第六章因子模型和套利定价 理论(APT)
第六章 因子模型和套利定价 理论（APT）
系统风险与非系统风险 ■单因子模型 ■多因子模型 套利和套利定价
◼ 系统风险与非系统风险 ◼ 单因子模型 ◼ 多因子模型 ◼ 套利和套利定价
1.系统风险与非系统风险 ■经济系统中的某些共同因素影响几乎所 有的公司 ■商业周期、利率、GDP增长率、技术进步 劳动和原材料的成本、通货膨胀率 ■这些变量不可预期的变化将导致整个证券市 场回报率的不可预期变化
1. 系统风险与非系统风险 ◼ 经济系统中的某些共同因素影响几乎所 有的公司 ◼ 商业周期、利率、GDP增长率、技术进步、 劳动和原材料的成本、通货膨胀率 ◼ 这些变量不可预期的变化将导致整个证券市 场回报率的不可预期变化
Therefore the risk of asset returns can be broken down into two sources a small number of common factors which proxy for economic events that affect almost all assets changes in interest rates inflation and productivit These represent systematic risk which cannot be diversified away. a risk component that is unique to the asset new product innovations changes in management, lawsuits labor strikes, etc These are Non-systematic idiosyncratic, or firm-specific risk which typically is diversifiable We call these equations which break down an asset's return into these two components factor models
◼ Therefore, the risk of asset returns can be broken down into two sources: ◼ A small number of common factors which proxy for economic events that affect almost all assets. ◼ changes in interest rates, inflation, and productivity. ◼ These represent Systematic risk, which cannot be diversified away. ◼ A risk component that is unique to the asset. ◼ new product innovations, changes in management, lawsuits, labor strikes, etc. ◼ These are Non-systematic idiosyncratic, or firm-specific risk, which typically is diversifiable. ◼ We call these equations which break down an asset's return into these two components factor models
例子:市玚模型 V=C;+);r+E 这里 F=在给定的时间区间,证券的回报率 r,=在同一时间区间,市场指标的回报 率 On=截矩项 Bn=斜率项 nE,=公司特有风险,满足 Ele =0 Cov(ei, 1=0 Cov[em, r=0
◼ 例子：市场模型 ◼ 这里 ◼ =在给定的时间区间，证券 i 的回报率 ◼ =在同一时间区间，市场指标 I 的回报 率 ◼ =截矩项 ◼ =斜率项 ◼ =公司特有风险，满足 i i I i I I i I r = + r + i r I r iI iIiI E iI = 0 Cov iI ,rI = 0 , = 0 iI jI Cov r
■例如:i为海尔股票,j为五粮液股票,I为 上证指数 ■海尔公司股票方差可以分解为 systematic risk non-systematic risk non-diversifiable risk diversifiable risk market risk unique or firm-specific risk
◼ 例如：i 为海尔股票，j 为五粮液股票，I 为 上证指数 ◼ 海尔公司股票方差可以分解为 ◼ = systematic risk + non-systematic risk ◼ = non-diversifiable risk + diversifiable risk ◼ = market risk + unique or firm-specific risk
■注意:市场模型与SML的区别 ■市场模型是统计模型,SML是理论结果 ■市场模型描述实现回报率,SML描述期望回 报率 ■市场模型可以分解为期望部分与非期望部分 r=an+B,1+B1(1-)+En B,r-r)+eu
◼ 注意：市场模型与SML的区别 ◼ 市场模型是统计模型， SML是理论结果 ◼ 市场模型描述实现回报率， SML描述期望回 报率 ◼ 市场模型可以分解为期望部分与非期望部分 ( ) i i I i I I i I i I i I r = + r + r − r + ( ) i i I i I i I = r + r − r +
例子:Fe公司股票的下一个月回报率 r=R+U 这里 R表示实际月回报率 R表示期望回报率 U表示回报率的非期望部分
◼ 例子：Flyer公司股票的下一个月回报率 ◼ 这里 ◼ 表示实际月回报率 ◼ 表示期望回报率 ◼ 表示回报率的非期望部分 R = R +U R R U
期望回报率是市场中投资者预期到的回报率, 依赖于投资者现在获得地关于该种股票的所有 信息,以及投资者对何种因素影响回报率地全 部了解
◼ 期望回报率是市场中投资者预期到的回报率， 依赖于投资者现在获得地关于该种股票的所有 信息，以及投资者对何种因素影响回报率地全 部了解
■回报率的非期望部分由下一个月内显示地信息导致, 例如 News about flyers'research Government figures released on the gross national product(Gnp) Results of the latest arms-control talks Discovery that a rival' s product has been tampered with News that Fleyers' sales figures are higher than expected a sudden drop in interest rates The unexpected retirement of Flyers founder and president
◼ 回报率的非期望部分由下一个月内显示地信息导致， 例如 ◼ News about Flyers’research ◼ Government figures released on the gross national product (GNP) ◼ Results of the latest arms-control talks ◼ Discovery that a rival’s product has been tampered with ◼ News that Fleyers’sales figures are higher than expected ◼ A sudden drop in interest rates ◼ The unexpected retirement of Flyers’founder and president