RiskandReturn投资分析与投资组合管理.ppt
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第十章风险与投资组合
E(R) B0 i Fi
小结
协方差对资产组合风险的影响：正的协方差 提高了资产组合的方差，而负的协方差降低 了资产组合的方差，它稳定资产组合的收益
相关系数 0.12 0.12
投资比重 30% 70%
组合P的期望收益 =( 0.1×0.3+0.05×0.7)×100%=6.5%
组合P的方差=(0.32×0.062) + (0.72 × 0.022 ) + (2 ×0.3×0.7×0.06×0.02×0.12 ) = 0.0327
协方差与相关系数
第九章 市场风险
第一节 收益与风险概述 第二节 投资组合与分散风险 第三节 资产定价理论
第一节 收益与风险概述
价格与回报率 期望收益率
单项资产的风险 投资组合的收益 投资组合的风险
一、价格与回报率
对于单期投资而言，假设你在时间0（今天） 以价格P0购买一种资产，在时间1（明天） 卖出这种资产，得到收益P1。那么，你的投 资回报率为： r=(P1-P0)/P0
证券组合的标准差，并不是单个证券标准差的简单加权平均，证券组合 的风险不仅取决于组合内的各证券的风险，还取决于各个证券之间的关系。
五、两项资产投资组合的风险
已知证券组合P是由证券A和B构成，证券A和B的期望收 益、标准差以及相关系数如下：
证券名称 A B
期望收益率 10% 5%
标准差 6% 2%
系统风险是指整个市场承受到的风险，如经济的景 气情况、市场总体利率水平的变化等因为整个市场 环境发生变化而产生的风险。
二、系统风险与非系统风险
系统风险：是指那些影响所有公司的因素引起的风险，也叫 市场风险。
非系统风险：是指发生于个别公司的特有事件造成的风险， 这种风险是可以通过多样化投资来分散的，因此，也叫可分 散风险。
小结
协方差对资产组合风险的影响：正的协方差 提高了资产组合的方差，而负的协方差降低 了资产组合的方差，它稳定资产组合的收益
相关系数 0.12 0.12
投资比重 30% 70%
组合P的期望收益 =( 0.1×0.3+0.05×0.7)×100%=6.5%
组合P的方差=(0.32×0.062) + (0.72 × 0.022 ) + (2 ×0.3×0.7×0.06×0.02×0.12 ) = 0.0327
协方差与相关系数
第九章 市场风险
第一节 收益与风险概述 第二节 投资组合与分散风险 第三节 资产定价理论
第一节 收益与风险概述
价格与回报率 期望收益率
单项资产的风险 投资组合的收益 投资组合的风险
一、价格与回报率
对于单期投资而言，假设你在时间0（今天） 以价格P0购买一种资产，在时间1（明天） 卖出这种资产，得到收益P1。那么，你的投 资回报率为： r=(P1-P0)/P0
证券组合的标准差，并不是单个证券标准差的简单加权平均，证券组合 的风险不仅取决于组合内的各证券的风险，还取决于各个证券之间的关系。
五、两项资产投资组合的风险
已知证券组合P是由证券A和B构成，证券A和B的期望收 益、标准差以及相关系数如下：
证券名称 A B
期望收益率 10% 5%
标准差 6% 2%
系统风险是指整个市场承受到的风险，如经济的景 气情况、市场总体利率水平的变化等因为整个市场 环境发生变化而产生的风险。
二、系统风险与非系统风险
系统风险：是指那些影响所有公司的因素引起的风险，也叫 市场风险。
非系统风险：是指发生于个别公司的特有事件造成的风险， 这种风险是可以通过多样化投资来分散的，因此，也叫可分 散风险。
投资学课件第3章风险与收益
3
31.3 7% 2
▪ 例：假定投资于某股票，初始价格1 0 0美元，持 有期1年，现金红利为4美元，预期股票价格由如 下三种可能，求其期望收益和方差。
r ( 1 ) ( 1 4 0 1 0 0 4 )/1 0 0 4 4 %
24
25
3.4.3 超额收益与风险溢价
风险资产投资收益=无风险收益+风险溢价
的一半，也就是 ▪ 几何平均值=算术平均值-1／2σ2
3.5.4 方差与标准差
▪ 方差 =期望值偏离的平方(expected value of squared deviations)
▪ 历史数据的方差估计：
2
1 n
n s 1
2
r(s) r
▪ 无偏化处理：
1
n
[r(s)r]2
n1s1
31
3.5.3 报酬-风险比率(夏普比率) The Reward-to-Volatility (Sharpe) Ratio
3.7 偏离正态
▪ 偏度，亦称三阶矩(third-order moments)
skewEr(s)3E(r)3
峰度：度量正态分布两侧尾部的厚度程度。
kurtoEsr(si)s4E(r)43
▪ 正态分布的这个比率为3，正态分布的峰度为0， 任何峰度大于0的分布，相对于正态分布存在厚 尾。
37
图 3.3A 正态与偏度分布 (mean = 6% SD = 17%)
38
图3.3B 正态与厚尾分布 (mean = .1, SD =.2)
39
▪ 在险价值(value at risk, VaR) ▪ 在一定概率下发生极端负收益所造成的损失
。 ▪ VaR即分布的分位数(q)，是指一个处在低于
31.3 7% 2
▪ 例：假定投资于某股票，初始价格1 0 0美元，持 有期1年，现金红利为4美元，预期股票价格由如 下三种可能，求其期望收益和方差。
r ( 1 ) ( 1 4 0 1 0 0 4 )/1 0 0 4 4 %
24
25
3.4.3 超额收益与风险溢价
风险资产投资收益=无风险收益+风险溢价
的一半，也就是 ▪ 几何平均值=算术平均值-1／2σ2
3.5.4 方差与标准差
▪ 方差 =期望值偏离的平方(expected value of squared deviations)
▪ 历史数据的方差估计：
2
1 n
n s 1
2
r(s) r
▪ 无偏化处理：
1
n
[r(s)r]2
n1s1
31
3.5.3 报酬-风险比率(夏普比率) The Reward-to-Volatility (Sharpe) Ratio
3.7 偏离正态
▪ 偏度，亦称三阶矩(third-order moments)
skewEr(s)3E(r)3
峰度：度量正态分布两侧尾部的厚度程度。
kurtoEsr(si)s4E(r)43
▪ 正态分布的这个比率为3，正态分布的峰度为0， 任何峰度大于0的分布，相对于正态分布存在厚 尾。
37
图 3.3A 正态与偏度分布 (mean = 6% SD = 17%)
38
图3.3B 正态与厚尾分布 (mean = .1, SD =.2)
39
▪ 在险价值(value at risk, VaR) ▪ 在一定概率下发生极端负收益所造成的损失
。 ▪ VaR即分布的分位数(q)，是指一个处在低于
财务管理英文第十三版ch 5shen.ppt
R = Dt + (Pt - Pt-1 )
Pt-1
5-3
Return Example
The stock price for Stock A was $10 per share 1 year ago. The stock is currently
trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year?
Chapter 5
Risk and Return
5-1
Risk and Return
Defining Risk and Return Using Probability Distributions to Measure Risk Attitudes Toward Risk Risk and Return in a Portfolio Context Diversification The Capital Asset Pricing Model (CAPM)
/
(
n
)
R is the expected return for the asset,
Ri is the return for the ith observation, n is the total number of observations.
5-14
Determining Standard Deviation (Risk Measure)
R=
$1.00 + ($9.50 - $10.00 ) $10.00
= 5%
5-5
Defining Risk
Pt-1
5-3
Return Example
The stock price for Stock A was $10 per share 1 year ago. The stock is currently
trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year?
Chapter 5
Risk and Return
5-1
Risk and Return
Defining Risk and Return Using Probability Distributions to Measure Risk Attitudes Toward Risk Risk and Return in a Portfolio Context Diversification The Capital Asset Pricing Model (CAPM)
/
(
n
)
R is the expected return for the asset,
Ri is the return for the ith observation, n is the total number of observations.
5-14
Determining Standard Deviation (Risk Measure)
R=
$1.00 + ($9.50 - $10.00 ) $10.00
= 5%
5-5
Defining Risk
投资学第7章最优风险资产组合v1
and the Optimal Risky Portfolio
33
图7.8 Determination of the Optimal Overall Portfolio
34
图7.9 The Proportions of the Optimal Overall Portfolio
35
小结：两种风险资产与无风险资产 组合的配置程序
▪ Covariance and the correlation coefficient provide a measure of the way returns of two assets vary
7-7
Two-Security Portfolio: Return
w r w r rp
DD
EE
rP Portfolio Return
（1）给定收益的条件下，风险最小化 （2）给定风险的条件下，收益最大化
38
11 ... 1n
若已知资产组合收益c、方差 协方差矩阵
M
O
M 和
1n L nn
组合各个资产期望收益向量r=(r1, r2,..., rn )T，求解组合中资产权重
向量w=(w1, w2,..., wn ),则有
nn
30
图7.6 债券与股票基金的可行集和两条可 行的CALs
31
最优风险资产组合P的求解
Max wi
S
P
E(rP ) rf
P
s.t. E(rP ) wD E(rD ) wE E(rE )
P
[ wD2
2 D
wE2
2 E
2wDwECov(rD , rE )]1/ 2
wD wE 1
33
图7.8 Determination of the Optimal Overall Portfolio
34
图7.9 The Proportions of the Optimal Overall Portfolio
35
小结：两种风险资产与无风险资产 组合的配置程序
▪ Covariance and the correlation coefficient provide a measure of the way returns of two assets vary
7-7
Two-Security Portfolio: Return
w r w r rp
DD
EE
rP Portfolio Return
（1）给定收益的条件下，风险最小化 （2）给定风险的条件下，收益最大化
38
11 ... 1n
若已知资产组合收益c、方差 协方差矩阵
M
O
M 和
1n L nn
组合各个资产期望收益向量r=(r1, r2,..., rn )T，求解组合中资产权重
向量w=(w1, w2,..., wn ),则有
nn
30
图7.6 债券与股票基金的可行集和两条可 行的CALs
31
最优风险资产组合P的求解
Max wi
S
P
E(rP ) rf
P
s.t. E(rP ) wD E(rD ) wE E(rE )
P
[ wD2
2 D
wE2
2 E
2wDwECov(rD , rE )]1/ 2
wD wE 1
金融经济学第五章 投资组合理论
24.6% 0.4070*24.6%=10.01%
C
0.3605
22.8%
0.3605*22.8%=8.22%
证券组合的期望回报率= r=p22.00%
20
（二）期望效用分析与均值－方差分析的关系
• 一般来说，资产回报的均值和方差并不能完全包含个 体做选择时所需要的全部信息
• 但在一定条件下，个体的期望效用函数能够仅仅表示 为资产回报的均值和方差的函数，从而投资者可以只 把均值和方差作为选择的目标
这等价于，投资者估计三种股票的期末价格分别 为46.48元[因为（46.48-40）/40=16.2%]、 43.61元[因为（43.61-35）/35=24.6%]和76.14 元[因为（76.14-62）/62=22.8%]。
证券组合期望回报率有几种计算方式，每种方式
得到相同的结果。
17
（1）证券和证券组合的值
掌握均值-方差前沿组合的相关性质.
•通过证券市场投资配置资源的两部分工作：
（１）证券与市场的分析，对投资者可能选择的所有 投资工具的风险及预期收益的特性进行评估。 （２）对资产进行最优的资产组合的构建，涉及在可 行的资产组合中决定最佳风险－收益机会，从可行的 资产组合中选择最好的资产组合。
3
一、现代投资组合理论的起源
• 投资者事先知道资产收益率的概率分布，并且收益率满足 正态分布的条件。
• 经济主体的效用函数是二次的，即u(w)=w-(1/2)αw2, α>0
• 经济主体以期望收益率来衡量未来实际收益率的总体水平， 以收益的方差（或标准差）来衡量收益率的不确定性(风 险)，因而经济主体在决策中只关心资产的期望收益率和 方差。
最后，通过求解二次规划，可以算出有效投资组合的集合，计算结果 指明各种资产在投资者的投资中所占份额，以便实现投资组合的有效性— —即对给定的风险使期望回报率最大化，或对于给定的期望回报使风险最 小化。
投资组合管理第1章
Get prepared for your career or further study Get prepared for the CFA exam Learn some investments knowledge for fun Maybe earn some money in the stock market Earn some credit for your study
of Economic Theory, 13(3):341-360, 1976.
TABLE OF CONTENTS (TENTATIVE)
第五章 普通股分析（（1）第十六、十七、十八章，（2）第十七、十八章） 宏观分析 行业分析 股权估值模型
*第六章 有效市场假说（（1）第四章，（2）第十一、十二章） 有效市场假说 关于效率市场假说的实证研究 行为金融
GRADING(1)
作业：本课程将布置几次平时作业，平时作业需在布 置后第二周上交(以小组为单位完成作业)。
课题：每个小组需完成一个课题，以PPT形式上交。 考试：期末考试闭卷笔试。 成绩计算方法：平时作业 (20%) + 期末课题(20%)
+ 期末考试（60%） 讲座：VC/PE，IPO，私募基金，大家的需求？
There are two reasons for not including advice on “guaranteed” ways to beat the market in this book.
First, to do so would make a successful system public and hence unsuccessful.
Work with financial assets(金融资产) such as stocks and bonds
of Economic Theory, 13(3):341-360, 1976.
TABLE OF CONTENTS (TENTATIVE)
第五章 普通股分析（（1）第十六、十七、十八章，（2）第十七、十八章） 宏观分析 行业分析 股权估值模型
*第六章 有效市场假说（（1）第四章，（2）第十一、十二章） 有效市场假说 关于效率市场假说的实证研究 行为金融
GRADING(1)
作业：本课程将布置几次平时作业，平时作业需在布 置后第二周上交(以小组为单位完成作业)。
课题：每个小组需完成一个课题，以PPT形式上交。 考试：期末考试闭卷笔试。 成绩计算方法：平时作业 (20%) + 期末课题(20%)
+ 期末考试（60%） 讲座：VC/PE，IPO，私募基金，大家的需求？
There are two reasons for not including advice on “guaranteed” ways to beat the market in this book.
First, to do so would make a successful system public and hence unsuccessful.
Work with financial assets(金融资产) such as stocks and bonds
MarketAnalysis(投资分析与投资组合管理).pptx
Questions to be answered:
• How do we apply the basic reduced form dividend discount model (DDM) to the valuation of the aggregate stock market?
• What would be the prevailing value of the market as presented by the S&P DM?
• What are some differences between stock market statistics for the U.S. versus other countries?
Applying the DDM Valuation Model to the Market
• The stream of expected returns
• What would be the prevailing value of the market (S&P 400) based upon the value of free cash flow to equity (FCFE) model?
Chapter 13 Stock Market Analysis
– Return on equity (ROE) – rate of return earned on investment
An increase in either or both of these variables causes an increase in the expected growth rate (g) and an increase in the earnings multiplier
• How do we apply the basic reduced form dividend discount model (DDM) to the valuation of the aggregate stock market?
• What would be the prevailing value of the market as presented by the S&P DM?
• What are some differences between stock market statistics for the U.S. versus other countries?
Applying the DDM Valuation Model to the Market
• The stream of expected returns
• What would be the prevailing value of the market (S&P 400) based upon the value of free cash flow to equity (FCFE) model?
Chapter 13 Stock Market Analysis
– Return on equity (ROE) – rate of return earned on investment
An increase in either or both of these variables causes an increase in the expected growth rate (g) and an increase in the earnings multiplier
投资组合(PPT)
一致。P74
第二十页，共二十九页。
证券市场线：
Ri= Rf＋i ·(Rm－Rf)
上式说明个别证券的报酬来自无风险报酬， 加上受系统风险影响的系统风险报酬。
Ri为证券i的期望收益率〔必要(bìyào)报酬率〕 i为其系统风险指标 〔Ri- Rf〕为证券i的期望超额收益率， (Rm－Rf)为风险的平均补偿水平
报酬的一种系数或倍数。
确定方法：
b=(R – Rf)/w w－标准离差率
b=(最高报酬率-最低报酬率)/〔最高标
准报酬率-最低标准离差率〕×100%
公司(ɡōnɡ sī)领导或者组织专家确定；
国家有关部门组织专家确定。
第五页，共二十九页。
计算风险报酬(bào 的方法： chou)
• 根据(gēnjù)投资额与风险报酬率计算：
• 多角经营(jīngyíng) • 多角筹资
第七页，共二十九页。
认识 投资组合 (rèn shi)
由一种以上的证券或资产构成(gòuchéng)的集合称为 投资组合。
投资组合的预期报酬率为所有个别资产预期
报酬率的加权平均数
E(Ri)＝W1·R1+ W2·R2+ · · · + Wn·Rn
第八页，共二十九页。
第二十一页，共二十九页。
例：无风险证券的报酬率为7%，市场证券 组合(zǔhé)的报酬率为13%。 问：1〕计算市场风险报酬率。
2〕如果某一投资方案的 系数0.8，其短
期的报酬率为12%，是否应该投资？ 3〕如果某证券的期望报酬率是16%，那么 其
系数是多少？
第二十二页，共二十九页。
解：
1〕市场风险报酬率〔市场平均的期望超额(chāo é)收益 率〕
第二十页，共二十九页。
证券市场线：
Ri= Rf＋i ·(Rm－Rf)
上式说明个别证券的报酬来自无风险报酬， 加上受系统风险影响的系统风险报酬。
Ri为证券i的期望收益率〔必要(bìyào)报酬率〕 i为其系统风险指标 〔Ri- Rf〕为证券i的期望超额收益率， (Rm－Rf)为风险的平均补偿水平
报酬的一种系数或倍数。
确定方法：
b=(R – Rf)/w w－标准离差率
b=(最高报酬率-最低报酬率)/〔最高标
准报酬率-最低标准离差率〕×100%
公司(ɡōnɡ sī)领导或者组织专家确定；
国家有关部门组织专家确定。
第五页，共二十九页。
计算风险报酬(bào 的方法： chou)
• 根据(gēnjù)投资额与风险报酬率计算：
• 多角经营(jīngyíng) • 多角筹资
第七页，共二十九页。
认识 投资组合 (rèn shi)
由一种以上的证券或资产构成(gòuchéng)的集合称为 投资组合。
投资组合的预期报酬率为所有个别资产预期
报酬率的加权平均数
E(Ri)＝W1·R1+ W2·R2+ · · · + Wn·Rn
第八页，共二十九页。
第二十一页，共二十九页。
例：无风险证券的报酬率为7%，市场证券 组合(zǔhé)的报酬率为13%。 问：1〕计算市场风险报酬率。
2〕如果某一投资方案的 系数0.8，其短
期的报酬率为12%，是否应该投资？ 3〕如果某证券的期望报酬率是16%，那么 其
系数是多少？
第二十二页，共二十九页。
解：
1〕市场风险报酬率〔市场平均的期望超额(chāo é)收益 率〕
第6章投资风险与投资组合123
证券投资风险的的界定及类型
• 证券投资风险来自哪里？
•市场风险 •利率风险 •通胀风险 •政治风险
•……
•系统性风 险
•风险化解方法
•期货、期 权
•经营风险 •财务风险 •道德风险 •流动性风 险
•……
•非系统风 险
•投资组合
风险溢价
•承担风险的报酬——风险溢价
– 风险溢价是投资者因承担风险而获得的超额 报酬
– 协方差的大小是无限的，从理论上来说，其 变化范围可以从负无穷大到正无穷大。
证券组合的风险
•相关系数
– 根据相关系数的大小，可以判定A、B两证券收益之 间的关联强度。
投资组合协方差的计算
证券A
证券B
年份
收益率 偏差 收益率 偏差
R1
R1k- R1
R2
R2k- R2
偏差 乘积
组合 收益率
(1) (2) (3) (4) (2)*(4)
– 统计上，一般用收益率的标准差（或方差）来度量风 险。
– 标准差反映了投资收益的各种可能结果相对于其期望 值的偏离程度的大小。
•σ——投资收益的标准差 •E（R）——预期收益率 •率Ri ——各种可能的投资收益 •Pi ——收益率事件发生的概率
单一资产期望收益率与风险
•投资风险的衡量指标——标准差（或方差）
•从预期收益率的计算公式可以发现，它是 一个以概率为权数的加权平均数。 •联系前述的历史的收益率的计算公式可以 发现，历史的收益率也是一个加权平均数 ，只是它的权数为1/n。
单一资产期望收益率与风险
•风险衡量——标准差（或方差）
– 为了计量的便利，一般将投资风险定义为投资预期收 益的变异性或波动性(Variability) 。
ManagementStrategies(投资分析与投资组合管理)
Chapter 17 - Equity Portfolio Management Strategies
• What techniques are used by active managers in an attempt to outperform their benchmark?
• What are differences between the integrated, strategic, tactical, and insured approaches to asset allocation?
• Over time value stocks have offered somewhat higher returns than growth stocks
Value versus Growth
• Growth-oriented investor will:
– focus on EPS and its economic determinants
• Replicate the performance of an index • May slightly underperform the target index
due to fees and commissions • Costs of active management (1 to 2 percent)
level
Style
• Construct a portfolio to capture one or more of the characteristics of equity securities
• Small-capitalization stocks, low-P/E stocks, etc…
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= reaction in asset i’s returns to movements in a common bik factor
= a common factor with a zero mean that influences the k returns on all assets
= a unique effect on asset i’s return that, by assumption, is i completely diversifiable in large portfolios and has a mean of zero
Assumptions of CAPM That Were Not Required by APT
APT does not assume • A market portfolio that contains all risky
assets, and is mean-variance efficient • Normally distributed security returns • Quadratic utility function
Arbitrage Pricing Theory (APT)
Rt Et bi1i bi2i ... bik k i
For i = 1 to N where:
Ri = return on asset i during a specified time period
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
Lecture Presentation Software
to accompany
Investment Analysis and Portfolio Management
Seventh Edition by
Frank K. Reilly & Keith C. Brown
Chapter 9
Chapter 9 – Multifactor Models of Risk and Return
– Inflation – Growth in GNP – Major political upheavals – Changes in interest rates – And many more….
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
For i = 1 to N where: Ri = return on asset i during a specified time period
Ei = expected return for asset i
bik = reaction in asset i’s returns to movements in a common factor
Arbitrage Pricing Theory (APT)
Bik determine how each asset reacts to this common factor
Each asset may be affected by growth in GNP, but the effects will differ
For i = 1 to N where: Ri = return on asset i during a specified time period
Ei = expected return for asset i
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP – Major political upheavals
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
• What are multifactor models and how are related to the APT?
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
= reaction in asset i’s returns to movements in a common bik factor
= a common factor with a zero mean that influences the k returns on all assets
= a unique effect on asset i’s return that, by assumption, is i completely diversifiable in large portfolios and has a mean of zero = number of assets N
– Inflation
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP
Arbitrage Pricing Theory (APT)
Ei = expected return for asset i
bik = reaction in asset i’s returns to movements in a common factor
= a common factor with a zero mean that influences the k returns on all assets
• An alternative pricing theory with fewer assumptions was developed:
• Arbitrage Pricing Theory
Arbitrage Pricing Theory - APT
Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
In application of the theory, the factors are not identified
Similar to the CAPM, the unique effects are independent and will be diversified away in a large portfolio
• Why do some authors contend that the APT model is untestable?
• What are the concerns related to the multiple factors of the APT model?
Chapter 9 - Multifactor Models of Risk and Return
– Inflation – Growth in GNP – Major political upheavals – Changes in interest rates
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
For i = 1 to N where: Ri = return riod Ei = expected return for asset i
• How is risk estimated in a multifactor setting?
Arbitrage Pricing Theory (APT)
• CAPM is criticized because of the difficulties in selecting a proxy for the market portfolio as a benchmark
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
For i = 1 to N where: Ri = return on asset i during a specified time period Ei = expected return for asset i
Arbitrage Pricing Theory (APT)
k Multiple factors expected to have an
impact on all assets:
Arbitrage Pricing Theory (APT)
= a common factor with a zero mean that influences the k returns on all assets
= a unique effect on asset i’s return that, by assumption, is i completely diversifiable in large portfolios and has a mean of zero
Assumptions of CAPM That Were Not Required by APT
APT does not assume • A market portfolio that contains all risky
assets, and is mean-variance efficient • Normally distributed security returns • Quadratic utility function
Arbitrage Pricing Theory (APT)
Rt Et bi1i bi2i ... bik k i
For i = 1 to N where:
Ri = return on asset i during a specified time period
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
Lecture Presentation Software
to accompany
Investment Analysis and Portfolio Management
Seventh Edition by
Frank K. Reilly & Keith C. Brown
Chapter 9
Chapter 9 – Multifactor Models of Risk and Return
– Inflation – Growth in GNP – Major political upheavals – Changes in interest rates – And many more….
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
For i = 1 to N where: Ri = return on asset i during a specified time period
Ei = expected return for asset i
bik = reaction in asset i’s returns to movements in a common factor
Arbitrage Pricing Theory (APT)
Bik determine how each asset reacts to this common factor
Each asset may be affected by growth in GNP, but the effects will differ
For i = 1 to N where: Ri = return on asset i during a specified time period
Ei = expected return for asset i
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP – Major political upheavals
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
• What are multifactor models and how are related to the APT?
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
= reaction in asset i’s returns to movements in a common bik factor
= a common factor with a zero mean that influences the k returns on all assets
= a unique effect on asset i’s return that, by assumption, is i completely diversifiable in large portfolios and has a mean of zero = number of assets N
– Inflation
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP
Arbitrage Pricing Theory (APT)
Ei = expected return for asset i
bik = reaction in asset i’s returns to movements in a common factor
= a common factor with a zero mean that influences the k returns on all assets
• An alternative pricing theory with fewer assumptions was developed:
• Arbitrage Pricing Theory
Arbitrage Pricing Theory - APT
Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
In application of the theory, the factors are not identified
Similar to the CAPM, the unique effects are independent and will be diversified away in a large portfolio
• Why do some authors contend that the APT model is untestable?
• What are the concerns related to the multiple factors of the APT model?
Chapter 9 - Multifactor Models of Risk and Return
– Inflation – Growth in GNP – Major political upheavals – Changes in interest rates
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
For i = 1 to N where: Ri = return riod Ei = expected return for asset i
• How is risk estimated in a multifactor setting?
Arbitrage Pricing Theory (APT)
• CAPM is criticized because of the difficulties in selecting a proxy for the market portfolio as a benchmark
Arbitrage Pricing Theory (APT) Rt Et bi1i bi2i ... bik k i
For i = 1 to N where: Ri = return on asset i during a specified time period Ei = expected return for asset i
Arbitrage Pricing Theory (APT)
k Multiple factors expected to have an
impact on all assets:
Arbitrage Pricing Theory (APT)