第10章 单一指数和多因素模型 Single index and multifactor models 10-1
10-1 第10章 单一指数和多因素模型 Single Index and Multifactor Models
单一指数和多因素模型 Single index and multifactor models 10.1单一指数证券市场 10.2CAPM模型与指数模型 10.3指数模型的行业性 104多因素模型 10-2
10-2 单一指数和多因素模型 Single Index and Multifactor Models 10.1 单一指数证券市场 10.2 CAPM模型与指数模型 10.3 指数模型的行业性 10.4 多因素模型
单一指数模型的优势 Advantages of the Single Index Model 假定证券分析人员能详细地分析50种股票,这意味着需要 输入如下这些数据: Suppose your security analysts can thoroughly analyze 50 stocks. This means that your input list will include the following n=50个期望收益的估计( estimates of expected returns) n=50个方差估计( estimates of variances) (n2-n)/2=1225个协方差估计( estimates of covariances 1325个估计值( estimates 10-3
10-3 假定证券分析人员能详细地分析50种股票,这意味着需要 输入如下这些数据： Suppose your security analysts can thoroughly analyze 50 stocks. This means that your input list will include the following: n＝50个期望收益的估计 (estimates of expected returns) n＝50个方差估计 (estimates of variances) (n 2 -n)/2＝1225 个协方差估计 (estimates of covariances) 1325个估计值 (estimates) 单一指数模型的优势 Advantages of the Single Index Model
单一指数模型的优势 Advantages of the Single Index Model ■减少输入数量 Reduces the number of inputs for diversification 简化证券分析 Easier for security analysts to specialize
10-4 减少输入数量 Reduces the number of inputs for diversification. 简化证券分析 Easier for security analysts to specialize. 单一指数模型的优势 Advantages of the Single Index Model
单一指数模型 Single Factor Model 证券的持有期收益: The holding- period return on security iis: r =E(ri+mi +e E(r)是证券持有期期初的期望收益,m;是在证券持有期间非预期 的宏观事件对证券收益的影响,e;是非预期的公司特有事件的影 E(r is the expected return on the security as of the beginning of the holding period, m is the impact of unanticipated macro events on the security's return during the period, and e is the impact of unanticipated firm-specific events 10-5
10-5 证券i的持有期收益： The holding-period return on security i is: ri = E(ri )+mi +ei E(ri )是证券持有期期初的期望收益, mi 是在证券持有期间非预期 的宏观事件对证券收益的影响，ei 是非预期的公司特有事件的影 响。 E(ri ) is the expected return on the security as of the beginning of the holding period, mi is the impact of unanticipated macro events on the security’s return during the period, and ei is the impact of unanticipated firm-specific events. 单一指数模型 Single Factor Model
单一指数模型 Single Factor Model B1=证券i对宏观因素的敏感度 the responsiveness of security i to macro events F=宏观因素的非预测成分,与证券收益有关 some macro factor; in this case F is unanticipated movement F is commonly related to security returns 假设:主要证券市场指数,譬如标准普尔500指数的收益率,是 般宏观因素的有效代表 Assumption a broad market index like the s&P500 is the common factor r=E(r)+βF+e1 10-6
10-6 ßi =证券 i 对宏观因素的敏感度 the responsiveness of security i to macro events F=宏观因素的非预测成分,与证券收益有关 some macro factor; in this case F is unanticipated movement; F is commonly related to security returns 假设：主要证券市场指数，譬如标准普尔500指数的收益率，是 一般宏观因素的有效代表。 Assumption: a broad market index like the S&P500 is the common factor. ri = E(ri )+βiF +ei 单一指数模型 Single Factor Model
单一指数模型 Single Factor Model 根据指数模型,依照与等式10-2相似的原理,我们可 以把实际的或已实现的证券收益率区分成宏观(系统) 的与微观(公司特有)的两部分。我们把每个证券的 收益率写成三个部分的总和: According to the index model, we can separate the actual or realized rate of return on a security into macro(systematic) and micro(firm-specific components in a manner similar to that in equation 10.2. We write the rate of return on each security as a sum of three components
10-7 根据指数模型，依照与等式 10-2相似的原理，我们可 以把实际的或已实现的证券收益率区分成宏观（系统） 的与微观（公司特有）的两部分。我们把每个证券的 收益率写成三个部分的总和： According to the index model, we can separate the actual or realized rate of return on a security into macro (systematic) and micro (firm-specific) components in a manner similar to that in equation 10.2. We write the rate of return on each security as a sum of three components: 单一指数模型 Single Factor Model
单一指数模型 Single Factor Model 项目 记号 如果市场是中性的,即市场超额收益ryr为零时的股票预期收益率 2随整个市场运动的收益成分,阝是证券对市场运动的敏感度 (y) 由于只与这个证券(公司特有)相关的非预期事件形成的非预期成分 Symbol 1. The stock's expected return if the market is neutral, that is if the market's excess return, IM-If is zero 2. The component of return due to movements in the overall market; B; is the security' s responsiveness to market movements β;(rM-t) 3. The unexpected component due to unexpected events that are relevant only to this security(firm specific)
10-8 单一指数模型 Single Factor Model
单一指数模型 Single Factor Model (r;-r)=o;+(r r)+ f 风险溢价 Risk Pren 市场风险溢价 Market risk pren 或指数风险溢价 or index risk pren 10-9
10-9 (ri - rf ) = i + ßi (rm - rf ) + e a i 风险溢价Risk Prem 市场风险溢价Market Risk Prem 或指数风险溢价or Index Risk Prem 单一指数模型 Single Factor Model
风险溢价格式 Risk Premium format Let: R =(r-r) 风险溢价格式 Risk premium Rm=(rmre format 尺代表超过无风险收益的超额收益 excess returns over the risk-free rate R;=01+B(Rm)+e;
10-10 Let: Ri = (ri - rf ) Rm = (rm - rf ) 风险溢价格式 Risk premium format Ri = ai + ßi (Rm) + ei 风险溢价格式 Risk Premium Format R代表超过无风险收益的超额收益 excess returns over the risk-free rate