断言与厌恶:两项最新实验对投资者的启示

2005 · report · 原文约 2569 词
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美盛资本管理公司 2005 年 8 月 9 日

Legg Mason Capital Management August 9, 2005

断言与厌恶 迈克尔·J·莫布森 最近两项实验对投资者意味着什么

Aver and Aversion Michael J. Mauboussin What Two Recent Experiments Mean for Investors

判断一个人是否拥有独立行动的自由,抑或总是屈从于群体压力,是决定其本质的关键事实。

It is a decisive fact about a person whether he possesses the freedom to act independently, or whether he characteristically submits to group pressures.

所罗门·E·阿施《群体压力对判断的修正与扭曲之影响》1

Solomon E. Asch Effects of Group Pressure Upon the Modification and Distortion of Judgments 1

有一种可能:那些……优秀的投资者,或许具备你所说的功能性心理病态。他们对事物不会产生情绪上的反应。

It’s possible that people who are . . . good investors may have what you call functional psychopathy. They don’t react emotionally to things.

安托万·贝沙拉:来自脑损伤投资者的教训 2

Antoine Bechara Lessons From the Brain-Damaged Investor 2

如今最迷人的一个研究领域,恰恰横跨了投资、决策与神经科学。尽管金融理论的大厦仍然严重依赖“理性投资者”这个假设,但实践者几百年来都清楚,投资者的行为常常并非最优。然而,直到最近,我们才拥有了一套连贯的理论来解释投资者的行为。

Scanning the Horizon One of the most fascinating areas of research today intersects investing, decision-making, and neuroscience. While the edifice of finance theory still leans heavily on the rational investor, practitioners have known for centuries that investors often act suboptimally. Until recently, however, we had no cohesive theory to explain investor behavior.

这一切在 1970 年代发生了改变,当时丹尼尔·卡尼曼和阿莫斯·特沃斯基提出了前景理论,该理论描述了人们如何系统性做出偏离理论最优的决策。他们发现,例如,个体始终过度自信,会锚定无关的数字且无法适当调整,还会根据问题呈现方式的不同而改变自己的决策。前景理论催生了行为金融学这一新领域,该领域专门研究商业与投资场景中的认知错误与决策偏误。

That all changed in the 1970s, when Daniel Kahneman and Amos Tversky developed prospect theory, which describes how people systematically make decisions that deviate from the theoretical ideal. They found, for example, that individuals are consistently overconfident, anchor on irrelevant figures and don’t adjust appropriately, and alter their decisions based on how problems are presented to them. Prospect theory catalyzed the new field of behavioral finance, dedicated to the study of cognitive errors and decision-making biases in business and investing settings.

虽然前景理论已迈出一大步,但它仍未揭示人们为何会做出那样的决策。神经科学的最新进展让研究人员得以窥探受试者的大脑,首次描绘出人们在决策时大脑内部的真实图景,虽只是惊鸿一瞥,却已令人心驰神往。经济学家科林·卡梅勒将神经科学的这股热潮比喻为 1950 年代街区里第一家有电视的家庭:画面也许模糊,还得时不时拨弄兔耳朵天线,但那些新图像和新发现带来的兴奋感,足以让人激动不已。

Though it represents a huge leap forward, prospect theory still fails to reveal why people make the decisions they do. Advances in neuroscience now allow researchers to peer into the brains of subjects, providing the first tantalizing glimpses of what’s actually going on as people decide. Economist Colin Camerer likens the plunge into neuroscience to the first family on the block to have a television in the 1950s: the picture may be fuzzy and you may need to tweak the rabbit ears, but the new images and insights are exhilarating.

近几个月来,研究人员发布了两篇对投资者有重要启示的新论文。第一篇论文借助最新的功能性磁共振成像(fMRI)技术,为一经典社会心理学研究提供了新的洞见。第二篇论文则通过展示某些脑部受损的受试者在投资游戏中表现优于健康个体,凸显了损失厌恶的强大影响力。以下我们对这两项研究进行简要回顾,并探讨其对投资过程的意义。

In recent months researchers released two new papers with important implications for investors. The first paper adds insight into a classic social psychology study by using the latest functional magnetic resonance imaging (fMRI) technology. The second underscores the power of loss aversion by showing that certain brain-damaged subjects do better than healthy individuals in an investing game. We briefly review both studies and discuss their significance for the investment process.

雷格·梅森资本管理公司

Legg Mason Capital Management

眼见为实(集团告诉你要相信什么)

Seeing is Believing (What the Group Tells You to Believe)

20 世纪 40 年代,心理学家所罗门·阿什(Solomon Asch)进行了一项如今已成为社会从众研究中最著名之一的实验。具体来说,阿什考察的是,当面对大多数人都明显给出错误答案的情况时,个体会有何反应。

In the 1940s, psychologist Solomon Asch conducted what is now one of the best-known studies of social conformity. Specifically, Asch examined how individuals react when faced with a majority clearly giving wrong answers.

阿什的实验小组由八名成员组成:七名知情者,一名受试者。实验开始时,阿什要求小组解决一个非常简单的问题:判断三条线中哪一条与标准线等长。(见图表 1。)按座位顺序,每位参与者大声说出自己的选择。在最初几轮对照试验中,所有参与者都给出了正确答案。

Asch’s experimental group consisted of eight members: seven in the know and one subject. To start, Asch asked the group to solve a very simple problem: determine which of three lines is of equal length to the standard line. (See Exhibit 1.) Going around the table, each participant named their choice aloud. In the first couple control trials, all of the participants got the right answers.

展示 1:阿施实验中的任务

Exhibit 1: The Task from Asch’s Experiment

X A B C

X A B C

该插图由美盛资本管理公司制作,用以复现所罗门·阿希实验中的概念——来源:S. E. 阿希,《群体压力对判断的修正与扭曲之影响》,载于哈罗德·格茨科编《群体、领导力与人》(宾夕法尼亚州匹兹堡:卡内基出版社,1951 年)。

Illustration created by Legg Mason Capital Management to replicate the concepts used in the Solomon Asch experiment— Source: S. E. Asch, “Effects of Group Pressure Upon the Modification and Distortion of Judgment,” in Harold Guetzkow, ed., Groups, Leadership and Men (Pittsburgh, PA: Carnegie Press, 1951).

试过几轮之后,阿希示意那七名成员开始犯明显错误。尽管许多受试者显露出情绪紧张的迹象——包括对小组明显错误感到震惊——但受试组中仍有整整 33% 的答案与多数人的回答保持一致。如此之高的从众比例,对于这样一项毫无歧义的任务而言,是一个令人震惊的结果。

After a few trials, Asch signaled the seven members to start making obvious mistakes. While many subjects showed signs of emotional strain, including shock at the group’s evident errors, a full 33 percent of the subject group’s answers stayed consistent with those of the majority. The high conformity level is a striking result, especially for such an unambiguous task. 3

阿什还注意到,受试者之间存在“极大的个体差异”。例如,四分之一的受试者始终完全独立,而三分之一的受试者则多半会顺应群体共识。

Asch also noticed “extreme individual differences” among the subjects. For example, one-quarter of the subjects remained completely independent while one-third went with the consensus more often than not.

今天,我们会说这些人有不同的接纳阈值——人们对新潮流、新观念或社会活动的接受速度各不相同。⁴ 这种个体行为上的差异引起了阿施的兴趣,他试图对不同的反应形式进行分类。

Today, we’d say the individuals had varying adoption thresholds—people embrace new fads, ideas, or social activities at different rates.4 This variation in individual behavior intrigued Asch, and he attempted to categorize the forms of reaction.

基于实验过程中对受试者行为的细致观察,阿希采用了纯粹描述性的分类方法,将那些多数情况下都跟随多数人的受试者行为划分为三类:

Using purely descriptive categorizations based on close observation during the trials, Asch devised three categories to explain the behavior of the subjects who mostly went with the majority:

• 感知扭曲。这一群体没有意识到,多数人扭曲了他们的估计。

• Distortion of perception. This group is unaware that the majority distorted their estimates.

判断扭曲。这类人得出结论:自己的感知是不准确的,而群体才是正确的。

• Distortion of judgment. These subjects conclude that their perceptions are inaccurate and the group is right.

• 行为扭曲。这些人压抑自己的观点,明知如此却故意随大流。

• Distortion of action. These individuals suppress their own views and knowingly go with the majority.

阿施实验的结果与市场有着明显的关联。群体的选择——仅仅通过股价表现来体现——会诱使投资者随大流,尽管程度因人而异。但阿施,这位

The results of Asch’s experiments have obvious relevance for markets. Group choices—revealed simply as stock price performance—tempt investors to go with the majority, albeit to varying degrees. But Asch, who

1996 年去世时,他始终没能彻底弄懂,那些受试者在面对多数人做出的错误选择时,脑子里到底在想什么。

died in 1996, never fully understood what went on in the minds of the subjects as they faced the majority’s wrong choices.

在最近发表的一项研究中,脑神经科学家接续了阿什的研究。5 科学家们对阿什原始实验进行了改良,要求受试者判断旋转后的三维几何形状是否相同。和原始实验一样,研究人员安排演员给出错误答案。与几十年前的主要结果一致,受试者在 41% 的情况下选择了群体的错误答案。

In a recently published study, brain researchers picked up where Asch left off. 5 The scientists ran a modified version of Asch’s original study, asking the subjects to decide whether rotated three-dimensional geometric shapes were the same or different. Like the original experiment, the researchers cued actors to give wrong answers. Consistent with the main result decades earlier, the subjects went with the group’s incorrect answers 41 percent of the time.

今天的科学家拥有阿施只能梦寐以求的东西——一台功能磁共振成像(fMRI)扫描仪,可以让他们看到受试者在做出选择时,大脑哪些区域被激活。科学家们首次得以将社会从众行为与大脑活动直接联系起来。

Today’s scientists had something Asch could only dream of—an fMRI machine, allowing them to see which brain regions were active as the subjects made their choices. For the first time, the scientists could directly link social conformity with brain activity.

实际上,科学家们可以验证阿施的描述性分类。如果受试者的扭曲是基于判断或行动,科学家预计前脑区域——负责监控冲突和规划的区域——会出现活动。另一方面,如果扭曲是由感知造成的——根据阿施的说法,属于这一类的“受试者极少”——变化则会出现在控制视觉和空间感知的后脑区域。 ⁶

In effect, the scientists could test Asch’s descriptive categories. If the subject’s distortions were based on judgment or action, the scientists would expect activity in the forebrain—an area that deals with monitoring conflict and planning. On the other hand, if the distortions were due to perception—a category to which “very few subjects” belonged, according to Asch—the changes would be in the posterior brain areas that control vision and spatial perception. 6

结果发现,在从众的受试者中,科学家们观察到负责心理旋转的大脑区域出现活动,表明多数人的选择确实影响了感知。此外,那些保持独立的受试者表现出的杏仁核与尾状核活动,正是与情绪显著性相关的区域。

As it turns out, in conforming subjects the scientists saw activity in the areas that work on mental rotation, suggesting the majority’s choice actually affects perception. Further, the subjects that remained independent showed activity in the amygdala and caudate nucleus, regions associated with emotional salience.

大多数人,尤其是投资者,都试图不带偏见地看清形势。但这项研究恰恰与这一目标背道而驰。研究负责人 格雷戈里·伯恩斯 总结了研究结论:“我们倾向于认为,眼见为实,”但研究显示,“眼见为实,其实是群体告诉你该相信什么。”

Most people, and especially investors, try to perceive situations clearly and without bias. But this research flies in the face of that objective. The study’s leader, Gregory Berns, summed up the findings: “We like to think that seeing is believing,” but the study suggests, “seeing is believing what the group tells you to believe.”

Damage = Good?

Damage = Good?

前景理论对金融学最重要的贡献之一是损失厌恶——即对大多数人而言,损失比等量收益带来的感受更强烈。7 实证证据表明,我们对损失的感受大约是等量收益的 2 到 2.5 倍。损失厌恶显然偏离了预期效用理论。

One of prospect theory’s most important contributions to finance is loss aversion, the idea that for most people, losses loom larger than corresponding gains. 7 The empirical evidence suggests we feel losses about two to two-and-a-half times more than we feel gains. Loss aversion is a clear-cut deviation from expected utility theory.

怎么回事?决策框架展示了预期效用理论与前景理论之间一个显著差异。预期效用理论从投资者总财富的角度考虑收益与损失,而前景理论则把收益与损失视为孤立的财富组成部分,比如股价的变动。投资者倾向于根据参照点来做决策,而不是从全局出发。

What gives? The decision frame shows one significant difference between expected utility theory and prospect theory. Expected utility considers gains and losses in the context of an investor’s total wealth, while prospect theory considers gains and losses versus isolated components of wealth, like changes in a stock price. Investors tend to make decisions based on reference points, not the big picture.

损失厌恶的涟漪波及投资领域的多个方面,包括禀赋效应 8、处置效应 9 和短视型损失厌恶 10。损失厌恶最根本的影响之一,就是投资者会自愿放弃具有正预期价值的金融机会。

Ripples from loss aversion touch many facets of investing, including the endowment effect, 8 the disposition effect, 9 and myopic loss aversion. 10 One of loss aversion’s most basic implications is that investors willingly turn down positive expected value financial propositions.

经济学家保罗·萨缪尔森在 1960 年代曾向一位同事提出一个简单诱人的赌注,这成了他著名的论断:猜对抛硬币的结果你赢 200 美元,猜错你输我 100 美元。他的同桌拒绝了这项正期望价值的提议,回答说:“我不赌,因为损失 100 美元的感觉比赢 200 美元更强烈。” 11

This point was famously made by economist Paul Samuelson, who in the 1960s offered a colleague a simple and attractive bet: call a fair coin toss right and you’ll get $200, call it wrong and you’ll pay me $100. His dining partner turned down the positive-expected-value proposition, replying, “I won’t bet because I would feel the $100 loss more than the $200 gain.” 11

因此,损失厌恶会导致一些非常次优的决策,尤其是在投资组合的环境中。此外,正如阿施发现存在广泛的从众阈值一样,投资者的损失厌恶比率可能也差异巨大。下面就是这项新研究登场的地方。

So loss aversion can lead to some very suboptimal decisions, especially in a portfolio setting. Further, just as Asch found a wide range of conformity thresholds, investors likely vary substantially in their loss aversion ratios. Here’s where the new study comes in. 12

研究人员决定让脑部受损的患者与正常人在一个投资游戏中一较高下。这些脑损患者的智商正常,他们大脑中与逻辑和认知推理相关的区域也完好无损。受损的部位是大脑控制情绪的区块:这些患者无法正常感知恐惧或焦虑。

Researchers decided to pit brain-damaged patients against normal subjects in an investment game. The brain-damaged patients had normal IQs, and the regions of their brains associated with logic and cognitive reasoning were fine. The damage was in the part of the brain controlling emotions: the patients didn’t have normal experiences of fear or anxiety.

在一项简单的实验中,研究者设计了 20 轮抛硬币游戏。每位玩家初始有 20 美元。每轮游戏中,参与者可以选择参赌或弃权。如果参赌,就交给实验员 1 美元。实验员抛一次硬币:如果抛出国徽面(tails),参与者获得 2.50 美元(扣除 1 美元参赌成本,净赚 1.50 美元);如果抛出数字面(heads),分文不得(相当于净亏 1 美元)。如果某轮不参赌,参与者就能保住自己那 1 美元。目标是最终手里剩下尽可能多的钱。

In a simple game, researchers set up 20 rounds of coin tosses. Each player started with $20. For every round, the individuals could play or sit out. If they played, they handed the experimenter $1. The experimenter flipped a coin, with a $2.50 payoff for a tails flip ($1.50 net of the dollar to play) and nothing for a heads (equivalent to a $1 loss). If they didn’t play a given round, the subjects got to keep their dollar. The goal was to end up with the most money possible.

这个游戏并不难理解。既然每轮投资获得的期望值(1.25 美元)都高于不投资(1.00 美元),那么最佳策略就是每轮都投。

The game is not hard to figure out. Since for each round the expected value is higher to invest than not to invest ($1.25 versus $1.00), the best strategy is to invest in every round.

那么谁做得更好,是脑损伤患者还是正常受试者?差距不大。脑损伤患者最终比正常患者多获得约 13% 的金额(25.70 美元对 22.80 美元)。原因何在?脑损伤患者参与的游戏轮数比正常玩家多出 45%。

So who did better, the brain-damaged or normal subjects? It wasn’t close. The brain-damaged patients ended up with about 13 percent more money than the normal patients ($25.70 versus $22.80). Why? The brain-damaged patients participated in 45 percent more rounds than the normal players.

尽管认知正常的受试者在理智上知道该怎么做,但损失厌恶心理还是占了上风。研究人员巴巴·希夫评论道:“他们知道正确的做法是每轮都投,可一旦真正进入游戏,就开始对前几轮的结果做出应激反应。”¹³ 正常参与者在经历亏损后,仅有 41% 的轮次会继续投资,不足脑损伤患者投资率的一半。

Even though the normal subjects intellectually knew what to do, loss aversion took over. Researcher Baba Shiv comments, “they know the right thing to do is invest in every single round, but when they actually get into the game, they just start reacting to the outcomes of previous rounds.” 13 Normal participants only invested in 41 percent of rounds following a loss, less than half the rate of the brain-damaged patients.

这项研究引出一个耐人寻味的问题:成功的投资者有没有可能只是比普通大众拥有更低的损失厌恶比率?如果是,这种差异在多大程度上归因于先天禀赋,又有多少归因于投资者所在公司的文化?

This research raises an intriguing question: is it possible that successful investors simply have a lower loss aversion ratio than the rest of the population? And if so, how much of the difference can we attribute to hard wiring versus the culture of the investor’s firm?

这并不是说健康的情绪不可取。事实上,研究中那些脑损伤患者的个人财务状况一塌糊涂。他们中有四分之三的人经历过破产,因为寻求风险的行为导致他们做出糟糕的决策,而情商缺失又让他们与一些不道德的人纠缠在一起。

None of this is to say healthy emotions are undesirable. In fact, the personal finances of the brain-damaged patients in the study were awful. Three-quarters of them had experienced bankruptcy because their risk-seeking behavior led to poor decisions and their lack of emotional intelligence allowed them to get involved with some unscrupulous people.

结论:自我认知、异质性与文化 我们认为,这些研究至少提供了三条经验教训。

Conclusion: Self-Awareness, Heterogeneity, and Culture We believe these studies provide at least three lessons.

首先,它们可能通过基本理解和识别行为陷阱,帮助提高自我意识。当你因为很多人都在参与而觉得某个投资机会有吸引力时,你需要意识到,你对这个问题的认知可能开始受损害。解药包括多元化你的信息来源,并量化资产价格所反映的预期。

First, they may help raise self-awareness, through a basic understanding and recognition of behavioral pitfalls. When you feel attracted to an investment opportunity because lots of other people are participating, you need to recognize that your perception of the problem may start to be jeopardized. The antidote includes diversifying your information sources and quantifying the expectations an asset price reflects.

应对损失厌恶,需要从投资组合而非单只股票的角度来思考,评估一家公司的价值要独立于该股票此前的交易价格(或你的买入成本),并且持续关注预期价值。

Coping with loss aversion requires thinking in terms of a portfolio instead of individual stocks, assessing a company’s value independent of where the stock has traded before (or your purchase price), and a constant focus on expected value.

第二,这些研究突显了个性与偏好的巨大差异。正如阿希实验所示,人们随大流的意愿程度各不相同。同样,你的损失厌恶比率会根据自身处境,要么助推你的投资业绩,要么拖累它。请确保你的性格与投资方法彼此合拍。

Second, these studies underscore the wide variation in personalities and preferences. As the Asch study showed, people follow the crowd with varying degrees of willingness. Likewise, your loss aversion ratio can help or hinder your investment results, based on your circumstances. Make sure your personality and investment approach are compatible.

最后,尽管采纳门槛和损失厌恶比率在某种程度上可能是与生俱来的,但投资公司的文化无疑对长期成功起着关键作用。健康文化的几个重要维度包括:充分的意见输入和认知多样性,在业绩困难时期(这是不可避免的)团队给予的支持,以及对投资过程而非结果的坚定关注。

Finally, while both adoption thresholds and loss aversion ratios may be hard-wired to some degree, investment firm culture undoubtedly plays a critical role in long-term success. Some important dimensions of a healthy culture include sufficient input and cognitive diversity, team support in periods of difficult results (which are inevitable), and an unyielding focus on investment process versus outcome.

尾注

1 S.E. 阿什,“群体压力对判断的修正与扭曲效应”,载哈罗德·格茨科夫编《群体、领导力与人类》(宾夕法尼亚州匹兹堡:卡内基大学出版社,1951 年),第 177 页。

2 简·斯宾塞,“脑损伤投资者带来的教训”,《华尔街日报》,2005 年 7 月 21 日。

3 阿什还测试了一些附带问题。首先,他让多数派公开说出答案,但要求受试者私下作答。在这种情况下,受试者没有遵从群体规范。其次,阿什改变了对立多数派的人数规模。他发现,受试者同意多数派意见的倾向基本不受绝对人数影响。他还发现,只要群体中哪怕有一个人与受试者意见一致,受试者就不太可能给出错误答案。即便只是微小的不一致,也能大幅减少错误答案的数量。

Endnotes 1 S.E. Asch, “Effects of Group Pressure Upon the Modification and Distortion of Judgments,” in Harold Guetzkow, ed., Groups, Leadership and Men (Pittsburgh, PA: Carnegie University Press, 1951), 177. 2 Jane Spencer, “Lessons From the Brain-Damaged Investor,” The Wall Street Journal, July 21, 2005. 3 Asch tested some side issues, as well. First, he allowed the majority to air their answers but asked the subject to answer in private. Under these conditions, the subjects did not conform to the norm. Second, Asch varied the size of the opposing majority. He found the tendency of the subject to agree with the majority was largely independent of the absolute number. He also found that if even one of the group members agreed with the subject, the subject was much less likely to provide an incorrect answer. Even a small crack in unanimity led to a sharp reduction in wrong answers.

4 邓肯·J·瓦茨,《六度:互联时代的科学》(纽约:W.W. 诺顿公司,2003 年),第 221-226 页。

4 Duncan J. Watts, Six Degrees: The Science of a Connected Age (New York: W.W. Norton & Company, 2003), 221-226.

5 格雷戈里·S·伯恩斯(Gregory S. Berns)、乔纳森·查普洛(Jonathan Chappelow)、卡罗琳·F·津克(Caroline F. Zink)、朱塞佩·帕尼奥尼(Giuseppe Pagnoni)、梅根·马丁-斯库尔斯基(Megan Martin-Skurski)和吉姆·理查兹(Jim Richards),《心理旋转过程中社会从众与独立性的神经生物学关联》,

5 Gregory S. Berns, Jonathan Chappelow, Caroline F. Zink, Giuseppe Pagnoni, Megan Martin-Skurski, and Jim Richards, “Neurobiological Correlates of Social Conformity and Independence During Mental Rotation,”

《生物精神病学》,2005 年 6 月 22 日。

Biological Psychiatry, June 22, 2005.

参见 http://staff.washington.edu/xtoph/anth469metro/metrop_readings/Berns_Conformity.pdf。

See http://staff.washington.edu/xtoph/anth469metro/metrop_readings/Berns_Conformity.pdf.

6 Sandra Blakeslee,“他人之言或能改变你所见”,《纽约时报》,2005 年 6 月 28 日。

6 Sandra Blakeslee, “What Other People Say May Change What You See,” The New York Times, June 28, 2005.

7 阿莫斯·特沃斯基和丹尼尔·卡尼曼,《无风险选择中的损失厌恶》,《经济学季刊》,第 106 卷,第 4 期,1991 年 11 月。

7 Amos Tversky and Daniel Kahneman, “Loss Aversion in Riskless Choice,” The Quarterly Journal of Economics, Vol. 106, 4, November 1991.

参见 http://loss-aversion.behaviouralfinance.net/TvKa91.pdf。

See http://loss-aversion.behaviouralfinance.net/TvKa91.pdf.

8 Daniel Kahneman, Jack L. Knetsch, and Richard H. Thaler,“禀赋效应、损失厌恶与现状偏见”,《经济展望杂志》,第 5 卷,第 1 期,1991 年。

8 Daniel Kahneman, Jack L. Knetsch, and Richard H. Thaler, “The Endowment Effect, Loss Aversion, and Status Quo Bias,” The Journal of Economic Perspectives, Vol. 5, 1, 1991.

9 Hersh Shefrin 和 Meir Statman,《过早卖出赢家、过久持有输家的倾向:理论与证据》,《金融学刊》,第 40 卷,1985 年。

9 Hersh Shefrin and Meir Statman, “The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence,” Journal of Finance, Vol. 40, 1985.

10 什洛莫·贝纳茨与理查德·H. 塞勒,《短视损失厌恶与股权风险溢价之谜》,《经济学季刊》,1995 年 2 月。

10 Shlomo Benartzi and Richard H. Thaler, “Myopic Loss Aversion and the Equity Risk Premium Puzzle,” The Quarterly Journal of Economics, February 1995.

11 Paul A. Samuelson, “Risk and Uncertainty: A Fallacy of Large Numbers,” Scientia, XCVIII, 1963. 12 Baba Shiv, George Loewenstein, Antoine Bechara, Hanna Damasio, and Antonio R. Damasio, “Investment Behavior and the Negative Side of Emotion,” Psychological Science, Vol. 16, 6, 2005.

11 Paul A. Samuelson, “Risk and Uncertainty: A Fallacy of Large Numbers,” Scientia, XCVIII, 1963. 12 Baba Shiv, George Loewenstein, Antoine Bechara, Hanna Damasio, and Antonio R. Damasio, “Investment Behavior and the Negative Side of Emotion,” Psychological Science, Vol. 16, 6, 2005.

13 Spencer.

13 Spencer.

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