1、第 13 章 报酬、风险与证券市场线Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.学会如何计算期望报酬率、方差和标准差 掌握多样性的影响 总结系统风险原则 描述证券市场线和风险报酬抉择学习目标Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or dis
2、tribution without the prior written consent of McGraw-Hill Education.期望报酬率和方差 投资组合 宣告、意外事项和期望报酬率 风险：系统的和非系统的 分散化与投资组合风险 系统风险与贝塔系数 证券市场线 证券市场线与资本成本：预习章节纲要Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education
3、.期望报酬率是基于未来可能结果的概率 在此情形中，“期望”是指该过程重复多次的平均值“期望”报酬甚至不一定是可能出现的报酬期望报酬率niiiRpRE1)(Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.假设你已经预测了以下三种可能的经济状况下股票C和T的收益，期望报酬率是多少？经济状况发生概率 C T_景气0.30.150.25正常0.50.100.
4、20萧条?0.02 0.01 RC=0.3(15)+0.5(10)+0.2(2)=9.9%RT=0.3(25)+0.5(20)+0.2(1)=17.7%示例:期望报酬率Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.方差和标准差衡量了报酬率的波动性 在整个可能性范围内使用不相等的概率 偏差平方的加权平均值方差和标准差niiiRERp122)(Copy
5、right 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.回到前面的例子，每只股票的方差和标准差是多少？股票 C 2=0.3(0.15-0.099)2+0.5(0.10-0.099)2+0.2(0.02-0.099)2=0.002029 =4.50%股票 T 2=0.3(0.25-0.177)2+0.5(0.20-0.177)2+0.2(0.01-0.177)2=0.
6、007441 =8.63%示例:方差和标准差Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.考虑以下信息:经济状况发生概率 报酬率景气0.25 0.15正常0.50 0.08放缓 0.15 0.04萧条 0.10-0.03 期望报酬率是多少？方差是多少？标准差是多少？另一示例Copyright 2019 McGraw-Hill Education.A
7、ll rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.投资组合是资产的集合 一项资产风险和报酬的重要性在于它们对投资组合的风险和报酬产生影响 与单个资产一样，投资组合的风险报酬通过投资组合的期望收益率和标准差来衡量投资组合Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior
8、 written consent of McGraw-Hill Education.假设你有15,000美元的投资资金，并且购买了以下金额的证券。你在每种证券中的投资组合权重是多少？$2000 的 C$3000 的 KO$4000 的 INTC$6000 的 BP示例:投资组合权重 C:2/15=0.133 KO:3/15=0.2 INTC:4/15=0.267 BP:6/15=0.4Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior
9、 written consent of McGraw-Hill Education.投资组合的期望报酬率是投资组合中各个资产的期望报酬率的加权平均值 你还可以像我们对单个资产所做的那样，通过查找每种可能经济状况下的投资组合报酬率来计算期望报酬率投资组合的期望报酬率mjjjPREwRE1)()(Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.考虑之前计
10、算的投资组合权重。如果单只股票具有以下期望报酬率，那么投资组合的期望报酬率是多少？C:19.69%KO:5.25%INTC:16.65%BP:18.24%E(RP)=0.133(19.69%)+0.2(5.25%)+0.267(16.65%)+0.4(18.24%)=15.41%示例:投资组合的期望报酬率Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education
11、.计算每种经济状况下投资组合的报酬率:RP=w1R1+w2R2+wmRm 使用与单个资产相同的公式来计算投资组合的期望报酬率 使用与单个资产相同的公式来计算投资组合的方差和标准差投资组合的方差Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.考虑以下有关报酬和概率的信息:投资你 50%的资金到 A资产经济状况发生概率AB投资组合景气 0.430%-5%
12、12.5%萧条 0.6 -10%25%7.5%单个资产的期望报酬率和标准差是多少？投资组合的期望报酬率和标准差是多少？示例:投资组合的方差Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.考虑以下有关报酬和概率的信息：经济状况 发生概率 XZ 景气0.2515%10%正常0.6010%9%萧条 0.155%10%如果投资组合中对资产X的投资为6,000
13、美元，对资产Z的投资为4,000美元，那么投资组合的期望报酬率和标准差是多少？另一示例:投资组合的方差Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.实际报酬率通常不同于期望报酬率 实际报酬有预期的部分和非预期的部分 在任何时候，非预期报酬可能是正数或负数 长期来看，非预期的部分平均值为0期望报酬率和非期望报酬率Copyright 2019 McGr
14、aw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.宣告和消息包含预期部分和意外事项 意外事项影响股价，继而影响报酬 当意外消息宣布或收益与预期不同时，我们会观察到股价的波动情况，这一点非常明显宣告和消息Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution withou
15、t the prior written consent of McGraw-Hill Education.有效的市场是投资者在接收到意外消息的基础上进行交易的结果 根据意外消息进行交易越容易，市场就越有效 我们无法预测意外情况，因此有效市场使得价格变动具有随机性有效市场Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.系统风险所影响的资产非常多 也称为
16、不可分散风险或市场风险 包括GDP、通货膨胀、利率等的变化。系统风险Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.非系统风险影响的是单个或是一小部分资产 也称作特有风险或具体资产风险 包括罢工，零件短缺等非系统风险Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduc
17、tion or distribution without the prior written consent of McGraw-Hill Education.实际报酬率=预期部分报酬率+意外部分报酬率 意外部分报酬率=系统部分报酬率+非系统部分报酬率 因此，实际报酬率能如下表达:实际报酬率=预期报酬率+系统部分报酬率+非系统部分报酬率报酬率Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of Mc
18、Graw-Hill Education.投资组合分散化是将投资分散到几种不同类别或行业的资产中 多元化不是指持有大量资产 例如，如果你持有50只互联网股票，那你就没有进行分散 但是，如果持有的50只股票跨20个不同行业，那么你的股票就会分散化分散化Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.表 13-7Copyright 2019 McGraw-
19、Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.分散化可大大减少报酬的波动性，而不会降低期望报酬 风险的降低是由于一项资产低于预期的回报会被另一项资产高于预期的回报所抵消 然而，存在着一个不能被分散的最低风险水平，那就是系统风险的部分。分散化原则Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or
20、 distribution without the prior written consent of McGraw-Hill Education.图 13-1Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.这类风险是可以通过投资组合而被化解掉的风险 通常被认为等同于非系统性风险，特有风险或具体资产风险 如果我们仅持有一项或单一行业的资产，那我们将面临
21、着的风险本可以通过分散投资来化解可分散风险Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.整体风险=系统风险+非系统风险 报酬率的标准差是对整体风险的一个度量 对于极度分散化的投资组合来说，非系统风险非常小 因此，分散化投资组合的整体风险实质上等于系统风险整体风险Copyright 2019 McGraw-Hill Education.All rig
22、hts reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.承担风险会有回报 承担不必要的风险是没有回报的 风险资产的预期回报仅取决于该资产的系统风险，因为非系统风险是可以分散的系统风险原则Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGra
23、w-Hill Education.怎样计量系统风险？使用贝塔系数 贝塔系数告诉我们什么？贝塔系数为1说明这项资产的系统风险等于市场整体的系统风险 贝塔系数小于1说明这项资产的系统风险小于市场整体的系统风险 贝塔系数大于1说明这项资产的系统风险大于市场整体的系统风险计量系统风险Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.表 13-8 贝塔系数Cop
24、yright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.考虑以下信息:标准差 贝塔系数资产 C 20%1.25资产 K30%0.95 哪项资产的整体风险较高？哪项资产的系统风险较高？哪项资产应该有更高的期望报酬率？整体风险和系统风险Copyright 2019 McGraw-Hill Education.All rights reserved.No reprodu
25、ction or distribution without the prior written consent of McGraw-Hill Education.许多网站都提供了公司的贝塔系数 雅虎财务在其“主要统计信息”部分提供了贝塔系数以及许多其他信息。输入股票代码并获得基本报价 点击“关键统计数据”WEB示例Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Educ
26、ation.考虑以下4项资产的信息资产权重 贝塔系数 C0.1331.685KO0.20.195INTC0.2671.161BP0.41.434 投资组合的贝塔系数是多少？0.133(1.685)+0.2(0.195)+0.267(1.161)+0.4(1.434)=1.147示例:投资组合的贝塔系数Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.风
27、险溢价=期望报酬率 无风险报酬率 贝塔系数越高，风险溢价应该越高 我们能否定义风险溢价与贝塔系数之间的关系，以便估计期望报酬率呢？可以！贝塔系数和风险溢价Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.示例:投资组合的期望报酬率和贝塔系数Expected Return,0,8%Expected Return,0.4,11%Expected Retur
28、n,0.8,14%Expected Return,1.2,17%Expected Return,1.6,20%Expected Return,2,23%Expected Return,2.4,26%0%5%10%15%20%25%30%00.511.522.53期望报酬率期望报酬率贝塔系数贝塔系数RfE(RA)ACopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Educa
29、tion.报酬风险比率是上面例子中直线的斜率 斜率=(E(RA)Rf)/(A 0)上面例子的报酬风险比率=(20 8)/(1.6 0)=7.5 如果资产的报酬风险比率为8会发生什么？（意味着该资产落在线的上方）如果资产的报酬风险比率为7会发生什么？（意味着该资产落在线的下方）报酬风险比率：定义和示例Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.在均
30、衡状态下，所有资产和投资组合具有相同的报酬风险比率，并且都等于市场的报酬风险比率市场均衡MfMAfARRERRE)()(Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.证券市场线(SML)是市场均衡的表现 证券市场线的斜率就是报酬风险比率:(E(RM)Rf)/M 但由于市场的贝塔系数始终等于，因此斜率能表示为 SML斜率=E(RM)Rf=市场风险溢价
31、证券市场线Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.资本资产定价模型定义了风险与报酬之间的关系 E(RA)=Rf+A(E(RM)Rf)如果我们知道一项资产的系统风险，那我们可以用CAPM模型确定其期望报酬率 不管是金融资产还是实物资产资本资产定价模型(CAPM)Copyright 2019 McGraw-Hill Education.All r
32、ights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.货币的纯粹时间价值:通过无风险利率来计量 承担系统风险的回报:通过市场风险溢价来计量 系统风险的大小:通过贝塔系数来计量影响期望报酬率的因素Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent o
33、f McGraw-Hill Education.考虑以下每项资产的贝塔系数，如果无风险利率3.15%，市场风险溢价是7.5%，每项资产的期望报酬率是多少？资产 贝塔系数期望报酬率 JNJ0.673.15+0.67(7.5)=8.18%TWTR0.853.15+0.85(7.5)=9.53%TSLA1.193.15+1.19(7.5)=12.08%CBS1.713.15+1.71(7.5)=15.98%示例-CAPMCopyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution wi
34、thout the prior written consent of McGraw-Hill Education.图 13-4Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.对于单个资产，如何计算其期望报酬率和标准差？对于一个投资组合呢？系统性风险和非系统性风险有什么区别？哪种风险决定了期望报酬率？一项资产的贝塔系数为1.2，无风险利率是5%，市场风
35、险溢价是13%.均衡状态下的报酬风险比率是多少？这项资产的期望报酬率是多少？快速测验Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.无风险利率为4%，市场要求的报酬率为12%一项资产的贝塔系数为1.5，那么其要求的报酬率是多少？报酬风险比率是多少？一项投资组合的40%由上述资产构成，余下资产的平均报酬率为承担系统风险的回报，这项投资组合要求的报酬率为
36、多少？综合性习题Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.本章结束 第 13 章Copyright 2019 McGraw-Hill Education.All rights reserved.No reproduction or distribution without the prior written consent of McGraw-Hill Education.
