单一指数模型 Single Factor Model 每种证券有两种风险来源:市场的或系统的风险,它们的区别源于它们对宏观 经济因素的敏感度,这个差异反映在RM上,以及对公司特有风险的敏感度, 这个差异反映在e上。如果我们记市场超额收益尺M的方差为o2M,则我们可以 把每个股票收益率的方差拆分成两部分 each security has two sources of risk: market or systematic risk, attributable to its sensitivity to macroeconomic factors as reflected in RM, and firm- specific risk, as reflected in e. If we denote the variance of the excess return on the market, RM, as o2M, then we can break the variance of the rate of return on each stock into two components 项目 记号 1.源于一般宏观经济因素的不确定性的方差 β02 2.源于公司特有不确定性的方差
10-11 单一指数模型 Single Factor Model 每种证券有两种风险来源：市场的或系统的风险，它们的区别源于它们对宏观 经济因素的敏感度，这个差异反映在RM上，以及对公司特有风险的敏感度， 这个差异反映在 e上。如果我们记市场超额收益RM的方差为σ2 M，则我们可以 把每个股票收益率的方差拆分成两部分： each security has two sources of risk: market or systematic risk, attributable to its sensitivity to macroeconomic factors as reflected in RM, and firmspecific risk, as reflected in e. If we denote the variance of the excess return on the market, RM, as σ2 M , then we can break the variance of the rate of return on each stock into two components:
单一指数模型 Single Factor Model Rn和e的协方差为零,因为e定义为公司特有的,即独立于 市场的运动。因此证券i的收益率的方差为: The covariance between RM and e i is zero because e; is defined as firm specific, that iS, independent of movements in the market hence the variance of the rate of return on security i equals the sum of the variances due to the common and the firm-specific components O=阝20M+0(e) 10-12
10-12 单一指数模型 Single Factor Model RM 和ei的协方差为零，因为ei定义为公司特有的，即独立于 市场的运动。因此证券i的收益率的方差为： The covariance between RM and e i is zero because e i is defined as firm specific, that is, independent of movements in the market. Hence the variance of the rate of return on security i equals the sum of the variances due to the common and the firm-specific components
单一指数模型 Single Factor Model 两个股票超额收益率的协方差,譬如尺与R;的协方差,仅仅 来自于一般因素RM,因为e和e;都是每个公司特有的,它们 显然不相关。所以,两个股票的协方差为 The covariance between RM and e; is zero because e; is defined as firm specific, that is, independent of movements in the market. Hence the variance of the rate of return on security i equals the sum of the variances due to the common and the firm-specific components Co(R,R,)=Cov(阝RM,B,Rn)=阝B,M 10-13
10-13 单一指数模型 Single Factor Model 两个股票超额收益率的协方差，譬如Ri与 R j 的协方差，仅仅 来自于一般因素RM， 因为e i和e j 都是每个公司特有的，它们 显然不相关。所以，两个股票的协方差为: The covariance between RM and ei is zero because e i is defined as firm specific, that is, independent of movements in the market. Hence the variance of the rate of return on security i equals the sum of the variances due to the common and the firm-specific components:
单一指数模型 Single Factor Model n个期望超额收益E(R)的估计, n个敏感度协方差)估计, n个公司特有方差o2e的估计, 1个(一般)宏观经济因素的方差σ2M的估计 那么,这一计算式就表明这些(3n+1)个估计值将为我们的单指数证券模型准备 好输入的数据。这样,对于有50种证券的资产组合,我们将需要151个估计值,而 不是1325个;对整个纽约证券交易所的大约3000个证券,我们将需要9001个估计 值,而不是大约450万个! These calculations show that if we have n estimates of the expected excess returns, E(Ri n estimates of the sensitivity coefficients, i n estimates of the firm-specific variances, o 1 estimate for the variance of the(common) macroeconomic factor,o then these(3n+1)estimates will enable us to prepare the input list for this single- index security universe. Thus for a 50-security portfolio we will need 151 estimates rather than 1, 325; for the entire New york stock Exchange, about 3, 000 securities we will need 9, 001 estimates rather than approximately 4.5 million!
10-14 单一指数模型 Single Factor Model n个期望超额收益 E(Ri)的估计， n个敏感度协方差 i的估计， n个公司特有方差 σ2 (ei)的估计， 1个（一般）宏观经济因素的方差 σ2 M的估计， 那么，这一计算式就表明这些（ 3n＋1）个估计值将为我们的单指数证券模型准备 好输入的数据。这样，对于有 50种证券的资产组合，我们将需要151个估计值，而 不是1325 个；对整个纽约证券交易所的大约 3000 个证券，我们将需要9001个估计 值， 而不是大约 450万个！ These calculations show that if we have n estimates of the expected excess returns, E(Ri) n estimates of the sensitivity coefficients, i n estimates of the firm-specific variances, σ2 (ei) 1 estimate for the variance of the (common) macroeconomic factor, σ2 M then these (3n+1) estimates will enable us to prepare the input list for this singleindex security universe. Thus for a 50-security portfolio we will need 151 estimates rather than 1,325; for the entire New York Stock Exchange, about 3,000 securities, we will need 9,001 estimates rather than approximately 4.5 million!
证券特征线 Security Characteristic Line 证券超额收益 Excess returns(i SCL 市场指数超额收益 Excess returns on market index R i=ai+B RM+e
10-15 证券特征线 Security Characteristic Line 证券i超额收益Excess Returns (i) SCL . . . .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 市场指数超额收益 Excess returns on market index Ri = a i + ßiRM + ei . .