實(shí)證金融 重慶課件1

1、實(shí)證金融西南財(cái)經(jīng)大學(xué)證券期貨學(xué)院重慶培訓(xùn)部課程概要引言實(shí)證金融的研究范例實(shí)證金融論文寫(xiě)作目標(biāo)通過(guò)實(shí)證金融學(xué)研究文獻(xiàn)的討論，了解相關(guān)領(lǐng)域的研究進(jìn)展，介紹資產(chǎn)定價(jià)領(lǐng)域的實(shí)證研究設(shè)計(jì)與方法體會(huì)金融論文寫(xiě)作選題規(guī)范實(shí)施通過(guò)課程的學(xué)習(xí)，獨(dú)立設(shè)計(jì)實(shí)施一個(gè)實(shí)證金融的研究項(xiàng)目，并規(guī)范地完成碩士論文的寫(xiě)作內(nèi)容實(shí)證金融研究的研究方法實(shí)證專題有效市場(chǎng)假說(shuō)的檢驗(yàn) 資產(chǎn)定價(jià)模型的檢驗(yàn) 價(jià)值投資，動(dòng)量效應(yīng)、反轉(zhuǎn)效應(yīng)的檢驗(yàn)如何設(shè)計(jì)研究計(jì)劃？論文的格式與要求I、引言什么是實(shí)證研究？ 以事實(shí)、實(shí)際情況和收集到的數(shù)據(jù)為對(duì)象，通過(guò)分析、計(jì)算、實(shí)驗(yàn)、研究，解釋和預(yù)測(cè)經(jīng)濟(jì)、會(huì)計(jì)、金融實(shí)務(wù)，回答“實(shí)際上是什么”的問(wèn)題。 實(shí)證研究要求客觀

2、、準(zhǔn)確、理性的描述現(xiàn)實(shí) 實(shí)證研究以解釋現(xiàn)實(shí)為目的，認(rèn)為存在就是事實(shí) 實(shí)證研究采用客觀中立的立場(chǎng) 目前，在國(guó)際上，實(shí)證研究方法廣泛的應(yīng)用在經(jīng)濟(jì)、金融、會(huì)計(jì)等社會(huì)學(xué)科的研究中-實(shí)證經(jīng)濟(jì)學(xué) 1953 弗里德曼實(shí)證經(jīng)濟(jì)學(xué)方法論發(fā)展歷程-實(shí)證會(huì)計(jì)學(xué) 1968 Ball，R.J., P.Brown An Empirical Evaluation of Accounting Income NumbersJournal of Accounting Research 1986 Watts， Zimmerman 實(shí)證會(huì)計(jì)理論趨勢(shì)由于金融市場(chǎng)每天都產(chǎn)生海量的數(shù)據(jù)，這些數(shù)據(jù)又是從真實(shí)的交易 過(guò)程中產(chǎn)生的, 這一特性使

3、實(shí)證研究成為現(xiàn)代金融研究的主流話語(yǔ)” Ross20世紀(jì)80年代以來(lái)，JF,JFE,RFS上實(shí)證性研究的論文占半數(shù)以上，有的年份還高達(dá)80以上?，F(xiàn)在實(shí)證研究已成為金融研究的主流。實(shí) 證 的 要 素 數(shù)據(jù)：反映客觀狀況的統(tǒng)計(jì)數(shù)據(jù)。 模型：刻畫(huà)客觀現(xiàn)象的數(shù)學(xué)方程。 假設(shè)：對(duì)所研究問(wèn)題的結(jié)果或狀態(tài)的一種預(yù)期。 檢驗(yàn)：利用數(shù)據(jù)，使用統(tǒng)計(jì)學(xué)知識(shí)對(duì)假設(shè)的統(tǒng)計(jì)顯著性作出判斷。 推理：基于知識(shí)和經(jīng)驗(yàn)對(duì)假設(shè)檢驗(yàn)結(jié)果進(jìn)行推理分析。 結(jié)論：利用假設(shè)檢驗(yàn)的結(jié)果，通過(guò)合理的邏輯推理得出結(jié)論，觀點(diǎn)。確立研究課題實(shí) 證 研 究 方 法 步 驟尋找相關(guān)理論提出命題假設(shè)設(shè)計(jì)研究方案搜集事實(shí)數(shù)據(jù)分析數(shù)據(jù)檢驗(yàn)命題得出研究結(jié)論實(shí)證金融

4、實(shí)證金融：以金融學(xué)理論為出發(fā)點(diǎn)和導(dǎo)向，分析實(shí)際金融數(shù)據(jù)，檢驗(yàn)理論、假說(shuō)或觀點(diǎn)，探索具有經(jīng)濟(jì)意義的新現(xiàn)象。金融理論實(shí)證檢驗(yàn)新的經(jīng)驗(yàn)證據(jù)新的理論實(shí)證檢驗(yàn)實(shí)證金融研究什么？從理論出發(fā) 理論 資產(chǎn)定價(jià)理論：CAPM 假說(shuō) 市場(chǎng)有效性假說(shuō) 觀點(diǎn) 基金經(jīng)理人的管理水平與其個(gè)人特征相關(guān)實(shí)證金融研究什么？從現(xiàn)象出發(fā) 封閉式基金折價(jià) 首次公開(kāi)發(fā)行股票的首日折價(jià) 股票收益的日歷效應(yīng)II、實(shí)證金融的研究范例三個(gè)主要的實(shí)證金融研究領(lǐng)域一、有效市場(chǎng)的實(shí)證檢驗(yàn)二、資本資產(chǎn)定價(jià)模型（CAPM)的實(shí)證檢驗(yàn)三、關(guān)于市場(chǎng)異象的實(shí)證經(jīng)驗(yàn)有效市場(chǎng)的實(shí)證檢驗(yàn)一、我國(guó)股市的實(shí)證檢驗(yàn)結(jié)果：自從全國(guó)性股票市場(chǎng)建立以來(lái)，對(duì)我國(guó)股票市場(chǎng)有效性的

5、討論和檢驗(yàn)從未間斷過(guò)，遺憾的是，至今仍未能形成統(tǒng)一的令人信服的結(jié)論。信息股票的歷史價(jià)格信息所有公開(kāi)的信息所有可獲得的信息（包括內(nèi)部或私人信息）有效市場(chǎng)假說(shuō)的類型弱式有效市場(chǎng)：如果所有關(guān)于過(guò)去價(jià)格變化的信息都反映在現(xiàn)行股價(jià)上。半強(qiáng)式有效市場(chǎng)：假定所有公開(kāi)可得的信息反映在股票價(jià)格上。強(qiáng)式有效市場(chǎng)：假定所有信息（尤其包括非公開(kāi)信息）都反映在股價(jià)上。假說(shuō)類型針對(duì)信息集（逐步擴(kuò)大）結(jié)論弱式EMH歷史信息技術(shù)分析無(wú)效半強(qiáng)式EMH公開(kāi)信息（歷史信息+基本面信息）基本面分析也無(wú)效強(qiáng)式EMH所有信息（歷史信息+基本面信息+內(nèi)幕信息）內(nèi)幕交易也無(wú)效相對(duì)市場(chǎng)有效并不簡(jiǎn)單是市場(chǎng)要么嚴(yán)格有效，要么嚴(yán)格無(wú)效的問(wèn)題，而是一

6、個(gè)有效的程度問(wèn)題。問(wèn)題的關(guān)鍵不是某個(gè)市場(chǎng)是否有效，而是多有效。二、弱式有效檢驗(yàn)背景：弱式有效檢驗(yàn)考察過(guò)去價(jià)格的時(shí)間序列是否能用于預(yù)測(cè)未來(lái)的股價(jià)。上證綜指: 12/19/199002/18/2011收益率: 12/19/199002/18/20111、回歸分析研究：Fama（1965），股票市場(chǎng)價(jià)格行為一文中對(duì)30支股票進(jìn)行了間隔一天的回歸分析。結(jié)論：過(guò)去價(jià)格序列確實(shí)包含一些有關(guān)未來(lái)股價(jià)行為的信息，但基于過(guò)去數(shù)據(jù)的任何交易方式可能不具價(jià)值，即便最小的交易費(fèi)用也會(huì)淹沒(méi)超額報(bào)酬。25有關(guān)回歸的基本介紹：最小二乘法 金融、經(jīng)濟(jì)變量之間的關(guān)系，大體上可以分為兩種： （1）函數(shù)關(guān)系：Y=f(X1,X2,.

7、,XP)，其中Y的值是由Xi（i=1,2.p）所唯一確定的。 （2）相關(guān)關(guān)系: Y=f(X1,X2,.,XP) ，這里Y的值不能由Xi（i=1,2.p）精確的唯一確定。26圖2-1 貨幣供應(yīng)量和GDP散點(diǎn)圖27圖2-1表示的是我國(guó)貨幣供應(yīng)量M2（y）與經(jīng)過(guò)季節(jié)調(diào)整的GDP（x）之間的關(guān)系（數(shù)據(jù)為1995年第一季度到2004年第二季度的季度數(shù)據(jù)）。28但有時(shí)候我們想知道當(dāng)x變化一單位時(shí)，y平均變化多少，可以看到，由于圖中所有的點(diǎn)都相對(duì)的集中在圖中直線周圍，因此我們可以以這條直線大致代表x與y之間的關(guān)系。如果我們能夠確定這條直線，我們就可以用直線的斜率來(lái)表示當(dāng)x變化一單位時(shí)y的變化程度，由圖中的點(diǎn)

8、確定線的過(guò)程就是回歸。 29對(duì)于變量間的相關(guān)關(guān)系，我們可以根據(jù)大量的統(tǒng)計(jì)資料，找出它們?cè)跀?shù)量變化方面的規(guī)律（即“平均”的規(guī)律），這種統(tǒng)計(jì)規(guī)律所揭示的關(guān)系就是回歸關(guān)系（regressive relationship）,所表示的數(shù)學(xué)方程就是回歸方程（regression equation）或回歸模型（regression model）。問(wèn)題：怎樣的擬合直線方程最好？答：保證這條直線與所有點(diǎn)的距離之和最近. 基于這種想法：最小二乘法問(wèn)題：怎么定義”與所有點(diǎn)的距離之和最近？答：設(shè)直線ya+bx，任意給定的一個(gè)樣本點(diǎn) （xi，yi） yi(a+bxi)2 刻畫(huà)這個(gè)樣本點(diǎn)與這條直線的 “距離”,表示了兩者

9、的接近程度.若有n個(gè)樣本點(diǎn)：（x1，y1）, ,（xn，yn），可以用下面的表達(dá)式來(lái)刻畫(huà)這些點(diǎn)與直線ya+bx的接近程度:使上式達(dá)到最小值的直線就是所求的直線.此時(shí)：32圖2-1中的直線可表示為 （2.1） 根據(jù)上式，在確定、的情況下，給定一個(gè)x值，我們就能夠得到一個(gè)確定的y值，然而根據(jù)式（2.1）得到的y值與實(shí)際的y值存在一個(gè)誤差（即圖2-1中點(diǎn)到直線的距離）。 33如果我們以表示誤差，則方程（2.1）變?yōu)椋?即： 其中t（=1,2,3,.,T）表示觀測(cè)數(shù)。 （2.2）（2.3）式（2.3）即為一個(gè)簡(jiǎn)單的雙變量回歸模型（因其僅具有兩個(gè)變量x, y）的基本形式。 34其中yt被稱作因變量（de

10、pendent variable）、 被解釋變量（explained variable）、 結(jié)果變量（effect variable）；xt被稱作自變量（independent variable）、解釋變量（explanatory variable）、 原因變量（causal variable）35、為參數(shù)（parameters）,或稱回歸系數(shù)（regression coefficients）；t通常被稱為隨機(jī)誤差項(xiàng)（stochastic error term）,或隨機(jī)擾動(dòng)項(xiàng)（random disturbance term）,簡(jiǎn)稱誤差項(xiàng)，在回歸模型中它是不確定的，服從隨機(jī)分布（相應(yīng)的，yt也是

11、不確定的，服從隨機(jī)分布）。 36為什么將t 包含在模型中？（1）有些變量是觀測(cè)不到的或者是無(wú)法度量的，又或者影響因變量yt的因素太多；（2）在yt的度量過(guò)程中會(huì)發(fā)生偏誤，這些偏誤在模型中是表示不出來(lái)的；（3）外界隨機(jī)因素對(duì)yt的影響也很難模型化，比如：恐怖事件、自然災(zāi)害、設(shè)備故障等。37參數(shù)的最小二乘估計(jì)(一) 方法介紹本章所介紹的是普通最小二乘法（ordinary least squares,簡(jiǎn)記OLS）;最小二乘法的基本原則是：最優(yōu)擬合直線應(yīng)該使各點(diǎn)到直線的距離的和最小，也可表述為距離的平方和最小。假定根據(jù)這一原理得到的、估計(jì)值為 、 ，則直線可表示為 。38直線上的yt值，記為 ，稱為擬

12、合值（fitted value）,實(shí)際值與擬合值的差，記為 ，稱為殘差（residual） ，可以看作是隨機(jī)誤差項(xiàng) 的估計(jì)值。 根據(jù)OLS的基本原則，使直線與各散點(diǎn)的距離的平方和最小，實(shí)際上是使殘差平方和（residual sum of squares, 簡(jiǎn)記RSS） 最小，即最小化： RSS= = （2.4） 39根據(jù)最小化的一階條件，將式2.4分別對(duì) 、求偏導(dǎo)，并令其為零，即可求得結(jié)果如下 :（2.5） （2.6） 40假設(shè)檢驗(yàn)假設(shè)檢驗(yàn)的程序是，先根據(jù)實(shí)際問(wèn)題的要求提出一個(gè)論斷，稱為零假設(shè)（null hypothesis）或原假設(shè)，記為H0（一般并列的有一個(gè)備擇假設(shè)（alternative

13、 hypothesis）,記為H1 ）然后根據(jù)樣本的有關(guān)信息，對(duì)H0的真?zhèn)芜M(jìn)行判斷，做出拒絕H0或不能拒絕H0的決策。41P值和t值t值越大，拒絕零假設(shè)的可能性就越大；t值越小，拒絕零假設(shè)時(shí)可能性就越小。 P值度量的是拒絕正確的零假設(shè)的概率。P值越大，錯(cuò)誤地拒絕零假設(shè)的可能性就越大；p值越小，拒絕零假設(shè)時(shí)就越放心?，F(xiàn)在許多統(tǒng)計(jì)軟件都能計(jì)算各種統(tǒng)計(jì)量的t值、p值，如Eviews、Stata等。對(duì)上證綜合指數(shù)的回歸檢驗(yàn)時(shí)間段：12/19/199012/13/199612/13/199606/13/200106/13/200101/04/200601/04/200611/04/200801/04/2

14、00602/18/201112/19/199012/13/1996結(jié)論：回歸系數(shù)為0.0071 0.1081，因此在0.05的置信水平下，拒絕一次項(xiàng)系數(shù)為零的原假設(shè)，表明有正相關(guān)。12/13/199606/13/2001結(jié)論：回歸系數(shù)為-0.0734 0.0449，因此在0.05的置信水平下，不能拒絕一次項(xiàng)系數(shù)為零的原假設(shè)。06/13/200101/04/2006結(jié)論：回歸系數(shù)為-0.0468 0.0714，因此在0.05的置信水平下，不能拒絕一次項(xiàng)系數(shù)為零的原假設(shè)。01/04/200611/04/2008結(jié)論：回歸系數(shù)為-0.0635 0.0866，因此在0.05的置信水平下，不能拒絕一次項(xiàng)

15、系數(shù)為零的原假設(shè)。01/04/200602/18/2011結(jié)論：回歸系數(shù)為-0.0453 0.0661，因此在0.05的置信水平下，不能拒絕一次項(xiàng)系數(shù)為零的原假設(shè)。時(shí)間段樣本數(shù)量H0：斜率為零斜率的置信區(qū)間12/19/199012/13/19961513拒絕0.0071 0.108112/13/199606/13/20011081無(wú)法拒絕-0.0734 0.044906/13/200101/04/2006 1102無(wú)法拒絕-0.0468 0.071401/04/200611/04/2008 687無(wú)法拒絕-0.0635 0.086601/04/200602/18/20111243無(wú)法拒絕-0.

16、0453 0.0661回歸檢驗(yàn)2、Autocorrelation Test：自相關(guān)檢驗(yàn)Ljung-Box的Q統(tǒng)計(jì)量：是通過(guò)計(jì)算序列自相關(guān)系數(shù)平方的加權(quán)平均來(lái)檢驗(yàn)序列是否獨(dú)立，是一種傳統(tǒng)直觀的方法。Q統(tǒng)計(jì)量如下式所示：其中rj是滯后為j的相關(guān)系數(shù)，T是樣本容量，p為滯后階數(shù)。其原假設(shè)為：序列獨(dú)立。LBQ-test(Series, Lags, Alpha)12/19/199012/13/1996Lbqtest: H=1; pValue =0.005212/13/199606/13/2001Lbqtest: H=0; pValue =0.057506/13/200101/04/2006Lbqtest

17、: H=0; pValue =0.878201/04/200611/04/2008Lbqtest: H=1; pValue =2.1192e-00401/04/200602/18/2011Lbqtest: H=1; pValue =0.0096時(shí)間段樣本數(shù)量HpValue12/19/199012/13/1996151310.005212/13/199606/13/2001108100.057506/13/200101/04/2006 110200.878201/04/200611/04/2008 68712.1192e-00401/04/200602/18/2011124310.0096Lju

18、ng-Box的Q統(tǒng)計(jì)量3、 Lo and MacKinlay (1988, RFS) 方差比檢驗(yàn)Random walk modelEfficient market prices follow random walkDoes stock market price follow random walk?Starting from mid 80s, studies starting showing that returns are predictable.Implication on market efficiency.Methodology: tests of random walkVarianc

19、e ratio testVariance Ratio Tests (1)Variance Ratio Tests (2)DataDo Stock prices follow random walk?Strong rejections on weekly equal weighted index (not value weighted)Few rejections for individual stocks二、半強(qiáng)式有效檢驗(yàn)背景：弱式有效檢驗(yàn)僅注重股票過(guò)去價(jià)格的信息，半強(qiáng)式有效檢驗(yàn)涉及所有公開(kāi)所得信息，當(dāng)然包括股票價(jià)格；如果市場(chǎng)是半強(qiáng)式有效，那么利好消息已經(jīng)反映在股價(jià)上，在披露信息后，無(wú)超額報(bào)酬

20、可掙。事件研究法背景：半強(qiáng)式有效市場(chǎng)的檢驗(yàn)可以采用事件研究法，事件如公司配股；拆股信息的頒布；盈利分紅信息的頒布；送轉(zhuǎn)股；基金經(jīng)理的變更；融資決策對(duì)股票價(jià)格(或企業(yè)價(jià)值) 的影響。事件研究概述定義指運(yùn)用金融市場(chǎng)的數(shù)據(jù)資料來(lái)測(cè)定某一特定經(jīng)濟(jì)事件對(duì)一公司價(jià)值的影響。基本原理 假設(shè)市場(chǎng)理性，則有關(guān)事件的影響將會(huì)立即反映在證券價(jià)格之中。于是，運(yùn)用相對(duì)來(lái)說(shuō)比較短期所觀察到的證券價(jià)格就可以測(cè)定某一事件的經(jīng)濟(jì)影響。 事件研究步驟1 事件定義（Event definition）確定所要研究的事件明確事件所涉及公司證券價(jià)格的研究期間事件窗 (event window) 2 取樣標(biāo)準(zhǔn)（Selection crit

21、eria） 歸納出一些樣本特征 (如公司市場(chǎng)資本化、行業(yè)代表、事件發(fā)布的時(shí)間分布等 )并注明通過(guò)選樣可能導(dǎo)致的任何偏差 。3 界定正常和非正常收益 正常收益是指假設(shè)不發(fā)生該事件條件下的預(yù)期收益。非正常收益即事件期間內(nèi)該證券事前或事后實(shí)際收益與同期正常收益之差。事件研究各時(shí)間窗T0T1T2T30估計(jì)窗口檢驗(yàn)窗口事件日L1L2市場(chǎng)模型（Market Model）中國(guó)證券分析師推薦價(jià)值研究數(shù)據(jù)：2005年5月31日起至2007年3月31日止wind資訊系統(tǒng)記錄的全部股票推薦，期間，收錄了來(lái)自32家研究機(jī)構(gòu)653名分析師共計(jì)4567個(gè)推薦評(píng)級(jí)樣本，涉及1035家上市公司，其中滬市617家，深市418家

22、。有效樣本2922個(gè)：剔除，如次新股、ST股票、重復(fù)推薦等所有推薦樣本按評(píng)級(jí)分類的統(tǒng)計(jì)性描述“買入”評(píng)級(jí)和“增持”評(píng)級(jí)的數(shù)量遠(yuǎn)多于“賣出”和“減持”評(píng)級(jí)的數(shù)量，分析師普遍表現(xiàn)出一種“樂(lè)觀”的傾向。所有推薦樣本按規(guī)模分類的統(tǒng)計(jì)性描述分析師對(duì)中小市值個(gè)股的偏好。事件研究法分別研究分析師推薦的短期效應(yīng)和長(zhǎng)期投資價(jià)值。估計(jì)窗口：推薦日前67天至前176天共110個(gè)交易日。短期檢驗(yàn)窗口：推薦日及前后5天共計(jì)11天作為事件期。長(zhǎng)期檢驗(yàn)窗口：推薦日起后推最長(zhǎng)6個(gè)月作為事件期。全部樣本推薦日起六個(gè)月內(nèi)的ACAR(平均累積異常收益)平均而言，6個(gè)月能夠獲得超過(guò)大盤將近2%的超額收益，整體而言，分析師具有一定的選

23、股擇時(shí)能力，其推薦具有一定的投資價(jià)值。大盤股、中盤股和小盤股自推薦日起六個(gè)月內(nèi)的ACAR平均來(lái)看，中等市值股票六個(gè)月能獲得相對(duì)大盤約7%的超額收益。分析師推薦的小盤股長(zhǎng)期的平均異常收益顯著為負(fù)，即長(zhǎng)期來(lái)看其表現(xiàn)不如市場(chǎng)指數(shù)。明星分析師和非明星分析師自2003年開(kāi)始，我國(guó)著名財(cái)經(jīng)雜志新財(cái)富借鑒國(guó)際慣例，每年由機(jī)構(gòu)投資者投票評(píng)選出當(dāng)年各個(gè)行業(yè)的“最佳分析師“。當(dāng)選“最佳分析師”，意味著該分析師推薦的價(jià)值得到了買方機(jī)構(gòu)投資者的高度認(rèn)可，同時(shí)，也會(huì)給當(dāng)選分析師帶來(lái)薪酬和行業(yè)地位的大幅提高，目前該頭銜已成為衡量國(guó)內(nèi)分析師水平高低的標(biāo)尺之一。當(dāng)年當(dāng)選的明星分析師與非明星分析師ACAR的比較 明星分析師并沒(méi)

24、有顯示出顯著超過(guò)一般分析師的推薦價(jià)值。2006年當(dāng)選的明星分析師與非明星分析師短期推薦效應(yīng)比較明星分析師短期內(nèi)的市場(chǎng)影響力顯著超過(guò)非明星分析師，說(shuō)明依據(jù)目前國(guó)內(nèi)”最佳分析師“機(jī)制選出的并不是長(zhǎng)期推薦價(jià)值最高的分析師，而是短期內(nèi)對(duì)市場(chǎng)影響力最強(qiáng)的分析師。股價(jià)和宏觀經(jīng)濟(jì)標(biāo)變量的關(guān)系Returns are predictableValuation ratios (D/P, E/P, B/M ratios)Interest rates (term spread, short-long T-bill rates, etc.)Decision of market participants (corpora

25、te financing, consumption).4.Cross-sectional equity pricing.5.Bond and foreign exchange returns are also predictable.Some funds seem to outperform simple indices, even after controlling for risk through market betas.Fama and French (1989), JFE: economic questionsEconomic questions:1. Do the expected

26、 returns on bonds and stocks move together? Do the same variables forecast bond and stock returns?2. Is the variation in expected returns related to business cycles?Motivation:1. Evidence shows that stock and bond returns are predictable.2. Interpretations: market inefficiency versus rational variat

27、ion in expected returns.Framework: Regress future returns on variables X(t) known at time t.r (t,t +) = () + () X(t) + (t,t +) (1)where can be one month, one quarter, and one to four years.r (t,t + ): value- and equal-weighted market portfolios of NYSE; value-weighted corporate bond portfolios.X(t)

28、variables:Dividend yields D(t)/P(t): summing monthly dividends for the year preceding time t divided by the value of the portfolio at time t (Discount rate intuition)Term Premium TERM(t): the difference between the returns on long- and short-term governance bonds. Default premium DEF(t): the differe

29、nce between the returns on corporate Baa bonds and long-term governance bonds.D/P has strongest effect (high t-stats and high R2) Regression coefficients and R2 rise with the forecast horizon.Rational time-variation of expected return:time-varying risk aversiontime-varying amount of risk資本資產(chǎn)定價(jià)模型的實(shí)證檢

30、驗(yàn)要點(diǎn)1. 資本資產(chǎn)定價(jià)模型（CAPM ）回顧2. 實(shí)證檢驗(yàn)CAPM的方法 （Empirical Tests of CAPM）橫截面回歸法 Cross Sectional approach 時(shí)間序列回歸法 Time-series approach3. 實(shí)例分析： Example for the Empirical Tests of CAPM : Fama and French (1992,1993, 1996) CAPM AssumptionsNo transactions costsNo taxesPerfect competitionNo individual can affect pri

31、cesInvestors have the same utility functionOnly expected returns and variances matterNormally distributed returnsUnlimited short sales and borrowing and lending at the risk free rate of returnFeasible portfolios withN risky assets Dominated and Efficient PortfoliosUtility MaximizationA world with on

32、e riskless asset and N risky assetsThree Important FundsThe riskless asset has a standard deviation of zeroThe minimum variance portfolio lies on the boundary of the feasible set at a point where variance is minimumThe market portfolio lies on the feasible set and on a tangent from the risk-free ass

33、etWhen the risk free asset is introduced,All investors prefer a combination of 1) The risk free asset and 2) The market portfolioSuch combinations dominate all other assets and portfoliosUtility maximization witha riskfree assetThe Capital Market LineAll investors face the same Capital Market Line (

34、CML) given by:The Capital Market Line (cont.)The CAPM and the Security Market Line (cont.)The expected return on any asset can be written as:This is the Security Market Line (SML).The CAPM and the Security Market Line (cont.)Graphical depiction of CAPM, the security market line.CAPMThe CAPM: the exp

35、ected return on the asset is determined from its Beta:Beta is the regression slope coefficient when the return on the asset is regressed on the return on the market.Empirical Tests of CAPM The CAPM assumes only one source of systematic risk: Market Risk. Systematic risk: Cannot be diversified The CA

36、PM is: Ri,t - rf = i + i (Rm,t - rf) + i,ti=1,.,N and t=1,TRi,t = return on asset i at time t.rf = return of riskless asset at time t. Rm,t = return on the market portfolio at time t.i and i are the coefficients to be estimated.Cov(Rm,t,i,t) = 0The model is also called the Security Characteristic Li

37、ne (SCL). If i = 0,. then ERi,t - rf = i E(Rm,t - rf)(This is the Sharpe-Litner CAPM.)E(Rm,t - rf) is called the market risk premium: the difference between the return on the market portfolio and the return on a riskless bond.The expected return on asset i over rf is the market excess return. i is t

38、he factor (sensitivity to market risk).If i = 0, asset i is not exposed to market risk. Thus, the investor is not compensated with higher return. Zero- asset, market neutral.If i 0, asset i is exposed to market risk and Ri,t rf , provided that ERm,t rf 0.Q: What is the Market Portfolio? It represent

39、s all wealth. We need to include not only all stocks, but all bonds, real estate, privately held capital, publicly held capital (roads, universities, etc.), and human capital in the world. (Easy to state, but complicated to form.)Q: How do we calculate ERm,t and rf?The CAPM can be represented as a r

40、elation between ER and :ERi = rf + i (Security Market Line=SML)Two test approaches for CAPMCross Sectional approach: Fama and French (1992)Time-series approach: Fama and French (1993, 1996)Early tests focused on the cross-section of stock returns. Test SML.If i is known, a cross-sectional regression

41、 with ERi and i can be used to test the CAPM:ERi = + i + i(SML)Test H0: 0.(The value of is also of importance. Why?)Problem: We do not know i. It has to be estimated. This will introduce measurement error: bias!Examples of the early tests: Black, Jensen and Scholes (1972), Fama and MacBeth (1973), F

42、indings: Support for CAPM.More modern tests focused on the time-series behavior. Two popular approaches: Ri,t - rf = i + i (Rm,t - rf) + i,t- Test H0: i=0 (i is the pricing error. Jensens alpha.)(Joint tests are more efficient H0: 1 = 2 = N=0 (for all i)- Add more explanatory variables Zi,t to the C

43、APM regression:Ri,t - rf = i + i (Rm,t - rf) + Zi,t + i,tTest: H0: =0.(We are testing CAPMs specification.) Findings: Negative for CAPM. is significant. First pass: time series estimation where security (or portfolio) returns were regressed against a market index :Ri,t - rf = i + i (Rm,t - rf) + i,t

44、(CAPM) Second pass: cross-sectional estimation where the estimated CAPM-beta from the first pass is related to average return:Ri = (1-i) + i + i,t(SML for security i)( equals rf in the CAPM and ER0m in the Black CAPM. While is the expected market return. Main problem: Measurement error in i. Solutio

45、n:Measure s based on the notion that portfolio p estimates will be less affected by measurement error than individual i estimates due to aggregation.CAPM Test- Cross Sectional approach: Two pass techniqueFama and French (1992) TestsMarket betas should explain the average returns on any asset.To test

46、 if beta completely explains the cross-section of average returns, us Fama and MacBeth (1973) cross-sectional regressions.Two steps for Fama and MacBeth regressions.Suppose there are N assets at time t, we know R(i,t), Beta (I,t), and X(i,t) other variables such as firm size, B/M ratio, P/E ratio wh

47、ere asset i=1,2,N; t=1,2,.T (1) The regression model for the cross section of N assets at time of t is: R(i,t)- RF(t)= a(t) + b(t)*Beta (i,t) + c(t)*X(i,t) (2) Aggregate the estimates in the time dimension, given T observations of a(t), b(t) , c(t) , test the null a(t)=0 , b (t)=RM(t)-RF(t) 0, and c

48、(t)=0 FM has become a staple in applied finance. - Very simple. No need to estimate SE in pass 2.- It can be easily adapted to introduce additional risk measures P/E, Size, B/M, Leverage, etc.- If coefficients are constant over time, it is equivalent to a FE panel estimation. General Issues: (1) Por

49、tfolios: each beta is estimated with error. If the estimation errors are uncorrelated across stocks, a portfolio reduces estimation error and improves second pass regression. The estimators are biased, but consistent.(2) Rolling Regression: To reduce the bias in estimation error, estimate a lot of b

50、etas!Motivation of Fama and French (1992)Banz (1981): Firm size (ME) can explain the cross-section of average returns in addition to Beta.Bhandari (1988): leverage helps explain the cross-section of average stock returns in tests that include size and Beta.Rosenberg, Reid, and Lanstein (1985): book-

51、to-market equity (BE/ME) also has a strong role in explaining the cross-section of average returns. Basu (1983) shows that earnings-price ratios (E/P) help explain the cross-section of average returns.Contribution of Fama and French (1992)Fama and French (1992): evaluate the joint roles of Beta, siz

52、e, E/P, leverage, and book-to-market equity in the cross-section of average returns.Their conclusion: Size and book-to-market combine to explain the cross-section of average returns; the relation between beta and average return is not significant.The Beta is dead.Fama and French (1992): Sample const

53、ructionAll nonfinancial firms in the intersection of (i) the NYSE, AMEX, and NASDAQ return files from CRSP and (ii) the merged COMPUSTAT annual industrial files of income statement and balance-sheet data from CRSP.Maintain the six-month gap between fiscal yearend and the return tests by matching the

54、 accounting data for all fiscal year ends in calendar year t1 with the returns for July of year t to June of t+1. (ensure that the accounting variables are known before the returns they are used to explain)Use a firms market equity at the end of December of year t1 to compute its book-to-market, lev

55、erage, and earnings-price ratios for t1, and use its market equity for June of year t to measure its size.Fama and French (1992): Beta estimation (1)Estimate beta for portfolios and then assign a portfolios beta to each stock in the portfolio. Why?Estimates of beta for portfolios are more precise fo

56、r portfolios than for individual stocksSize, E/P, leverage, B/M measured precisely for individual stocksIn June of each year, all NYSE stocks on CRSP are sorted by size to determine the NYSE decile breakpoints for size. Stocks that have the required CRSP- OMPUSTAT data are then allocated to 10 size

57、portfolios based on the NYSE breakpointsWhy use size portfolios?Fama and French (1992): Beta estimation (2)To allow for variation in Beta unrelated to size, subdivide each size decile into 10 portfolios on the basis of pre-ranking Beta for individual stocksThe pre-ranking Betas are estimated on 24 t

58、o 60 monthly observations (as available) in the 5 years before July of year tSet the Beta breakpoints for each size decile using only NYSE stocksAfter assigning firms to the size-Beta portfolios in June, calculate the equal-weighted monthly portfolio returns from July to June.Fama and French (1992):

59、 Beta estimation (3)Estimate Beta using the full sample (330 months) of post-ranking returns on each of the 100 portfolios, with CRSP value-weighted portfolio of NYSE,AMEX, and NASDAQ stocks as proxy for the market.Estimate Beta as the sum of the slopes in the regression of the portfolio return on t

60、he current and prior months market return (nonsynchronous trading)Allocate the full-period post-ranking Beta of a size- portfolio to each stock in the portfolioFama and French (1992): Fama-MacBeth cross sectional regressions Table III The CAPM is very simple: Only one source of risk market risk affe