套利定价理论与多因素模型

1、CHAPTER 10,Arbitrage Pricing Theory and Multifactor Models of Risk and Return 套利定价理论与多因素模型,Single Factor Model单因素模型,Returns on a security come from two sources 证券收益有两大源泉 Common macro-economic factor 公共宏观经济因素 Firm specific events 公司特有事件 Possible common macro-economic factors 可能的公共宏观经济因素 Gross Domestic Product Growth 国内生产总值的增长 Interest Rates 利率,Single Factor Model Equation单因素模型公式,ri = Return for security I = Factor sensitivity or factor loading or factor beta F = Surprise in macro-economic factor

2、(F could be positive, negative or zero) ei = Firm specific events,Multifactor Models多因素模型,Use more than one factor in addition to market return 除市场收益外,不止使用一个因素 Examples include gross domestic product, expected inflation, interest rates etc. 例子包括国内生产总值,期望的通货膨胀,利率等 Estimate a beta or factor loading for each factor using multiple regression. 使用多元回归去估计一个贝塔值或每个因素的因子载荷,Multifactor Model Equation多因素模型公式,ri = E(ri) + GDP GDP + IR IR + ei ri = Return for security i GDP= Factor sensitivity for GDP IR = Fa

3、ctor sensitivity for Interest Rate ei = Firm specific events,Multifactor SML Models多因素证券市场线的模型,E(r) = rf + GDPRPGDP + IRRPIR GDP = Factor sensitivity for GDP RPGDP = Risk premium for GDP IR = Factor sensitivity for Interest Rate RPIR = Risk premium for Interest Rate,Arbitrage Pricing Theory套利定价理论,Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit 套利-通过零投资组合而获得无风险利润 Since no investment is required, an investor can create large positions to secure large

4、levels of profit 由于没有投资是必需的，投资者可以构建大量的投资组合以确保大的利润水平 In efficient markets, profitable arbitrage opportunities will quickly disappear 在有效市场中,这种套利机会会迅速消失,APT & Well-Diversified Portfolios套利定价理论及充分分散的投资组合,rP = E (rP) + bPF + eP F = some factor For a well-diversified portfolio: eP approaches zero Similar to CAPM,Figure 10.1 Returns as a Function of the Systematic Factor作为系统因素函数的收益,Figure 10.2 Returns as a Function of the Systematic Factor: An Arbitrage Opportunity出现了套利机会,Figure 10.3 An Arbitrage Oppo

5、rtunity套利机会,Figure 10.4 The Security Market Line证券市场线,APT applies to well diversified portfolios and not necessarily to individual stocks 套利定价理论可应用于充分分散的投资组合,不必用于单个股票 With APT it is possible for some individual stocks to be mispriced - not lie on the SML 套利定价理论使一些单个股票被错误标价成为可能,而不依靠证券市场线 APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio APT更普遍,因为它可以不经市场投资组合假设而达到预期回报和贝塔的关系 APT can be extended to multifactor models APT能够拓展

6、到多因素模型,APT and CAPM Compared套利定价理论与资本资产定价模型的对照,Multifactor APT多因素套利定价理论,Use of more than a single factor 不止利用一个因素 Requires formation of factor portfolios 需要形成因素投资组合 What factors? 哪些因素? Factors that are important to performance of the general economy 那些对于整体经济的绩效很重要的因素 Fama-French Three Factor Model 法玛-弗伦奇的三因素模型,Two-Factor Model双因素模型,The multifactor APR is similar to the one-factor case 多因素套利定价规则与单因素相似 But need to think in terms of a factor portfolio 但是须以单因素投资组合进行考虑 Well-diversified 充分分散化 Beta of

7、1 for one factor Beta of 0 for any other,Example of the Multifactor Approach以多因素方法为例,Work of Chen, Roll, and Ross 陈,罗尔和罗斯的工作 Chose a set of factors based on the ability of the factors to paint a broad picture of the macro-economy 根据因素描述整个宏观经济的能力选择以下因素的集合,Another Example:Fama-French Three-Factor Model又如:法玛-弗伦奇三因素模型,The factors chosen are variables that on past evidence seem to predict average returns well and may capture the risk premiums Where: SMB = Small Minus Big, i.e., the return of a portfo

8、lio of small stocks in excess of the return on a portfolio of large stocks HML = High Minus Low, i.e., the return of a portfolio of stocks with a high book to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratio,The Multifactor CAPM and the APM多因素资本资产定价和套利定价模型,A multi-index CAPM will inherit its risk factors from sources of risk that a broad group of investors deem important enough to hedge 多指数CAPM模型从广大投资者认为足够重要的风险因素中导出可以对冲的风险因素 The APT is largely silent on where to look for priced sources of risk APT没有指明何处寻找风险定价来源

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