/span><\/strong>\u00a0zerobondu toti\u017e odpad\u00e1 velmi pracn\u00e1 pas\u00e1\u017e s diskontov\u00e1n\u00edm kup\u00f3nov\u00fdch plateb a z\u016fstane pouze \u010d\u00e1st, kter\u00e1 vyjad\u0159uje diskontov\u00e1n\u00ed Face Value. Bezkup\u00f3nov\u00e9 dluhopisy toti\u017e \u017e\u00e1dn\u00fd kup\u00f3n nenab\u00edz\u00ed, nen\u00ed tak co diskontovat :c). N\u00e1kupem zerobondu m\u011b \u010dek\u00e1 pouze jedin\u00e9 budouc\u00ed cash flow a t\u00edm je jeho budouc\u00ed prodej nebo vypo\u0159\u00e1d\u00e1n\u00ed ve v\u00fd\u0161i Face Value p\u0159i splatnosti, v m\u00e9m p\u0159\u00edpad\u011b druh\u00e1 mo\u017enost, proto\u017ee hled\u00e1m v\u00fdnos „do splatnosti“ dluhopisu. Potom, p\u0159i vylou\u010den\u00ed \u010d\u00e1sti vzorce ozna\u010den\u00e9 \u010derven\u00fdm k\u0159\u00ed\u017ekem reprezentuj\u00edc\u00ed diskontov\u00e1n\u00ed pr\u016fb\u011b\u017en\u00fdch kup\u00f3n\u016f, mohu pozorovat:<\/span><\/p>\n

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\u00a0\u00a0\u00a0 Hled\u00e1n\u00ed v\u00fdnosu do splatnosti se tak velmi p\u0159\u00edjemn\u011b smrsklo do jednoduch\u00e9 algebry, kde budu cht\u00edt vyhledat hodnotu \u00farok<\/span><\/em><\/strong> z v\u00fd\u0161e uveden\u00e9ho vzorce, bude to hodnota takov\u00e9 \u00farokov\u00e9 sazby, kter\u00e1 zp\u016fsobuje, \u017ee budouc\u00ed Face Value m\u00e1 sou\u010dasnou hodnotu SH<\/em><\/span><\/strong>:<\/span><\/p>\n

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\u00a0\u00a0 Po p\u0159\u00edslu\u0161n\u00fdch \u00faprav\u00e1ch, mohu vypozorovat, \u017ee se mi poda\u0159ilo \u201evyseparovat\u201c hodnotu \u00farok do velmi dobr\u00e9ho form\u00e1tu pro stanoven\u00ed v\u00fdnosu do splatnosti<\/strong> (YTM) jak\u00e9hokoliv zerobondu takto:<\/span><\/p>\n

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\u00a0\u00a0 N\u00e1kup zerobondu se splatnost\u00ed za \u010dty\u0159i roky s Face Value 1000 USD<\/strong> a aktu\u00e1ln\u00ed cenou 880 USD<\/strong>, by pak p\u0159ineslo tento v\u00fdsledek p\u0159i vyhled\u00e1n\u00ed YTM:<\/span><\/p>\n

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\u00a0\u00a0 T\u00edmto jednoduch\u00fdm v\u00fdpo\u010dtem bych pak mohl zjistit, \u017ee takto nab\u00edzen\u00fd zerobond by poskytoval v\u00fdnos 3.24 % p.a<\/strong>. Za jak\u00fdch podm\u00ednek? Zerobond poskytuje tento v\u00fdnos za jedin\u00e9 podm\u00ednky, tedy mus\u00ed b\u00fdt dr\u017een do splatnosti<\/strong>, kdy obdr\u017e\u00edm p\u0159i vypo\u0159\u00e1d\u00e1n\u00ed Face Value ve v\u00fd\u0161i 1000 USD, tento \u00farokov\u00fd v\u00fdnos mi tak ji\u017e nikdo p\u0159i spln\u011bn\u00ed t\u00e9to podm\u00ednky nevezme. Odpad\u00e1 tak vliv pohybu jeho ceny, pokud bych se rozhodl tento dluhopis prodat p\u0159ed jeho splatnost\u00ed a nemus\u00edm se zab\u00fdvat ot\u00e1zkou reinvestov\u00e1n\u00ed kup\u00f3n\u016f, jako u klasick\u00e9ho kup\u00f3nov\u00e9ho dluhopisu. \u00a0<\/span><\/p>\n

\u00a0\u00a0 V praktick\u00e9 uk\u00e1zce a s pot\u0159ebou v\u00edce v\u00fdpo\u010det v\u00fdnos ze zerobondu plasti\u010dt\u011bji p\u0159ibl\u00ed\u017eit, je na obr\u00e1zku n\u00ed\u017ee patrn\u00e9, \u017ee jsem 29.12.2022 nakoupil na obchodn\u00ed \u00fa\u010det 50 ks zerobond\u016f \u2013 Treasury Bills APR25 2023.<\/span><\/p>\n

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\u00a0\u00a0 Jednalo se o dluhopisy se splatnost\u00ed 25.4.2023 a za tyto dluhopisy jsem po zapo\u010dten\u00ed komis\u00ed zaplatil 98,5793% jejich Face Value, tedy nakoupil jsem jeden kus<\/strong>\u00a0za 985.793 USD, <\/strong>tato cena je zobrazena na obr\u00e1zku z obchodn\u00ed platformy TWS n\u00ed\u017ee \u010dervenou \u0161ipkou:\u00a0\u00a0<\/span><\/p>\n

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\u00a0 Proto\u017ee se jedn\u00e1 o dluhopisov\u00e9 cenn\u00e9 pap\u00edry dr\u017een\u00e9 krat\u0161\u00ed dobu ne\u017e jeden rok, mus\u00edm prov\u00e9st m\u00edrnou \u00fapravu vzorce pro v\u00fdpo\u010det YTM tak, aby vyjad\u0159ovala pr\u00e1v\u011b takovou dobu do splatnosti krat\u0161\u00ed ne\u017e kalend\u00e1\u0159n\u00ed rok. V\u00a0\u010dl\u00e1nku Dluhopisy \u2013 I.<\/a><\/strong><\/span> jsem popisoval, jak mohu vypo\u010d\u00edtat hodnotu pen\u011bz pro obdob\u00ed krat\u0161\u00ed nebo del\u0161\u00ed ne\u017e jeden rok, budu aplikovat tento postup tak\u00e9 na sv\u00e9 zerobondy. N\u00e1kup zerobond\u016f 29.12.2022 se splatnost\u00ed 25.4.2023 ur\u010duje dobu do splatnosti t\u011bchto zerobond\u016f ve v\u00fd\u0161i 117 kalend\u00e1\u0159n\u00edch dn\u016f. Mohu pak na v\u00fdpo\u010det YTM t\u011bchto dubnov\u00fdch zerobond\u016f aplikovat vzorec: \u00a0<\/span><\/p>\n

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\u00a0\u00a0 Po\u0159\u00edzen\u00edm t\u011bchto zerobond\u016f m\u011b v\u00fdnos do splatnosti (YTM)<\/strong> ve v\u00fd\u0161i 4.565 % p.a.<\/strong> nemine. Mohu tak porovnat tuto hodnotu s\u00a0obr\u00e1zkem z\u00a0v\u00fdpisu \u00fa\u010dtu v\u00fd\u0161e, kde \u010dervenou \u0161ipkou je odhadovan\u00e1 v\u00fd\u0161e YTM u tohoto zerobondu tak\u00e9 vyzna\u010dena podle v\u00fdpo\u010dtu m\u00e9ho brokera.<\/span><\/p>\n

\u00a0\u00a0 Mohu toto v\u0161e samoz\u0159ejm\u011b sv\u011b\u0159it excelovsk\u00e9mu se\u0161itu, kde budu m\u00edt cel\u00fd v\u00fdpo\u010det okam\u017eit\u011b k dispozici. Na n\u00ed\u017ee uveden\u00e9m obr\u00e1zku je v uk\u00e1zce excelovsk\u00e9ho se\u0161itu pops\u00e1n zp\u016fsob v\u00fdpo\u010dtu YTM nakoupen\u00e9ho zerobondu spole\u010dn\u011b s mo\u017enost\u00ed modelovat v\u00fdnos do jak\u00e9koliv po\u017eadovan\u00e9 po\u0159izovac\u00ed ceny.<\/span><\/p>\n

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\u00a0\u00a0 V\u00fdpo\u010det YTM<\/strong> zerobondu (1)<\/span><\/strong> je prost\u00fdm p\u0159eveden\u00edm vzorce popsan\u00e9ho v\u00fd\u0161e do excelovsk\u00e9ho vzorce. Mohu ale tak\u00e9, za pou\u017eit\u00ed p\u016fvodn\u00edho vzorce pro hled\u00e1n\u00ed po\u017eadovan\u00e9 sou\u010dasn\u00e9 hodnoty dluhopisu podle zadan\u00e9ho \u00farokov\u00e9ho v\u00fdnosu (2)<\/strong>,<\/span><\/span> modelovat situaci, kdy budu cht\u00edt nakoupit za ur\u010ditou cenu, kter\u00e1 bude charakterizovat po\u017eadovan\u00fd v\u00fdnos. Pokud bych tedy cht\u011bl po nakupovan\u00e9m zerobondu dne 29.12.2022 se splatnost\u00ed 25.4.2023, aby mi p\u0159inesl vy\u0161\u0161\u00ed v\u00fdnos nap\u0159\u00edklad 5% p.a<\/strong>. (3)<\/strong><\/span>, musela by b\u00fdt jeho po\u0159izovac\u00ed hodnota ni\u017e\u0161\u00ed, tedy na \u00farovni nejv\u00fd\u0161e 984,4821 USD<\/strong>. Zm\u011bnou po\u017eadovan\u00e9 \u00farokov\u00e9 sazby pak mohu tento \u00farok m\u011bnit a pozorovat, jak se prom\u00edt\u00e1 do po\u017eadovan\u00e9 ceny nakupovan\u00e9ho zerobondu.<\/span><\/p>\n

\u00a0\u00a0\u00a0Dluhopisy s\u00a0kup\u00f3nem<\/strong><\/span><\/h1>\n

\u00a0\u00a0 Stanovit v\u00fdnos dluhopisu vypl\u00e1cej\u00edc\u00edho kup\u00f3n v\u00a0pravideln\u00fdch intervalech je \u00fakol, kter\u00fd by m\u011bl \u0159e\u0161it ji\u017e vzpom\u00ednan\u00fd vzorec pro v\u00fdpo\u010det sou\u010dasn\u00e9 hodnoty cenn\u00e9ho dluhov\u00e9ho pap\u00edru diskontov\u00e1n\u00edm budouc\u00edch pen\u011b\u017en\u00edch tok\u016f.<\/span><\/p>\n

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\u00a0\u00a0 U\u017e bylo nazna\u010deno, \u017ee prom\u011bnn\u00e1 \u00farok<\/em><\/span><\/strong> je hledan\u00fd YTM<\/strong> a \u017ee v\u00fdpo\u010det nen\u00ed jednoduch\u00fd, pokud bych cht\u011bl pou\u017e\u00edt tu\u017eku a pap\u00edr, nicm\u00e9n\u011b pomoc\u00ed Excelu toto probl\u00e9m nen\u00ed. V \u201erozlo\u017een\u00e9\u201c form\u011b tohoto vzorce je pak patrn\u00e9, \u017ee pro stanoven\u00ed YTM bude sta\u010dit zn\u00e1t po\u0159izovac\u00ed cenu dluhopisu, Face Value, v\u00fd\u0161i vypl\u00e1cen\u00e9ho kup\u00f3nu a jeho periodu, a nakonec po\u010det period do splatnosti dluhopisu. Potom, za p\u0159edpokladu pou\u017eit\u00ed vhodn\u00e9ho v\u00fdpo\u010detn\u00edho n\u00e1stroje, budu moci stanovit YTM pozorovan\u00e9ho dluhopisu. Na obr\u00e1zku n\u00ed\u017ee je op\u011bt zobrazen dluhopis spole\u010dnosti Ford se z\u00e1kladn\u00edmi \u00fadaji:<\/span><\/p>\n

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\u00a0\u00a0 Pokud bych nyn\u00ed tento dluhopis nakoupil za 1042.50 USD, tak mohu inkasovat kup\u00f3n ve v\u00fd\u0161i 6.625% p.a. v pravideln\u00fdch p\u016flro\u010dn\u00edch intervalech ve v\u00fd\u0161i +33,125 USD a\u017e do jeho splatnosti, tedy do 15.2.2028. Proto\u017ee do splatnosti dluhopisu ode dne\u0161n\u00edho dne je p\u011bt let, \u010dek\u00e1 m\u011b deset v\u00fdplat kup\u00f3n\u016f \u2013 po\u010det period je tak 10. Toto mi posta\u010d\u00ed ke zb\u011b\u017en\u00e9mu<\/strong> v\u00fdpo\u010dtu v\u00fdnosu do splatnosti pomoc\u00ed excelu. \u00a0\u00a0<\/span><\/p>\n

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\u00a0\u00a0 V\u00a0excelovsk\u00e9 tabulce vypln\u00edm modr\u00e9 bu\u0148ky, v\u0161e ostatn\u00ed obstaraj\u00ed v\u00fdpo\u010dty. Zad\u00e1n\u00ed Face Value<\/strong>, aktu\u00e1ln\u00ed ceny<\/strong>, data po\u0159\u00edzen\u00ed<\/strong> a data splatnosti<\/strong> dluhopisu net\u0159eba v\u00fdznamn\u011b komentovat (1.)<\/strong><\/span>. Datum po\u0159\u00edzen\u00ed a datum splatnosti mi vygeneruje po\u010det let do splatnosti<\/strong> dluhopisu (hodnota 5 let). Proto\u017ee se jedn\u00e1 o dluhopis s\u00a0frekvenc\u00ed p\u0159ipisov\u00e1n\u00ed kup\u00f3n\u016f pololetn\u011b<\/strong>, je v\u00a0bu\u0148ce \u201eFrekvence za rok\u201c uvedeno \u010d\u00edslo 2 (2.)<\/span><\/strong>. Po\u010det period<\/strong> je automaticky vypo\u010dten na hodnotu (5*2) 10<\/strong>. Posledn\u00ed, co zad\u00e1m do p\u0159ipraven\u00e9 tabulky je kup\u00f3nov\u00e1 sazba<\/strong> dluhopisu, tak jak je vyzna\u010dena v\u00a0platform\u011b, v\u00a0m\u00e9m p\u0159\u00edpad\u011b u dluhopisu Ford \u010din\u00ed 6,625 % p.a. (3.)<\/span><\/strong>. V\u00fdpo\u010det mi ukazuje, \u017ee pravideln\u00fd pololetn\u00ed kup\u00f3n<\/strong> (Kup\u00f3n za periodu) bude \u010dinit 33,125 USD<\/strong>. Celkovou kalkulaci mi umo\u017en\u00ed excelovsk\u00e1 funkce =\u00daROKOV\u00c1.M\u00cdRA <\/em>(4.)<\/strong><\/span>, jej\u00edmi\u017e argumenty jsou (po\u010det period; kup\u00f3n za periodu; aktu\u00e1ln\u00ed cena se znam\u00e9nkem m\u00ednus; Face Value; 0)<\/em>. Toto zad\u00e1n\u00ed mi vypo\u010d\u00edt\u00e1 YTM, tedy v\u00fdnos do splatnosti dluhopisu podle m\u00e9ho velmi zjednodu\u0161en\u00e9ho zad\u00e1n\u00ed. Mohu tak konstatovat, \u017ee pokud nakoup\u00edm<\/strong> tento dluhopis Ford skute\u010dn\u011b za cenu 1042,50 USD<\/strong>, mohl bych, p\u0159i kup\u00f3nov\u00fdch platb\u00e1ch, kter\u00e9 budu reinvestovat (tedy neutr\u00e1cet), vyd\u011blat na tomto dr\u017een\u00ed dluhopisu do jeho splatnosti \u010d\u00e1stku p\u0159edstavuj\u00edc\u00ed zhodnocen\u00ed vlo\u017een\u00e9 investice na \u00farovni 5,638% p.a.<\/strong><\/span><\/p>\n

\u00a0\u00a0 Je to zcela p\u0159esn\u00e9? Ne zcela, proto jsem tak\u00e9 v\u00fd\u0161e uvedl, \u017ee se jedn\u00e1 o zb\u011b\u017en\u00fd v\u00fdpo\u010det YTM a opravdu mohu ve zcela hrub\u00fdch obrysech takto o v\u00fdnosu uva\u017eovat. Probl\u00e9mem, se kter\u00fdm tato \u00favaha nepo\u010d\u00edt\u00e1, je rozlo\u017een\u00ed kup\u00f3nov\u00fdch plateb s p\u0159ihl\u00e9dnut\u00edm k datu po\u0159\u00edzen\u00ed dluhopisu. Pohledem do analytick\u00e9 platformy mohu zjistit, \u017ee kup\u00f3ny se vypl\u00e1cej\u00ed v t\u011bchto term\u00ednech:<\/span><\/p>\n

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\u00a0 \u00a0Je 25.1.2023 a nejbli\u017e\u0161\u00ed v\u00fdplata kup\u00f3nu<\/strong> dluhopisu Ford je 15.\u00fanora 2023<\/strong>, tedy za 21 dn\u016f<\/strong>. P\u0159edchoz\u00ed \u201ezb\u011b\u017en\u00fd\u201c v\u00fdpo\u010det po\u010d\u00edtal s t\u00edm, \u017ee jsem kup\u00f3n obdr\u017eel p\u0159esn\u011b za p\u016fl roku od n\u00e1kupu dluhopisu, dal\u0161\u00ed kup\u00f3n za rok atd.., toto je v\u0161ak nep\u0159esn\u00e1 nebo velmi zjednodu\u0161en\u00e1 \u00favaha, proto\u017ee do v\u00fdplaty prvn\u00edho kup\u00f3nu mi zb\u00fdv\u00e1 pouze 21 dn\u016f (nikoliv tedy zjednodu\u0161en\u00e9ho p\u016fl roku) a dal\u0161\u00ed kup\u00f3nov\u00e1 platba se uskute\u010dn\u00ed 15.8.2023, pot\u00e9 budou n\u00e1sledovat dal\u0161\u00ed pravideln\u00e9 platby kup\u00f3n\u016f a\u017e do maturity dne 15.2.2028. Co t\u00edm chci nazna\u010dit? Inkasovat vyzna\u010den\u00fd kup\u00f3n m\u00e1 ten dr\u017eitel dluhopisu, kter\u00fd je jeho vlastn\u00edkem v okam\u017eiku rozhodn\u00e9m pro jeho v\u00fdplatu. N\u00e1kupem dluhopisu, kter\u00fd m\u00e1 p\u016flro\u010dn\u00ed frekvenci vypl\u00e1cen\u00ed, si dnes, jedenadvacet dn\u016f p\u0159ed nejbli\u017e\u0161\u00ed v\u00fdplatou, zajist\u00edm jeho inkaso v pln\u00e9 v\u00fd\u0161i, p\u0159esto\u017ee jej budu dr\u017eet jen 21 kalend\u00e1\u0159n\u00edch dn\u016f, a nikoliv cel\u00fd p\u016flrok jako ve zjednodu\u0161en\u00e9m v\u00fdpo\u010dtu v\u00fd\u0161e. Bylo by ale asi podivn\u00e9, kdyby se prodejce dluhopisu zbavoval t\u011bsn\u011b p\u0159ed jeho v\u00fdplatou a daroval tak t\u00e9m\u011b\u0159 celou kup\u00f3novou p\u016flro\u010dn\u00ed v\u00fdplatu nov\u00e9mu vlastn\u00edkovi. Jak to tedy funguje?<\/span><\/p>\n

Accrued Interest a Clean Price<\/strong><\/span><\/h2>\n

\u00a0\u00a0 V\u00fd\u0161e popsan\u00e1 situace, tedy n\u00e1kup kup\u00f3nov\u00e9ho dluhopisu mezi periodami v\u00fdplaty kup\u00f3nu, je samoz\u0159ejm\u011b o\u0161et\u0159ena. Nem\u016f\u017eu se tedy spol\u00e9hat, \u017ee zachytra\u010d\u00edm a takticky nakoup\u00edm dluhopis p\u0159ed v\u00fdplatou kup\u00f3nu, sl\u00edznu smetanu a prodejce dluhopisu vyjde napr\u00e1zdno. Jak to funguje uk\u00e1\u017eu na zcela praktick\u00e9m p\u0159\u00edkladu, kdy jsem na sv\u016fj obchodn\u00ed \u00fa\u010det nakoupil pr\u00e1v\u011b tento dluhopis spole\u010dnosti Ford. Na obr\u00e1zku n\u00ed\u017ee je vid\u011bt aktu\u00e1ln\u00ed cenovou nab\u00eddku ze dne 25.1.2023.<\/span><\/p>\n

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\u00a0\u00a0 Mohu pozorovat, \u017ee aktu\u00e1ln\u011b mohu dluhopis po\u0159\u00eddit za 104,75% Face Value, tedy za 1047,50 USD<\/strong> za jeden kus. Na obr\u00e1zku n\u00ed\u017ee je zadan\u00fd p\u0159\u00edkaz k\u00a0n\u00e1kupu za Ask cenu.<\/span><\/p>\n

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\u00a0\u00a0 Pro ka\u017ed\u00fd dluhopis je definovan\u00e1 jin\u00e1 velikost nejmen\u0161\u00edho lotu, kter\u00fd mohu po\u0159\u00eddit, v p\u0159\u00edpad\u011b dluhopisu Ford mohu nakoupit nejm\u00e9n\u011b p\u011bt kus\u016f (\u010derven\u00e1 \u0161ipka). Takto zad\u00e1v\u00e1m p\u0159\u00edkaz do platformy, aby jeho v\u00fdsledkem bylo po\u0159\u00edzen\u00ed t\u011bchto dluhov\u00fdch cenn\u00fdch pap\u00edr\u016f.<\/span><\/p>\n

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\u00a0\u00a0 V\u00fdsledkem je po\u0159\u00edzen\u00ed p\u011bti dluhopis\u016f spole\u010dnosti Ford<\/strong>, ka\u017ed\u00fd s\u00a0pr\u016fm\u011brnou cenou se zapo\u010d\u00edtan\u00fdmi poplatky za obchod ve v\u00fd\u0161i 1048,50 USD<\/strong>. Pokud jsem tedy zaplatil za n\u00e1kup ka\u017ed\u00e9ho dluhopisu -1.00 USD na komis\u00edch, opravdu jsem dluhopis nakoupil za Ask cenu 1047.50 USD, tak jak jsem po\u017eadoval. <\/span><\/p>\n

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\u00a0 \u00a0Na obr\u00e1zku v\u00fd\u0161e cel\u00e1 situace ze statementu m\u00e9ho obchodn\u00edho \u00fa\u010dtu, p\u011bt dluhopis\u016f, zaplacen\u00fdch p\u011bt dolar\u016f poplatk\u016f, opravdu jsem tedy po\u0159\u00eddil tyto dluhopisy za -1047.50 USD ka\u017ed\u00fd. T\u00e9to cen\u011b se \u0159\u00edk\u00e1 Clean Price<\/strong>. Tato cena ale nep\u0159edstavuje v\u0161echny n\u00e1klady<\/strong>, kter\u00e9 m\u011b tento dluhopis st\u00e1l, je toti\u017e o\u010di\u0161t\u011bna pr\u00e1v\u011b od nahromad\u011bn\u00e9 \u010d\u00e1stky \u00farok\u016f z nejbl\u00ed\u017ee splatn\u00e9ho kup\u00f3nu, kter\u00e1 mi nepat\u0159\u00ed a kter\u00e1 n\u00e1le\u017e\u00ed prodejci dluhopisu. Je pravdou, \u017ee za 21 kalend\u00e1\u0159n\u00edch dn\u016f (15.2.2023) inkasuji celou pololetn\u00ed kup\u00f3novou v\u00fdplatu ve v\u00fd\u0161i +33.125 USD, budu toti\u017e v danou chv\u00edli dr\u017eitelem dluhopisu, nicm\u00e9n\u011b valn\u00e1 \u010d\u00e1st t\u00e9to sumy mi nepat\u0159\u00ed, proto\u017ee p\u0159edch\u00e1zej\u00edc\u00ed vlastn\u00edk dluhopisu jej dr\u017eel t\u00e9m\u011b\u0159 po celou dobu t\u00e9to v\u00fdplatn\u00ed periody, tedy konkr\u00e9tn\u011b (16.8.2022 \u2013 25.1.2023) dobu v d\u00e9lce 162 dn\u016f.<\/span> Nab\u011bhl\u00fd \u00farok za obdob\u00ed, kdy dluhopis nevlastn\u00edm, b\u00fdv\u00e1 ozna\u010dov\u00e1n term\u00ednem Accrued Bond Interest<\/strong> a je po zobchodov\u00e1n\u00ed dluhopisu jeho nov\u00e9mu nabyvateli za\u00fa\u010dtov\u00e1n a pat\u0159i\u010dn\u011b sra\u017een, aby byl p\u0159ed\u00e1n jeho p\u0159edchoz\u00edmu dr\u017eiteli. Na obr\u00e1zku n\u00ed\u017ee je vid\u011bt jeho celkov\u00e1 hodnota pro mnou po\u0159\u00edzen\u00fdch p\u011bt dluhopis\u016f Ford:<\/span><\/p>\n

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\u00a0\u00a0 Mohu vypozorovat, \u017ee mi bylo z\u00a0m\u00e9ho \u00fa\u010dtu str\u017eeno -149,06 USD<\/strong> s\u00a0koment\u00e1\u0159em Purchased Accrued Interest<\/strong>, tedy zaplatil jsem za p\u011bt dluhopis\u016f jeho p\u0159edch\u00e1zej\u00edc\u00edmu dr\u017eiteli tyto pen\u00edze a p\u0159edstavuj\u00ed \u010d\u00e1stku (-149,06 USD\/5) ve v\u00fd\u0161i -29.812 USD<\/strong> na jeden dluhopis Ford. Plat\u00ed, \u017ee Clean Price + Accrued Interest = Dirty Price, takto se pak ozna\u010duje kone\u010dn\u00e1 po\u0159izovac\u00ed cena dluhopisu, kter\u00e1 p\u0159edstavuje cenu, kterou nevid\u00edm ve sv\u00e9 obchodn\u00ed platform\u011b, proto\u017ee k n\u00ed mus\u00edm p\u0159ipo\u010d\u00edtat je\u0161t\u011b hodnotu nab\u011bhl\u00fdch \u00farok\u016f, kter\u00e9 mi nepat\u0159\u00ed a kter\u00e9 budu muset p\u0159edchoz\u00edmu vlastn\u00edkovi odevzdat. Pokud bych tento dluhopis prod\u00e1val, mohu pak se stejnou logikou o\u010dek\u00e1vat, \u017ee krom\u011b prodejn\u00ed ceny obdr\u017e\u00edm na sv\u016fj \u00fa\u010det tak\u00e9 \u010d\u00e1st \u00farok\u016f, kter\u00e9 odpov\u00eddaj\u00ed dob\u011b, po kterou jsem dluhopis dr\u017eel a m\u011bl n\u00e1rok na p\u0159\u00edslu\u0161nou \u010d\u00e1st kup\u00f3nov\u00e9ho \u00faroku.<\/span><\/p>\n

\u00a0\u00a0 Jak byla hodnota Accrued Interest stanovena lze vypo\u010d\u00edtat pom\u011b\u0159en\u00edm d\u00e9lky kup\u00f3nov\u00e9 periody<\/strong> a d\u00e9lky n\u00e1roku na odpov\u00eddaj\u00edc\u00ed \u00faroky<\/strong>. V m\u00e9m konkr\u00e9tn\u00edm p\u0159\u00edpad\u011b je d\u00e9lka periody pololet\u00ed, tak\u017ee p\u0159i konvenci 30\/360 (rok pro korpor\u00e1tn\u00ed dluhopisy m\u00e1 360 dn\u016f, pololet\u00ed 180 dn\u016f) \u010din\u00ed tato d\u00e9lka 180 dn\u016f. Nen\u00e1le\u017e\u00ed mi kup\u00f3nov\u00fd \u00farok za obdob\u00ed, kdy jsem nebyl vlastn\u00edkem dluhopisu, tedy za obdob\u00ed od p\u0159edch\u00e1zej\u00edc\u00ed v\u00fdplaty do dne po\u0159\u00edzen\u00ed dluhopisu (16.8.2022 \u2013 25.1.2023), tedy konkr\u00e9tn\u011b za 162 dn\u016f (po\u010d\u00edt\u00e1 se ode dne n\u00e1sleduj\u00edc\u00edho po v\u00fdplat\u011b p\u0159edch\u00e1zej\u00edc\u00edho kup\u00f3nu 15.8.2022, v m\u00e9m p\u0159\u00edpad\u011b tak od 16.8.2022). Potom, p\u0159i kup\u00f3nov\u00e9 v\u00fdplat\u011b +33.125 USD p\u0159ipadaj\u00edc\u00ed na cel\u00e9 toto pololet\u00ed, mi nepat\u0159\u00ed \u010d\u00e1stka (+33.125 USD\/180)*162 = 29.8125 USD<\/strong> pro ka\u017ed\u00fd nakoupen\u00fd dluhopis Ford. Pro p\u011bt nakoupen\u00fdch dluhopis\u016f je mi pak str\u017eeno (5*29.8125 USD), co\u017e je \u010d\u00e1stka -149,0625 USD, tedy p\u0159esn\u011b str\u017een\u00e1 suma, kter\u00e1 je k vid\u011bn\u00ed v\u00fd\u0161e na obr\u00e1zku z v\u00fdpisu z m\u00e9ho obchodn\u00edho \u00fa\u010dtu. Mohu tak ve shrnut\u00ed konstatovat, \u017ee jsem za ka\u017ed\u00fd dluhopis zaplatil o 29,8125 USD v\u00edce, nekoupil jsem jej tak za cenu Ask (-1047,50 USD), kterou jsem zadal do obchodn\u00ed platformy, ale kompletn\u00ed po\u0159izovac\u00ed cena<\/strong> (Dirty Price) je tak (-1047,50 USD cena Ask – poplatek 1.00 USD \u2013 odevzdan\u00e9 \u00faroky -29.8125 USD) celkov\u011b ve v\u00fd\u0161i -1.078,313 USD<\/strong>.<\/span><\/p>\n

\u00a0\u00a0 M\u016f\u017eu tak sv\u016fj v\u00fdpo\u010det YTM v\u00edce up\u0159esnit a pou\u017e\u00edt k n\u011bmu excelovskou pom\u016fcku pro v\u00fdpo\u010det vnit\u0159n\u00edho v\u00fdnosov\u00e9ho procenta, tak jak bylo pops\u00e1no v \u010dl\u00e1nc\u00edch d\u0159\u00edve. Excelovsk\u00fd v\u00fdpo\u010det je na obr\u00e1zku n\u00ed\u017ee.<\/span><\/p>\n

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\u00a0\u00a0 V\u00fdpo\u010det zhodnocen\u00ed m\u00e9 investice do jej\u00ed splatnosti (YTM) je tak +4.980% p.a. Jak mohu tuto skute\u010dnost interpretovat a jak\u00fdm zp\u016fsobem ji dos\u00e1hnu? Dos\u00e1hnout takov\u00e9ho zhodnocen\u00ed vy\u017eaduje spln\u011bn\u00ed t\u0159ech z\u00e1kladn\u00edch podm\u00ednek a z jejich dodr\u017een\u00ed vyplyne, \u017ee vypo\u010d\u00edtan\u00fd YTM je pouze hodnotou, kter\u00e1 odr\u00e1\u017e\u00ed o\u010dek\u00e1v\u00e1n\u00ed takov\u00e9ho zhodnocen\u00ed a nikoliv jeho p\u0159esn\u00e9ho ur\u010den\u00ed tak, jak ve skute\u010dnosti v budoucnosti nastane. Pro dosa\u017een\u00ed hodnoty zhodnocen\u00ed ve v\u00fd\u0161i +4.980% p.a. mus\u00ed b\u00fdt spln\u011bno:<\/span><\/p>\n

\u00a0 \u00a01\/ Budu dr\u017eet dluhopis a\u017e do jeho splatnosti.<\/strong> Nebudou m\u011b tak zaj\u00edmat cenov\u00e9 pohyby zp\u016fsoben\u00e9 tr\u017en\u00edmi vlivy (pohyb \u00farokov\u00fdch sazeb na dluhopisov\u00fdch trz\u00edch apod.). Je patrn\u00e9, \u017ee pokud bych prodal dluhopis p\u0159ed jeho splatnost\u00ed za vy\u0161\u0161\u00ed cenu ne\u017e jsem jej koupil, mohu utr\u017eit mimo ji\u017e p\u0159ijat\u00e9 kup\u00f3ny dal\u0161\u00ed kapit\u00e1lov\u00fd v\u00fdnos a hodnotu projektovan\u00e9ho YTM m\u00edrn\u011b vylep\u0161it a naopak, p\u0159i jeho prodeji za ni\u017e\u0161\u00ed ne\u017e po\u0159izovac\u00ed cenu toto YTM sn\u00ed\u017eit.<\/span><\/p>\n

\u00a0 \u00a02\/ Budu reinvestovat v\u0161echny obdr\u017een\u00e9 kup\u00f3ny<\/strong>, a to okam\u017eit\u011b po jejich obdr\u017een\u00ed.<\/span><\/p>\n

\u00a0 \u00a03\/ Reinvestice kup\u00f3n\u016f<\/strong> se bude prov\u00e1d\u011bt s \u00farokovou sazbou rovnaj\u00edc\u00ed se vypo\u010d\u00edtan\u00e9mu YTM<\/strong> (+4.980%). Nemohu odhadnout, jak\u00e9 budou aktu\u00e1ln\u00ed p\u0159\u00edle\u017eitosti \u00faro\u010den\u00ed na trz\u00edch pevn\u011b \u00faro\u010den\u00fdch cenn\u00fdch pap\u00edr\u016f v horizontu n\u011bkolika let, kter\u00e9 p\u0159edstavuje dr\u017een\u00ed m\u00e9ho dluhopisu Ford se splatnost\u00ed v roce 2028. Jedno je jist\u00e9, pokud by se mi poda\u0159ilo inkasovan\u00e9 kup\u00f3ny zhodnocovat vy\u0161\u0161\u00ed sazbou ne\u017e +4.980% p.a., dos\u00e1hnu celkov\u011b vy\u0161\u0161\u00ed zhodnocen\u00ed m\u00e9ho dluhopisu ne\u017e jsem si nyn\u00ed vypo\u010d\u00edtal a naopak, pokud se mi toto postupn\u00e9 zhodnocov\u00e1n\u00ed nebude da\u0159it za podm\u00ednek vypo\u010d\u00edtan\u00e9ho YTM, dos\u00e1hnu celkov\u011b ni\u017e\u0161\u00edho zhodnocen\u00ed, ne\u017e jsem si sv\u00fdm v\u00fdpo\u010dtem ur\u010dil. \u00a0<\/span><\/p>\n

\u00a0\u00a0 Z dan\u00e9ho popisu podm\u00ednek je jasn\u00e9, \u017ee spln\u011bn\u00ed prvn\u00ed z nich nen\u00ed nic nemo\u017en\u00e9ho, druh\u00e1 podm\u00ednka je ot\u00e1zkou obchodn\u00ed techniky, ov\u0161em t\u0159et\u00ed podm\u00ednka je zcela z\u00e1sadn\u00ed p\u0159i vyhl\u00eddk\u00e1ch na dosa\u017een\u00ed o\u010dek\u00e1van\u00e9ho v\u00fdnosu. Z popsan\u00e9ho vypl\u00fdv\u00e1, \u017ee a\u010dkoliv nakoup\u00edm dluhopis jako \u201ecenn\u00fd pap\u00edr s pevn\u00fdm v\u00fdnosem\u201c, nemohu jednozna\u010dn\u011b prohl\u00e1sit, kolik na t\u00e9to investici vyd\u011bl\u00e1m optikou tohoto p\u0159\u00edstupu. Nen\u00ed tak zcela ur\u010duj\u00edc\u00ed, za kolik cenn\u00fd pap\u00edr nakoup\u00edm, jakou m\u00e1 hodnotu kup\u00f3nu a za jak dlouho je jeho splatnost, p\u0159esto\u017ee toto jsou z\u00e1kladn\u00ed faktory tvo\u0159\u00edc\u00ed z\u00e1klad budouc\u00edho v\u00fdnosu, mus\u00edm je\u0161t\u011b, p\u0159i p\u0159esv\u011bd\u010den\u00ed, \u017ee dluhopis budu dr\u017eet do splatnosti, po\u010d\u00edtat s aktu\u00e1ln\u00edm v\u00fdvojem \u00farokov\u00fdch sazeb na trz\u00edch, kter\u00e9 ur\u010d\u00ed dal\u0161\u00ed (a podstatn\u00fd) v\u00fdnos z p\u0159ijat\u00fdch budouc\u00edch cash flow.<\/span><\/p>\n

YTM, kup\u00f3n a cena dluhopisu<\/strong><\/span><\/h2>\n

\u00a0\u00a0 K jednoduch\u00e9 interpretaci a vztahu vypo\u010d\u00edtan\u00e9ho YTM k aktu\u00e1ln\u00ed cen\u011b dluhopisu s definovan\u00fdm kup\u00f3nem mohu, ve sv\u011btle p\u0159edch\u00e1zej\u00edc\u00ed v\u00fdpo\u010dt\u016f, zaznamenat z\u00e1kladn\u00ed pravidla, kter\u00e1 mi pomohou se z\u00e1kladn\u00ed interpretac\u00ed YTM.<\/span><\/p>\n

\u00a0\u00a0 A\/ Pokud je YTM ni\u017e\u0161\u00ed ne\u017e hodnota kup\u00f3nov\u00e9 sazby dluhopisu<\/strong>, mus\u00edm o\u010dek\u00e1vat, \u017ee cena dluhopisu<\/strong> bude vy\u0161\u0161\u00ed ne\u017e Face Value<\/strong>, v\u00a0m\u00e9m p\u0159\u00edpad\u011b je vypo\u010d\u00edtan\u00e1 hodnota YTM +4.980% p.a. a kup\u00f3nov\u00fd v\u00fdnos p\u0159edstavuje 6.625% p.a. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

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\u00a0 Tato situace odpov\u00edd\u00e1 m\u00e9mu konkr\u00e9tn\u00edmu obchodu. Vysok\u00fd kup\u00f3n (+6.625% p.a.) zp\u016fsobuje, \u017ee se nemohu divit, \u017ee nakupuji za hodnotu vy\u0161\u0161\u00ed ne\u017e Face Value, tedy za -1.078,313 USD. Mohu tak\u00e9 konstatovat, \u017ee pokud je cena dluhopisu vy\u0161\u0161\u00ed ne\u017e Face Value, bude YTM ni\u017e\u0161\u00ed ne\u017e vyzna\u010den\u00fd \u00farok vypl\u00fdvaj\u00edc\u00ed z kup\u00f3nu.<\/span><\/p>\n

\u00a0\u00a0\u00a0 B\/ Pokud by hodnota YTM byla stejn\u00e1, jako je hodnota kup\u00f3nov\u00e9 sazby dluhopisu<\/strong>, tedy pokud by kup\u00f3n m\u011bl sazbu +6.625% p.a. a stejn\u00e1 by byla hodnota YTM +6.625% p.a., pak bych m\u011bl tento dluhopis b\u00fdt schopen nakoupit p\u0159esn\u011b za Face Value<\/strong>.<\/span><\/p>\n

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\u00a0\u00a0 Jin\u00fdmi slovy, pokud se dluhopis nab\u00edz\u00ed za Face Value, jeho YTM bude rovna \u00farokov\u00e9 sazb\u011b odpov\u00eddaj\u00edc\u00ed vyzna\u010den\u00e9mu kup\u00f3nu.<\/span><\/p>\n

\u00a0\u00a0 C\/ Pokud je YTM vy\u0161\u0161\u00ed ne\u017e hodnota kup\u00f3nov\u00e9 sazby dluhopisu<\/strong>, mus\u00edm o\u010dek\u00e1vat, \u017ee cena dluhopisu bude ni\u017e\u0161\u00ed ne\u017e Face Value<\/strong>, v\u00a0m\u00e9m p\u0159\u00edpad\u011b si mohu namodelovat vypo\u010d\u00edtanou hodnotu YTM nap\u0159\u00edklad na +8.00% p.a. p\u0159i kup\u00f3nov\u00e9m v\u00fdnosu p\u0159edstavuj\u00edc\u00edm +6.625% p.a. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

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\u00a0\u00a0 Op\u011bt by m\u011blo platit, \u017ee pokud budu pozorovat cenu sledovan\u00e9ho dluhopisu a tato bude ni\u017e\u0161\u00ed ne\u017e Face Value, mohu o\u010dek\u00e1vat YTM vy\u0161\u0161\u00ed, ne\u017e je vyzna\u010den\u00e1 kup\u00f3nov\u00e1 sazba. V konkr\u00e9tn\u00edm modelov\u00e9m p\u0159\u00edkladu je p\u0159i kup\u00f3nu +6.625% p.a. a vypo\u010d\u00edtan\u00e9m modelov\u00e9m YTM na \u00farovni +8.00% p.a. patrn\u00e9, \u017ee dluhopis by m\u011bl st\u00e1t m\u00e9n\u011b ne\u017e 1.000 USD, konkr\u00e9tn\u011b pouze 939,77 USD.<\/span><\/p>\n

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\u00a0\u00a0 Zm\u011b\u0159it v\u00fdnos dluhopisu je celkem v\u00fdzva a nab\u00edzej\u00ed se nejr\u016fzn\u011bj\u0161\u00ed metody, jak se k takov\u00e9mu v\u00fdpo\u010dtu postavit. Mohu si samoz\u0159ejm\u011b vymyslet jin\u00e9 zp\u016fsoby, jak se k celkov\u00e9mu v\u00fdnosu dobrat, d\u016fle\u017eit\u00e9 ale z m\u00e9ho pohledu je pochopit z\u00e1kladn\u00ed princip takov\u00e9ho ocen\u011bn\u00ed a tento pak d\u00e1le rozv\u00edjet. Mohu vyu\u017e\u00edt vysoce sofistikovan\u00e9 cenov\u00e9 modely, mohu vyu\u017e\u00edt publikovan\u00e9 internetov\u00e9 kalkul\u00e1tory nebo si vymyslet sv\u016fj vlastn\u00ed v\u00fdpo\u010det nap\u0159\u00edklad pomoc\u00ed VBA skriptu zdokonaluj\u00edc\u00edho uveden\u00fd excelovsk\u00fd v\u00fdpo\u010det, mohu cel\u00fd v\u00fdpo\u010det sv\u011b\u0159it vlastn\u00edmu naprogramovan\u00e9mu \u0159e\u0161en\u00ed, z\u00e1kladn\u00ed \u00favaha a principy budou ale patrn\u011b vych\u00e1zet ze stejn\u00fdch z\u00e1klad\u016f, kter\u00e9 byly pops\u00e1ny v\u00fd\u0161e\u2026:c) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

\u00a0 \u00a0Koment\u00e1\u0159e a p\u0159\u00edsp\u011bvky k tomuto \u010dl\u00e1nku pros\u00edm sm\u011brujte do Diskuzn\u00edho f\u00f3ra do tohoto vl\u00e1kna<\/a><\/span>, <\/strong>zde tak\u00e9 najdete ke sta\u017een\u00ed excelovsk\u00fd se\u0161it, ze kter\u00e9ho jsou uk\u00e1zky k tomuto \u010dl\u00e1nku \u00a0:c) \u00a0<\/span><\/p>\n

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

\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u00a0\u00a0 Kupuji dluhopis. Prvn\u00ed v\u011bta z\u00a0minul\u00e9ho \u010dl\u00e1nku se tak opakuje, a proto\u017ee jsem si v\u00a0tomto p\u0159edch\u00e1zej\u00edc\u00edm \u010dl\u00e1nku ud\u011blal svou anal\u00fdzu z\u00e1kladn\u00edch vlastnost\u00ed dluhopisu, nyn\u00ed je m\u00e9 rozhodov\u00e1n\u00ed ji\u017e zam\u011b\u0159eno na vlastn\u00ed v\u00fdkon zam\u00fd\u0161len\u00e9 investice. Jak zm\u011b\u0159it investici do cenn\u00e9ho pap\u00edru s pevn\u00fdm v\u00fdnosem je opravdu v\u00fdzva a z nab\u00edzen\u00e9ho \u0159e\u0161en\u00ed Continue Reading<\/i><\/a><\/p>\n","protected":false},"author":1,"featured_media":6127,"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-6122","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-1AK","jetpack-related-posts":[{"id":6668,"url":"https:\/\/dobretrejdy.com\/?p=6668","url_meta":{"origin":6122,"position":0},"title":"Dluhopisy \u2013 XII.","author":"dobretrejdy :c)","date":"14.10.2023","format":false,"excerpt":"\u00a0\u00a0 V\u00a0hrnci dluhopisov\u00fdch trh\u016f to za\u010d\u00edn\u00e1 p\u011bkn\u011b bublat. Pry\u010d jsou doby nev\u00fdznamn\u00fdch v\u00fdnos\u016f \u010di dokonce z\u00e1porn\u00fdch \u00farokov\u00fdch sazeb, investo\u0159i za\u010d\u00ednaj\u00ed v\u011bt\u0159it zaj\u00edmav\u00e9 p\u0159\u00edle\u017eitosti a po dlouh\u00e1 l\u00e9ta p\u0159ehl\u00ed\u017een\u00fd segment cenn\u00fdch pap\u00edr\u016f s\u00a0pevn\u00fdm v\u00fdnosem za\u010d\u00edn\u00e1 nab\u00edrat na zaslou\u017een\u00e9 pozornosti. N\u00e1sleduj\u00edc\u00ed \u0159\u00e1dky dal\u0161\u00edho d\u00edlu dluhopisov\u00e9ho seri\u00e1lu pak budou o projasn\u011bn\u00ed n\u011bkter\u00fdch probl\u00e9m\u016f\u2026","rel":"","context":"V \u201eDluhopisy\u201c","block_context":{"text":"Dluhopisy","link":"https:\/\/dobretrejdy.com\/?cat=60"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/10\/main.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/10\/main.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/10\/main.jpg?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":6010,"url":"https:\/\/dobretrejdy.com\/?p=6010","url_meta":{"origin":6122,"position":1},"title":"Dluhopisy \u2013 III.","author":"dobretrejdy :c)","date":"14.12.2022","format":false,"excerpt":"\u00a0\u00a0N\u00e1kupem dluhopisu p\u016fj\u010duji pen\u00edze. Nejjednodu\u0161\u0161\u00ed definice, kterou by si mohla zaslou\u017eit odpov\u011b\u010f na ot\u00e1zku, co to vlastn\u011b dluhopis je. Emitent dluhopisu \u2013 dlu\u017en\u00edk - vstupuje do pr\u00e1vn\u00edho svazku s v\u011b\u0159itelem (t\u0159eba se mnou), kter\u00fd je zalo\u017een na z\u00e1vazku dlu\u017en\u00edka platit v\u011b\u0159iteli periodick\u00fd \u00farok ve form\u011b kup\u00f3nu a splatit celou p\u016fvodn\u011b\u2026","rel":"","context":"V \u201eDluhopisy\u201c","block_context":{"text":"Dluhopisy","link":"https:\/\/dobretrejdy.com\/?cat=60"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2022\/12\/main.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2022\/12\/main.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2022\/12\/main.jpg?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":6340,"url":"https:\/\/dobretrejdy.com\/?p=6340","url_meta":{"origin":6122,"position":2},"title":"Dluhopisy – IX.","author":"dobretrejdy :c)","date":"26.4.2023","format":false,"excerpt":"\u00a0 \u00a0Obchody s dluhopisy maj\u00ed sv\u016fj smysl a nen\u00ed od v\u011bci porozum\u011bt jejich fungov\u00e1n\u00ed. Pozn\u00e1n\u00ed teorie je skv\u011bl\u00e1 v\u011bc, nicm\u00e9n\u011b nesm\u00edm zapomenout v p\u0159em\u00ed\u0159e teoretizov\u00e1n\u00ed tak\u00e9 na praktickou str\u00e1nku tohoto typu obchodov\u00e1n\u00ed, tedy jak skute\u010dn\u011b dluhopis po\u0159\u00eddit. Dne\u0161n\u00ed \u010dl\u00e1nek pak bude o dluhopisech v prost\u0159ed\u00ed m\u00e9ho brokera Interactive Brokers, kde\u2026","rel":"","context":"V \u201eDluhopisy\u201c","block_context":{"text":"Dluhopisy","link":"https:\/\/dobretrejdy.com\/?cat=60"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/04\/SC1.jpg?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/04\/SC1.jpg?resize=350%2C200 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/04\/SC1.jpg?resize=525%2C300 1.5x"},"classes":[]},{"id":6047,"url":"https:\/\/dobretrejdy.com\/?p=6047","url_meta":{"origin":6122,"position":3},"title":"Dluhopisy \u2013 IV.","author":"dobretrejdy :c)","date":"24.12.2022","format":false,"excerpt":"\u00a0\u00a0 Kupuji dluhopis. Plat\u00edm za n\u011bj n\u011bjakou cenu a m\u00e1m od n\u011bj n\u011bjak\u00e9 o\u010dek\u00e1v\u00e1n\u00ed, zejm\u00e9na co se t\u00fd\u010de finan\u010dn\u00edho potenci\u00e1lu, kter\u00fd mi m\u016f\u017ee p\u0159in\u00e9st. Pokud nejsem \u00fapln\u00fd ignorant a nakupuji akcie n\u011bjak\u00e9 spole\u010dnosti, v\u017edy m\u00e1m n\u011bjakou, alespo\u0148 mlhavou p\u0159edstavu nebo d\u016fvod, pro\u010d jsem u\u010dinil rozhodnut\u00ed do takov\u00e9ho obchodu vstoupit. Mohu\u2026","rel":"","context":"V \u201eDluhopisy\u201c","block_context":{"text":"Dluhopisy","link":"https:\/\/dobretrejdy.com\/?cat=60"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2022\/12\/WMT1.jpg?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2022\/12\/WMT1.jpg?resize=350%2C200 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2022\/12\/WMT1.jpg?resize=525%2C300 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2022\/12\/WMT1.jpg?resize=700%2C400 2x"},"classes":[]},{"id":6742,"url":"https:\/\/dobretrejdy.com\/?p=6742","url_meta":{"origin":6122,"position":4},"title":"Dluhopisy \u2013 XIII.","author":"dobretrejdy :c)","date":"28.10.2023","format":false,"excerpt":"\u00a0\u00a0 Poznat a pochopit dluhopisov\u00fd trh, porozum\u011bt z\u00e1kladn\u00edm princip\u016fm spojen\u00fdch s nakl\u00e1d\u00e1n\u00ed s dluhopisy a zjednodu\u0161en\u00fd vhled do mo\u017enost\u00ed, jak je u sv\u00e9ho brokera nakoupit a co to m\u016f\u017ee pro m\u011b znamenat, bylo p\u0159edm\u011btem p\u0159edchoz\u00edch \u010dl\u00e1nk\u016f. Nabyt\u00e9 poznatky pak mohu aplikovat na zapojen\u00ed dluhopis\u016f do sv\u00e9ho obchodov\u00e1n\u00ed a nemus\u00ed to\u2026","rel":"","context":"V \u201eDluhopisy\u201c","block_context":{"text":"Dluhopisy","link":"https:\/\/dobretrejdy.com\/?cat=60"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/10\/main-1.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/10\/main-1.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/10\/main-1.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/10\/main-1.jpg?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":6561,"url":"https:\/\/dobretrejdy.com\/?p=6561","url_meta":{"origin":6122,"position":5},"title":"Dluhopisy \u2013 XI.","author":"dobretrejdy :c)","date":"26.8.2023","format":false,"excerpt":"\u00a0\u00a0Dluhopisov\u00fd seri\u00e1l pokra\u010duje, p\u00ed\u0161e se jeho dal\u0161\u00ed d\u00edl. Pokud se zd\u00e1, \u017ee se podrobn\u011b a mo\u017en\u00e1 zbyte\u010dn\u011b v\u011bnuji americk\u00fdm vl\u00e1dn\u00edm dluhopis\u016fm, tak tento \u010dl\u00e1nek op\u011bt nebude o ni\u010dem jin\u00e9m, n\u011b\u017e pr\u00e1v\u011b o t\u00e9to kategorii dluhov\u00fdch cenn\u00fdch pap\u00edr\u016f. Pro\u010d tomu tak je vypl\u00fdv\u00e1 z m\u00e9ho praktick\u00e9ho pohledu na v\u011bc. Krom\u011b toho,\u2026","rel":"","context":"V \u201eDluhopisy\u201c","block_context":{"text":"Dluhopisy","link":"https:\/\/dobretrejdy.com\/?cat=60"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/08\/Aukce1.jpg?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/08\/Aukce1.jpg?resize=350%2C200 1x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/08\/Aukce1.jpg?resize=525%2C300 1.5x, https:\/\/i0.wp.com\/dobretrejdy.com\/wp-content\/uploads\/2023\/08\/Aukce1.jpg?resize=700%2C400 2x"},"classes":[]}],"jetpack_featured_media_url":"https:\/\/dobretrejdy.com\/wp-content\/uploads\/2023\/01\/main-2.jpg","_links":{"self":[{"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/posts\/6122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6122"}],"version-history":[{"count":33,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/posts\/6122\/revisions"}],"predecessor-version":[{"id":7313,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/posts\/6122\/revisions\/7313"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=\/wp\/v2\/media\/6127"}],"wp:attachment":[{"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dobretrejdy.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

\u00a0\u00a0 V\u00a0\u010d\u00e1sti (1)<\/strong><\/span> jsou zad\u00e1ny do modr\u00fdch bun\u011bk parametry dluhopisu<\/strong>, tak jak je mohu vypozorovat z obchodn\u00ed platformy. Je zde vypo\u010d\u00edt\u00e1na na \u0159\u00e1dku \u010d.8 hodnota nab\u011bhl\u00e9ho \u00faroku (Accrued Interest), kter\u00e1 mi nepat\u0159\u00ed. V \u010d\u00e1sti (2)<\/strong><\/span> jsou zaps\u00e1ny v\u0161echny budouc\u00ed pen\u011b\u017en\u00ed toky<\/strong> spojen\u00e9 s dr\u017een\u00edm dluhopisu, v \u0159\u00e1dku \u201eInvestice\u201c je ji\u017e spo\u010d\u00edt\u00e1na cel\u00e1 vstupn\u00ed investice do dluhopisu, tedy Clean Price + poplatek za po\u0159\u00edzen\u00ed + Accrued Interest. N\u00e1sleduj\u00ed v\u0161echny kup\u00f3nov\u00e9 platby, kter\u00e9 p\u0159ijmu na sv\u016fj \u00fa\u010det spole\u010dn\u011b s v\u00fdplatou Face Value u maturity. V\u0161echny tyto polo\u017eky jsou sumarizov\u00e1ny pomoc\u00ed excelovsk\u00e9 funkce =M\u00cdRA.V\u00ddNOSNOSTI<\/em> (3)<\/strong><\/span> do hodnoty Vnit\u0159n\u00edho V\u00fdnosov\u00e9ho Procenta, kter\u00e9 stanov\u00ed hodnotu o\u010dek\u00e1van\u00e9ho v\u00fdnosu do splatnosti (YTM)<\/strong>, proto\u017ee se jedn\u00e1 o pololetn\u00ed frekvenci budouc\u00edch tok\u016f, je vypo\u010d\u00edtan\u00e1 hodnota YTM v tomto vzorci n\u00e1sobena po\u010dtem period za rok (hodnotou 2). Mohu tak vypozorovat, \u017ee vypo\u010d\u00edtan\u00fd YTM<\/strong> je 4.980% p.a.<\/strong>, takov\u00e9 zhodnocen\u00ed bych pak mohl od sv\u00e9ho dluhopisu o\u010dek\u00e1vat p\u0159i spln\u011bn\u00ed podm\u00ednek, kter\u00e9 v\u00fdpo\u010det respektuje. V sekci ozna\u010den\u00e9 (4)<\/span><\/strong> a popsan\u00e9 jako \u201eModelov\u00e1n\u00ed\u201c mohu zad\u00e1vat do \u0161ed\u011b podbarven\u00e9 bu\u0148ky hodnotu YTM, kterou bych si p\u0159\u00e1l dos\u00e1hnout a p\u0159i jak\u00e9 po\u0159izovac\u00ed cen\u011b (modr\u00e1 \u0161ipka) by se mi toto vyplnilo. Pokud bych tedy cht\u011bl od tohoto dluhopisu Ford, aby mi vynesl 7.5 % p.a., musel bych jej po\u0159\u00eddit za -961.15 USD. \u010c\u00e1st (5)<\/strong> <\/span>ozna\u010den\u00e1 jako \u201eSou\u010dasn\u00e1 hodnota\u201c je pak kontroln\u00edm v\u00fdpo\u010dtem<\/strong>, kter\u00fd diskontuje v\u0161echny budouc\u00ed pen\u011b\u017en\u00ed toky k datu v\u00fdpo\u010dtu YTM do sou\u010dasn\u00e9 hodnoty dluhopisu, mus\u00ed tedy platit, \u017ee sou\u010det t\u011bchto diskontovan\u00fdch cen (hn\u011bd\u00e1 \u0161ipka) se mus\u00ed rovnat hodnot\u011b m\u00e9 investice do po\u0159izovan\u00e9ho dluhopisu vyzna\u010den\u00e9ho v \u0159\u00e1dku \u201eInvestice\u201c. Cel\u00fd tento Excel si m\u016f\u017eete st\u00e1hnout v diskuzn\u00edm f\u00f3ru ve vl\u00e1kn\u011b k tomuto \u010dl\u00e1nku<\/a><\/strong><\/span>.<\/span><\/p>\n