套利定价理论与多因素模型.ppt

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1、CHAPTER 10Arbitrage Pricing Theory and Multifactor Models of Risk and Return套利定价理论与多因素模型10-2Single 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 Pr

2、oduct Growth 国内生产总值的增长Interest Rates 利率10-3Single Factor Model Equation单因素模型公式ri=Return for security I =Factor sensitivity or factor loading or factor betaF=Surprise in macro-economic factor(F could be positive,negative or zero)ei=Firm specific events10-4Multifactor Models多因素模型Use more than one fact

3、or 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10-5Multifactor Model Equation多因素模型公式ri=E(ri)+GDP GD

4、P +IR IR+ei ri =Return for security i GDP=Factor sensitivity for GDP IR =Factor sensitivity for Interest Rate ei =Firm specific events10-6Multifactor 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 RateRPIR =R

5、isk premium for Interest Rate10-7Arbitrage 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 levels of profit 由于没有投资是必需的，投资者可以构建大量的

6、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10-8APT&Well-Diversified Portfolios套利定价理论及充分分散的投资组合rP=E(rP)+bPF+ePF=some factorFor a well-diversified portfolio:eP approaches zeroSimilar to CAPM,10-9Figure 10.1 Returns as a Function of the

7、 Systematic Factor作为系统因素函数的收益10-10Figure 10.2 Returns as a Function of the Systematic Factor:An Arbitrage Opportunity出现了套利机会10-11Figure 10.3 An Arbitrage Opportunity套利机会10-12Figure 10.4 The Security Market Line证券市场线10-13APT applies to well diversified portfolios and not necessarily to individual sto

8、cks 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

9、达到预期回报和贝塔的关系 APT can be extended to multifactor modelsAPT能够拓展到多因素模型APT and CAPM Compared套利定价理论与资本资产定价模型的对照10-14Multifactor 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?1.Factors that are important to performance of the gener

10、al 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10-15Two-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 1 for one factor Beta of 0 for any other1

11、0-16Example 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10-17Another Example:Fama-French Three-Factor Model又如:法玛-弗伦奇三因素模型The factors chosen are

12、variables that on past evidence seem to predict average returns well and may capture the risk premiumsWhere:SMB=Small Minus Big,i.e.,the return of a portfolio of small stocks in excess of the return on a portfolio of large stocksHML=High Minus Low,i.e.,the return of a portfolio of stocks with a high

13、 book to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratio10-18The 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 riskAPT没有指明何处寻找风险定价来源