Monday, April 1, 2019

Prospect theory in decision making

Prospect supposition in conclusion doProspect possibleness is an important opening for conclusiveness-making amongst alternatives that involve luck. The theory departs from the traditional judge advantage theory because it attempts to condone how muckle legitimately make decisions among risky alternatives, which attempts to model optimum decisions. This vital difference leads to the picture theory departing from the traditional framework in important ways. Unlike the traditional approach, it attempts to incorporate psychology into the consideration plow to provide a behavioural approach to portfolio selection (Barberis, Nichola, Huang, Santos, 2001). During the course of this report, we entrust first look at how face theory differs from the traditional anticipate utility theory to march on a chamferrupt at a lower placestanding of the concept. sideline this will be, a discussion of the expose elements of anticipation theory the range constituent includi ng a sm solely reference to endowment marrow and the experimental condition quo bow, reflection and framing put, isolation effect and probabi bunkencyic redress. Towards the end, we will cause a precise look at the applications of prospect theory put updour premium paradox and home bias.The traditional finance theory assumes that investors separate out to maximize judge utility of wealthiness when they argon making decisions under un currentty. However, many studies have shown that the underlying assumptions of the traditional theory do not accurately describe how concourse actu tout ensembley behave when choosing among risky alternatives. This want leads to the weak cor parity betwixt the utility theory model and real decisions.There are four key features that distinguish prospect theory from mean-variance theory, which is the traditional approach to modelling decision-making. First, match to the traditional theory battalion choose among alternatives based on h ow the outcomes will affect their all overall wealth. However, according to prospect theory people evaluate outcomes in terms of gives and losings relative to a reference evince. So decisions are based on how the outcome changes their income, in relation to their reference point. (Han Hsu, 2004).Second, the mean variance digest makes the assumption that people are risk indisposed(predicate) in all their pickaxs. In contrast, prospect theory agents are risk-averse in the domain of gains except are risk seeking when all changes in income are frame in as losings.The third feature of prospect theory is passing play de quization. An single is hurt averse if she or he dislikes symmetric 50-50 bets and their degree of plague amplifications with the absolute size of the stakes. In some other words, prospect agents dont perceive gains and wantes of equal amounts evenly. For example, the loss of a particular amount is more than dire then the pleasure received from the gain of an equal amount. This is similarly cognise as the endowment affect. People place a higher(prenominal) mensurate on a good that they own than goods that they do not, and are free to accept a higher risk if it means that they can deflect the loss.Finally, in utility theory risk is treated objectively, by its probabilities. In contrast, the utility under prospect theory is not dependant on the original hazard barely rather on the transformed luck also known as decision weights. They do not middling measure the perceived likelihood of an detail. Instead, they measure how events will impact the desirability of prospects. (Han Hsu, 2004)This feature of the prospect theory helps explain a turn of events of violations of expected utility theory, including the famous Allais paradox. People in prospect theory course to overweight small probabilities. This overweighting explains why people buy drawing tickets vortexing a small medical prognosis of large gain, and indemnific ation protecting against a small portion of a large loss (Kahneman Tversky, 1979).The four elements explained higher up and how risk is evaluated is usually explained by the entertain function. The concept of the value function is based on gains and losses from a reference point, as explained in the first element of prospect theory above. Value function stresses the sizeableness of the reference point (starting point) although changes and movement are observed more compared to the resting point, referable to the concept of gains and loss. The followers is the prospect theory value function= non-linear weighting functionV(x-r) = the value functionR= the reference pointPT = (pi) v(xi r)This function creates an S-shaped curve (Figure 1.1)Figure 1.1The curve clearly highlights the reference point, from where onward gains and losses can be observed. It displays that as your gain increases the desire for it decreases demonstrating that people are risk averse when it comes to ga ins. On the contrary, as the loss increases the consternation for more loss increases hence showing that people are risk seeking regarding losses. These two concomitantors are highlighted in the graph by the brusqueness of the relevant sides. As gains increase the steepness decreases (in channelizely proportional) and as losses increase the steepness increases (directly proportional) (Maher, 2010).An example for this ir wise behaviour is how a random ingest would prefer to spend their $400.Gain survival of the fittest A, where you will have a blow% chance of gaining $200Option B, where you will have 50% chance of gaining $400 and a 50% chance of gaining $0 injuryOption A, where you will have 100% chance of losing $ five hundredOption B, where you will have 50% chance of losing $1000 and 50% of losing $0In this scenario the vast majority of people would choose option A for gain and option B for loss confirming that people weight their losses more compared to their gains. As they would settle for a rational gain (even if it is small) barely when it comes to losses they would prefer risk seeking to limit their loss. The last of utility relating to the gain or loss mirrors the concept of psychophysical principle concerning the valuation of outcomes.This reflects loss aversion which then implicates two specific aspects. Firstly, the endowment effect i.e. people would be willing to demand a higher value on crop that they themselves own rather than a similar product that they do not. The second implication is status quo bias, in this case people like things to stay relatively in the same position they are in so they remain at the status quo they are in. In this scenario any sort of change either good or harmful is taken to be a disadvantage.Another key element of prospect theory is the reflection effect, which states that succession investors are risk averse over prospects involving gains, they are risk seeking over prospects involving losses. This effect explains the observed druthers for definite small gains over uncertain large gains and in showdown preference for uncertain large losses over small certain losses.A remarkable interpretation of the reflection effect is that, a switch of all positive offsprings by their negatives (reflection around zero) reverses the choice patterns. For example, a choice between a 90% choice of getting 2000 and a 45% chance of getting 4000 would be replaced by a choice between a 90% chance of losing 2000 and a 45% chance of losing 4000. This effect implies a risk-averse preference for high probability of the relatively safe 3000 gain, yet a reversed preference for the risky option in the loss domain. Reflected choice patterns reported by Kahneman and Tversky (1979) were fairly high, i.e. 86% of subjects chose the safe lottery (90% chance of 3000) in the gain domain but only 8% chose the safe lottery when all payoffs were transformed into losses. (Laury Holt, 2000).An important implication of th is is the S shape of the value function in prospect theory that is umbilicate for gains and convex for losses.It was also identified, that if the same decision conundrum was worded differently, the preferences of decision makers differed as well. This was referred to as the framing effect. Prospect theory implies a unique kinship of risk seeking to positive and negative framing- negatively framed problem encourage risk seeking.For example When a group of investors were faced with the following two propositionsA put on the line that offers a 10% chance of attractive $95 and a 90% chance of losing $5 and another gamble B offering a 10% chance of winning $100 and a 90% chance of winning nothing. It was found that although the outcomes on both(prenominal) the gambles were the same, 74% of investors chose option B as stipendiary $5(negative as compared to a loss) for the gamble than simply losing made the gamble more acceptable.Von Restorff created the concept of the isolation ef fect, a way to make aroundthing that conforms at bottom a similar a group stand out like a sore thumb. An quarantined stop, in a list of other similar items, is better remembered than an item in the same relative position in a list where all items are similar. This is a way of distracting help from one event when the alternative constipates exactly the same probability and can be of some help in explaining the prospect theory in decision making in relation to investments.Kahneman and Tversky (1979) used the example of a two-stage test to better explain the use of the isolation effect practically in a behavioral finance situation. Isolation effect is important to show the irrationality of investors in situations that would normally produce a rational effect. This typifies the psychology of an investor having their attention diverted away from using a mean variance analysis of a situation.The first step of the test is a .25 chance of promotion to the second stage and a .75 cha nce of gaining nothing. The participant is asked to decide sooner the first stage whether, if successful, they would take 3000 or a 0.8 chance of taking 4000. It must be noted that in this game, the participant is choosing between 0.2 chance of 4000 or a 0.25 chance of 3000, the expected value of the former existence greater (800 rather than 750). Of the 141 participants that Kahneman and Tversky (1979) tested, 78% chose the first option of the guaranteed 3000. The reasoning back end this is the greater appeal of the sequential certainty of the choice most participants disregard the first stage of the experiment and just looked at the second test as a basis for their decision rather than weighing up the potential outcomes.The concept is a dependable indicator to suggest against all investors being mean variance optimising, thither is clear evidence that addicted the right circumstances people will ignore the obvious rational choice and accept a decision based on the higher va luation of certain prospects. This evidence of irrational preference conforms to the reflection theory where the certainty of a small gain is valued higher than a chance of a large gain. Using this psychological weakness in peoples logic the Von Restorff effect distracted attention from the overall probability and coerced the decision maker into accept a decision based on something that s in like mannerd out.The emergent popularity of amends policies has been used by supporters of the utility function as strong evidence of the concavity of the utility curve for money. However Kahneman and Tversky (1979) demonstrated that not all redress policy policies support this idea, basing their argument around the example of probabilistic insurance. Probabilistic insurance has also been used to highlight that decision weights tend to overweight small probabilities and large probabilities, but underweight moderate probabilities (Wakker, Thaler and Tversky, 1997). hackneyed insurance provide s the purchasers with a zero percent chance of any loss after a given incident, however a probabilistic insurance policy leaves the purchasers open to a small possibility that they will not be fully reimbursed. Following is an example of standard versus probabilistic insurance. imagine you want to insure i visit4 for the coming year, you can either insure your phone with Natwest bank for 10 a month or with first rudiment insurance who offer to insure the phone ever other day passim the year for 4.50 per month. Most people would view the offer by ABC as unattractive and prefer to go with the deal offered by the bank of 10 per month. In this situation the purchaser is underweighting the fifty percent chance of damage to the phone occurring on a day that he or she is covered by the ABC insurance policy. This example demonstrates that reducing the probability of a loss from p to p over 2, is less priceless than reducing the probability of a loss from p over 2 to zero (Tomas and Viila r, 2002).In contrast to the iphone4 insurance example given above, expected utility theory implies that probabilistic insurance is superior to regular insurance. This aversion towards probabilistic insurance is noteworthy because the most avid purchaser of insurance is still subjected to some level of risk. For example, most household contents insurance policies are void if the purchaser forgets to lock their front door.This type of insurance represents many types of protective action, where the user pays a certain cost to abase the probability of an undesirable event. For example, the purchase of a steering wheels lock or a carbon monoxide detector (Kahneman Tversky, 1979).Applications of Prospect theoryThe underlying principles bottom of the inning Prospect theory have been used on a number of occasions to explain a range of financial anomalies. The real earth aspect of the model means it offers genuine explanations for some of the most vainglorious puzzles such as the justn ess Premium Puzzle and nucleotide Bias.Equity Premium PuzzleThe equity premium puzzle refers to the empirical fact that shoots have outperformed bonds over the last century by a surprisingly large margin. Since 1926, the annual return on stocks has been around 7% while the return on bonds has been around 1% so, $1 invested in the SP 500 on January 1, 1926 was worth $1100 by the end of 1995, while $1 invested in T-bills was worth $12.87. In 1985, Mehra and Prescott noted that under the assumptions of Expected Utility Theory, these abnormally high and low returns are difficult to explain. In 1995, Banartzi and Thaler offered an explanation to the puzzle based on key features of Prospect Theory. They claimed that the puzzle is caused mainly by two factors derived from the Prospect theory loss aversion (investors being more sensitive to losses than gain) and a short evaluation period (investors checking their portfolio too often). This combination they termed Myopic Loss Aversion. Th ey argue that the attractiveness, and therefore value of a stock depends on the time horizon of the investor and frequency of evaluation. The more oft somebody evaluates their portfolio, the more likely they see their losses and suffer from loss aversion.Putting this application into more contexts, a risky addition paying 7% per year with a standard deviation on 20%, like the average stock, has a probability of loss or gain of around 50%. For a loss averse investor who evaluates frequently, the stock grocery store appears very risky. Considering this, an investor who is prepared to wait a long time between evaluating will find stocks much more appealing as there is an increased chance of them closing their position with a positive return. In turn, long-term investors will be willing to pay more for an uniform stock than a short term, frequently evaluating investor.Prospect theory has other various applications associated with it apart from the above mentioned equity premium puzzl e. The Home bias phenomenon is another such example. This phenomenon contradicts the mean variance framework, which elucidates the benefits of international diversification lot in the minimization of risk of a given securitys expected return. Home bias states that investors hold more domestic stocks and few foreign stocks than the optimum amounts actually predicted by the mean variance optimization (French and Poterba, 1991). Prospect theory explains this tendency of investors to choose domestic stocks. It says that one of the reasons for this could be a greater familiarity of investors with domestic assets and lower downside risk. This compels investors who may think globally to act locally (Campbell and Kraussl, 2006). Consider a foreign stock and a domestic stock with identical distribution payoffs. Since the foreign stock seem less familiar than the domestic one, investors may perceive it as having higher variance of payoff leading to low allocation to the foreign stock. Howev er a direct implication of this is derived from the portfolio choice theory that home bias would decline as investors became more familiar with foreign stocks ( (Han Hsu, 2004).Thus, while the prospect theory can explain this behaviour of investors to concentrate risks on single assets rather than to hold a well diversified portfolio, it fails to explain why the single asset chosen by investors are domestic ones. In addition, the argument present by Stracca (2002) says that if prospect theory is an accurate description of human stance towards risk, the benefits of international diversification would be reduced to a significant extent. cultureWe have looked over the principal elements behind the prospect theory proposed by Kahneman and Tversky in 1979. Prospect Theory is an alternative descriptive model of decision making under uncertainty, which incorporates real life choices and psychological analysis. Firstly, within prospect theory investors evaluate their outcomes in accordanc e with a reference point and make decisions based on how the outcome changes their wealth in relation to this unique reference. Within the expected utility theory, this relative level of wealth is not accounted for. Another key assumption behind prospect theory is the risk averse and seeking behaviour of investors under different circumstances. Investors are risk seeking in terms of losses and risk averse when it comes to profits. The assumptions of an endowment effect and decision weights are also included within the theory, where people place a higher value on a good that they already own and, in contrast to expected utility theory, risk is incorporated not by the original probability but by transformed decision weights. The S-shaped value function curve for prospect theory show this risk seeking and averse behaviour in investors, a reflection effect. The idea of framing is also a key element of prospect theory, where if the same decision problem is described in different words, i t can lead to different preferences. Within the theory also is an isolation effect, where devices are used to draw additional attention to something that would otherwise conform, and probabilistic insurance, where decision weights tend to overweight small and large probabilities, but underweight moderate probabilities. The real world assumptions behind prospect theory have been used to explain a number of financial anomalies. We eventually looked into prospect theorys applications to the equity premium puzzle and home bias which offer explanations to these anomalies.

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