第10章 套利定价理论与多因素模型
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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
10-7
APT & Well-Diversified Portfolios 套利定价理论及充分分散的投资组合
rP = E (rP) + βPF + eP F = some factor • For a well-diversified portfolio: eP approaches zero Similar to CAPM,
10-8
Figure 10.1 Returns as a Function of the Systematic Factor 作为系统因素函数的收益
10-13
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? 1. 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
10-14
Two-Factor Model 双因素模型
ri = E (ri ) + β i1 F1 + β i 2 F2 + ei
• The multifactor APR is similar to the onefactor 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
10-16
Another Example: Fama-French Thre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 rit = α i + βiM RMt + βiSMB SMBt + βiHML HMLt + eit
10-9
Figure 10.2 Returns as a Function of the Systematic Factor: An Arbitrage Opportunity 出现了套利机会
10-10
Figure 10.3 An Arbitrage Opportunity 套利机会
10-11
Figure 10.4 The Security Market Line 证券市场线
10-5
Multifactor SML Models 多因素证券市场线的模型 E(r) = rf + βiGDPRPGDP + βiIRRPIR
βGDP = Factor sensitivity for GDP i
RPGDP = Risk premium for GDP βi IR = Factor sensitivity for Interest Rate RPIR = Risk premium for Interest Rate
• Where: – SMB = Small Minus Big, i.e., the return of a portfolio 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 10-17
10-6
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 levels of profit
• Well-diversified 充分分散化 • Beta of 1 for one factor • Beta of 0 for any other
10-15
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
10-12
APT and CAPM Compared 套利定价理论与资本资产定价模型的对照
• 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能够拓展到多因素模型
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
10-3
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.
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
10-18
使用多元回归去估计一个贝塔值或每个因素的因子载荷
10-4
Multifactor Model Equation 多因素模型公式 ri = E(ri) + βiGDP GDP + βi IR IR + ei
= Return for security i βi GDP= Factor sensitivity for GDP βiIR = Factor sensitivity for Interest Rate ei = Firm specific events ri
10-2
ri = E (ri ) + βi F + ei
Single Factor Model Equation 单因素模型公式
ri = Return for security I = Factor sensitivity or factor loading or factor βi beta F = Surprise in macro-economic factor (F could be positive, negative or zero) ei = Firm specific events
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
• 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
10-7
APT & Well-Diversified Portfolios 套利定价理论及充分分散的投资组合
rP = E (rP) + βPF + eP F = some factor • For a well-diversified portfolio: eP approaches zero Similar to CAPM,
10-8
Figure 10.1 Returns as a Function of the Systematic Factor 作为系统因素函数的收益
10-13
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? 1. 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
10-14
Two-Factor Model 双因素模型
ri = E (ri ) + β i1 F1 + β i 2 F2 + ei
• The multifactor APR is similar to the onefactor 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
10-16
Another Example: Fama-French Thre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 rit = α i + βiM RMt + βiSMB SMBt + βiHML HMLt + eit
10-9
Figure 10.2 Returns as a Function of the Systematic Factor: An Arbitrage Opportunity 出现了套利机会
10-10
Figure 10.3 An Arbitrage Opportunity 套利机会
10-11
Figure 10.4 The Security Market Line 证券市场线
10-5
Multifactor SML Models 多因素证券市场线的模型 E(r) = rf + βiGDPRPGDP + βiIRRPIR
βGDP = Factor sensitivity for GDP i
RPGDP = Risk premium for GDP βi IR = Factor sensitivity for Interest Rate RPIR = Risk premium for Interest Rate
• Where: – SMB = Small Minus Big, i.e., the return of a portfolio 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 10-17
10-6
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 levels of profit
• Well-diversified 充分分散化 • Beta of 1 for one factor • Beta of 0 for any other
10-15
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
10-12
APT and CAPM Compared 套利定价理论与资本资产定价模型的对照
• 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能够拓展到多因素模型
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
10-3
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.
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
10-18
使用多元回归去估计一个贝塔值或每个因素的因子载荷
10-4
Multifactor Model Equation 多因素模型公式 ri = E(ri) + βiGDP GDP + βi IR IR + ei
= Return for security i βi GDP= Factor sensitivity for GDP βiIR = Factor sensitivity for Interest Rate ei = Firm specific events ri
10-2
ri = E (ri ) + βi F + ei
Single Factor Model Equation 单因素模型公式
ri = Return for security I = Factor sensitivity or factor loading or factor βi beta F = Surprise in macro-economic factor (F could be positive, negative or zero) ei = Firm specific events
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