投資學(xué)第三講投資的收益與風(fēng)險(xiǎn)課件

2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers1

投資學(xué)第三講

投資的收益與風(fēng)險(xiǎn)陳善昂2022/11/2412022/11/22CopyRight?ShanAngChe問(wèn)題1.市民24年前（1989年）存2000元預(yù)期收益22萬(wàn),銀行只付8400元.2.某人6年前信用卡欠銀行900元,現(xiàn)在銀行要收19000元.計(jì)算：兩個(gè)案例的年算術(shù)平均收益與幾何平均收益.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers2問(wèn)題1.市民24年前（1989年）存2000元預(yù)期收益22萬(wàn)Part1

收益的來(lái)源及其類型2022/11/243Copyright?Shanangchen,DepartmentOfFinance,XiamenUniversityPart1

收益的來(lái)源及其類型2022/11/223Cop2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers4一.持有期收益1.收益來(lái)源：定期現(xiàn)金流（如利息股息）+價(jià)差收入2.持有期收益：2022/11/244CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity注：羅伯特.清崎強(qiáng)調(diào)投資于現(xiàn)金流而不是資本利得！2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers5利息收入：幾種投資品的比較股票：股息收益,可以與債券當(dāng)期收益、存款利息比較債券：當(dāng)期收益（I/P）、息票收益（I/F）,可以與存款利息比較房產(chǎn)：租售比,可以與債券當(dāng)期收益、股息收益比較黃金：沒(méi)有利息收入.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity52022/11/22CopyRight?ShanAngChe價(jià)差收入：區(qū)分投資與投機(jī)的一個(gè)標(biāo)準(zhǔn)2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers6問(wèn)題：A股投資者能指望現(xiàn)金分紅來(lái)獲取收益嗎？參與者應(yīng)當(dāng)重點(diǎn)關(guān)注什么？?jī)r(jià)差收入：區(qū)分投資與投機(jī)的一個(gè)標(biāo)準(zhǔn)2022/11/22Cop2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers7舉例3-1假定你的投資在四年內(nèi)有如下的收益：那么,四年內(nèi)的年平均收益為9.58%.HPR=44.21%.公式：HPR=（1+r1）（1+r2）（1+r3）（1+r4）-1年平均收益=［（1+r1）（1+r2）（1+r3）（1+r4）］^0.25-12022/11/247CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity年收益110%2-5%320%415%2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers8幾何平均與算術(shù)平均幾何平均不同于算術(shù)平均.算術(shù)平均持有期收益率是按照單利原理計(jì)算的年均收益率.一般地,算術(shù)平均不低于幾何平均；在各期持有期收益率均相等時(shí),幾何平均等于算術(shù)平均.上例的算術(shù)平均收益率=10%（高于幾何平均的9.58%）.（10%-5%+20%+15%）/4=10%.2022/11/248CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe舉例3-21.市民24年前存2000元約定22萬(wàn),銀行只付8400元.用計(jì)算器計(jì)算幾何平均收益.輸入n=24,pv=-2000,fv=8400,pmt=0.輸出i=6.16（%）算術(shù)平均收益：13.33%2.某人6年前信用卡欠銀行900元,現(xiàn)在銀行要收19000元.用計(jì)算器計(jì)算幾何平均收益.輸入n=6,pv=-900,fv=19000,pmt=0.輸出i=66.24（%）算術(shù)平均收益：120.67%2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers9舉例3-21.市民24年前存2000元約定22萬(wàn),銀行只付82022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers10歷史收益率（幾何平均與算術(shù)平均）2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers11考慮匯率影響的持有期收益率舉例：2002-2004年,歐元兌美元的實(shí)際匯率變化從1.05變?yōu)?.35（即歐元相對(duì)美元升值28.57%）.假設(shè)2002年末EurTel股票的價(jià)格為75歐元,此時(shí)美元成本為78.75美元.在2004年末,該股票的價(jià)格漲至105歐元（股票漲了40%）,相當(dāng)于141.75美元.以美元計(jì)算的投資收益率可以通過(guò)兩種方法計(jì)算得出：2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity11股價(jià)上漲貢獻(xiàn)歐元上漲貢獻(xiàn)注：匯率風(fēng)險(xiǎn)對(duì)投資的影響是顯著的.人民幣匯率與跨境投資！2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers12二.貨幣的時(shí)間價(jià)值用復(fù)利衡量收益是投資的本質(zhì)要求！單利只考慮到利息；而復(fù)利考慮到了利息以及利息的利息.2022/11/2412CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers132022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity言論艾伯特?愛(ài)因斯坦:“宇宙中最強(qiáng)大的力量是什么?……是復(fù)利.”羅思柴爾德:“我不知道世界七大奇跡是哪些,但我知道第八大奇跡是復(fù)利.”132022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers14美麗的財(cái)富曲線問(wèn)題：中美投資收益對(duì)比.1926年投資于美國(guó)小盤(pán)股1美元,到2004年底變成了9248美元,投資于美國(guó)大盤(pán)股1美元,到2004年底變成了1992美元.1907年福建林先生用洋銀100元購(gòu)買(mǎi)了福建鐵路優(yōu)先股20股,去年其孫持此憑證希望了解其目前值多少錢(qián).您能幫助林先生的孫子算算嗎？2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers152022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity三.有效年收益率-有效年收益率-連續(xù)復(fù)利連續(xù)復(fù)利是既定利率水平下最大的名義利率.

152022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers162022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity年名義利率為6%的有效年利率復(fù)利頻率n有效年利率年16.00000半年26.09000季46.13636月126.16778周526.17998日3656.18313連續(xù)復(fù)利611/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers17舉例3-3一張面值為100元、半年期的零息票債券目前售價(jià)為97.36元.計(jì)算：銀行貼現(xiàn)收益率、持有期收益與有效年收益.銀行貼現(xiàn)收益率（年）=（100-97.36）/100*2=5.28%持有期收益（半年）=（100-97.36）/97.36=2.71%有效年收益=（1.0271）^2-1=5.49%.（不是5.42%）銀行貼現(xiàn)收益率會(huì)低估收益.2022/11/2417CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers18四.要求收益率投資決策取決于預(yù)期收益率與要求收益率之間的對(duì)比.要求收益率主要受三個(gè)因素的影響,即：貨幣的時(shí)間價(jià)值（真實(shí)無(wú)風(fēng)險(xiǎn)收益率）+預(yù)期通貨膨脹率+風(fēng)險(xiǎn)溢價(jià)；作為對(duì)延期消費(fèi)的補(bǔ)償,這是進(jìn)行一項(xiàng)投資可能接受的最低收益率.2022/11/2418CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers19通貨膨脹與稅收對(duì)投資收益的影響案例1：1977年湯女士存入銀行300元,2009年連本帶息取出來(lái)是843元.案例2：1954年王先生存入銀行10萬(wàn)元,2011年底其孫子持憑證到銀行要求兌付,您猜可以兌到多少錢(qián)？案例3：名義收益率=3.5%,預(yù)期通貨膨脹率=6.5%.粗略計(jì)算真實(shí)收益率為-3%,但精確計(jì)算真實(shí)收益率為-2.82%.進(jìn)入負(fù)利率時(shí)代.案例4：稅后收益＝稅前收益*（1－稅率）2022/11/2419CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe通貨膨脹猛于虎2022/11/24Copyright?Shanangchen,DepartmentOfFinance,XiamenUniversity20鐘偉：今天100萬(wàn)的購(gòu)買(mǎi)力不及30年前的1萬(wàn)元.建設(shè)銀行（CBC）：存不存？中國(guó)銀行（BC）：不存！農(nóng)業(yè)銀行（ABC）：?。坎淮?？工商銀行（ICBC）：愛(ài)存不存！民生銀行（CMSB）：存么,傻B！國(guó)家開(kāi)發(fā)銀行（CDB）：存點(diǎn)吧！興業(yè)銀行（CIB）：存一百！北京市商業(yè)銀行（BCCB）：白存,存不？匯豐銀行（HSBC）：還是不存！通貨膨脹猛于虎2022/11/22Copyright?Sha2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers212022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity五.到期收益率(YTM)YTM是指使得從證券上獲得的收入的現(xiàn)值與其當(dāng)前市場(chǎng)價(jià)格相等時(shí)的利率水平.它是一個(gè)全期利率,即它是假定投資者能夠持有證券直至到期日為止.YTM是一個(gè)非常重要的收益率,它適用于任何現(xiàn)金流的貼現(xiàn).但是,它的缺陷在于買(mǎi)入證券后持有至到期日.212022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers222022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity22附息債券的到期收益率到期收益率的計(jì)算公式如果是零息票債券與永久性債券,其計(jì)算公式就是其特例.到期收益率也就是IRR.當(dāng)?shù)狡谑找媛蚀笥谝笫找媛蕰r(shí),現(xiàn)金流的凈現(xiàn)值大于0,顯示項(xiàng)目可行.反之反是.2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers23舉例：到期收益率的計(jì)算例3-4：20年期政府債券的息票率6%,每半年付息一次,當(dāng)前每1000元售價(jià)為980元.計(jì)算其到期收益率.計(jì)算過(guò)程：在財(cái)務(wù)計(jì)算品上輸入n=40,pmt=30,pv=-980,fv=1000,輸出1/y=3.0878%.例3-5：2年期零息票債券,當(dāng)前每1000元售價(jià)為800元.計(jì)算其到期收益率.計(jì)算過(guò)程：在財(cái)務(wù)計(jì)算品上輸入n=2,pmt=0,pv=-800,fv=1000,輸出1/y=11.8034%.也可以用EXCEL中的函數(shù)來(lái)計(jì)算.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity232022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers242022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity六.預(yù)期收益率未來(lái)充滿著不確定性.前面討論的都是事后收益.未來(lái)的持有期收益率也稱期望收益率.人們進(jìn)行投資決策取決于預(yù)期收益率與要求收益率的對(duì)比.包括單資產(chǎn)的期望收益率與投資組合的預(yù)期收益率.242022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers252022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity單一資產(chǎn)的預(yù)期收益在任何情況下,資產(chǎn)的預(yù)期收益就是其收益的概率加權(quán)平均值.公式如下:說(shuō)明:權(quán)重為未來(lái)狀態(tài)s發(fā)生的可能性的概率,它是一個(gè)主觀概率;且假設(shè)概率的分布符合正態(tài)分布.252022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers26舉例3-6某投資品未來(lái)的收益有三種可能情形：2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity26情形收益概率經(jīng)濟(jì)繁榮0.340.3正常0.140.5經(jīng)濟(jì)蕭條-0.160.2預(yù)期收益為0.14,最大可能收益為0.34,最小可能收益為-0.2.2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers272022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity資產(chǎn)組合的預(yù)期收益率資產(chǎn)組合的收益率是構(gòu)成資產(chǎn)組合的每個(gè)資產(chǎn)收益率的加權(quán)平均值,資產(chǎn)組合的構(gòu)成比例為權(quán)重.表明資產(chǎn)組合的預(yù)期收益率就是每個(gè)資產(chǎn)的預(yù)期收益率的加權(quán)平均值.公式為：272022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers28舉例3-7某投資組合由三種證券組成,它們的預(yù)期收益及其投資比例如下：2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity28資產(chǎn)收益在組合中的比重資產(chǎn)10.20.5資產(chǎn)20.150.3資產(chǎn)30.100.22022/11/22CopyRight?ShanAngChePart2

風(fēng)險(xiǎn)及其類型2022/11/2429Copyright?Shanangchen,DepartmentOfFinance,XiamenUniversityPart2

風(fēng)險(xiǎn)及其類型2022/11/2229Copyr問(wèn)題1.一提“風(fēng)險(xiǎn)”你首先能想到的有哪些詞？2.在法庭上,法官問(wèn)搶銀行嫌疑人的一段對(duì)話.法官問(wèn)“你為什么搶銀行？”嫌疑人答“因?yàn)殂y行有錢(qián).”法官再問(wèn)“你搶銀行時(shí)就沒(méi)看到有保安和別的人嗎？”嫌疑人答“當(dāng)時(shí)我就只看到錢(qián)了.”問(wèn)題：從這段對(duì)話里你能解讀出哪些信息？3.“不入虎穴,焉得虎子”能否反過(guò)來(lái)說(shuō)？為什么？2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity30問(wèn)題1.一提“風(fēng)險(xiǎn)”你首先能想到的有哪些詞？2022/11/一.風(fēng)險(xiǎn)的定義風(fēng)險(xiǎn)（Risk）：

風(fēng)險(xiǎn)是指“可度量的不確定性”,不確定性是指“不可度量的風(fēng)險(xiǎn)”.與可度量或可預(yù)見(jiàn)的風(fēng)險(xiǎn)不同,不確定性是指人們?nèi)狈?duì)事件的基本知識(shí),對(duì)事件可能的結(jié)果知之甚少,因此,不能通過(guò)現(xiàn)有理論或經(jīng)驗(yàn)進(jìn)行預(yù)見(jiàn)和定量分析.－富蘭克·H·奈特在《風(fēng)險(xiǎn)、不確定性和利潤(rùn)》（1921）一個(gè)事件如果只有一個(gè)結(jié)果,那就是確定的,無(wú)風(fēng)險(xiǎn)的.一個(gè)事件如果有兩個(gè)或兩個(gè)以上的可能結(jié)果,那就是不確定的,有風(fēng)險(xiǎn)的.因此,可以將風(fēng)險(xiǎn)定義為“收益的不確定性”.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity31一.風(fēng)險(xiǎn)的定義風(fēng)險(xiǎn)（Risk）：2022/11/22Copy2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity32二.風(fēng)險(xiǎn)的來(lái)源系統(tǒng)風(fēng)險(xiǎn)是指由于某種全局性的因素而對(duì)所有投資收益都產(chǎn)生作用的風(fēng)險(xiǎn).又稱為市場(chǎng)風(fēng)險(xiǎn)、宏觀風(fēng)險(xiǎn)、不可分散風(fēng)險(xiǎn).具體包括利率風(fēng)險(xiǎn)、匯率風(fēng)險(xiǎn)、購(gòu)買(mǎi)力風(fēng)險(xiǎn)、政策風(fēng)險(xiǎn)等.

非系統(tǒng)風(fēng)險(xiǎn)是因個(gè)別上市公司特殊情況造成的風(fēng)險(xiǎn).也稱微觀風(fēng)險(xiǎn)、可分散風(fēng)險(xiǎn).具體包括財(cái)務(wù)風(fēng)險(xiǎn)、經(jīng)營(yíng)風(fēng)險(xiǎn)、信用風(fēng)險(xiǎn)、偶然事件風(fēng)險(xiǎn)等.

注：系統(tǒng)風(fēng)險(xiǎn)與非系統(tǒng)風(fēng)險(xiǎn)沒(méi)有確定的界限.問(wèn)題：你能列舉出系統(tǒng)風(fēng)險(xiǎn)與非系統(tǒng)風(fēng)險(xiǎn)相互轉(zhuǎn)換的例子嗎？2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity322022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity33資本的逐利本性《資本論》里引用了托.約.登寧的一句話：“如果有10％的利潤(rùn),資本就會(huì)保證到處被使用；有20％的利潤(rùn),資本就能活躍起來(lái)；有50％的利潤(rùn),資本就會(huì)鋌而走險(xiǎn)；為了100％的利潤(rùn),資本就敢踐踏一切人間法律；有300％以上的利潤(rùn),資本就敢犯任何罪行,甚至去冒絞首的危險(xiǎn).”

點(diǎn)評(píng)：投資者要求較高的收益從而對(duì)不確定性作出補(bǔ)償,否則就不會(huì)投資.風(fēng)險(xiǎn)溢價(jià)或補(bǔ)償：超出無(wú)風(fēng)險(xiǎn)收益率之上的要求收益率.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity332022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity342022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity三.風(fēng)險(xiǎn)的衡量

-過(guò)去值的方差與標(biāo)準(zhǔn)差對(duì)于n個(gè)歷史數(shù)據(jù),計(jì)算方差的公式如下：342022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity352022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity風(fēng)險(xiǎn)的衡量

-預(yù)期值的方差與標(biāo)準(zhǔn)差沿用例2-5的方差與標(biāo)準(zhǔn)差計(jì)算如下35離差平方情形收益概率經(jīng)濟(jì)繁榮0.340.3正常0.140.5經(jīng)濟(jì)蕭條-0.160.2注：預(yù)期收益為14%.2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity36收益率的分布

-正態(tài)分布2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity36正態(tài)分布

[E(R)-,

E(R)+]：概率為68.26%[E(R)-2,

E(R)+2]：概率為95.44%[E(R)-3,

E(R)+3]：概率為99.74%2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity37舉例3-8承2-5為例,假如它符合正態(tài)分布.計(jì)算：1.收益為［0-31.32%］的概率是多少？2.收益為［0-48.64%］的概率是多少？3.收益低于50%的概率是多少？4.收益超過(guò)50%的概率是多少？答案：1.34.13%.2.47.72%.3.用EXCEL當(dāng)中的NORMDIST（臨界值,均值,標(biāo)準(zhǔn)差,TRUE）函數(shù)來(lái)求小于臨界值的概率.在EXCEL中輸入=NORMDIST（50,14,17.32,TRUE）=0.98124.1.88%.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity372022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity38收益率的分布

-非正態(tài)分布1.風(fēng)險(xiǎn)價(jià)值（也稱在險(xiǎn)價(jià)值,ValueatRisk,VaR）2.尾部條件期望（conditionaltailexpectation,CTE）3.下半標(biāo)準(zhǔn)差（lowerpartialstandarddeviation,LPSD）2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity382022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity392022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity四、資產(chǎn)組合的標(biāo)準(zhǔn)差組合的標(biāo)準(zhǔn)差取決于三個(gè)因素：方差、協(xié)方差、權(quán)重如果是負(fù)相關(guān)或不相關(guān)的資產(chǎn)構(gòu)建組合,那么就可以降低組合的風(fēng)險(xiǎn).但如果是完全正相關(guān)的資產(chǎn)構(gòu)建組合,組合的風(fēng)險(xiǎn)不會(huì)降低.392022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity402022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity協(xié)方差與相關(guān)系數(shù)40注：協(xié)方差與相關(guān)系數(shù)是決定組合降低風(fēng)險(xiǎn)的重要變量！2022/11/22CopyRight?ShanAngChePart3

收益與風(fēng)險(xiǎn)的權(quán)衡2022/11/2441Copyright?Shanangchen,DepartmentOfFinance,XiamenUniversityPart3

收益與風(fēng)險(xiǎn)的權(quán)衡2022/11/2241Cop一.風(fēng)險(xiǎn)厭惡假設(shè)追求收益最大化的同時(shí),希望風(fēng)險(xiǎn)（不確定性）最小.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers42標(biāo)準(zhǔn)差：風(fēng)險(xiǎn)預(yù)期收益ABCD說(shuō)明：從圖中可以看出,B優(yōu)于A,A優(yōu)于C,B優(yōu)于D問(wèn)題：在A與D之間如何選擇？一.風(fēng)險(xiǎn)厭惡假設(shè)追求收益最大化的同時(shí),希望風(fēng)險(xiǎn)（不確定性）最2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity432022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity二.變異系數(shù)及其運(yùn)用變異系數(shù)（CV）=標(biāo)準(zhǔn)差/預(yù)期收益指標(biāo)的涵義：獲取單位收益需要承擔(dān)的風(fēng)險(xiǎn)大小.該指標(biāo)可以用來(lái)評(píng)價(jià)投資項(xiàng)目,越小越好.舉例3-9：假定有四項(xiàng)投資可供選擇,如右表所示.A的CV值為0.67(=10/15).B的CV值為1(=15/15).C的CV值為1(=10/10).D的CV值為0.75(=15/20).B與C的CV值相同,都為1.A的風(fēng)險(xiǎn)/收益權(quán)衡要比D稍好.項(xiàng)目預(yù)期收益%標(biāo)準(zhǔn)差%A1510B1515C1010D2015432022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity44三.總風(fēng)險(xiǎn)與夏普比率可以用夏普比率來(lái)評(píng)價(jià)證券或組合的業(yè)績(jī)夏普比率=（預(yù)期收益-無(wú)風(fēng)險(xiǎn)收益）/標(biāo)準(zhǔn)差衡量的是每承擔(dān)一單位總風(fēng)險(xiǎn)可以獲取的超額收益大小.該指標(biāo)越大越好.下圖中,證券A的夏普比率優(yōu)于證券C與證券B.2022/11/2444CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity452022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity資本市場(chǎng)線E(r)E(rM)rfCML45ABCM2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity462022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity四.證券市場(chǎng)線與系統(tǒng)性風(fēng)險(xiǎn)E(r)E(rM)rfSMLbbM=1.046ABCM體現(xiàn)的是具體的某個(gè)證券對(duì)市場(chǎng)組合風(fēng)險(xiǎn)的貢獻(xiàn)度.大于1意味著投資于該證券要承擔(dān)高于市場(chǎng)組合的波動(dòng)敏感度；小于1意味著其相對(duì)于市場(chǎng)組合波動(dòng)水平不敏感,是保守型投資.2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity47貝塔系數(shù)2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity協(xié)方差只能衡量證券或組合與市場(chǎng)組合收益變化的相關(guān)性,無(wú)法衡量其系統(tǒng)性風(fēng)險(xiǎn)的大小,因而,夏普進(jìn)一步引入了貝塔系數(shù),從而可以比較證券或組合的系統(tǒng)風(fēng)險(xiǎn)大小.市場(chǎng)組合的貝塔系數(shù)恒等于1.組合的貝塔系數(shù)等于構(gòu)成該組合所有證券貝塔系數(shù)的加權(quán)平均值.2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity48五.特雷納比率可以用特雷納比率來(lái)評(píng)價(jià)投資或投資組合特雷納比率=（預(yù)期收益-無(wú)風(fēng)險(xiǎn)收益）/貝它值衡量的是每承擔(dān)一單位系統(tǒng)風(fēng)險(xiǎn)可以獲取的超額收益大小.該指標(biāo)越大越好.上圖中,證券A的特雷諾比率優(yōu)于證券C與證券B.2022/11/2448CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe六.風(fēng)險(xiǎn)偏好與投資選擇投資者對(duì)風(fēng)險(xiǎn)有三種態(tài)度：風(fēng)險(xiǎn)厭惡、風(fēng)險(xiǎn)中性和風(fēng)險(xiǎn)喜好.投資者的風(fēng)險(xiǎn)偏好將直接影響其投資選擇.效用函數(shù)可分為三類：凹性效用函數(shù)、凸性效用函數(shù)和線性效用函數(shù),分別表示投資者對(duì)風(fēng)險(xiǎn)持回避態(tài)度、喜好態(tài)度和中性態(tài)度.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers49六.風(fēng)險(xiǎn)偏好與投資選擇投資者對(duì)風(fēng)險(xiǎn)有三種態(tài)度：風(fēng)險(xiǎn)厭惡、風(fēng)險(xiǎn)2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity50風(fēng)險(xiǎn)態(tài)度的測(cè)定－賭徒心態(tài)舉例3-10：設(shè)一賭局,G(a,b,

),其中a

和b

為結(jié)果,為結(jié)果a

發(fā)生的概率.對(duì)于一給定賭局G($100,0,40%), 終盤(pán)的期望值=$1000.4+00.6=$40問(wèn)題：拿走確定的$40,還是“開(kāi)賭”？2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity502022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity51賭徒的選擇A愿意拿走$40: U($40)>0.4U($100)+0.6U(0)=>風(fēng)險(xiǎn)厭惡（Riskaverse）B愿意開(kāi)賭：U($40)<0.4U($100)+0.6U(0)=>風(fēng)險(xiǎn)喜好（Riskloving）C無(wú)所謂：U($40)=0.4U($100)+0.6U(0)=>風(fēng)險(xiǎn)中性（Riskneutral）2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity512022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity52風(fēng)險(xiǎn)厭惡程度與投資選擇方差減少效用的程度取決于風(fēng)險(xiǎn)厭惡系數(shù)A,即投資者個(gè)人對(duì)風(fēng)險(xiǎn)的厭惡程度.A=0,為中性投資者,他們只關(guān)心期望收益率.A<0,為風(fēng)險(xiǎn)喜好投資者,風(fēng)險(xiǎn)的存在增加效用,他們當(dāng)中A越小的人（或者說(shuō)絕對(duì)值越大）越喜歡風(fēng)險(xiǎn).投資者都會(huì)選擇效用值最大的證券或組合.顯然,風(fēng)險(xiǎn)厭惡程度對(duì)投資者在風(fēng)險(xiǎn)-收益間的權(quán)衡會(huì)產(chǎn)生重大影響.效用函數(shù)U＝E(R)-0.005*A*(方差)^22022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity522022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity53效用值的計(jì)算：舉例3-112022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity53注：不考慮投資者的風(fēng)險(xiǎn)偏好,顯然,組合H最好,因?yàn)樗芴峁┳畲蟮氖找?在考慮變異系數(shù)的前提下,組合L最優(yōu),因?yàn)槠渥儺愊禂?shù)最小（單位收益承擔(dān)的風(fēng)險(xiǎn)最?。?在考慮不同風(fēng)險(xiǎn)偏好的條件下,當(dāng)風(fēng)險(xiǎn)厭惡系數(shù)為2時(shí),組合H最優(yōu)；當(dāng)風(fēng)險(xiǎn)厭惡系數(shù)為3.5時(shí),組合M最優(yōu)；但當(dāng)風(fēng)險(xiǎn)厭惡系數(shù)上升至5時(shí),組合L最優(yōu).預(yù)期收益標(biāo)準(zhǔn)差A(yù)=2A=3.5A=52022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity54舉例3-12問(wèn)題：一項(xiàng)風(fēng)險(xiǎn)資產(chǎn)的期望收益率為20%,標(biāo)準(zhǔn)差為30%.國(guó)債能提供的無(wú)風(fēng)險(xiǎn)收益率為7%.一個(gè)風(fēng)險(xiǎn)厭惡系數(shù)為4的投資者更愿意投資國(guó)債還是風(fēng)險(xiǎn)資產(chǎn)？如果風(fēng)險(xiǎn)厭惡系數(shù)為2的投資者呢？風(fēng)險(xiǎn)資產(chǎn)有正的風(fēng)險(xiǎn)溢價(jià),但會(huì)否選擇風(fēng)險(xiǎn)資產(chǎn),還得看投資者的風(fēng)險(xiǎn)態(tài)度.無(wú)風(fēng)險(xiǎn)資產(chǎn)的效用值就是其期望收益率,即7%.對(duì)于風(fēng)險(xiǎn)厭惡系數(shù)為4的投資者,風(fēng)險(xiǎn)資產(chǎn)的效用是U=20-（0.005*4*30^2)=-30%小于7%.不會(huì)選擇風(fēng)險(xiǎn)資產(chǎn).對(duì)于風(fēng)險(xiǎn)厭惡系數(shù)為2的投資者,風(fēng)險(xiǎn)資產(chǎn)的效用是U=20-（0.005*2*30^2)=11%大于7%.會(huì)選擇風(fēng)險(xiǎn)資產(chǎn).2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity542022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity552022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity舉例3-13假設(shè)某投資者要在兩項(xiàng)風(fēng)險(xiǎn)資產(chǎn)A與B之間進(jìn)行投資選擇.如果運(yùn)用前面的變異系數(shù)進(jìn)行分析可以得出A的風(fēng)險(xiǎn)/收益權(quán)衡好于B的結(jié)論.但投資是否就應(yīng)當(dāng)選擇A呢?關(guān)鍵還要看投資者的風(fēng)險(xiǎn)厭惡程度.即投資者在選擇風(fēng)險(xiǎn)資產(chǎn)時(shí)應(yīng)當(dāng)遵循最大化收益的同時(shí)最小化風(fēng)險(xiǎn).在此引入無(wú)差異曲線進(jìn)行分析.效用的無(wú)差異曲線由效用函數(shù)給出.項(xiàng)目預(yù)期收益%標(biāo)準(zhǔn)差%A1018B1525552022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity562022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity效用的無(wú)差異曲線無(wú)差異曲線就是指在該曲線上的任何一點(diǎn)給投資者帶來(lái)的效用值無(wú)差異.無(wú)差異曲線可以用來(lái)分析投資者厭惡風(fēng)險(xiǎn)的程度.下頁(yè)圖中,無(wú)差異曲線斜率表示投資者厭惡風(fēng)險(xiǎn)的程度.斜率越大(L2)表明投資者越厭惡風(fēng)險(xiǎn),因?yàn)樗袚?dān)風(fēng)險(xiǎn)要求更高的報(bào)酬.而斜率越小(L1)表明投資者比較不厭惡風(fēng)險(xiǎn).對(duì)于L1的投資者而言,兩項(xiàng)資產(chǎn)的效用值相同,因而兩者無(wú)差異,選擇哪一個(gè)都一樣.而對(duì)于L2的投資者而言,兩項(xiàng)資產(chǎn)所能提供預(yù)期收益的效用值低于其預(yù)期水平,因而,兩者都不會(huì)考慮.即如果要他投資于標(biāo)準(zhǔn)差為18%的資產(chǎn)的話,他要求得到遠(yuǎn)高于10%的收益.562022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversityCopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity572022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity無(wú)差異曲線預(yù)期收益(效用)方差(標(biāo)準(zhǔn)差)不同投資者對(duì)于承擔(dān)同樣的風(fēng)險(xiǎn),要求的風(fēng)險(xiǎn)溢價(jià)不同,使得無(wú)差異曲線的斜率明顯不同.斜率越大,表明投資者越厭惡風(fēng)險(xiǎn),亦即要求的風(fēng)險(xiǎn)溢價(jià)越高..A.BL1L257CL2’2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers58思考題1.一家銀行提供給你兩種三年定期存款1萬(wàn)元的利率選擇：（1）月利率1%.（2）年復(fù)利12%.你會(huì)選擇哪種方式？2.你投資2.7萬(wàn)元于一個(gè)公司債券,每1000元面值的債券售價(jià)為900元.在來(lái)年,1000元債券能夠提供的利息為75元.年末債券價(jià)格有三種可能（0.2的概率為850元,0.5的概率為915元,0.3的概率為985元）.你的另一種投資選擇是國(guó)庫(kù)券,它能提供5%的收益率.計(jì)算：每種情況的持有期收益率、期望收益率和投資的風(fēng)險(xiǎn)溢價(jià).你投資的年末期望價(jià)值是多少？3.比較算術(shù)平均收益與幾何平均收益的差異.4.某銀行推出的一款理財(cái)產(chǎn)品過(guò)去取得的收益能否作為選擇其新推出同類型產(chǎn)品的依據(jù)？為什么？5.比較變異系數(shù)、夏普比率、特雷諾比率之間的差別6.一項(xiàng)風(fēng)險(xiǎn)資產(chǎn)的期望收益率為22%,標(biāo)準(zhǔn)差為30%.國(guó)債能提供的無(wú)風(fēng)險(xiǎn)收益率為7%.一個(gè)風(fēng)險(xiǎn)厭惡系數(shù)為4的投資者更愿意投資國(guó)債還是風(fēng)險(xiǎn)資產(chǎn)？如果風(fēng)險(xiǎn)厭惡系數(shù)為2的投資者呢？2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity582022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers59

投資學(xué)第三講

投資的收益與風(fēng)險(xiǎn)陳善昂2022/11/24592022/11/22CopyRight?ShanAngChe問(wèn)題1.市民24年前（1989年）存2000元預(yù)期收益22萬(wàn),銀行只付8400元.2.某人6年前信用卡欠銀行900元,現(xiàn)在銀行要收19000元.計(jì)算：兩個(gè)案例的年算術(shù)平均收益與幾何平均收益.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers60問(wèn)題1.市民24年前（1989年）存2000元預(yù)期收益22萬(wàn)Part1

收益的來(lái)源及其類型2022/11/2461Copyright?Shanangchen,DepartmentOfFinance,XiamenUniversityPart1

收益的來(lái)源及其類型2022/11/223Cop2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers62一.持有期收益1.收益來(lái)源：定期現(xiàn)金流（如利息股息）+價(jià)差收入2.持有期收益：2022/11/2462CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity注：羅伯特.清崎強(qiáng)調(diào)投資于現(xiàn)金流而不是資本利得！2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers63利息收入：幾種投資品的比較股票：股息收益,可以與債券當(dāng)期收益、存款利息比較債券：當(dāng)期收益（I/P）、息票收益（I/F）,可以與存款利息比較房產(chǎn)：租售比,可以與債券當(dāng)期收益、股息收益比較黃金：沒(méi)有利息收入.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity632022/11/22CopyRight?ShanAngChe價(jià)差收入：區(qū)分投資與投機(jī)的一個(gè)標(biāo)準(zhǔn)2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers64問(wèn)題：A股投資者能指望現(xiàn)金分紅來(lái)獲取收益嗎？參與者應(yīng)當(dāng)重點(diǎn)關(guān)注什么？?jī)r(jià)差收入：區(qū)分投資與投機(jī)的一個(gè)標(biāo)準(zhǔn)2022/11/22Cop2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers65舉例3-1假定你的投資在四年內(nèi)有如下的收益：那么,四年內(nèi)的年平均收益為9.58%.HPR=44.21%.公式：HPR=（1+r1）（1+r2）（1+r3）（1+r4）-1年平均收益=［（1+r1）（1+r2）（1+r3）（1+r4）］^0.25-12022/11/2465CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity年收益110%2-5%320%415%2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers66幾何平均與算術(shù)平均幾何平均不同于算術(shù)平均.算術(shù)平均持有期收益率是按照單利原理計(jì)算的年均收益率.一般地,算術(shù)平均不低于幾何平均；在各期持有期收益率均相等時(shí),幾何平均等于算術(shù)平均.上例的算術(shù)平均收益率=10%（高于幾何平均的9.58%）.（10%-5%+20%+15%）/4=10%.2022/11/2466CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe舉例3-21.市民24年前存2000元約定22萬(wàn),銀行只付8400元.用計(jì)算器計(jì)算幾何平均收益.輸入n=24,pv=-2000,fv=8400,pmt=0.輸出i=6.16（%）算術(shù)平均收益：13.33%2.某人6年前信用卡欠銀行900元,現(xiàn)在銀行要收19000元.用計(jì)算器計(jì)算幾何平均收益.輸入n=6,pv=-900,fv=19000,pmt=0.輸出i=66.24（%）算術(shù)平均收益：120.67%2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers67舉例3-21.市民24年前存2000元約定22萬(wàn),銀行只付82022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers68歷史收益率（幾何平均與算術(shù)平均）2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers69考慮匯率影響的持有期收益率舉例：2002-2004年,歐元兌美元的實(shí)際匯率變化從1.05變?yōu)?.35（即歐元相對(duì)美元升值28.57%）.假設(shè)2002年末EurTel股票的價(jià)格為75歐元,此時(shí)美元成本為78.75美元.在2004年末,該股票的價(jià)格漲至105歐元（股票漲了40%）,相當(dāng)于141.75美元.以美元計(jì)算的投資收益率可以通過(guò)兩種方法計(jì)算得出：2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity69股價(jià)上漲貢獻(xiàn)歐元上漲貢獻(xiàn)注：匯率風(fēng)險(xiǎn)對(duì)投資的影響是顯著的.人民幣匯率與跨境投資！2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers70二.貨幣的時(shí)間價(jià)值用復(fù)利衡量收益是投資的本質(zhì)要求！單利只考慮到利息；而復(fù)利考慮到了利息以及利息的利息.2022/11/2470CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers712022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity言論艾伯特?愛(ài)因斯坦:“宇宙中最強(qiáng)大的力量是什么?……是復(fù)利.”羅思柴爾德:“我不知道世界七大奇跡是哪些,但我知道第八大奇跡是復(fù)利.”712022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers72美麗的財(cái)富曲線問(wèn)題：中美投資收益對(duì)比.1926年投資于美國(guó)小盤(pán)股1美元,到2004年底變成了9248美元,投資于美國(guó)大盤(pán)股1美元,到2004年底變成了1992美元.1907年福建林先生用洋銀100元購(gòu)買(mǎi)了福建鐵路優(yōu)先股20股,去年其孫持此憑證希望了解其目前值多少錢(qián).您能幫助林先生的孫子算算嗎？2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers732022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity三.有效年收益率-有效年收益率-連續(xù)復(fù)利連續(xù)復(fù)利是既定利率水平下最大的名義利率.

732022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers742022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity年名義利率為6%的有效年利率復(fù)利頻率n有效年利率年16.00000半年26.09000季46.13636月126.16778周526.17998日3656.18313連續(xù)復(fù)利611/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers75舉例3-3一張面值為100元、半年期的零息票債券目前售價(jià)為97.36元.計(jì)算：銀行貼現(xiàn)收益率、持有期收益與有效年收益.銀行貼現(xiàn)收益率（年）=（100-97.36）/100*2=5.28%持有期收益（半年）=（100-97.36）/97.36=2.71%有效年收益=（1.0271）^2-1=5.49%.（不是5.42%）銀行貼現(xiàn)收益率會(huì)低估收益.2022/11/2475CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers76四.要求收益率投資決策取決于預(yù)期收益率與要求收益率之間的對(duì)比.要求收益率主要受三個(gè)因素的影響,即：貨幣的時(shí)間價(jià)值（真實(shí)無(wú)風(fēng)險(xiǎn)收益率）+預(yù)期通貨膨脹率+風(fēng)險(xiǎn)溢價(jià)；作為對(duì)延期消費(fèi)的補(bǔ)償,這是進(jìn)行一項(xiàng)投資可能接受的最低收益率.2022/11/2476CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers77通貨膨脹與稅收對(duì)投資收益的影響案例1：1977年湯女士存入銀行300元,2009年連本帶息取出來(lái)是843元.案例2：1954年王先生存入銀行10萬(wàn)元,2011年底其孫子持憑證到銀行要求兌付,您猜可以兌到多少錢(qián)？案例3：名義收益率=3.5%,預(yù)期通貨膨脹率=6.5%.粗略計(jì)算真實(shí)收益率為-3%,但精確計(jì)算真實(shí)收益率為-2.82%.進(jìn)入負(fù)利率時(shí)代.案例4：稅后收益＝稅前收益*（1－稅率）2022/11/2477CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity2022/11/22CopyRight?ShanAngChe通貨膨脹猛于虎2022/11/24Copyright?Shanangchen,DepartmentOfFinance,XiamenUniversity78鐘偉：今天100萬(wàn)的購(gòu)買(mǎi)力不及30年前的1萬(wàn)元.建設(shè)銀行（CBC）：存不存？中國(guó)銀行（BC）：不存！農(nóng)業(yè)銀行（ABC）：??？不存？工商銀行（ICBC）：愛(ài)存不存！民生銀行（CMSB）：存么,傻B！國(guó)家開(kāi)發(fā)銀行（CDB）：存點(diǎn)吧！興業(yè)銀行（CIB）：存一百！北京市商業(yè)銀行（BCCB）：白存,存不？匯豐銀行（HSBC）：還是不存！通貨膨脹猛于虎2022/11/22Copyright?Sha2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers792022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity五.到期收益率(YTM)YTM是指使得從證券上獲得的收入的現(xiàn)值與其當(dāng)前市場(chǎng)價(jià)格相等時(shí)的利率水平.它是一個(gè)全期利率,即它是假定投資者能夠持有證券直至到期日為止.YTM是一個(gè)非常重要的收益率,它適用于任何現(xiàn)金流的貼現(xiàn).但是,它的缺陷在于買(mǎi)入證券后持有至到期日.792022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers802022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity80附息債券的到期收益率到期收益率的計(jì)算公式如果是零息票債券與永久性債券,其計(jì)算公式就是其特例.到期收益率也就是IRR.當(dāng)?shù)狡谑找媛蚀笥谝笫找媛蕰r(shí),現(xiàn)金流的凈現(xiàn)值大于0,顯示項(xiàng)目可行.反之反是.2022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers81舉例：到期收益率的計(jì)算例3-4：20年期政府債券的息票率6%,每半年付息一次,當(dāng)前每1000元售價(jià)為980元.計(jì)算其到期收益率.計(jì)算過(guò)程：在財(cái)務(wù)計(jì)算品上輸入n=40,pmt=30,pv=-980,fv=1000,輸出1/y=3.0878%.例3-5：2年期零息票債券,當(dāng)前每1000元售價(jià)為800元.計(jì)算其到期收益率.計(jì)算過(guò)程：在財(cái)務(wù)計(jì)算品上輸入n=2,pmt=0,pv=-800,fv=1000,輸出1/y=11.8034%.也可以用EXCEL中的函數(shù)來(lái)計(jì)算.2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity812022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers822022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity六.預(yù)期收益率未來(lái)充滿著不確定性.前面討論的都是事后收益.未來(lái)的持有期收益率也稱期望收益率.人們進(jìn)行投資決策取決于預(yù)期收益率與要求收益率的對(duì)比.包括單資產(chǎn)的期望收益率與投資組合的預(yù)期收益率.822022/11/22CopyRight?ShanAngChe2022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUnivers832022/11/24CopyRight?ShanAngChen,DepartmentOfFinance,XiamenUniversity單一資產(chǎn)的預(yù)期收益在任何情況下,