Should Investors Update Reference Points Utility

Prospect Theory

Prospect theory reveals that when faced with uncertainty and risk people choose on the footing of a reference point (e.thousand., their current wealth) and treat potential gains and losses differently.

From: Behavioral Economic science for Tourism , 2021

Ambiguity and Nonexpected Utility

Edi Karni , ... Massimo Marinacci , in Handbook of Game Theory with Economical Applications, 2015

17.four.i Introduction

Prospect theory was introduced by Kahneman and Tversky (1979) as an alternative to expected utility theory. Intended as tractable model of conclusion making under risk capable of accommodatinglarge set of systematic violations of the expected utility model, the theory has several special features: First, payoffs are specified in terms of gains and losses relative to a reference point rather than as ultimate outcomes. 2nd, payoffs are evaluated by a real-valued value function that is concave over gains and convex over losses and steeper for losses than for gains, capturing a holding dubbed loss aversion. Third, the probabilities of the dissimilar outcomes are transformed using a probability weighting function which overweight small probabilities and underweight moderate and big probabilities. ²⁵

In its original conception the weighting function in prospect theory transformed the probabilities of the outcomes every bit in [17.1] and, consequently, violates monotonicity. To overcome this difficulty, cumulative prospect theory is proposed as a synthesis of the original prospect theory and the rank-dependent utility model. ²⁶

In what follows we nowadays a version of cumulative prospect theory axiomatized by Chateauneuf and Wakker (1999).

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Behavioral Public Sector Economics

Richard W. Tresch , in Public Finance (Third Edition), 2015

Applying Prospect Theory

In his review of prospect theory, Nicholas Barberis notes that other researchers using always more sophisticated experiments have confirmed the 4 elements of prospect theory. As noted before in the chapter, Barberis believes that prospect theory best explains how subjects behave in experimental settings involving risk. ^eleven That said, the theory has not as all the same been widely applied to actual settings, although inquiry along those lines is start to gain some momentum. Most applications to engagement have been in finance and insurance, which makes sense given that information technology is a theory of behavior under dubiety. It has had very little impact on public finance.

The main difficulty in applying the theory has been in capturing the property of reference dependence in real-life settings. Reference points are piece of cake to ascertain and dispense in experimental settings, but often very difficult to determine with much conviction in actual situations. The difficulties are such that the vast majority of empirical inquiry still favors expected utility maximization every bit the underlying theoretical foundation. This may change, all the same, should more convincing ways of defining actual reference points evolve, given prospect theory's overwhelming success in laboratory settings.

The i potential application we will consider hither concerns annuities. As noted in Affiliate 21 on social insurance, private annuity markets are exceedingly sparse in the United States, such that annuities are too expensive. Peter Diamond uses this fact in support to his position that the public annuities under the Social Security System should be retained. Diamond attributes the thinness of the annuity markets to a simple mistake: People do non empathize that annuities are the cheapest way to provide a given stream of income during the retirement years Diamond (2004). Prospect theory offers ii other possibilities for fugitive private annuities: loss aversion and overweighting of extreme outcomes. Purchasing a retirement annuity is a gamble. Assume that the purchase price is actuarially off-white, equal to the nowadays value of the annuity income stream to the expected yr of death. If the purchaser dies before reaching the average life expectancy, he or she loses. If the purchaser lives longer than the average life expectancy, he or she gains. Under loss disfavor, the possible loss of a shorter-than-expected life outweighs the possible proceeds of a longer-than-expected life. The overweighting of extreme outcomes enhances the hesitancy to purchase an annuity because of loss aversion. Suppose that a quite healthy person at 65 years of age is considering buying an annuity. Provisional on reaching age 65, the life expectancy in the United States is in the mid-80s. The probability of the person dying presently later on buying the annuity is quite small. But the person overweights the probability and, combined with loss aversion, foregoes the annuity.

Why, then, are people reluctant to buy retirement annuities? Is their reluctance a fault, a la Diamond, that could possibly exist overcome with an educational campaign nearly the advantages of retirement annuities? Or is it a more fundamental reluctance caused by people'southward underlying psychological tendencies, and thus much more than difficult to overcome? The answer is unclear, but it likely matters in the debate near whether public pension systems should exist privatized.

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Behavioral Public Sector Economic science

Richard W. Tresch , in Public Finance (Quaternary Edition), 2023

Applying Prospect Theory

In his review of prospect theory, Nicholas Barberis noted that other researchers using e'er more than sophisticated experiments confirmed the four elements of prospect theory. As previously noted in the chapter, Barberis believes that prospect theory best explains how subjects deport in experimental settings involving risk. ¹² That said, the theory has non as notwithstanding been widely applied to bodily settings, although enquiry along those lines is beginning to gain some momentum. Well-nigh applications to date have been in finance and insurance, which makes sense given that it is a theory of behavior nether dubiety. It has had very piffling touch on on public finance.

The main difficulty in applying the theory has been in capturing the holding of reference dependence in real-life settings. Reference points are easy to define and dispense in experimental settings only often very hard to determine with much confidence in actual situations. The difficulties are such that the vast majority of empirical research still favors expected utility maximization as the underlying theoretical foundation. However, this may alter should more convincing ways of defining actual reference points evolve, given prospect theory's overwhelming success in laboratory settings.

The i potential application we consider here concerns annuities. Every bit noted in Affiliate 21 on social insurance, private annuity markets are exceedingly thin in the United States, such that annuities are overly expensive. Peter Diamond used this fact to support his position that public annuities under the Social Security System should exist retained. Diamond attributed the thinness of the annuity markets to a elementary mistake: People do not understand that annuities are the cheapest style to provide a given stream of income during retirement years (Diamond, 2004). Prospect theory offers two other possibilities for avoiding private annuities—loss disfavor and overweighting of farthermost outcomes. Purchasing a retirement annuity is a chance. Presume the purchase price is actuarially fair, equal to the present value of the annuity income stream to the expected year of death. If the purchaser dies before reaching the average life expectancy, she loses. If the purchaser lives longer than the average life expectancy, she gains. Under loss aversion, the possible loss of a shorter-than-expected life outweighs the possible gain of a longer-than-expected life. The overweighting of extreme outcomes enhances the hesitancy to purchase an annuity considering of loss aversion. Suppose a quite healthy person at historic period 65 is considering buying an annuity. Conditional on reaching age 65, the life expectancy in the United States is in the mid-80s. The probability of the person dying shortly later on buying the annuity is quite pocket-sized. However, the person overweights the probability and, combined with loss aversion, foregoes the annuity.

Why, and then, are people reluctant to purchase retirement annuities? Is their reluctance a mistake, a la Diamond, that could possibly be overcome with an educational campaign about the advantages of retirement annuities? Or is information technology a more than primal reluctance caused by people's underlying psychological tendencies and thus much more than difficult to overcome? The answer is unclear just probable matters in the debate about whether public alimony systems should be privatized.

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Handbook of the Economics of Risk and Uncertainty

Howard Kunreuther , Erwann Michel-Kerjan , in Handbook of the Economics of Adventure and Uncertainty, 2014

xi.iv.3 A Goal-based Model of Choice

Both expected utility theory and prospect theory assume that financial considerations decide a person's decisions regarding insurance purchase. Simply people ofttimes construct or select insurance plans designed to achieve multiple goals, not all of which are purely financial ( Krantz and Kunreuther, 2007). The relative importance of these goals varies with the determination maker likewise as the context in which the decision to purchase insurance may be triggered. For case, an insurance purchaser may think chiefly about the goals of satisfying the requirements of the depository financial institution that holds the mortgage loan. Simply when that same person reflects on her valuable works of art, she may recollect chiefly almost reducing anxiety and fugitive regret.

To illustrate how the plan/goal representation captures the insurance decision-making process, consider beliefs that is often observed: people purchase flood insurance after suffering damage in a alluvion, but then cancel their policies when several sequent years pass with no flood. 1 explanation is that avoiding feet and feeling justified are both important goals. Post-obit flood damage, feet is loftier, and reducing it is a salient goal; information technology is also easy to justify buying the insurance because a overflowing has just occurred and the experience is deeply etched in the purchaser'southward contempo retentivity. But a couple of years after, many people may observe that the prospect of a inundation no longer intrudes on their peace of mind, so anxiety avoidance takes on less importance.

In a similar spirit, insured individuals do not feel justified in continuing to pay premiums when they do non collect on their policy. The differential weighting of these goals at the time 1 suffers a overflowing and several years without experiencing some other loss can lead to a decision to cancel the existing policy. These individuals view insurance as a poor investment rather than celebrating the fact that they have not suffered any losses for the by few years.

Four of the main goal categories that may influence insurance purchase using the plans/goals model are (1) investment goals, (2) satisfying legal or other official requirements, (3) worry or regret, and (4) satisfying social and/or cognitive norms. Two other goals—maintaining a relationship with a trusted agent/advisor and affording insurance protection—may likewise play a role. These goal categories do non themselves constitute a complete theory of demand for insurance, only do seem to capture some aspects of beliefs inconsistent with expected utility theory.

Investment goals. Many homeowners view insurance through an investment lens rather than as a protective measure. These individuals purchase coverage with the expectation that they volition collect on their policy often enough and then that it is considered to exist a worthwhile expenditure. It is difficult for them to appreciate the maxim that "the all-time return on one'due south insurance policy is no render at all," meaning that one was spared harm from an effect for which one was insured. At one level, everyone agrees that a person is improve off not suffering a loss than experiencing one. But for those who care for insurance as an investment, each year that they practice not collect on their policy, they regret having bought coverage.

Satisfying requirements. Insurance coverage is often mandatory: Automobile liability insurance is required by near states; homeowners' insurance is normally required by mortgage lenders; flood insurance must be purchased as a condition for a federally insured mortgage in special overflowing hazard areas; and malpractice insurance is needed for several different professions. In these cases, purchase of insurance may be viewed as a subgoal for coming together cease goals, such as owning a auto or a dwelling or practicing ane's profession. The amount of coverage and size of the deductible are frequently discretionary then that the relative importance of specific goals will play a cardinal role in these decisions.

Emotion-related goals: worry or regret. There is an established literature on how touch and emotional goals influence an individual'south decisions nether risk (Lowenstein et al., 2001; Finucane et al., 2000). Three goals in this category with relevance to insurance are reduction of anxiety (i.e., peace of mind), abstention of anticipated regret, and consolation. Because emotions —even anticipation of anxiety or regret—have considerable immediate presence, individuals sometimes buy an insurance policy that has a high loading cost if doing so satisfies emotional goals, even if information technology leads to a shortage of funds to pursue other goals in the more afar futurity. Long-term care insurance is a good example. Elderly households of modest means can more frequently become financially stressed by trying to keep upwardly loftier nursing home insurance payments than past paying for nursing habitation care—which will somewhen exist covered by Medicaid. Merely still some people buy the individual insurance.

For low-probability, loftier-impact events, individuals may purchase coverage to reduce their anxiety about experiencing a large fiscal loss. Information technology is important to separate the following two goals: financial protection from the loss, and reduction of anxiety about the loss. Situations vary in the degree to which financial losses are made brilliant and to which they provoke or relieve anxiety. Hence, the relative importance of these goals may alter over time.

Ane may also anticipate feet and take measures to avoid it. For case, some people claim that they refuse to fly, not because they fear a crash, but because they anticipate and dislike feeling broken-hearted virtually a crash while they are on the aeroplane. Merely if i cannot avoid anxiety about a loss, i may however find opportunities to reduce this emotion past taking protective measures, including insurance, where appropriate. This feeling may partially explain the demand by the few who purchase flight insurance.

Regret (Bell, 1982; Loomes and Sugden, 1982; Braun and Muermann, 2004) and disappointment (Bell, 1985) are quite different from anxiety, in that they are primarily experienced after a loss occurs rather than earlier. Consider the instance of mailing a packet worth $50. If you do not purchase insurance, and so if the package is lost or badly damaged, you likely wish that you had purchased the coverage. If, at the time of mailing, you lot anticipate unpleasant regret or disappointment if an uninsured loss occurs, then you may make up one's mind to purchase insurance as a way of avoiding the possibility of such emotions.

Individuals may also purchase insurance as a form of consolation should they suffer a loss. In detail, if you accept special affection for an item, such as a piece of fine art, then the knowledge that you can brand a claim should the item be destroyed or stolen has special meaning. Hsee and Kunreuther (2000) attribute the need for consolation every bit the reason individuals are willing to pay higher premiums for the aforementioned corporeality of coverage for objects they love than for those for which they accept no special feeling.

With respect to negative feelings about a situation, experimental findings indicate that people focus on how astringent the outcome volition be rather than on its probability when they have strong emotional feelings attached to the upshot (Rottenstreich and Hsee, 2001; Sunstein, 2003). In the case of terrorism, a national field survey conducted in November 2001 revealed that Americans living within 100   miles of the World Trade Center felt a greater personal risk from terror than if they lived farther away (Fischhoff et al., 2003). This may explain the large New York surface area demand for terrorism insurance coverage immediately after 9/xi even at extremely high premiums (U.South. Government Accountability Part, 2002; Wharton Take a chance Management Center, 2005).

Satisfying social and/or cognitive norms. Many insurance decisions are based on what other people are doing, or on what those whom one respects believe is an appropriate action to take. For case, a new parent may purchase life insurance because his or her ain parent, partner, or financial adviser thinks that it is important to provide protection for the spouse and child. The amount purchased might follow some standard guideline (east.g., iii times annual income) regardless of the loading on the insurance or the buyer's risk-aversion. One time once again, multiple goals may come up into play: the new parent may be trying to achieve the goal of financial protection for the family against a depression-probability, high-impact event, merely trying also to satisfy what others look or wish them to do.

There is also empirical testify that purchase of insurance, like adoption of new products, is based on knowledge of what friends and neighbors accept done, even if the purchaser'due south own beliefs about the probabilities or consequences of a loss event accept not changed. Someone who purchases insurance soon subsequently suffering damage from a disaster may exercise so in role because it is easy to justify the expenditure to others by pointing to the event that just occurred. Similarly, some may cancel their insurance coverage after being protected for some years considering it is hard to justify an expenditure that has not paid off. The importance of justification as part of the determination procedure has been demonstrated in experiments that suggest social norms are an important determinant of selection (Shafir et al., 1993). In the process, people oftentimes use arguments that have little to practise with the merchandise-offs betwixt the cost of insurance and the expected loss that forms the footing of economic analyses of insurance or warranty transactions (Hogarth and Kunreuther, 1995).

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The contingent focus model and bad decisions

Kazuhisa Takemura , in Escaping from Bad Decisions, 2021

16.4 Prospect theory explains the framing issue and its problem

Tversky and Kahneman (1981) , using prospect theory, which they proposed ( Kahneman & Tversky, 1979; Tversky & Kahneman, 1992), explained why the framing effect occurs. They identified differences of respondents' subjective values for gain and loss. The value function is a concave role in the gain area, so information technology is take a chance-balky, and it is hazard-taking in the loss area because it is a convex function. Furthermore, the slope of the value role is steeper in the loss expanse than the gain area.

According to a revised theory (cumulative prospect theory) by Tversky and Kahneman (1992), the prospect theory using the Choquet integral is placed under the category of contempo nonlinear utility theory (Fishburn, 1988) with respect to its mathematical description. Whereas the detailed explanation of the cumulative prospect theory will executed into the side by side chapter, the special signal of prospect theory is that the reference indicate corresponds to the origin of utility theory, and prospect theory assumes that the reference point shifts easily depending on the mode of framing in a controlling problem. Prospect theory explains that by shifting the reference point, risk is avoided in a positive frame condition and risk is preferred in a negative frame condition of the same conclusion trouble. In addition, another cause of the framing issue is explained by Tversky and Kahneman (1981): the weighting value of the probability that is assigned to a preference is nonlinear. Therefore the framing consequence becomes more prominent as the value of proceeds or loss for a sure alternative increases, according to the relation.

Accordingly, concepts of these prospect theories explain why description invariance—that decision-making issues that are identical in form have the same preference order—is not met. That the nature of the value function differs between the gain area and the loss area, or alternatively, that the probability affects preference effect nonadditively, are adopted past many other theories such as nonlinear theories (eastward.1000., Fishburn, 1988). Nevertheless, a necessary point in prospect theory is that the shift of the reference point engenders reference reversal.

So, what kind of formulation tin can theoretically explain the shift of the reference signal? To engagement, no positive answer has been plant. Prospect theory cannot tell how the reference point shifts only has a difficulty in predicting the preference or choice outcome. That is, a trouble exists: although prospect theory postulates that a decision maker changes the coordinate system, it cannot elucidate how a decision maker changes the coordinate system.

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Prospect Theory, Asset Pricing, and Market Dynamics

Moshe Levy , ... Sorin Solomon , in Microscopic Simulation of Financial Markets, 2000

ix.3.3 Equilibrium Pricing

The equilibrium cost of the stock (which is a proxy for the market portfolio) is determined by investors' portfolio optimization and by market clearance. Permit us elaborate. Suppose that the market place portfolio's end-of-catamenia value is a stochastic variable ${\tilde{V}}_{\mathrm{one}}$ , and that the total aggregate wealth of investors at fourth dimension 0 is W ₀. (At this stage nosotros assume that investors are homogeneous; this assumption is later on relaxed.) The investors' investment proportion in the stock, p, determines the market portfolio'southward value at time 0. Namely, V ₀  = prisoner of war ₀ (otherwise the market is not cleared). Therefore, the investment proportion p determines the market portfolio'due south charge per unit of return distribution:

(nine.nineteen) $\tilde{R}=\frac{{\tilde{V}}_1}{V_0}-1,\mathrm{or}\tilde{R}=\frac{{\widetilde{\mathrm{Five}}}_{\mathrm{i}}}{p{\mathrm{West}}_0}-\mathrm{i}$

For a given end-of-period value distribution ${\tilde{V}}_1$ , the investment proportion north the stock, p, determines the charge per unit of return distribution, but on the other hand, the charge per unit of return distribution determines the optimal investment proportion in the stock For an expected utility maximize the optimal investment proportion in the stock is the proportion that maximizes the expected utility— that is, the investment proportion, p, which maximizes the expression:

(nine.xx) $\mathit{EU}=\int U\left[\left(1-p\right)r+\mathit{pR}\right]f\left(R\right)\mathit{dR}$

For a PT expected value maximizer, the optimal investment proportion is the proportion that maximizes the expectation of the value function (as given in Eq. (9.9)). In both cases, for the marketplace to exist in equilibrium, the investment proportion in the stock must be cocky-consistent (i.e., it must generate a rate of return distribution that justifies this investment proportion as optimal). Thus, similar in Lintner'due south version of the CAPM, the distribution of returns "adjusts and readjusts" until investors are at their optimal investment proportion, and the market is cleared simultaneously (see Lintner, 1965b, p. 598). Namely, in equilibrium there must exist an equality between the marketplace immigration investment proportion and optimal investment proportion. It is convenient to view both the market clearing investment proportion and the optimal investment proportion as a function of the expected charge per unit of return, μ. The marketplace clearance status dictates the following relation between the expected rate of render and the investment proportion:

(9.21) $\mu =\frac{\overline{V_1}}{p{\mathrm{Due\; west}}_0}-1$

(which is obtained by taking the expectation of Eq. (9.19)). Alternatively, one can view the marketplace clearing investment proportion equally the following function of the expected rate of return:

(9.22) $p=\frac{\overline{V_1}}{\left(1+\mu \right){\mathrm{Due\; west}}_0}$

For given preferences (characterized either past an expected utility function or a PT value function), the expected return μ also implies an optimal investment proportion in the stock ¹⁰ The equilibrium expected return, μ*, is that for which the market immigration investment proportion (given by Eq. (9.22)) is equal to the optimal investment proportion (given by the optimization of Eq. (9.20) for expected utility maximizers and by the optimization of Eq. 9.nine for expected value maximizers). Graphically, μ* is given by intersection of the line describing the marketplace clearing investment proportion as a function of μ with the line describing the optimal investment proportion as a function of μ. Figure 9.6 shows the marketplace clearing investment proportion given by Eq. (9.22) for the following parameters:

Figure 9.six. (a). Equilibrium expected return (b) Equilibrium expected return.

Westward ₀  =   1, ${\overline{V}}_1$ = i.5.

The optimal investment proportion is calculated for two cases:

1.

An expected utility (European union) maximize with a log utility function

2.

A prospect theory expected Value (EV) maximize with α   =   β =  0.88, λ   =   2.25

(The EU optimal investment proportion is calculated by numerically maximizing the EU as given in Eq. (nine.20) with U(·)   =   log(·). The PT optimal investment proportion is calculated past numerically maximizing the expected value as given in Eq. (9.ix).) The hazard-free real interest rate is taken as 0.8%, and the cease-of-period value, ${\tilde{V}}_1$ , is usually distributed with a hateful of ane.5 and standard deviation of 0.165 ¹¹ The equilibrium expected return is depicted in Figure ix.6a by μ _EU * for the example of the expected utility Eu maximizer and by μ _EV * for the case of the expected value maximizer.

When ${\overline{V}}_1$ =   ane.5, which is the situation depicted in Figure 9.6a, the equilibrium expected rate of return in a marketplace of Eu maximizers, μ _EU *, is lower than the equilibrium expected charge per unit of return in an identical market with EV maximizers. Different values of the end-of-period expected value, ${\overline{5}}_1$ , correspond to unlike market clearing investment proportion lines (come across Eq. (9.22)). The higher ${\overline{\mathrm{Five}}}_1$ , the higher the line describing the market immigration investment proportion. Figure nine.6b describes the same market place scenario as depicted in Figure 9.6a, with the exception that ${\overline{5}}_{\mathrm{i}}$ is higher ( ${\overline{V}}_{\mathrm{one}}$ =  2.0). Since the optimal investment proportion line for EV maximizers is almost vertical in the relevant range, the dissimilar value of ${\overline{V}}_1$ has nigh no effect on μ _EV *. In dissimilarity, the line describing the optimal investment proportion for EU maximizers is moderately upward sloping, and equally a consequence when ${\overline{V}}_1$ is increased, μ _{European union} * also increases (run across Figure nine.6b). If the value of ${\overline{V}}_{\mathrm{ane}}$ is such that the market place clearing investment proportion crosses the European union and EV optimal investment proportion lines at their intersection point (point ten in Figure ix.6b), the stock is priced the same by European union maximizers and by EV maximizers. For lower values of ${\overline{\mathrm{Five}}}_{\mathrm{one}}$ , the stock is priced higher by the EU maximizers. Even so, the situation is reversed for college values of ${\overline{V}}_1$ . In this instance μ _EU * > μ _EV *, which implies that the stock is priced higher past the EV maximizers (see Figure 9.6b). Thus, the higher ${\overline{5}}_1$ , the larger the difference between the price of a stock in a market place of EV maximizers and the price of an identical stock in a market of Eu maximizers.

To sum up, the main findings from our theoretical analysis of asset allocation and equilibrium pricing in the PT framework are as follows:

ane.

Given a risky stock with a given rate of return distribution and a riskless asset, the asset allocation decision of a PT investor characterized by the Tversky and Kahneman value office (in the relevant case where α = β). is contained of the investor's wealth. Namely, the optimal investment proportion in the stock is not a part of the investor's wealth.

ii.

The diversification policy unsaid by PT is rather extreme: given i riskless asset (bond). and one risky nugget (stock). with arbitrary rate of return distribution parameters, an investor with the Tversky and Kahneman value function will typically be in ane of the following ii states: (a) Fully invested in the bail or (b) fully invested in the stock. The crossover between these 2 states is abrupt: a small alter in one of the rate of return distribution parameters may lead to a switch from one state to the other. Nonetheless, the sharp crossover does not imply that investors flip-flop from bonds to stocks. Rather, it enables the states to narrate a relationship that must hold between the parameters of the rate of return distribution in equilibrium when all investors are informed (i.eastward., the distribution of ${\stackrel{\sim }{V}}_1$ is known).

3.

A risky security with some distribution of end-of-menses value, ${\widetilde{\mathrm{Five}}}_1$ , will exist priced higher by EV maximizers (relative to the pricing by Eu maximizers) if the expectation regarding the end-of-period value, ${\overline{V}}_1$ , is loftier. In contrast, if ${\overline{V}}_1$ is low, EV maximizers will toll the security lower than European union maximizers.

In the next section nosotros utilize these theoretical results in order to investigate the implications of PT to asset pricing and to market place dynamics in a dynamic market place model. As the dynamics are analytically intractable, we utilise the microscopic simulation (MS) method in our analysis. We apply the framework of the LLS model, described in Affiliate seven. To examine the with simulations of a market that has Eu maximizers with simulations of a market place that is identical apart from the fact that investors' beliefs is described by PT (rather than EUT).

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The Beliefs of Private Online Investors Before and After the 2007 Financial Crisis: Lessons From the French Example

Daniel Haguet , in Handbook of Investors' Behavior During Financial Crises, 2017

20.iv.3 Impact of the Financial Crisis on the Selling Beliefs

One of the main differences between behavioral finance and traditional finance is the selling behavior of individuals. Behavioral finance research and Prospect theory ( Kahneman and Tversky, 1979; Tversky and Kahneman, 1992) bear witness that, in situations of loss, people take a tendency to increase their risk (Fig. 20.2). Therefore, we decided to focus on the selling beliefs of our sample compared to the render of the market.

We analyze the selling beliefs based on the number of sales from which we take the logarithm. Therefore, our explained variable is log(number of sales). Our hypothesis is that there is a difference between the selling beliefs of our sample before and after the start of the fiscal crunch.

Our objective will be to verify if the switch between positive and negative returns of the CAC twoscore index has a significant impact on the selling behavior of our private investor sample.

We wanted to analyze the touch of the switch between a "bull" period before June 2007 and a "bear" catamenia after June 2007. The global sample was divided between two subsamples: the first one uses the daily trades from January 1, 2006 to the end of May 2007 ("bull" period). The second subsample uses the daily trades between June 2, 2007 and the end of June 2008 ("bear" period).

We apply ii measure of the CAC 40 index performance: the get-go one is merely the return of the alphabetize between the 24-hour interval of the trade and the twenty-four hours before; the 2nd i is the return of the CAC 40 on a yearly basis showing a positive or a negative trend during the "bull" menses and the "conduct" menstruation.

Our regression is as follows.

$y_i=a_{\mathrm{i}}{X}_{\mathrm{one}}+a_2{X}_{\mathrm{two}}+{\varepsilon }_i$

Where y _i is the logarithm of the number of sales, X ₁ is the daily render of the CAC 40, and X ₂ the yearly render of the CAC 40. Results are displayed in Table 20.10.

Table 20.ten. Regression on the two subsamples.

Explained Variable: Log (Number of Sales)	Earlier the Financial Crisis (01/02/2006–06/01/2007)	Afterward the Fiscal Crisis (06/01/2007–06/30/2008)
Explaining variables
Constant (t-stat)	6.882 (167.482)	half dozen.702 (405.449)
CAC 40 daily (t-stat)	2.091 (1.329)	iv.265 (3.617)***
CAC 40 12 months (t-stat)	−84.268 (−2.359)	95.985 (3.305)***
Number of observations	360	274

** and *** denote significant at the 5% and 10% levels, respectively.

Tabular array twenty.ten shows 2 regressions. The results are quite interesting. Offset, the two explaining factors (short-term render and long-term return of the CAC twoscore) are not significant before the financial crisis and get pregnant later on the financial crunch. This information is of involvement, showing that individuals are more sensitive to the return of the market when it falls.

Second, the coefficient for the daily render of the CAC xl is positive and shows that our individual online investors increase their sales when the market is ascent and decrease their sales when the market is falling. This beliefs is in line with Prospect theory that states that individuals become risk seekers in loss situations.

The third and terminal comment is about the long-term return of the CAC 40. This factor becomes significant after the first of the financial crisis and has at present a very high coefficient compared to that of the short-term return. Our estimation is that individual investors get much more than sensitive to the long-term tendency of the marketplace after the financial crisis than earlier. In a "bear" marketplace, they tend to decrease their sales.

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fMRI in Economics: What Functional Imaging of the Brain Tin Add to Behavioral Economic science Experiments

Niree Kodaverdian , in Biophysical Measurement in Experimental Social Science Research, 2019

Loss Aversion

Along with the above neural bear witness for the phenomenon of subjective probability weighting, there is neural back up for another conjecture of prospect theory. While standard economic theory suggests that people will have a mixed chance if the potential gain is equal to the potential loss, behavioral prove suggests an asymmetric sensitivity to losses—specifically, by a gene of ii, and then that the potential gain must be at least twice as large equally the potential loss for the gamble to be accepted ( Tom, Fox, Trepel, & Poldrack, 2007). This phenomenon, called loss aversion, is captured in prospect theory by an asymmetric value function that is relatively steeper for losses than for gains.

One question is whether the same neural regions are involved in evaluating losses and gains. If common regions are institute to be involved in the evaluation of each, then the question is whether at that place is evidence for a steeper loss function than gain role, or as Kahneman and Tversky (1979) originally put it, whether "losses loom larger than gains." If unlike regions are activated in the evaluation of losses and gains, a question we can accost using neural testify is whether the avoidance of potential losses reflects a fearful overreaction at the fourth dimension of pick, or rather a stable component of preferences.

There is prove for a common neural organization underlying the evaluation of potential gains and potential losses. Several neuroimaging studies, where subjects make gambling choices in the scanner, find that action in a broad set of areas displays joint sensitivity to prospective gains and losses (Canessa et al., 2013; Tom et al., 2007). While some of these areas (such every bit the ventral striatum, vmPFC, OFC, and aCC) displayed increased activation with potential gains and decreased activation with potential losses (Canessa et al., 2013; Tom et al., 2007), another areas (posterior insula, parietal operculum) displayed decreased activation with potential gains and increased activation with potential losses (Canessa et al., 2013). In a neuroimaging report where subjects fabricated intertemporal choices in the scanner (Xu, Liang, Wang, Li, & Jiang, 2009), it has again been found that mutual regions (lPFC, posterior parietal) are activated when evaluating potential gains and losses, with stronger activation when evaluating future losses as compared to when evaluating hereafter gains.

With common regions of activation for losses and for gains, the shape of the value part tin exist interrogated: is prospect theory correct in proposing a steeper function for the loss domain every bit compared to the proceeds domain? Tom et al. (2007) find that a number of regions (including the ventral striatum) take a decrease in activity for losses that is steeper than their increase in activity for gains. Similarly, Canessa et al. (2013) discover that the slope of the activation (in the correct posterior insula and parietal operculum) for increasing losses is greater than the slope of the deactivation in these regions for increasing gains.

Conversely, there is evidence for the activation of singled-out systems for the evaluation of losses. In line with a lesion written report, where two patients with amygdala damage showed a dramatic reduction in loss aversion compared to normal controls (De Martino, Camerer, & Adolphs, 2010), Sokol-Hessner, Camerer, and Phelps (2012) detect that amygdala activity is indicative of one's caste of loss aversion during a gambling task in the scanner: specifically, they find that amygdala activity in response to loss versus gain outcomes correlates with estimates of behavioral loss aversion, although due to their blueprint it was not possible to independently analyze Bold responses to potential losses versus potential gains at the betoken of a subject's decision.

Other studies also find support for dissociable systems for evaluating gain- and loss-related value. Employing a guessing chore in the scanner, Yacubian et al. (2006) find that activation in the ventral striatum activation correlates with expected value (and prediction fault) but only for the proceeds domain. In contrast, loss-related expected value and the associated prediction error are correlated with activity in the amygdala. Weber et al. (2007) utilise a pattern in which participants either buy or sell MP3 songs in a BDM auction. In their procedure, an individual bid his minimum buying or selling price in a second-toll auction against a randomly drawn number. Comparing selling trials and buying trials revealed greater amygdala and dorsal striatal activity in the former, and greater activity in the parahippocampal gyrus (the region surrounding the hippocampus) in the latter. The researchers interpret the comparatively stronger activation of the amygdala during selling trials relative to ownership trials every bit neural testify for loss aversion. A lesion study by Weller, Levin, Shiv, and Bechara (2007) provides more evidence for dissociable systems, but the office of the amygdala appears to be the opposite of that found in the to a higher place studies. They find that patients with lesions to the amygdala display impaired decision making involving the consideration of potential gains but are unimpaired in making decisions involving the consideration of potential losses (Weber et al., 2007).

As the amygdala is instrumental in emotional processing and learning (every bit reviewed in Sergerie, Chochol, & Armony, 2008 and in Phelps & LeDoux, 2005), these findings suggest that loss anticipation may activate a Pavlovian response, inhibiting action to avoid the potentially aversive result (Phelps & LeDoux, 2005). Findings by Xu et al. (2009) support the determination that potential losses appoint emotional systems. They find that regions previously constitute to exist associated with emotion processing (e.g., the insula, thalamus, and dorsal striatum) were more than activated during intertemporal choices involving losses as compared to those involving gains, leading to the inference that "enhanced sensitivity to losses may be driven by negative emotions" (Xu et al., 2009, p. 65).

The engagement of these structures in the processing of aversive stimuli and experiences raises the question of whether loss represents a transient fearful overreaction elicited by choice-related information, or rather a stable component of preferences. In a contempo study, Canessa et al. (2017) scanned subjects' brains during a resting land: when they were not making decisions, but simply lying down in the scanner. They constitute that activity during this resting state in the same regions (ventral striatum, right posterior insula/supramarginal gyrus) that previously demonstrated patterns consistent with neural loss aversion was correlated with subjects' degree of behavioral loss aversion. This finding indicates that loss disfavor may be a stable component of an individual's preferences.

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The mental ruler model: Qualitative and mathematical representations of contingent judgment

Kazuhisa Takemura , in Escaping from Bad Decisions, 2021

19.4.3 Construction of mental ruler

I hereby ascertain the mental ruler. This ruler approximately differs with positive and negative areas, simply like the value function in the prospect theory. The greater number, the improve it is in one case and the worse it is in some other. Still, as stated earlier, the objects of the mental ruler model too include rather neutral ones such equally probability judgment, not only the gain and loss areas. For simplification, withal, this affair is only discussed in the positive area. Moreover, the writer first discusses the mental ruler model for a case in which the evaluation object as an element of subjective situation Due south can be described objectively using an condiment measurement such as price, length, or size. And so I describe the mental ruler equally a set function from the subsets of the subjective state of affairs S to one-dimensional real number space R.

Start consider a case in which an element x is of the subjective state of affairs; S can exist described objectively as an additive function to price, length, proportion, probability, and then forth, every bit m(x)∈R. Consider a part m from S to one-dimensional real number space R, m: South→R. For instance, let chiliad(x) denote the discount rate m for an commodity 10. Moreover, consider the mental ruler using the part v from one-dimensional real number space R, which is mapped by yard, to 1-dimensional existent number space R, which describes the evaluation value v: R→R. Here, v has the following property.

(19.1) $k\left(\mathrm{ten}\right)=0\to v\left(m\left(x\right)\right)=0$

(19.2) $x^{*}=\underset{\mathrm{ten}\in S}{\text{arg}\max }k\left(\mathrm{ten}\right)\to 5\left(m\left(x^{*}\right)\right)=k,$

where k is a positive abiding.

(xix.3) $\mathrm{thou}\left(\mathrm{10}\right)\ge m\left(y\right)\to v\left(g\left(x\right)\right)\ge \mathrm{five}\left(m\left(y\right)\right)$

Eqs. (nineteen.1) and (xix.2) denote the boundedness of the mental ruler. For example, the evaluation for the relative income of $0 is 0, where the evaluation for the evaluation object that has the most value in the subjective situation is a real number chiliad. Here, 10* denotes 10 which maximizes chiliad(x). For example, when the upper limit of a relative income is considered to be $10,000, the alternative which gives the $10,000 is x*. Alternatively, considering the evaluation for a price using the mental ruler, if the upper limit of the budget is $100, then the article equivalent to the $100 is equivalent to x*. Eq. (nineteen.3) describes the monotonicity of the mental ruler. Information technology suggests that evaluation using the mental ruler does non exceed k in the subjective situation S. Moreover, if the mental ruler is unique with regard to the positively proportional transformation (the similarity transformation), past an adequate calibration transformation, then

(19.iv) $v\left(\mathrm{yard}\left(x^{*}\right)\right)=\mathrm{i},$

where $x^{*}=\underset{x\in S}{\text{arg}\max }\mathrm{thou}\left(\mathrm{ten}\right).$

As stated earlier, x* denotes ten which maximizes m(x), where x* always denotes the aforementioned quantity in the following discussion. Additionally, for simplification, the evaluation role of the mental ruler is presumed to hold always for Eq. (19.iv) in the discussion afterward.

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Why financial literacy matters for socio-economic wellbeing

Morris Altman , in Smart Economical Controlling in a Complex World, 2020

Errors and biases and 'irrational' heuristics

Dominating behavioural economics at present is the perspective adult by Daniel Kahneman and Amos Tversky, that individual conclusion-making is likewise often characterized by persistent biases and errors in choice behaviour. Humans develop heuristics to appoint in decision making. Because these differ from the neoclassically prescribed norms for choice behaviour, they are deemed to represent mistake-decumbent or biased means of acting, and are considered past many scholars to exist irrational (for a more recent rendition of this perspective see Kahneman, 2011).

Tversky and Kahneman (1974, p. 1130) stress the importance of neoclassical norms equally the benchmarks for rational behaviour. What is disquisitional to the popular and pervasive Kahneman and Tversky arroyo is the central role of emotion and intuition every bit the footing of choice irrationality in decision making, as opposed to the physiological and ecology variables stressed by the Simon-March arroyo to behavioural economics. Emotion and intuition can effect in determination making that is short-sighted and field of study to regret in the longer run; that is, in behaviour that is inconsistent with rationality, according to Tversky and Kahneman (1981). However, the emotional and intuitive side to the controlling procedure might exist subject to some control and re-teaching (Tversky & Kahneman, 1981, p. 458).

In a nutshell, Kahneman and Tversky's primal proffer (encounter Kahneman, 2011 , for an updated elaboration of this argument), much of information technology articulated in prospect theory, relates to how emotive factors, rather than objective determination-making benchmarks, drive the decision-making procedure. The critical empirics that underlie prospect theory are:

1.

On average, individuals have a preference for outcomes that are certain, even if their budgetary value is less than that of the uncertain outcome. For example, a person prefers a certain (100% probability) $100 pick over an option where there is an lxxx% chance of obtaining $140 and a twenty% chance of ending upwardly with nix. The latter yields an expected return of $112. Individuals are 'irrationally' willing to sacrifice $12 to gain a certain event.

2.

On average, individuals weight losses more than gains. For example, based upon Kahneman's and Tversky'southward research, a $100 loss would be given a weight of 2.5 and a $100 proceeds would be given a weight of 1. If ane gains $100 and loses $100, ane ends up with no net change in income or wealth. Objectively speaking, from a materialist (neoclassical) perspective, this type of event does not and should not affect ane's well-being. Even so, prospect theory suggests that an individual'southward well-being will autumn by quite a lot in this scenario as a result of the subjective (emotionally based) weights that individuals differentially adhere to losses and gains. This causes individuals to be loss-agin—to feel particularly bad nearly losses.

iii.

Individuals' subjective well-being is affected past their relative continuing and changes to their relative continuing in terms of losses and gains. Absolute levels of wealth are less important than changes to wealth. For this reason, the reference point that the private uses when making decisions is important, and these reference points are subjectively (thus not rationally) determined.

iv.

The framing of options or prospect affects decision making. When events are framed positively, individuals tend to choose them over the same events framed negatively. This should non happen when the different frames take no substantive issue on events—packaging should not affect conclusion making. Since such frames practice affect decision making, individuals are subject to perceptual or cognitive illusions. Related to this, individuals tin be hands manipulated by frames. This is referred to as the framing issue. Such behaviour is considered to be irrational or biased. However, one should note that it is non clear that differential framing volition touch choice behaviour when prospects or rates of return are substantively dissimilar. People tin be fooled when the cost of being tricked is non all that great. In the aforementioned vein, Gigerenzer (2007) makes the point that in a world of imperfect information and dubiety or of divisional rationality (the real globe), frames point information about the effect. When an event is positively or negatively framed, individuals read betwixt the lines, attempting to excerpt surplus information from the frames. A positive frame suggests a better choice than a negative frame. This is a judgement call that might prove to be wrong. Only information technology is a rational choice in a world of bounded rationality and uncertainty. However, this does not distract from the suggestion that frames can be manipulated such that smart people can end up making rational errors in their decisions, yielding choices that they might not take made had in that location been improve cerebral frames in place (Gigerenzer, 2007, pp. 99–100).

Every bit part of the Kahneman–Tversky perspective, the following are identified as primal cognitive biases (there are said to be many others) in conclusion making:

1.

Overconfidence: Individuals overestimate their decision-making capabilities. As a result, individuals engage in risky behaviour in activities across their objective chapters to succeed.

2.

Herding: The tendency of individuals to mimic the behaviour of others tin can event in cascades of detail choices. Herd behaviour occurs even when other individuals' behaviours are error-decumbent in the long run.

3.

Loss aversion (related to prospect theory).

iv.

Status quo bias and the endowment consequence: Individuals bear witness a preference for the status quo fifty-fifty when information technology does not yield college levels of material welfare. Ane example would exist an individual valuing an asset by more than its purchase price even though its marketplace value is not increasing. Possession in itself increases the value of the item possessed in the optics of the individual endowed with this asset.

5.

Framing effect (related to prospect theory).

vi.

Anchoring: Individuals tend to anchor their choices to reference points that are not objectively relevant to the conclusion at hand. This relates to what is referred to as the recognition heuristic (run across beneath).

7.

Adopting the wrong heuristic: This represents a more recent contribution Kahneman (2011), in this thinking dull and thinking fast narrative. Thinking fast (analogous to fast and frugal heuristics), might exist okay in some circumstances, only it can lead to disastrous or, at best, sub-optimal decisions in other circumstances when thinking irksome, taking i's time to remember things through can yield superior decisions and choices. Kahneman argues that which heuristic is best is context dependent. So, one has to re-focus on context to appreciate which arrangement of thinking is most effective and efficient.

One important implication of the Kahneman and Tversky perspective to behavioural economics is that considering individual decision-making is all too often irrational, mistake-decumbent or biased for emotive reasons—and, related to this, considering of the role heuristics play in decision making (which can involve intuition)—external intervention tin can exist justified in selection behaviour. Experts (or bureaucrats informed past experts), coming from a rational benchmark, can affect the conclusion outcomes or choices of individuals by regulating choice behaviour or past encouraging particular choices based upon what is taken by an expert to be optimal choices, which the proficient believes to be in the best involvement of the private. Such intervention could take place even if an private's choices are not burdened by negative externalities and, therefore, cause no harm to others.

This line of thinking is expressed quite eloquently by Thaler and Sunstein (2008, p. six): 'Individuals make pretty bad decisions in many cases because they exercise not pay total attending in their conclusion making (they make intuitive choices based on heuristics), they don't have self-control, they are lacking in total information, and they suffer from limited cerebral abilities'. As a event, individuals should exist nudged towards rational choices. People who oppose choice compages, they debate, do and then because they make the simulated supposition that (Thaler & Sunstein, 2008, p. eleven): 'almost all people, nearly all of the time, brand choices that are in their best interest or at the very least are better than the choices that would be fabricated by someone else. We merits that this assumption is simulated. In fact, we practice not think that anyone believes this on reflection'. This implies that instruction cannot exist expected, with any caste of confidence, to do the trick in affecting choice behaviour. Pick architecture is a mode of framing pick options so that people tin can exist nudged or manipulated into making the 'right' or rational choices.

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