资产定价第二讲投资的收益风险与投资决策原理

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,*,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,1,资产定价第二讲,-,投资的收益与风险,陈善昂,2024/10/8,1,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,2,第一节 收益的来源及其类型,2024/10/8,2,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,3,一,.,持有期收益,1.,收益来源：定期现金流（如利息股息）,+,价差收入,2.,持有期收益：,2024/10/8,3,CopyRightShanAngChen,Department Of Finance,Xiamen University,注：罗伯特,.,清崎强调投资于现金流而不是资本利得！,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,4,利息收入：几种投资品的比较,股票：股息收益,可以与债券当期收益、存款利息比较,债券：当期收益（,I/P,）、息票收益（,I/F,）,可以与存款利息比较,房产：租售比,可以与债券当期收益、股息收益比较,黄金：没有利息收入,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,4,价差收入：区分投资与投机的一个标准,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,5,问题：,A,股投资者能指望现金分红来获取收益吗？参与者应当重点关注什么？,郭树清主席上任伊始就推出了强制分红制度,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,6,举例,2-1,假定你的投资在四年内有如下的收益：,那么,四年内的年平均收益为,9.58%.HPR=44.21%.,公式：,HPR=,（,1+r1,）（,1+r2,）（,1+r3,）（,1+r4,）,-1,年平均收益,=,（,1+r1,）（,1+r2,）（,1+r3,）（,1+r4,）,0.25-1,2024/10/8,6,CopyRightShanAngChen,Department Of Finance,Xiamen University,年,收益,1,10%,2,-5%,3,20%,4,15%,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,7,几何平均与算术平均,几何平均不同于算术平均,.,算术平均持有期收益率是按照单利原理计算的年均收益率,.,一般地,算术平均不低于几何平均；在各期持有期收益率均相等时,几何平均等于算术平均,.,上例的算术平均收益率,=10%,（高于几何平均的,9.58%,）,.,（,10%-5%+20%+15%,）,/4=10%.,2024/10/8,7,CopyRightShanAngChen,Department Of Finance,Xiamen University,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,8,历史收益率（几何平均与算术平均）,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,9,考虑汇率影响的持有期收益率,举例：,2002-2004,年,欧元兑美元的实际汇率变化从,1.05,变为,1.35,（即欧元相对美元升值,28.57%,）,.,假设,2002,年末,EurTel,股票的价格为,75,欧元,此时美元成本为,78.75,美元,.,在,2004,年末,该股票的价格涨至,105,欧元（股票涨了,40%,）,相当于,141.75,美元,.,以美元计算的投资收益率可以通过两种方法计算得出：,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,9,股价上涨贡献,欧元上涨贡献,注：汇率风险对投资的影响是显著的,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,10,二,.,货币的时间价值,用,复利,衡量收益是投资的本质要求！,单利只考虑到利息；而复利考虑到了,利息以及利息的利息,.,2024/10/8,10,CopyRightShanAngChen,Department Of Finance,Xiamen University,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,11,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,言论,艾伯特,爱因斯坦,:“,宇宙中最强大的力量是什么,?,是复利,.”,罗思柴尔德,:“,我不知道世界七大奇迹是哪些,但我知道第八大奇迹是复利,.”,11,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,12,美丽的财富曲线,问题：中美投资收益对比。,1926,年投资于美国小盘股,1,美元，到,2004,年底变成了,9248,美元，投资于美国大盘股,1,美元，到,2004,年底变成了,1992,美元。,1907,年福建林先生用洋银,100,元购买了福建铁路优先股,20,股，去年其孙持此凭证希望了解其目前值多少钱。您能帮助林先生的孙子算算吗？,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,13,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,三,.,有效年收益率,-,有效年收益率,-,连续复利,连续复利是既定利率水平下最大的名义利率,.,13,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,14,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,年名义利率为,6%,的有效年利率,复利频率,n,有效年利率,年,1,6.00000,半年,2,6.09000,季,4,6.13636,月,12,6.16778,周,52,6.17998,日,365,6.18313,连续复利,6.18365,14,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,15,举例,2-2,一张面值为,100,元、半年期的零息票债券目前售价为,97.36,元,.,计算：银行贴现收益率、持有期收益与有效年收益,.,银行贴现收益率（年）,=,（,100-97.36,）,/100,*,2=5.28%,持有期收益（半年）,=,（,100-97.36,）,/97.36=2.71%,有效年收益,=,（,1.0271,）,2-1=5.49%.,（不是,5.42%,）,银行贴现收益率会低估收益,.,2024/10/8,15,CopyRightShanAngChen,Department Of Finance,Xiamen University,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,16,四,.,要求收益率,投资决策取决于,预期,收益率与,要求,收益率之间的对比,.,要求收益率主要受三个因素的影响,即：,货币的时间价值（真实无风险收益率）,+,预期通货膨胀率,+,风险溢价；,作为对延期消费的补偿,这是进行一项投资可能接受的最低收益率,.,2024/10/8,16,CopyRightShanAngChen,Department Of Finance,Xiamen University,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,17,通货膨胀与税收对投资收益的影响,罗伯特,.,清崎在,富人的阴谋,一书揭露了,4,个阴谋，即：,税收、债务、通货膨胀与退休金,案例,1,：,1977,年汤女士存入银行,300,元，,2009,年连本带息取出来是,843,元。,案例,2,：,1954,年王先生存入银行,10,万元，,2011,年底其孙子持凭证到银行要求兑付，您猜可以兑到多少钱？,案例,3,：名义收益率,=3.5%,预期通货膨胀率,=6.5%.,粗略计算真实收益率为,-3%,但精确计算真实收益率为,-2.82%.,进入,负利率,时代,.,案例,4,：税后收益税前收益,*,（,1,税率）,2024/10/8,17,CopyRightShanAngChen,Department Of Finance,Xiamen University,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,18,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,五,.,到期收益率,(YTM),YTM,是指使得从证券上获得的收入的现值与其当前市场价格相等时的利率水平,.,它是一个全期利率,即它是假定投资者能够持有证券直至到期日为止,.,YTM,是一个非常重要的收益率,它适用于任何现金流的贴现,.,但是,它的缺陷在于买入证券后持有至到期日,.,18,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,19,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,19,附息债券的到期收益率,到期收益率的计算公式,如果是零息票债券与永久性债券,其计算公式就是其特例,.,到期收益率也就是,IRR.,当到期收益率大于要求收益率时,现金流的净现值大于,0,显示项目可行,.,反之反是,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,20,举例：到期收益率的计算,例,2-3,：,20,年期政府债券的息票率,6%,每半年付息一次,当前每,1000,元售价为,980,元,.,计算其到期收益率,.,计算过程：在财务计算品上输入,n=40,pmt=30,pv=-980,fv=1000,输出,1/y=3.0878%.,例,2-4,：,2,年期零息票债券,当前每,1000,元售价为,800,元,.,计算其到期收益率,.,计算过程：在财务计算品上输入,n=2,pmt=0,pv=-800,fv=1000,输出,1/y=11.8034%.,也可以用,EXCEL,中的函数来计算,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,20,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,21,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,六,.,预期收益率,未来充满着不确定性,.,前面讨论的都是,事后收益,.,未来的持有期收益率也称,期望收益率,.,人们进行投资决策取决于预期收益率与要求收益率的对比,.,包括单资产的期望收益率与投资组合的预期收益率,.,21,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,22,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,单一资产的预期收益,在任何情况下,资产的预期收益就是其收益的概率加权平均值,.,公式如下,:,说明,:,权重为未来状态,s,发生的可能性的概率,它是一个主观概率,;,且假设概率的分布符合正态分布,.,22,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,23,举例,2-5,某投资品未来的收益有三种可能情形：,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,23,情形,收益,概率,经济繁荣,0.34,0.3,正常,0.14,0.5,经济萧条,-0.16,0.2,预期收益为,0.14,最大可能收益为,0.34,最小可能收益为,-0.2.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,24,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,资产组合的预期收益率,资产组合的收益率是构成资产组合的每个资产收益率的加权平均值,资产组合的构成比例为权重,.,表明资产组合的预期收益率就是每个资产的预期收益率的加权平均值,.,公式为：,24,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,25,举例,2-6,某投资组合由三种证券组成,它们的预期收益及其投资比例如下：,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,25,资产,收益,在组合中的比重,资产,1,0.2,0.5,资产,2,0.15,0.3,资产,3,0.10,0.2,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,26,第二节 风险及其类型,2024/10/8,26,问题,1.,一提“风险”你首先能想到的有哪些词？,2.,在法庭上，法官问抢银行嫌疑人的一段对话。法官问“你为什么抢银行？”嫌疑人答“因为银行有钱。”法官再问“你抢银行时就没看到有保安和别的人吗？”嫌疑人答“当时我就只看到钱了。”,问题：,从这段对话里你能解读出哪些信息？,3.,“不入虎穴，焉得虎子”能否反过来说？为什么？,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,27,一,.,风险的定义,风险（,Risk,）：,风险是指“可度量的不确定性”，不确定性是指“不可度量的风险”。与可度量或可预见的风险不同，不确定性是指人们缺乏对事件的基本知识，对事件可能的结果知之甚少，因此，不能通过现有理论或经验进行预见和定量分析。,富兰克,H,奈特在,风险、不确定性和利润,（,1921,）,一个事件如果只有一个结果，那就是确定的，无风险的。一个事件如果有两个或两个以上的可能结果，那就是不确定的，有风险的。,因此，可以将风险定义为,“收益的不确定性”,。,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,28,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,29,二,.,风险的来源,系统风险,是指由于某种全局性的因素而对所有投资收益都产生作用的风险,.,又称为市场风险、宏观风险、不可分散风险,.,具体包括利率风险、汇率风险、购买力风险、政策风险等,.,非系统风险,是因个别上市公司特殊情况造成的风险,.,也称微观风险、可分散风险,.,具体包括财务风险、经营风险、信用风险、偶然事件风险等,.,注：,系统风险与非系统风险没有确定的界限。,问题：,你能列举出系统风险与非系统风险相互转换的例子吗？,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,29,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,30,资本的逐利本性,资本论,里引用了托,.,约,.,登宁的一句话：“如果有,10,的利润，资本就会保证到处被使用；有,20,的利润，资本就能活跃起来；有,50,的利润，资本就会铤而走险；为了,100,的利润，资本就敢践踏一切人间法律；有,300,以上的利润，资本就敢犯任何罪行，甚至去冒绞首的危险。”,点评：,投资者要求较高的收益从而对不确定性作出补偿,否则就不会投资,.,风险溢价或补偿：超出无风险收益率之上的要求收益率。,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,30,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,31,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,三,.,风险的衡量,-,过去值的方差与标准差,对于,n,个历史数据,计算方差的公式如下：,31,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,32,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,风险的衡量,-,预期值的方差与标准差,沿用例,2-5,的方差与标准差计算如下,32,离差平方,情形,收益,概率,经济繁荣,0.34,0.3,正常,0.14,0.5,经济萧条,-0.16,0.2,注：预期收益为,14%,。,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,33,收益率的分布,-,正态分布,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,33,正态分布,E,(,R,)-,E,(,R,)+,：概率为,68,.26,%,E,(,R,)-2,E,(,R,)+2,：概率为,95,.44,%,E,(,R,)-3,E,(,R,)+3,：概率为,99.7,4,%,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,34,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,四、资产组合的标准差,组合的标准差取决于三个因素：方差、,协方差,、权重,如果是,负相关或不相关的,资产构建组合,那么就可以,降低,组合的风险,.,但如果是完全正相关的资产构建组合,组合的风险不会降低,.,34,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,35,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,协方差与相关系数,35,注：协方差与相关系数是决定组合降低风险的重要变量！,证券收益之间的协方差,协方差衡量资产之间的相互关系对收益的影响,.,公式为：,其中,COV(X,Y),表示,X,和,Y,的协方差,也可以用,XY,表示,.,协方差为正,两种资产收益率具有同向变动关系；为负则反向变动关系；为零则二者没有关联,.,2024/10/8,36,CopyRightShanAngChen,Department Of Finance,Xiamen University,两证券组合的方差,当两证券完全正相关时,当两证券完全不相关时,当两证券完全负相关时,2024/10/8,37,CopyRightShanAngChen,Department Of Finance,Xiamen University,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,38,第三节 收益与风险之间的关系与投资选择,2024/10/8,38,一,.,风险厌恶假设,追求收益最大化的同时，希望风险（不确定性）最小。,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,39,标准差：风险,预期收益,A,B,C,D,说明：,从图中可以看出，,B,优于,A,A,优于,C,B,优于,D,问题：,在,A,与,D,之间如何选择？,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,40,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,二,.,变异系数及其运用,变异系数（,CV,）,=,标准差,/,预期收益,指标的涵义：获取单位收益需要承担的风险大小,.,该指标可以用来评价投资项目,越小越好,.,举例,2-8,：,假定有四项投资可供选择,如右表所示,.,A,的,CV,值为,0.67(=10/15).,B,的,CV,值为,1(=15/15).,C,的,CV,值为,1(=10/10).,D,的,CV,值为,0.75(=15/20).,B,与,C,的,CV,值相同,都为,1.,A,的风险,/,收益权衡要比,D,稍好,.,项目,预期收益,%,标准差,%,A,15,10,B,15,15,C,10,10,D,20,15,40,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,41,三,.,总风险与夏普比率,可以用夏普比率来评价证券或组合的业绩,夏普比率,=,（预期收益,-,无风险收益）,/,标准差,衡量的是每承担,一单位总风险可以获取的超额收益大小,.,该指标越大越好,.,下图中,证券,A,的夏普比率优于证券,C,与证券,B.,2024/10/8,41,CopyRightShanAngChen,Department Of Finance,Xiamen University,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,42,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,资本市场线,E(r),E(r,M,),r,f,CML,42,A,B,C,M,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,43,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,四,.,证券市场线与系统性风险,E(r),E(r,M,),r,f,SML,b,b,M,= 1.0,43,A,B,C,M,体现的,是具体的某个证券对市场组合风险的贡献度,.,大于,1,意味着投资于该证券要承担高于市场组合的波动敏感度；,小于,1,意味着其相对于市场组合波动水平不敏感,是保守型投资,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,44,贝塔系数,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,协方差只能衡量证券或组合与市场组合收益变化的相关性,无法衡量其系统性风险的大小,因而,夏普进一步引入了贝塔系数,从而可以比较证券或组合的系统风险大小,.,市场组合的贝塔系数恒等于,1.,组合的贝塔系数等于构成该组合所有证券贝塔系数的加权平均值,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,45,五,.,特雷纳比率,可以用特雷纳比率来评价投资或投资组合,特雷纳比率,=,（预期收益,-,无风险收益）,/,贝它值,衡量的是每承担,一单位系统风险,可以获取的,超额收益大小,.,该指标越大越好,.,上图中,证券,A,的特雷诺比率优于证券,C,与证券,B.,2024/10/8,45,CopyRightShanAngChen,Department Of Finance,Xiamen University,六,.,风险偏好与投资选择,投资者对风险有三种态度：风险厌恶、风险中性和风险喜好,.,投资者的风险偏好将直接影响其投资选择。,效用函数可分为三类：凹性效用函数、凸性效用函数和线性效用函数,分别表示投资者对风险持回避态度、喜好态度和中性态度,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen Univers,46,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,47,风险态度的测定赌徒心态,举例,2-9,：设一赌局,G(a,b,),其中,a,和,b,为结果,为结果,a,发生的概率,.,对于一给定赌局,G($100,0,40%),终盘的期望值,=,$100,0.4 + 0,0.6 = $40,问题,：拿走确定的,$40,还是,“,开赌,”,？,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,47,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,48,赌徒的选择,A,愿意拿走,$40:,U($40) 0.4U($100)+0.6U(0),=,风险厌恶（,Risk averse,）,B,愿意开赌：,U($40) ,风险喜好,（,Risk loving,）,C,无所谓：,U($40) = 0.4U($100)+0.6U(0),=,风险中性,（,Risk neutral,）,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,48,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,49,风险厌恶程度与投资选择,方差减少效用的程度取决于风险厌恶系数,A,即投资者个人对风险的厌恶程度,.,A=0,为中性投资者,他们只关心期望收益率,.,A0,为风险喜好投资者,风险的存在增加效用,他们当中,A,越小的人（或者说绝对值越大）越喜欢风险,.,投资者都会选择效用值最大的证券或组合,.,显然,风险厌恶程度对投资者在风险,-,收益间的权衡会产生重大影响,.,效用函数,U,E(R)-0.005*A*(,方差,)2,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,49,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,50,效用值的计算：举例,2-10,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,50,注：不考虑投资者的风险偏好,显然,组合,H,最好,因为它能提供最大的收益,.,在考虑变异系数的前提下,组合,L,最优,因为其变异系数最小（单位收益承担的风险最小）,.,在考虑不同风险偏好的条件下,当风险厌恶系数为,2,时,组合,H,最优；当风险厌恶系数为,3.5,时,组合,M,最优；但当风险厌恶系数上升至,5,时,组合,L,最优,.,预期收益,标准差,A=2,A=3.5,A=5,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,51,举例,2-11,问题：,一项风险资产的期望收益率为,20%,标准差为,30%.,国债能提供的无风险收益率为,7%.,一个风险厌恶系数为,4,的投资者更愿意投资国债还是风险资产？如果风险厌恶系数为,2,的投资者呢？,风险资产有正的风险溢价,但会否选择风险资产,还得看,投资者的风险态度,.,无风险资产的效用值就是其期望收益率,即,7%.,对于风险厌恶系数为,4,的投资者,风险资产的效用是,U=20-,（,0.005,*,4,*,302)=-30%,小于,7%.,不会选择风险资产,.,对于风险厌恶系数为,2,的投资者,风险资产的效用是,U=20-,（,0.005,*,2,*,302)=11%,大于,7%.,会选择风险资产,.,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,51,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,52,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,举例,2-12,假设某投资者要在两项风险资产,A,与,B,之间进行投资选择,.,如果运用前面的变异系数进行分析可以得出,A,的风险,/,收益权衡好于,B,的结论,.,但投资是否就应当选择,A,呢,?,关键还要看投资者的风险厌恶程度,.,即投资者在选择风险资产时应当遵循最大化收益的同时最小化风险,.,在此引入无差异曲线进行分析,.,效用的无差异曲线由效用函数给出,.,项目,预期收益,%,标准差,%,A,10,18,B,15,25,52,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,53,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,效用的无差异曲线,无差异曲线就是指在该曲线上的任何一点给投资者带来的效用值无差异,.,无差异曲线可以用来分析投资者厌恶风险的程度,.,下页图中,无差异曲线斜率表示投资者厌恶风险的程度,.,斜率越大,(L2),表明投资者越厌恶风险,因为他承担风险要求更高的报酬,.,而斜率越小,(L1),表明投资者比较不厌恶风险,.,对于,L1,的投资者而言,两项资产的效用值相同,因而两者无差异,选择哪一个都一样,.,而对于,L2,的投资者而言,两项资产所能提供预期收益的效用值低于其预期水平,因而,两者都不会考虑,.,即如果要他投资于标准差为,18%,的资产的话,他要求得到远高于,10%,的收益,.,53,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen UniversityCopyRightShanAngChen,Department Of Finance,Xiamen University,54,2024/10/8,CopyRightShanAngChen,Department Of Finance,Xiamen University,无差异曲线,预期收益,(,效用,),方差,(,标准差,),不同投资者对于承担同样的风险,要求的风险溢价不同,使得无差异曲线的斜率明显不同,.,斜率越大,表明投资者越厌恶风险,亦即要求的风险溢价越高,.,.,A,.,B,L1,L2,54,C,L2,