1、Arbitrage Pricing Theory and Multifactor Models of Risk and Return套利定價理論與多因素模型10-2Single Factor Model單因素模型Returns on a security come from two sources 證券收益有兩大源泉 Common macro-economic factor 公共宏觀經(jīng)濟(jì)因素 Firm specific events 公司特有事件Possible common macro-economic factors 可能的公共宏觀經(jīng)濟(jì)因素 Gross Domestic Product G

2、rowth 國內(nèi)生產(chǎn)總值的增長 Interest Rates 利率10-3Single Factor Model Equation單因素模型公式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 events( )iiiirE rFei10-4Multifactor Models多因素模型 Use m

3、ore than one factor in addition to market return 除市場收益外,不止使用一個因素 Examples include gross domestic product, expected inflation, interest rates etc. 例子包括國內(nèi)生產(chǎn)總值,期望的通貨膨脹,利率等 Estimate a beta or factor loading for each factor using multiple regression.使用多元回歸去估計一個貝塔值或每個因素的因子載荷10-5Multifactor Model Equation多

4、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 = Factor sensitivity for Interest Rate ei = Firm specific eventsiiii10-6Multifactor SML Models多因素證券市場線的模型E(r) = rf + GDPRPGDP + IRRPIR GDP = Factor sensitivity for GDP RPGDP = Risk premium for GDP I

5、R = Factor sensitivity for Interest RateRPIR = Risk premium for Interest Rateiiii10-7Arbitrage Pricing Theory套利定價理論 Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit 套利-通過零投資組合而獲得無風(fēng)險利潤 Since no investment is required, an investor can create large position

6、s to secure large levels of profit 由于沒有投資是必需的，投資者可以構(gòu)建大量的投資組合以確保大的利潤水平 In efficient markets, profitable arbitrage opportunities will quickly disappear 在有效市場中,這種套利機(jī)會會迅速消失10-8APT & Well-Diversified Portfolios套利定價理論及充分分散的投資組合rP = E (rP) + PF + ePF = some factor For a well-diversified portfolio: eP a

7、pproaches zeroSimilar to CAPM,10-9Figure 10.1 Returns as a Function of the Systematic Factor作為系統(tǒng)因素函數(shù)的收益10-10Figure 10.2 Returns as a Function of the Systematic Factor: An Arbitrage Opportunity出現(xiàn)了套利機(jī)會10-11Figure 10.3 An Arbitrage Opportunity套利機(jī)會10-12Figure 10.4 The Security Market Line證券市場線10-13APT a

8、pplies to well diversified portfolios and not necessarily to individual stocks 套利定價理論可應(yīng)用于充分分散的投資組合,不必用于單個股票With APT it is possible for some individual stocks to be mispriced - not lie on the SML 套利定價理論使一些單個股票被錯誤標(biāo)價成為可能,而不依靠證券市場線APT is more general in that it gets to an expected return and beta relati

9、onship without the assumption of the market portfolio APT更普遍,因為它可以不經(jīng)市場投資組合假設(shè)而達(dá)到預(yù)期回報和貝塔的關(guān)系 APT can be extended to multifactor modelsAPT能夠拓展到多因素模型APT and CAPM Compared套利定價理論與資本資產(chǎn)定價模型的對照10-14Multifactor APT多因素套利定價理論Use of more than a single factor 不止利用一個因素Requires formation of factor portfolios 需要形成因素投

10、資組合What factors? 哪些因素?1. Factors that are important to performance of the general economy 那些對于整體經(jīng)濟(jì)的績效很重要的因素Fama-French Three Factor Model法瑪-弗倫奇的三因素模型10-15Two-Factor Model雙因素模型 The multifactor APR is similar to the one-factor case 多因素套利定價規(guī)則與單因素相似 But need to think in terms of a factor portfolio 但是須以單

11、因素投資組合進(jìn)行考慮 Well-diversified 充分分散化 Beta of 1 for one factor Beta of 0 for any other1122( )iiiiirE rFFe10-16Example of the Multifactor Approach以多因素方法為例 Work of Chen, Roll, and Ross 陳,羅爾和羅斯的工作Chose a set of factors based on the ability of the factors to paint a broad picture of the macro-economy根據(jù)因素描述整

12、個宏觀經(jīng)濟(jì)的能力選擇以下因素的集合10-17Another Example:Fama-French Three-Factor Model又如:法瑪-弗倫奇三因素模型 The factors chosen are variables that on past evidence seem to predict average returns well and may capture the risk premiumsWhere: SMB = Small Minus Big, i.e., the return of a portfolio of small stocks in excess of t

13、he 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 ratioitiiMMtiSMBtiHMLtitrRSMBHMLe10-18The Multifactor CAPM and the APM多因素資本資產(chǎn)定價和套利定價模型 A multi-index CAPM will inherit its risk factors f