投资学第六章

1、6-1第六章6-2n 马克维茨模型的缺陷：- 计算量过大.假定分析n种股票,需要计算n个预期值、n个方差以及(n2 n)/2个协方差.- 相关系数确定或者估计中的误差会导致无效结果.n 指数模型的优势：- 大大降低了马克维茨模型的计算量,它把精力放在了对证券的专门分析中.- 指数模型以一种简单的方式来计算协方差,证券间的协方差由单个一般因素的影响生成,为市场指数收益所代表,从而为系统风险与公司特有的性质提供了重要的新视角. 指数模型的优势6-3Announcements, Surprises, and Expected Returnsn任一证券的收益由两部分组成（The return on a

2、ny security consists of two parts）. 1) 预期或一般收益（the expected or normal return）: the return that shareholders in the market predict or expect2) 非预期或风险收益（the unexpected or risky return）: the portion that comes from information that will be revealed .6-4Announcements, Surprises, and Expected Returnsn 任何

3、信息的公布可以被分成两个部分，预期到的部分和异常部分（Any announcement can be broken down into two parts, the anticipated or expected part and the surprise or innovation）:n Announcement = Expected part + Surprise.n 任何公布的信息中预期部分是市场用来形成股票预期收益（ E(ri). ）的信息（The expected part of any announcement is part of the information the mark

4、et uses to form the expectation of the return on the stock , E(ri).）n异常部分是那些影响股票非预期收益（ U. ）的信息（The surprise is the news that influences the unanticipated return on the stock, U.）6-5有关信息的例子Examples of relevant information- Statistics China figures (e.g., GNP)- A sudden drop in interest rates- News th

5、at the companys sales figures are higher than expected6-6因素模型Factor ModelsnA way to write the return on a stock in the coming month is:return theofpart unexpected theis return theofpart expected theis )(where)(UrEUrErii6-7实际总收益的构成n ri = E(ri) +U = E(ri) +m+eiri ：下个月的实际总收益E（ ri ）：实际总收益中的期望收益部分U：实际总收益

6、中的非期望收益部分m：系统性风险ei：非系统性风险公布信息公布信息= =期望部分期望部分+ +异动部分异动部分6-8风险：系统性和非系统性风险Risk: Systematic and Unsystematicn 系统性风险会影响到大部分资产A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree.n 非系统性风险只会影响到单一资产或某一小类的资产。非系统性风险可以被分散掉。An unsystematic risk is a risk that s

7、pecifically affects a single asset or small group of assets. Unsystematic risk can be diversified away.n 系统性风险包括那些一般经济状态的不确定性，如GNP、利率、通货膨胀等。Examples of systematic risk include uncertainty about general economic conditions, such as GNP, interest rates, or inflation. n 换句话说，一个公司特定的消息，如金矿开采公司发现黄金，就是非系统

8、性风险。On the other hand, announcements specific to a company, such as a gold mining company striking gold, are examples of unsystematic risk.6-9因素模型的特点n作为一种回报率产生过程，因素模型具有以下几个特点。- 第一，因素模型中的因素应该是系统影响所有证券价格的因素。- 第二，在构造因素模型中，我们假设两个证券的回报率相关一起运动仅仅是因为它们对因素运动的共同反应导致的。- 第三，证券回报率中不能由因素模型解释的部分是该证券所独有的，从而与别的证券回报率

9、的特有部分无关，也与因素的运动无关。6-10n因素模型在证券组合管理中的应用- 在证券组合选择过程中，减少估计量和计算量- 刻画证券组合对因素的敏感度n如果假设证券回报率满足因素模型，那么证券分析的基本目标就是，辨别这些因素以及证券回报率对这些因素的敏感度。6-11 ri = E(ri) + iF + eii = index of a securities particular return to the factorF= some macro factor; in this case F is unanticipated movement; F is commonly related to

10、security returnsAssumption: a broad market index like the S&P500 is the common factor.单一因素模型Single Factor Model6-12随机误差项RANDOM ERROR TERMS- ei 被称为随机误差项CAN BE CONSIDERED A RANDOM VARIABLEuDISTRIBUTION:MEAN = 0,即E(ei)=0VARIANCE = s 2ei 任意证券 i 的随机项 ei 与因素F不相关; 任意证券 i 与证券 j 的随机项 ei与 ej 不相关,cov(ei,ej

11、)=06-13- 表表6-1 因素模型数据因素模型数据n年份 GDP增长率 A股票回报率n 1 5.7% 14.3%n 2 6.4 19.2n 3 7.9 23.4n 4 7.0 15.6n 5 5.1 9.2n 6 2.9 13.06-14n4%trtGDP%0 .136r%2 . 36e%9 . 26GDP6-15n上图中，横轴表示GDP的预期增长率，纵轴表示证券A的回报率。图上的每一点表示表6-1中，在给定的年份，A的回报率与GDP增长率的关系。通过线性回归分析，我们得到一条符合这些点的直线:rt=a+GDPt+et。这条直线的斜率为2，说明A的回报率与GDP增长率有正的关系。GDP增长

12、率越大，A的回报率越高。6-16n在上图中，零因素是4%，这是GDP的预期增长率为零时，A的回报率。A的回报率对GDP增长率的敏感度为2，这是图中直线的斜率。这个值表明，高的GDP的预期增长率一定伴随着高的A的回报率。如果GDP的预期增长率是5%，则A的回报率为14%。如果GDP的预期增长率增加1%为6%时，则A的回报率增加2%，或者为16%。6-17n在这个例子里，第六年的GDP的预期增长率为2.9%，A的实际回报率是13%。因此，A的回报率的特有部分（由 ei 给出）为3.2%。给定GNP的预期增长率为2.9%，从A的实际回报率13%中减去A的期望回报率9.8%，就得到A的回报率的特有部分

13、3.2%。6-18市场模型THE MARKET MODELn在实际应用过程中常用证券市场组合来作为影响证券价格的单因素，此时的单因素模型被称为市场模型。市场模型实际上是单因素模型的一个特例。 ri = E(ri ) + i rM-E（ rM ）+ eirM ：市场组合的实际收益率E（ rM ）：市场组合的期望收益率6-19(ri - rf) = i + i(rm - rf) + eia aRisk Prem（股票持有期超额收益）（股票持有期超额收益）Market Risk Prem or Index Risk Premi= the stocks expected return if the m

14、arkets excess return is zeroi(rm - rf) = the component of return due to movements in the market index(rm - rf) = 0 ei = firm specific component, not due to market movementsa a单一指数模型Single Index Model6-20Let: Ri = (ri - rf) Rm = (rm - rf)Risk premiumformatRi = a ai + i(Rm) + eiRisk Premium Format6-21

15、证券特征线Security Characteristic LineExcess Returns (i)SCL. . . .Excess returnson market indexRi = a a i + iRm + ei. .Ri =i + iRm6-22Jan.Feb.DecMeanStd Dev5.41-3-.604.9.901.753.32ExcessMkt. Ret.ExcessGM Ret.Using the Text Example from Table 8-56-23Estimated coefficientStd error of esti

16、mateVariance of residuals = 12.601Std dev of residuals = 3.550R-SQR = 0.575-2.590(1.547)1.1357(0.309)rGM - rf = + (rm - rf)a aa a回归结果Regression Results6-24n市场风险或系统风险Market or systematic risk: risk related to the macro economic factor or market index.n非系统性风险或公司特有的风险Unsystematic or firm specific risk:

17、 risk not related to the macro factor or market index.nTotal risk = Systematic + Unsystematic风险构成Components of Risk6-25风险：系统性和非系统性风险Risk: Systematic and Unsystematicn 系统性风险会影响到大部分资产A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree.n 非系统性风险只会影响到单一

18、资产或某一小类的资产。非系统性风险可以被分散掉。An unsystematic risk is a risk that specifically affects a single asset or small group of assets. Unsystematic risk can be diversified away.n 系统性风险包括那些一般经济状态的不确定性，如GNP、利率、通货膨胀等。Examples of systematic risk include uncertainty about general economic conditions, such as GNP, int

19、erest rates, or inflation. n 换句话说，一个公司特定的消息，如金矿开采公司发现黄金，就是非系统性风险。On the other hand, announcements specific to a company, such as a gold mining company striking gold, are examples of unsystematic risk.6-26风险各组成部分的衡量Measuring Components of Risksi2 = i2 sm2 + s2(ei)where;si2 = 总方差（total variance）i2 sm2

20、 = 系统性方差（systematic variance）s2(ei) = 非系统性方差（unsystematic variance）sij=cov(ri,rj)=i j sm26-27随机误差项ei THE RANDOM ERROR TERMS einTHE RANDOM ERROR TERMS ei- 显示因素模型不能解释的部分shows that the factor model cannot explain perfectly- 实际收益和因素模型预期的收益之间的差异就是ei （the difference between what the actual return value is

21、 and what the model expects it to be is attributable to ei）6-28Total Risk = Systematic Risk + Unsystematic RiskSystematic Risk/Total Risk = R2i2 s m2 / s2 = R2i2 sm2 / i2 sm2 + s2(ei) = R2Examining Percentage of Variance6-29风险分散国际经验 6-306-31)(22221222)(11PMPNieieNiiiPNiiiPPmPPPeXXXeRRpiPssssaaas指数模型

22、和分散化Index Model and Diversification6-32分散化DIVERSIFICATIONuUnique Riskmathematically can be expressed asNieiePN12221ssNNeNee22221.1sss6-33分散化DIVERSIFICATIONn总组合的风险TOTAL PORTFOLIO RISK- also has two parts: market and uniqueuMarket Risk分散化会导致市场风险的平均化（diversification leads to an averaging of market risk

23、）uUnique Risk越是分散化的组合，其非系统性的风险越小（as a portfolio becomes more diversified, the smaller will be its unique risk）6-34风险降低和分散化Risk Reduction with DiversificationNumber of SecuritiesSt. DeviationMarket RiskUnique Risks s2(eP)=s s2(e) / n P2s sM26-35nReduces the number of inputs for diversification.nEasie

24、r for security analysts to specialize.单一指数的优点Advantages of the Single Index Model6-36Determining the inputs needed for locating the efficient set 1nMarkowitz: expected returns: N variances: N covariances: (N2-N)/2 Total: (N2+3N)/26-37Determining the inputs needed for locating the efficient set 2n In

25、dex model:n For the market index:n expected return 1n variance 1n For each securityn vertical intercept Nn Beta Nn Variance of random error term Nn TOTAL 3N+26-38n 假定有反映中国股市整体情况的中证300指数，有无风险利率存在。估算期为1年，计算出每月同方公司的平均收益水平和中国股市月平均收益水平（虚拟数据），结果如下。6-39n 同方股票的超额收益与市场超额收益的关系有下式：n RTFt=TF+TFRMt+eTFt n 将这12组数

26、据带入上式进行回归，得到结果如下：6-40 截距为截距为-0.11%，斜率为，斜率为0.36，残值的方差反映了同，残值的方差反映了同方公司特有因素对同方股票收益的影响程度，表中的方公司特有因素对同方股票收益的影响程度，表中的R2表示的是表示的是rI与与rM之间的相关性的平方，它是总方差之间的相关性的平方，它是总方差上的系统方差，它告诉我们公司股价小量波动是由市上的系统方差，它告诉我们公司股价小量波动是由市场波动造成的。场波动造成的。6-41n 美林公司用S&P500指数作为市场资产组合，以最近60个月的每月均值来计算回归参数。为了简便，用总收益代替了模型中的超额收益，要估计的模型变成n

27、 r =+ rM +e* n 只要rf是常数，回归结果就是一样的。式中的值和市场风险s2M与公司特有风险s2(e)，都可以从证券特征线中估计出来，美林公司将其评估结果按月刊登在它出版的月刊证券风险评估中，人们通常将其称为“手册”。以下是手册中的几行。n 6-42多因素模型Multifactor Modelsn 单因素模型（市场模型）假设市场组合收益的变化包括了所有的风险因素，而且（不正确地）假设任何一种股票对每种风险的相对敏感度都一样 Use factors in addition to market return Estimate a beta for each factor using m

28、ultiple regressionuse more than one explanatory variable in the return-generating process6-43系统性风险和 Systematic Risk and BetasnFor example, suppose we have identified three systematic risks on which we want to focus: Inflation GDP growth spot interest rate6-44多因素模型Rt = a a t + GDPGDPt + IFIFt+ INTINT

29、t+et 6-45Examplen Suppose we have made the following estimates:1.IF = -2.302.GDP = 1.503.INT= 0.50.n Finally, the firm was able to attract a “superstar” CEO and this unanticipated development contributes 1% to the return.n e=1%150. 050. 130. 2SGDPIFFFRR6-46We must decide what surprises took place in

30、 the systematic factors. If it was the case that the inflation rate was expected to be 3%, but in fact was 8% during the time period, then IF = Surprise in the inflation rate= actual expected= 8% - 3%= 5%150. 050. 1%530. 2SGDPFFRR6-47If it was the case that the rate of GDP growth was expected to be

31、4%, but in fact was 1%, then FGDP = Surprise in the rate of GDP growth = actual expected = 1% - 4% = -3%150. 0%)3(50. 1%530. 2SFRR6-48If it was the case that spot interest rate, S, was expected to increase by 10%, but in fact remained stable during the time period, then FS = Surprise in the interest

32、 rate = actual expected = 0% - 10% = -10%1%)10(50. 0%)3(50. 1%530. 2 RR6-49n Finally, if it was the case that the expected return on the stock was 8%, then%8R%12%1%)10(50. 0%)3(50. 1%530. 2%8RR6-50Multifactor ModelsnUse factors in addition to market return- Examples include industrial production, ex

33、pected inflation etc.- Estimate a beta for each factor using multiple regression.6-51MULTIPLE-FACTOR MODELSnMULTIPLE-FACTOR MODELS- some of these factors may includeuTHE GROWTH RATE OF GDPuTHE LEVEL OF INTEREST RATESuTHE YIELD SPREAD BETWEEN CERTAIN VARIABLESuTHE INFLATION RATEuTHE LEVEL OF OIL PRICES6-52多因素模型的应用1n Studies by Roll and Ross and by Chen - 行业生产变动百分比Change in industrial production- 预期通胀变动百分比Change in Unanticipated inflation- 非预期通胀变动百分比Change in expected inflation- 长期公司债券对长期政府债券的超额收益Excess return of lo