12-1
第 11章套利定价理论
Arbitrage Pricing Theory
12-2
套利定价理论
Arbitrage Pricing Theory
11.1 套利机会与利润
11.2 套利定价理论 与充分分散的资产组合
11.3 单一资产与 套利定价理论
11.4 套利定价理论 与 CAPM模型
11.5 多因素套利定价理论
12-3
套利定价理论
Arbitrage Pricing Theory
利用证券定价之间的不一致进行资金转移，从中赚取无风险利润的行为称为套利
Arbitrage - arises if an investor can construct a zero
investment portfolio with a sure profit.
无投资需要,投资者可建立大的头寸来获取高利润
Since no investment is required,an investor can
create large positions to secure large levels of profit.
在有效市场内,有利的套利机会会很快消失
In efficient markets,profitable arbitrage opportunities
will quickly disappear.
12-4
当前价格 期望收益 标准差 关系矩阵股票 Current Expected Standard
Stock Price$ Return% Dev.%
A 10 25.0 29.58
B 10 20.0 33.91
C 10 32.5 48.15
D 10 22.5 8.58
套利举例
Arbitrage Example from Text
12-5
均值 标准差 相关系数
Mean S.D,Correlation
ABC组合
Portfolio
A,B,C 25.83 6.40 0.94
D 22.25 8.58
套利组合
Arbitrage Portfolio
12-6
套利行为和收益
Arbitrage Action and Returns
预期收益
E,Ret.
标准方差 St.Dev.
* P
* D
卖空 3份 D股票和 A,B,C股票各买 1份形成组合 P
Short 3 shares of D and buy 1 of A,B & C to form P.
投资者将获取比卖空更高额的回报
You earn a higher rate on the investment than you pay
on the short sale.
12-7
套利定价理论和组合投资
APT & Well-Diversified Portfolios
rP = E (rP) + bPF + eP
F = 一些因素 some factor
对完善的资产组合
For a well-diversified portfolio,
eP 约为零 approaches zero
类似 CAPM Similar to CAPM
12-8
单个证券与投资组合的比较
Comparing a Portfolio with an Individual Security
F
E(r)%
证券组合
Portfolio
F
E(r)%
单个证券
Individual Security
12-9
非均衡举例
Disequilibrium Example
E(r)%
Beta for F
10
7
6无风险
Risk Free 4
AD
C
.5 1.0
12-10
非均衡举例
Disequilibrium Example
卖空组合 C Short Portfolio C
用资金构建一个均衡风险高收益的组合 D
-D与 A和无风险资产相比
Use funds to construct an equivalent risk
higher return Portfolio D.
– D is comprised of A & Risk-Free Asset
百分之一的套利 Arbitrage profit of 1%
12-11
E(r)%
Beta (市场指数 Market
Index)
无风险
Risk Free
M
1.0
[E(rM) - rf]
市场风险益价
Market Risk Premium
套利定价理论和市场指数组
APT with Market Index Portfolio
12-12
套利定价理论有很好的动态组合功能 -除个别股票外。
APT applies to well diversified portfolios and not necessarily to
individual stocks.
套利定价理论是可行的 -对一些不在 SML线上的被错估价格的单个股票。
With APT it is possible for some individual stocks to be mispriced -
not lie on the SML.
套利定价理论在不假设市场组合的条件下可以得出期望收益和 beta 关系。
APT is more general in that it gets to an expected return and beta
relationship without the assumption of the market portfolio.
套利定价理论可以延伸到多因素模型
APT can be extended to multifactor models.
套利定价理论和资本资产定价模型比较
APT and CAPM Compared
12-13
小结当存在两种或两种以上的证券价格能使投资者构造一个能获得无风险利润的零 投资组合时，（无风险）套利机会就会出现。
A (risk-free) arbitrage opportunity
arises when two or more security
prices enable investors to construct
a zero net investment portfolio that
will yield a sure profit.
12-14
小结理性的投资者将不考虑风险厌恶程度，愿意对套利资产组合拥有尽可能大的头寸。
Rational investors will want to take
infinitely large positions in
arbitrage portfolios regardless of
their degree of risk aversion.
12-15
小结套利机会的存在和大量交易的结果将对证券价格产生压力。这种压力会持续存在直至价格达到排除掉套利的水平。由于会引起巨额的交易，所以只需有一小部分投 资者留意到套利机会就可以启动这个过程。
The presence of arbitrage opportunities and
the resulting large volume of trades will
create pressure on security prices,This
pressure will continue until prices reach
levels that preclude arbitrage,Only a few
investors need to become aware of arbitrage
opportunities。
12-16
小结当证券的价格使无风险套利机会无法存在时，我们便称它们满足了无套利条件。 满足无套利条件的价格关系是重要的，因为我们希望它们在实际的市场中是有效的。
When securities are priced so that there
are no risk-free arbitrage opportunities,
we say that they satisfy the no-
arbitrage condition,Price relationships
that satisfy the no- arbitrage condition
are important because we expect them to
hold in real-world markets.
12-17
小结当一个投资组合包含了大量不同的证券,并且每一种证券占的比例充分小时,我们称这个投资组合为,充分分散化的,。 一种证券的比例在充分分散化的投资组合中是如此之小,以致在所有的实际运作中,该证券收益率的一次理性的变动对该资产组合收益率的影响是可以忽略不计的 。
Portfolios are called,well-diversified” if they
include a large number of securities and the
investment proportion in each is sufficiently small.
The proportion of a security in a well-diversified
portfolio is small enough so that for all practical
purposes a reasonable change in that security’s rate
of return will have a negligible effect on the
portfolio’s rate of return.
12-18
小结在单因素证券市场中，为了满足无套利条件，所有充分分散化的投资组合必须 满足证券市场曲线的期望收益 - 关系。
In a single-factor security market,all
well-diversified portfolios have to satisfy
the expected return–beta relationship of
the security market line to satisfy the no-
arbitrage condition.
12-19
小结如果所有充分分散化的投资组合满足期望收益 -关系，那么除了一小部分以外,所有的证券也必须满足该关系。
If all well-diversified portfolios
satisfy the expected return–beta
relationship,then all but a small
number of securities also must
satisfy this relationship.
12-20
小结无套利条件与在套利定价理论的简单形式下作出的单因素证券市场假定一起,包含了与资本资产定价模型中相同的期望收益 - 关系,但它并不要求以 CAPM中的严格假定和 （ 难以观测的 ） 市场投资组合为基础 。 这个一般化的代价是 APT不能保证期望收益 - 关系在所有时候对所有的证券都成立 。
The assumption of a single-factor security market
made in the simple version of the APT,together
with the no-arbitrage condition,implies the same
expected return–beta relationship as does the CAPM,
yet it does not require the restrictive
assumptions of the CAPM and its (unobservable)
market portfolio,The price of this generality is
that the APT does not guarantee this relationship
for all securities at all times.
12-21
小结多因素 APT将单因素模型一般化，使其适用于有多种风险来源的情况。
A multifactor APT generalizes the
single-factor model to accommodate
several sources of systematic risk.
第 11章套利定价理论
Arbitrage Pricing Theory
12-2
套利定价理论
Arbitrage Pricing Theory
11.1 套利机会与利润
11.2 套利定价理论 与充分分散的资产组合
11.3 单一资产与 套利定价理论
11.4 套利定价理论 与 CAPM模型
11.5 多因素套利定价理论
12-3
套利定价理论
Arbitrage Pricing Theory
利用证券定价之间的不一致进行资金转移，从中赚取无风险利润的行为称为套利
Arbitrage - arises if an investor can construct a zero
investment portfolio with a sure profit.
无投资需要,投资者可建立大的头寸来获取高利润
Since no investment is required,an investor can
create large positions to secure large levels of profit.
在有效市场内,有利的套利机会会很快消失
In efficient markets,profitable arbitrage opportunities
will quickly disappear.
12-4
当前价格 期望收益 标准差 关系矩阵股票 Current Expected Standard
Stock Price$ Return% Dev.%
A 10 25.0 29.58
B 10 20.0 33.91
C 10 32.5 48.15
D 10 22.5 8.58
套利举例
Arbitrage Example from Text
12-5
均值 标准差 相关系数
Mean S.D,Correlation
ABC组合
Portfolio
A,B,C 25.83 6.40 0.94
D 22.25 8.58
套利组合
Arbitrage Portfolio
12-6
套利行为和收益
Arbitrage Action and Returns
预期收益
E,Ret.
标准方差 St.Dev.
* P
* D
卖空 3份 D股票和 A,B,C股票各买 1份形成组合 P
Short 3 shares of D and buy 1 of A,B & C to form P.
投资者将获取比卖空更高额的回报
You earn a higher rate on the investment than you pay
on the short sale.
12-7
套利定价理论和组合投资
APT & Well-Diversified Portfolios
rP = E (rP) + bPF + eP
F = 一些因素 some factor
对完善的资产组合
For a well-diversified portfolio,
eP 约为零 approaches zero
类似 CAPM Similar to CAPM
12-8
单个证券与投资组合的比较
Comparing a Portfolio with an Individual Security
F
E(r)%
证券组合
Portfolio
F
E(r)%
单个证券
Individual Security
12-9
非均衡举例
Disequilibrium Example
E(r)%
Beta for F
10
7
6无风险
Risk Free 4
AD
C
.5 1.0
12-10
非均衡举例
Disequilibrium Example
卖空组合 C Short Portfolio C
用资金构建一个均衡风险高收益的组合 D
-D与 A和无风险资产相比
Use funds to construct an equivalent risk
higher return Portfolio D.
– D is comprised of A & Risk-Free Asset
百分之一的套利 Arbitrage profit of 1%
12-11
E(r)%
Beta (市场指数 Market
Index)
无风险
Risk Free
M
1.0
[E(rM) - rf]
市场风险益价
Market Risk Premium
套利定价理论和市场指数组
APT with Market Index Portfolio
12-12
套利定价理论有很好的动态组合功能 -除个别股票外。
APT applies to well diversified portfolios and not necessarily to
individual stocks.
套利定价理论是可行的 -对一些不在 SML线上的被错估价格的单个股票。
With APT it is possible for some individual stocks to be mispriced -
not lie on the SML.
套利定价理论在不假设市场组合的条件下可以得出期望收益和 beta 关系。
APT is more general in that it gets to an expected return and beta
relationship without the assumption of the market portfolio.
套利定价理论可以延伸到多因素模型
APT can be extended to multifactor models.
套利定价理论和资本资产定价模型比较
APT and CAPM Compared
12-13
小结当存在两种或两种以上的证券价格能使投资者构造一个能获得无风险利润的零 投资组合时，（无风险）套利机会就会出现。
A (risk-free) arbitrage opportunity
arises when two or more security
prices enable investors to construct
a zero net investment portfolio that
will yield a sure profit.
12-14
小结理性的投资者将不考虑风险厌恶程度，愿意对套利资产组合拥有尽可能大的头寸。
Rational investors will want to take
infinitely large positions in
arbitrage portfolios regardless of
their degree of risk aversion.
12-15
小结套利机会的存在和大量交易的结果将对证券价格产生压力。这种压力会持续存在直至价格达到排除掉套利的水平。由于会引起巨额的交易，所以只需有一小部分投 资者留意到套利机会就可以启动这个过程。
The presence of arbitrage opportunities and
the resulting large volume of trades will
create pressure on security prices,This
pressure will continue until prices reach
levels that preclude arbitrage,Only a few
investors need to become aware of arbitrage
opportunities。
12-16
小结当证券的价格使无风险套利机会无法存在时，我们便称它们满足了无套利条件。 满足无套利条件的价格关系是重要的，因为我们希望它们在实际的市场中是有效的。
When securities are priced so that there
are no risk-free arbitrage opportunities,
we say that they satisfy the no-
arbitrage condition,Price relationships
that satisfy the no- arbitrage condition
are important because we expect them to
hold in real-world markets.
12-17
小结当一个投资组合包含了大量不同的证券,并且每一种证券占的比例充分小时,我们称这个投资组合为,充分分散化的,。 一种证券的比例在充分分散化的投资组合中是如此之小,以致在所有的实际运作中,该证券收益率的一次理性的变动对该资产组合收益率的影响是可以忽略不计的 。
Portfolios are called,well-diversified” if they
include a large number of securities and the
investment proportion in each is sufficiently small.
The proportion of a security in a well-diversified
portfolio is small enough so that for all practical
purposes a reasonable change in that security’s rate
of return will have a negligible effect on the
portfolio’s rate of return.
12-18
小结在单因素证券市场中，为了满足无套利条件，所有充分分散化的投资组合必须 满足证券市场曲线的期望收益 - 关系。
In a single-factor security market,all
well-diversified portfolios have to satisfy
the expected return–beta relationship of
the security market line to satisfy the no-
arbitrage condition.
12-19
小结如果所有充分分散化的投资组合满足期望收益 -关系，那么除了一小部分以外,所有的证券也必须满足该关系。
If all well-diversified portfolios
satisfy the expected return–beta
relationship,then all but a small
number of securities also must
satisfy this relationship.
12-20
小结无套利条件与在套利定价理论的简单形式下作出的单因素证券市场假定一起,包含了与资本资产定价模型中相同的期望收益 - 关系,但它并不要求以 CAPM中的严格假定和 （ 难以观测的 ） 市场投资组合为基础 。 这个一般化的代价是 APT不能保证期望收益 - 关系在所有时候对所有的证券都成立 。
The assumption of a single-factor security market
made in the simple version of the APT,together
with the no-arbitrage condition,implies the same
expected return–beta relationship as does the CAPM,
yet it does not require the restrictive
assumptions of the CAPM and its (unobservable)
market portfolio,The price of this generality is
that the APT does not guarantee this relationship
for all securities at all times.
12-21
小结多因素 APT将单因素模型一般化，使其适用于有多种风险来源的情况。
A multifactor APT generalizes the
single-factor model to accommodate
several sources of systematic risk.
