The Role of Emotions on Risk Aversion: A prospect theory experiment

The Role of Emotions on Risk Aversion: A prospect theory experiment

Date:	2013-03
By:	Campos-Vazquez, Raymundo M. Cuilty, Emilio
URL:	http://d.repec.org/n?u=RePEc:pra:mprapa:48280&r=net
	This study measures risk and loss aversion using Prospect Theory and the impact of emotions on those parameters. Our controlled experiment at two universities in Mexico City, using uncompensated students as research subjects, found results similar to those obtained by Tanaka et al. (2010). In order to study the role of emotions, we provided subjects with randomly varied information on rising deaths due to drug violence in Mexico and also on youth unemployment. In agreement with previous studies, we find that risk aversion on the gains domain decreases with age and income. We also find that loss aversion decreases with income and is less for students in public universities. With regard to emotions, risk aversion increases with sadness and loss aversion is negatively influenced by anger. On the loss domain, anger dominates sadness. On average, anger reduces loss aversion by half.
Keywords:	Risk Aversion; Emotions; Prospect Theory; Experiment; Mexico
JEL:	C93

Prospect theory: An analysis of decision under risk

Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society, 263-291. uoregon.edu 提供的 [PDF]; [PDF] albacharia.ma] ;

==notes by yinung==

近數十年來, 影響最大的文章之一, 修正了期望效用理論的一些不合理的部份。

本文大量使用機率組合之選擇，以實驗 (問受試者) 的選擇，來解釋 EU 的不合理。

==original Abstract==

This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low probabilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling.

Do financial advisors exhibit myopic loss aversion?*

Kristoffer W. Eriksen, and Ola Kvaløy (2010) “Do financial advisors exhibit myopic loss aversion?."  Financial Markets and Portfolio Management, June 2010, Volume 24, Issue 2, pp 159-170.

==original Abstract==

Myopic loss aversion (MLA) has been proposed as an explanation for the equity premium puzzle, and a number of experiments on students indicate that people do exhibit MLA. However, many people do not rely on their own judgment when making investment decisions, but obtain help from financial investment advisors on how to allocate their wealth. The preferences and choices of financial advisors are thus important for understanding investment behavior. In this paper we make use of 50 professional financial advisors to examine whether they exhibit behavior consistent with MLA. Indeed, we find that they behave consistently with MLA to a larger extent than students.

==selected references==

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Myopic Loss Aversion and the Equity Premium Puzzle

Shlomo Benartzi and Richard H. Thaler  (1995) “Myopic Loss Aversion and the Equity Premium Puzzle.” Quarterly Journal of Economics, Vol. 110, No. 1 (Feb., 1995), pp. 73-92. ; doi: 10.2307/2118511 ;nyu.edu 提供的 [PDF]

==notes by yinung==

Prospect theory, myopic loss aversion (MLA) 和 equity premium puzzle 的重要文獻

==original Abstract==

The equity premium puzzle refers to the empirical fact that stocks have outperformed bonds over the last century by a surprisingly large margin. We offer a new explanation based on two behavioral concepts. First, investors are assumed to be “loss averse,” meaning that they are distinctly more sensitive to losses than to gains. Second, even long-term investors are assumed to evaluate their portfolios frequently. We dub this combination “myopic loss aversion.” Using simulations, we find that the size of the equity premium is consistent with the previously estimated parameters of prospect theory if investors evaluate their portfolios annually.

Stationary Concepts for Experimental 2×2-Games

Selten, Reinhard; Chmura, Thorsten (2008) “Stationary Concepts for Experimental 2×2-Games." American Economic Review, Volume 98, Number 3, June 2008 , pp. 938-966(29). DOI: http://dx.doi.org/10.1257/aer.98.3.938; zju.edu.cn 提供的 [PDF];

==notes by yinung==

此文之觀念, 適用於 長期 或 repeated 賽局之均衡解

mixed equilibrium 可視為是動態均衡解 (stationary concept)

Mixed equilibrium has several interpretations. One interpretation is that of a rational recommendation for a one-shot game. Another  interpretation  looks at mixed equilibrium as a result of evolutionary or learning processes in a situation of frequently repeated play with two populations of randomly matched opponents. One may speak of mixed equilibrium as a behavioral stationary concept.

這篇以 2×2 賽局實驗, 比較5種 stationary concept:

Quantal response equilibrium (Richard D. McKelvey and Thomas R. Palfrey 1995)

策略選擇比例是 exponential form

assumes that players give quantal best  responses  to  the behavior of  the others  (see Section  IB).  In  the exponential form of quantal response equilibrium considered here, the probabilities are proportional to an exponential with the expected payoff times a parameter in the exponent.

Action-sampling  equilibrium

從觀察對手的 7 種 (神奇數字) 可能的策略, 來決定自己的最佳策略

…in  a  stationary  situation,  a player takes a sample of seven observations of the strategies played on the other side, and then optimizes against this sample.

Payoff-sampling equilibrium  (Osborne and Rubinstein 1998)

這個還不太懂…

…envisions a  stationary  situation in which a player takes two samples of equal size, one for each of her pure strategies. She then compares the sum of her payoffs in the two samples and plays the strategy with the higher payoff sum…. The best fitting sample size turns out to be six for each of both samples. The name  “payoff-sampling equilibrium" refers to the sampling of own payoffs for each pure strategy.

Impulse balance  equilibrium

和 prospect theory 觀念結合的均衡

proposed  by Selten  is  based  on  learning direction  theory  (Selten  and  Joachim Buchta 1999)…   is  applicable  to the repeated choice of  the same parameter  in  learning situations  in which  the decision maker receives feedback, not only about the payoff for the choice taken, but also for the payoffs connected to alternative actions.
…. The decision maker is assumed to have a tendency to move in the direction of the impulse….

此觀念有別於 reinforcement learning

… that impulse learning is very different from reinforcement learning.

In reinforcement learning, the payoff obtained for a pure strategy played in the preceding period determines the increase of the probability for this strategy. … 完全取決於自己的報酬 (is  entirely based on observed own payoffs)

In  impulse  learning  it  is not  the payoff  in  the preceding period  that  is of crucial importance. It is the difference between what could have been obtained and what has been received, which moves the behavior in the direction of the higher payoff. … 取決於對手的策略和自己的報酬 (requires feedback on the other player’s choice and the knowledge of the player’s own payoff)

均衡成立時, 期望向上和期望向下 impulses 相同, losses 時 impulses 加倍計算
In  the  stationary distribution, expected upward impulses are equal to expected downward impulses. … losses are counted double in the computation of impulses as in prospect theory (Daniel Kahnemann and Amos Tversky 1979).

===五種 equilibrium 之差異===

The five concepts can be thought of as stationary states of dynamic learning models. Learning models differ with respect to their requirements on prior knowledge of the game and on feedback after each period.

reinforcement learning: Nash, quantal response, pay-off sampling equil. 屬之

其它兩種皆需要更多資訊: 自己的報酬 + 對手之選擇

one needs knowledge of one’s own payoff matrix, as well as feedback on the other player’s choice

==original Abstract:==

Five stationary concepts for completely mixed 2×2-games are experimentally compared: Nash equilibrium, quantal response equilibrium, action-sampling equilibrium, payoff-sampling equilibrium (Martin J. Osborne and Ariel Rubinstein 1998), and impulse balance equilibrium. Experiments on 12 games, 6 constant sum games, and 6 nonconstant sum games were run with 12 independent subject groups for each constant sum game and 6 independent subject groups for each nonconstant sum game. Each independent subject group consisted of four players 1 and four players 2, interacting anonymously over 200 periods with random matching. The comparison of the five theories shows that the order of performance from best to worst is as follows: impulse balance equilibrium, payoff-sampling equilibrium, action-sampling equilibrium, quantal response equilibrium, Nash equilibrium.

Psychologists at the Gate: A Review of Daniel Kahneman’s Thinking, Fast and Slow*

Shleifer, Andrei. 2012. “Psychologists at the Gate: A Review of Daniel Kahneman’s Thinking, Fast and Slow." Journal of Economic Literature, 50(4): 1080-91. link to AEAWeb;

==Notes by yinung==

這篇文章回顧 Daniel Kahneman 的書  “Thinking, Fast and Slow”

… because the  book mentions few economic applications, I  will describe some of the economic research that has been substantially infuenced by  this work.

作者認為 Kahneman and Tversky 影響最大者在於 財務學 (或稱行為財務) … this work. My feeling is that the most profound infuence of Kahneman and Tversky’s work on economics has been in fnance, on what has now become the field of behavioral finance…

兩種常見反對將心理學引進經濟學的理由:

…two common objections to the introduction of psychology into economics,…

A. 經濟學較著重研究人類行為的一般觀點，而非特殊行為
… economists should focus on “first order things”rather than quirks （quirk 這個字原意是）.

1. 反例1，人們花太多錢在保險，只為了很小的可能損失 (這可不是特殊現象)，
individuals pay large multiples of actuarially fair value to buy insurance against small losses, as well as to reduce their deductibles (Sydnor 2010).

2. 反例2，廣告 （？？還沒看懂）
the standard economic view that persuasion is conveyance of information seems to run into a rather basic problem that advertising is typically emotional, associative, and misleading— yet nonetheless effective (Bertrand et al. 2010; DellaVigna and Gentzkow 2010; Mullainathan, Schwartzstein, and Shleifer 2008).

3. 反例3，財務理論說，投資者應選 low-cast index fund, 但事實上大部份人卻是選 high-cost actively managed funds

B. 市場力量可消除心理因素對價格和分配之影響 （價格和效率）
… market forces eliminate the influence of psychological factors on prices and allocations.

1. 反例，Real-world arbitrage is costly and risky, and hence limited, … Dozens of empirical studies confirm that, even in markets with relatively inexpensive arbitrage, identical, or nearly identical, securities trade at different prices. With costlier arbitrage, pricing is even less efficient.

2. 市場參與者大多不理性，即是有專家之協助 （專家的動機通常值得懷疑，見(Chalmers and Reuter 2012; Gennaioli,
Shleifer, and Vishny 2012)）
Market forces often work to strengthen, rather than to eliminate, the influence of psychology.
List 研究棒球卡交易，發現專家沒有 endowment effects, 支持了此一觀點。

兩個思考體系 （two systems)

System 1: 直覺、自動、非意識性、容易 （intuitive, automatic, unconscious, and effortles）；快速反應，透過聯想、組合

System 2: 具意識性、緩慢、受控制 …但不容易 （conscious, slow, controlled, deliberate, effortful, statistical, suspicious, and lazy (costly to use)）；這是經濟學家認為的思考

Heuristics and Biases

Anchoring effects: 對未知的問題，容易受到前置性的影響 （擲俄羅斯輪盤，看到數字後，猜非洲國家佔聯合國之比例…, 看到輪盤數字小者猜小， 看到數字大者猜大)

… respondents receive all the information they need, but nonetheless do not use it correctly.

===一些結論…===

人類注意和聯想到的資訊，並非皆是在最佳決策中所需要的… 系統 1 的思考是自動反應，而非最佳化： 選擇性認知與記憶之決策行為（highly selective perception and memory … before we make decisions and choice)
… the fundamental feature of System 1 is that what our attention is drawn to, what we focus on, and what we recall is not always what is most necessary or needed for optimal decision making.

==original Abstract==

The publication of Daniel Kahneman’s book, Thinking, Fast and Slow, is a major intellectual event. The book summarizes, but also integrates, the research that Kahneman has done over the past forty years, beginning with his path-breaking work with the late Amos Tversky. The broad theme of this research is that human beings are intuitive thinkers and that human intuition is imperfect, with the result that judgments and choices often deviate substantially from the predictions of normative statistical and economic models. In this review, I discuss some broad ideas and themes of the book, describe some economic applications, and suggest future directions for research that the book points to, especially in decision theory. (JEL A12, D03, D80, D87)

==References==

有關 prospect theory

• Barberis, Nicholas. Forthcoming. “Thirty Years of Prospect Theory in Economics.” Journal of Economic Perspectives.
• Bordalo, Pedro, Nicola Gennaioli, and Andrei Shleifer. 2012b. “Salience in Experimental Tests of the Endowment Effect.” American Economic Review 102 (3): 47–52.
• Bordalo, Pedro, Nicola Gennaioli, and Andrei Shleifer. 2012c. “Salience Theory of Choice Under Risk.” Quarterly Journal of Economics 127 (3): 1243–85.
• Hart, Oliver, and John Moore. 2008. “Contracts as Reference Points.” Quarterly Journal of Economics 123 (1): 1–48.
• Koszegi, Botond, and Matthew Rabin. 2006. “A Model of Reference-Dependent Preferences.” Quarterly Journal of Economics 121 (4): 1133–65.
• *List, John A. 2003. “Does Market Experience Eliminate Market Anomalies?” Quarterly Journal of Economics 118 (1): 41–71.
• Pope, Devin G., and Maurice E. Schweitzer. 2011. “Is Tiger Woods Loss Averse? Persistent Bias in the Face of Experience, Competition, and High Stakes.” American Economic Review 101 (1): 129–57.

有關財務

• Barberis, Nicholas, and Ming Huang. 2008. “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices.” American Economic Review 98 (5): 2066–2100.
• Barberis, Nicholas, Andrei Shleifer, and Robert W. Vishny. 1998. “A Model of Investor Sentiment.” Journal of Financial Economics 49 (3): 307–43.
• Benartzi, Shlomo, and Richard H. Thaler. 1995. “Myopic Loss Aversion and the Equity Premium Puzzle.” Quarterly Journal of Economics 110 (1): 73–92.
• De Bondt, Werner F. M., and Richard H. Thaler. 1985. “Does the Stock Market Overreact?” Journal of Finance 40 (3): 793–805.
• Frazzini, Andrea, and Owen A. Lamont. 2008. “Dumb Money: Mutual Fund Flows and the Cross-Section of Stock Returns.” Journal of Financial Economics 88 (2): 299–322.
• Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny. 1994. “Contrarian Investment, Extrapolation, and Risk.” Journal of Finance 49 (5): 1541–78.
• Sydnor, Justin. 2010. “(Over)insuring Modest Risks.” American Economic Journal: Applied Economics 2 (4): 177–99.

其它

• Gennaioli, Nicola, and Andrei Shleifer. 2010. “What Comes to Mind.” Quarterly Journal of Economics 125 (4): 1399–1433.
• House money effects
  Thaler, Richard H., and Eric J. Johnson. 1990. “Gambling with the House Money and Trying to Break Even: The Effects of Prior Outcomes on Risky Choice.” Management Science 36 (6): 643–60.
• Framming
  Tversky, Amos, and Daniel Kahneman. 1981. “The Framing of Decisions and the Psychology of Choice.” Science 211 (4481): 453–58.

What is the actual shape of perception utility?

What is the actual shape of perception utility?

Date:	2011-06-20
By:	Kontek, Krzysztof
URL:	http://d.repec.org/n?u=RePEc:pra:mprapa:31715&r=net
	Cumulative Prospect Theory (Kahneman, Tversky, 1979, 1992) holds that the value function is described using a power function, and is concave for gains and convex for losses. These postulates are questioned on the basis of recently reported experiments, paradoxes (gain-loss separability violation), and brain activity research. This paper puts forward the hypothesis that perception utility is generally logarithmic in shape for both gains and losses, and only happens to be convex for losses when gains are not present in the problem context. This leads to a different evaluation of mixed prospects than is the case with Prospect Theory: losses are evaluated using a concave, rather than a convex, utility function. In this context, loss aversion appears to be nothing more than the result of applying a logarithmic utility function over the entire outcome domain. Importantly, the hypothesis enables a link to be established between perception utility and Portfo-lio Theory (Markowitz, 1952A). This is not possible in the case of the Prospect Theory value function due its shape at the origin.
Keywords:	Prospect Theory; value function; perception utility; loss aversion; gain-loss separability violation; neuroscience; Portfolio Theory; Decision Utility Theory.
JEL:	D81