茲維博迪金融學(xué)第二版課件Chapter08

Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall1第8章：

已知現(xiàn)金流估值：債券目標(biāo)估值固定收入證券解釋為什么債券價格變化Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall2內(nèi)容8.1用現(xiàn)值公式給已知現(xiàn)金流賦值8.2基本構(gòu)件：純貼現(xiàn)債券【零息債券】8.3付息債券、當(dāng)期收益率、到期收益率8.4解讀債券行情表8.5為什么相同到期期限的債券的收益率可能不同？8.6時間上的債券價格行為Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall38.1用現(xiàn)值公式給已知現(xiàn)金流賦值你有機(jī)會購買一項(xiàng)抵押貸款。該貸款剩余期限60個月，每月還款$400。你要求的收益率是每月1.5%。Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall4計算使用第4章討論的年金現(xiàn)值公式，你將支付不超過Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall5金融計算器或者，使用你的金融計算器（記得設(shè)定正確的默認(rèn)選項(xiàng)）得到Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall6變化所要求的收益率如果你要求的收益率增加到每月1.6%Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall7用現(xiàn)值公式給已知現(xiàn)金流賦值觀察到你為債券【抵押貸款】最大愿意支付的金額減少了要求收益率的提高永遠(yuǎn)使固定收益證券的價值減少證明非常容易Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall8利率下降時債券價格上升將固定收入證券的現(xiàn)值寫為各項(xiàng)之和Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall9利率下降時債券價格上升若i上升，1+i上升，1/(1+i)下降（i>-1），(1/(1+i))j

下降（i>0）。于是，若支付均為正，各項(xiàng)之和一定也下降

類似地，i下降推出PV上升Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall10利率下降時債券價格上升估值已知現(xiàn)金流的基本原則市場利率的改變引起所有承諾未來固定支付的現(xiàn)存合約市值的反向改變Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall11注易變的市場利率意味著易變的市場價值Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall12尋找正確的貼現(xiàn)率債券分析不像看起來那么容易我們需要在公式中使用一個利率我們在第2章看到，利率是到期時間【time-to-maturity】的函數(shù)兩個相同到期日【maturity】的無違約風(fēng)險債券可能有不同的到期收益率Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall13收益率曲線（YieldCurve）Atypicalyieldcurve:Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall14```8.2基本構(gòu)件：純貼現(xiàn)債券【零息債券】我們永遠(yuǎn)可以將任意固定收益合約視為一些純貼現(xiàn)債券的組合純貼現(xiàn)債券（purediscountbond）承諾在被稱為到期日的指定日期，支付指定的現(xiàn)金流（面值），且只有這一筆支付。Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall15純貼現(xiàn)債券注表面上沒有利息支付純貼現(xiàn)債券以其面值的一個折扣價購買Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall16純貼現(xiàn)債券純貼現(xiàn)債券是我們在第4章分析的一次性總付現(xiàn)金流的現(xiàn)值的一個例子解相關(guān)方程，純貼現(xiàn)債券的到期收益率由下式給出：Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall17純貼現(xiàn)債券其中，P是債券的現(xiàn)值或價格F是面值或未來值

n是投資期數(shù)i是到期收益率Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall18純貼現(xiàn)債券例花9000美元購買一張零息債券，兩年后到期，面值1萬美元到期收益率是多少？Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall19純貼現(xiàn)債券Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall208.3付息債券、當(dāng)期收益率、到期收益率付息債券責(zé)令發(fā)行者定期支付利息（稱“息票支付”）給債券持有者，直到債券到期

此時債券面值也支付給債券持有者且合約被履行Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall21票面利率（CouponRate）票面利率是應(yīng)用于票面價值計算息票支付的利率面值1000美元、票面利率10%的債券每年的息票支付是100美元在到期日，總支付=1000美元+100美元Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall22CashFlowsfor10%$1,000CouponBondCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall23```平價、溢價和貼現(xiàn)債券當(dāng)前價格等于面值的付息債券稱平價債券（parbond）若付息債券以低于面值的價格交易，稱貼現(xiàn)債券（discountbond）若付息債券以高于面值的價格交易，稱溢價債券（premiumbond）(nottobeconfusedwiththeU.K.lotterybondofthesamename!)Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall24平價債券債券定價原理1：（平價債券）如果債券價格等于其面值，則其到期收益率=當(dāng)期收益率=票面利率

證明：

Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall25付息債券、當(dāng)期收益率、到期收益率到期收益率是使源于債券的現(xiàn)金流的現(xiàn)值等于債券當(dāng)前價格的貼現(xiàn)率【此定義不如p16的定義直觀；這兩個定義等價】一個很好的計算到期收益率的方法在第4章給出Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall26使用純貼現(xiàn)債券賦值其他債券賦值一個債券——每年末支付100美元利息，支付3年；3年后支付1000美元面值你已經(jīng)找到3個零息債券（面值均為1000美元），分別在1、2、3年后到期，以960、890、810美元交易Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall27解法一Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall28解法二Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall29結(jié)論解法一利用了付息債券是多個零息債券的組合這一事實(shí)快速且直觀解法二首先求出每一個零息債券的到期收益率接著用這些貼現(xiàn)率給付息債券的現(xiàn)金流賦值Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall30付息債券的到期收益率我們有付息債券的價格和未來現(xiàn)金流的時序及大小，這樣就能決定其到期收益率對這類問題，我們使用金融計算器，但一個數(shù)值方法在第4章給出Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall31TheYTMoftheCouponBondCopyright?2009PearsonEducation,Inc.PublishingasPrenticeHall32觀察3年期零息債券的到期收益率是7.28%，而3年期付息債券的到期收益率是7.10%無違約風(fēng)險債券的收益率曲線不是唯一的值Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall33債券定價原理2和3原理2：溢價債券

債券價格>面值T到期收益率<當(dāng)期收益率<票面利率原理3：貼現(xiàn)債券

債券價格<面值T到期收益率>當(dāng)期收益率>票面利率Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall34到期收益率與當(dāng)期收益率關(guān)系的證明【證法一】對付息債券，我們有如下關(guān)系注意對變量取值范圍的（合理）限制注意1/((1+i)^n-1)永遠(yuǎn)為正Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall35【兩邊同乘i(1+i)^n，解i】Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall36當(dāng)期和票面收益率關(guān)系的證明【證法二】對付息債券，我們有從債券公式中推出的如下關(guān)系注意若倒數(shù)之差一與倒數(shù)之差二的符號相同，則原數(shù)之差一與原數(shù)之差二的符號也相同注意大小關(guān)系由貼現(xiàn)因子永遠(yuǎn)小于1決定Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall37Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall38怎樣記憶原理想象債券平價發(fā)行到期收益率從票面利率開始隨【發(fā)行】價格反向變動票面利率不變下圖可能有幫助：Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall39Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall408.4解讀債券行情TherearetraditionsforreportingyieldsandcomputingearnedinterestthatneedtobeunderstoodbeforetradingCouponbondsareoftenquotedintermsoftheannualratecompoundedsemi-annuallyT-billsareoftenquotedonadiscountbasise.g.,a1yearT-billhas364daysoutstanding,butayearhasonly360days…(itgetsnasty)Copyright?2009PearsonEducation,Inc.PublishingasPrenticeHall41ReadingBondListings

TakecarethatthefractionalpartofanumberisunderstoodIsit16ths,32nds,64ths,100thsorsomeotherconvention?Askprice:dealer’ssellingpriceBidprice:dealer’sbuyingpriceCopyright?2009PearsonEd