中财网甜心英文怎么说:行为金融学的理论框架
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行为金融学的理论框架 200607
自1980年代以来，行为金融学逐渐受到重视，此研究领域相关理论的起源有二：一方面是因为许多实证研究发现传统理论无法解释的异常现象；另一方面则是和Kahneman and Tverskey（1979，以下简称为KT）所发表的展望理论有关。本文试图针对展望理论与其他相关理论作详尽的介绍。文章的这一部分只是作者预期的最后成稿的一个基础，希望在接下来的一段时间之内给出展望理论的相关研究结果，和行为金融学的其他理论发展。
一、展望理论
（一）理论发展
KT（1979）指出传统预期效用理论无法完全描述个人在不确定情况下的决策行为。他们以大学教授和学生为基础进行问卷调查，发现大部分受访者的回答显示许多偏好违反传统预期效用理论的现象，并据此提出另一种经济行为的模型，称为展望理论。
KT将这些违反传统预期效用理论的部分归纳出下列三个效应来说明：
⑴确定性效应（certainty effect）
此效应是指相对与不确定的结局（outcome）来说，个人对于结果确定的结局会过度重视。KT设计了两个问题来说明确定效应。第一个问题是，假设有两个赌局：第一个赌局有33％的机会得到2,500元，66%的机会得到2,400元，另外1％的机会什么也没有，第二个督军是确定得到2,400，问卷的结果显示有82％的受访者选择第二个赌局。第二个问题也假设有两个赌局：第一个赌局有33％的机会得到2,500元，67％的机会什么也没有。第二个赌局有34％的机会得到2,400元，66％的机会什么也没有。问卷的结果显示有83％的受访者选择第一个赌局。比较以上两个问题可知，根据预期效用理论，第一个问题的偏好为?u(2,400)>0.33u(2,500)+0.66u(2,400)或0.34u(2,400)>0.33u(2,500)，其中u(.)为效用函数。第二个问题的偏好却是0.34u(2,400)
⑵反射效应（reflection effect）
若考虑负的结局，即损失（loss），可发现个人对利得和损失的偏好刚好相反，称为反射效应。个人在面对损失是，有风险偏好（risk seeking），对于利得则有风险规避（risk aversion）的倾向。这和预期效用理论并不一致，可以看出个人注重的是相对于某个参考点（preference point）的财富变动而不是最终财富部位的预期效用。KT设计了一个问题来说明反射效应。假设有两个赌局：第一个赌局有80％的概率得到4,000元，第二个赌局是确定得到3,000元，问卷的结果显示有80％的受访者选择第二个赌局。若将结局改成负的，即第一个赌局有80％的概率损失4,000元，第二个赌局是确定损失3,000元，问卷的结果显示有92％的受访者选择第一个赌局。
⑶分离效应（isolation effect）
若一组prospects可以用不只一种方法被分解成共同和不同的因子，则不同的分解方式可能会造成不同的偏好，这就是分离效应。KT设计了一个两阶段的赌局来说明分离效应。在赌局的第一个阶段，个人有75％的概率会不得到任何奖品而出局，只有25％的概率可以进入第二阶段。到了第二阶段有有两个选择：一个选择是有80％的概率得到4,000元，另外一个选择是确定得到3,000元。从整个赌局来看，个人有20％（25％×80％）的概率得到4,000元，有25％的概率得到3,000元。对于这个二阶段赌局的问题，有78％的受访者选择得到3,000元。但KT若问受访者另一个问题：“两个选择：20％的概率得4,000元和25％的概率得到3,000元”，大部分的人会选择前者。由此可知，在两阶段的赌局当中，个人会忽略第一个阶段只考虑到第二个阶段的选择，既是有短视（myopia）现象。在这种情况，个人面临的是一个不确定的prospect和一个确定的prospect。若只考虑最后的结果和概率，个人面临的是两个不确定的prospects。虽然这两种情况的预期值相同，但是由于个人不同的分解方式，会得到不同的偏好。由此可知，若以预期效用理论的观点来看，这两个赌局是相同的，个人的选择应该相同。但是实际上却不是如此，个人会因为问题描述方式的不同而有不同的选择，这就是所谓框架依赖的现象。
除了利用问卷来说明之外，KT也提出理论模型来说明个人的选择问题。他们利用两种函数来描述个人的选择行为：一种是价值函数（value function）v(x)。另一种是决策权数函数（decision weighting function）π（p）。其中价值函数取代了传统的预期效用理论中的效用函数，决策权数函数将预期效用函数的概率转变成决策权数。
KT定义一个prospect为一个赌局，表示为（x,p;y,q），这个赌局最多只有两个非零的结局。在这个赌局中，个人得到x的概率p，得到y的概率为q，另外一个人有1-p-q的概率得不到任何东西，因此p+q≤1。若赌局中所有的结局皆为正（positive）也就是x,y>0且p+q=1,则这种赌局被称为严格为正(strictly positive)；若赌局中所有的结局皆为负，也就是x,y<0且p+q=1,则这种赌局被称为严格为负（strictly negative）；若赌局中的结局不是严格为正也不是严格为负，也就是p+q<1或x≥0≥y或x≤0≤y，则这种赌局被称为常态（regular）。个人在作选择的时候会经历两个阶段：编辑（editing phase）和评价（evaluation phase）。
编辑是为了对不同的prospects作简化和重新编码（encode），编辑阶段主要包含四个部分：
⑴编码（coding）：个人所认知的结局是利得和损失，而不是期末财富部位，利得和损失是相对于某个参考点所决定的，通常参考点是根据目前财富的部位所决定的，但是有时候参考点位置的决定是受到目前面临的prospects的情况和决策者对未来的预期所影响的。
⑵合并（combination）：合并相同结局的概率，可以简化问题。
⑶分解（segregation）：将prospects分解无风险因子和风险性因子，以下在评价的部分将有进一步的说明。
⑷删除（cancellation）：删除的情况可能有两种：第一种是前面所提到的分离效应，个人对于一个两阶段的赌局，会只考虑第二个阶段的部分。另一种情况是个人对于不同赌局种的相同因子会不予考虑。例如，若有两个赌局可供选择：（200,0.2;100,0.5;-50,0.3）和（200,0.2;150,0.5;-100,0.3）。个人可能会将这两种选择中相同的因子（200,0.2）删除，使这两种选择变成（100,0.5;-50,0.3）和(150,0.5;-100,0.3)，再予以评价。
在展望理论中，第二个阶段是评价，也就是假设决策这对每一个被编辑过的prospects加以评价，然后选择最高价值的prospect。
根据展望理论，假如赌局是常态的，也就是p+q<1或x≥0≥y或x≤0≤y，则prospect的价值为：
V（x,p;y,q）=л(p)v(x)+ л(q)v(y) (1)
展望理论认为个人对于严格为正或严格为负的赌局的评价原则和（1）式不同。在编辑的阶段，这种严格为正或严格为负的prospects可以被分解成两个因子，一个因子式务风险因子，譬如确定获得的最小利得或确定支付的最小损失；另一个因子式风险性因子，譬如可能的发生的利得或损失。这种prospects的评价可利用下式说明：
假如p+q=1且x>y>0或x
V（x,p;y,q）= v(y)+ л(p)[ v(x)-v(y)] (2)
也就是说，严格为正的prospects和严格为负的prospects的价值等于无风险因子的价值加上结局之间的价值差异乘上和比较极端（概率较低）的结局相关的权数。从（2）式可看出风险性因子是v(x)- v(y)，v(y)代表的是无风险因子。（2）式的右边可化成л(p)v(x)+ [ 1-л(p)] v(y)。因此，假如л(p)+ л(1-p)＝1，则（2）式可简化成（1）。
价值函数有下列三个重要的特性：
(1) 价值函数是定义在相对于某个参考点的利得和损失，而不是一般传统理论所重视的期末财富或消费。参考点的决定通常是以目前的财富水准为基准，但是有时不一定是如此。KT认为参考点可能会因为投资人对未来财富部位预期的不同，而有不同的考虑。譬如一个对于损失不甘心的投资人，可能会接受他原来不会接受的局面。
(2) 价值函数为S型的函数。在面对利得时是凹函数（concave,v?(x)<0,x>0），损失是凸函数（convex,v?(x)>0,x<0），这表示投资者每增加一单位的损失，其失去的效用也低于前一单位所失去的效用。
(3) 此价值函数，损失的斜率比利得的斜率抖。即投资者在相对应的利得与损失下，其边际损失比边际利得敏感。例如：损失一单位的边际痛苦大于获取一单位的边际利润，也就是个人有损失趋避（loss aversion）的倾向。Thaler（1980）将这种情况称之为禀赋效应（endowment effect）。有关于禀赋效应在下一节会有进一步的说明。
决策权数函数有下列两个特性：
（1） 决策权数不是概率，π是p的递增函数，它并不符合概率公理，也不应被解释为个人预期的程度。
（2） 对于概率p很小的时候，π（p）>p。这表示个人对于概率很小的事件会有过度重视（overweighted），但是当一般概率或概率很大时，π（p）
KT所讨论的主要是单一赌局的选择，但是个人实际上常常是同时面对多个赌局的选择。譬如，投资这在买卖股票时，可能会同时买进或卖出多种不同的股票。据此，Tverskey and Kehneman（1981）认为个人对于多个不同赌局的反应，必须视为一种心理帐户（mental account）之表达。所谓心理帐户，既是指每个人皆根据其自身的参考点，而投资人面对此一现象，便会根据其自身之心理帐户做出最适的决策。
个人在同时面对多个赌局时，要如何将之编辑并评价呢？Thaler（1985）以个人在确定性下，同时面对两个不同的赌局为例。个人将这两个不同的赌局视为一种联合现象（x,y），个人会根据心理帐户的观念将这种联合结局以合并v(x+y)或分开v(x)+v(y)的方式来编辑[1]。一般而言，个人会以让价值达到最大的原则来决定要合并编辑或是分开编辑。Thaler（1985）提出一个衡量模式来说明个人可能面临的四种可能的组合：
（1） 多重利得（multiple gains）：假如个人面临的两个赌局价值都为利得，即x>0,y>0。因为v在面对利得时时凹函数，所以v(x)+v(y)>v(x+y)，因此分开编辑对个人而言价值会比较大。
（2） 多重损失（multiple losses）：假如个人面临的两个赌局价值抖为损失，即x<0,y<0。因为v在面对损失时是凸函数，所以v(x)+v(y)
（3） 混合利得（mixed gain）：假设个人所面临的两个赌局中，一个价值为正，另一个价值为负，即x>0,y<0。这里假设x+y>0，所以是整体而言是净利得，Thaler将这种情况称为混合利得。因为损失函数较利得函数为陡，因此v(x)+v(y)
（4） 混合损失（mixed loss）：假如个人所面临的两个赌局中，一个价值为正，另一个价值为负，即x>0,y<0。但是这里假设x+y<0，所以是整体而言是净损失，Thaler将这种情况成为混合损失。在这种情况之下，没有进一步的信息无法判断哪一种编辑方式好。假如v(x)+v(y)
除了上述的理论发展之外，Tverskey and Kahneman（1991）认为展望理论会遇到两个问题：（1）不一定会满足随机优势（stochastic dominance）[2]原则；（2）无法扩充到有树木很大的结局的情况。为了解决上述问题，Tverskey and Kahneman（1992）提出累计展望理论（cumulative prospect theory,以下简称CPT）来克服相关问题。CPT满足随机优势理论，而且可运用于任何数量的结局的prospects之间的选择，以及运用到连续分配，并保留了大部分展望理论的论点。不过，累积展望理论似乎为受到学术界的重视，这可能是因为它只是将原始的展望理论复杂化，无法提供更进一步的经济内涵。
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[1]这里将x, y定义为prospects，v(x), v(y)为prospects的价值，这和前面KT的定义不同。
[2]KT（1979）指出，当权数π（p）并非概率p的线性函数时，随机优势可能会被违反。但他们认为人们在编辑阶段，即会将赌局中不具优势（dominated）的部分加以删除，在此假设下，上述问题便不会发生。Tverskey and Kahneman（1992）所采用的CPT不需要上述假设，因此可避免随机优势原则被违反的问题。