The History Of Isolation Effect

Published Date: 02 Nov 2017

Certainty Effect

In an attempt to test whether professional investors in Mauritius behave in accordance with the certainty effect proposed by Kahneman and Tversky (1979), five games are described below. It is important to note that in order to test whether certainty effect is appropriate in the Mauritian context, only positive prospects have been taken into consideration.

Game 1

In Game 1, participants were given a choice between a 50% chance to win Rs 1000 and 50% chance to win nothing and winning Rs 600 with certainty. As depicted in the chart given, nearly everyone (91.8%) preferred the second choice. As such, in Game 1 we see the certainty effect in full display, with participants in Kanhneman and Tversky (1979) research opting for certain prospects instead of risky prospect.

Game 2

In Game 2, subjects were required to choose between an 80% chance to win Rs4000 and 20% to win nothing and winning Rs3000 with certainty. Once again, the respondents preferred the certain outcome (80.3%) over the one offering only 80% chance of winning Rs4000. It is interesting to note that the results obtained in this study are almost similar to the findings of Kanhneman and Tversky (1979) where 80% of the subjects in his study chose the second option. Besides, by selecting "irrational pattern of preferences", Kanhneman and Tversky (1979) pointed out that the majority of his subjects were not complying with the principles of Expected Utility Theory (EUT). It should be recalled that u(0)=0 and for simplicity purposes, an 80% chance of winning Rs4000 will be denoted by A and winning Rs3000 with certainty will be denoted by B. Therefore, the choice of B, in this case, would imply that U (3000)> 0.8U (4000) violating the axioms of EUT since under EUT one should prefer A to B. This could be explained by the fact that under EUT, 0.8U (4000)> U (3000).

Game 3

In the following game (Game 3), the choice was between a 20% chance to win Rs4000 and a 80% chance to win nothing and a 25% chance to win Rs3000 and a 75% chance to win nothing. In this case, even though the final wealth at stake is the same, a contradictory result has been obtained. 77% of the respondents chose the first option while the remaining 23% preferred a 25% chance to win Rs3000. This result is in line with the findings of Kanhneman and Tversky (1979). However, it should be noted that the percentage of respondents opting for the first choice in the current study (77%) is more than that of Kanhneman and Tversky(65%).

One important aspect observed in Game 3 as opposed to Game 2 is that when the probability of winning changes from winning Rs4000 with certainty to 25% chance to win Rs3000, the risk profile of the investors also changes from risk aversion to attractiveness to risk. As seen in Game 3, the respondents preferred the riskier prospect (the one offering a 20% chance of winning instead of a 25% chance of winning). Thus, when winning becomes less probable, the respondents tend to take into account the final wealth at stake and ignore the probability of winning.

Another violation of EUT can be noted here since according to EUT, an individual will have only one attitude towards risk, that is, averse, attracted or neutral to risk. However, by comparing Game 2 and Game 3, the risk profile of the participants changed according to the circumstances they faced.

Despite the majority of respondents adhered to the principles of certainty effect, it can be pointed out that out of 15 participants in the Banking sector, 7 chose the 25% chance of winning Rs3000 option implying that nearly half of the investors in the Banking sector is less prone to certainty effect as compared to investors in other sectors.

Game 4

This trend can also be applied for non-monetary outcomes as shown by the results obtained in Game 4 and Game 5. In Game 4 , the respondents were asked to choose between a 50% chance to win a three week tour to England, Italy and France and winning a one week tour to England with certainty. Once again for simplicity purposes, let us denote the first option by A and the second one by B. The following chart demonstrates that the respondents steered away from the risky prospect A (14.8%) to the certain prospect B (85.2%). Here, we can observe that the results obtained by Kanhneman and Tversky (1979) are roughly the same (14.8% V 22%). The rationale behind such behaviour is that people are satisfied with a smaller gain if the gain is guaranteed. Thus, in this scenario, we can say that investors are averse to risk.

Game 5

In Game 5, the same opportunities are given. The only difference is that the probability of winning a three week tour to England, Italy and France is reduced to 5% while the probability of winning a one week tour to England is reduced to 10%.

With reference to the chart, it can be seen that 75.4% has chosen the first option while the remaining 24.6% opted for the second one. Once again, the results obtained coincide with the findings of Kanhneman and Tversky (1979). By comparing Game 4 and Game 5, we can observe that when the probability of winning is reduced from certain to risky (5%), the respondents preferred the gain offering a higher payoff. Therefore, the results obtained confirm that investors are prone to the certainty effect.

General Comment

The results obtained in Game 2, 3, 4 and 5 shows that there is the presence of the certainty effect for both monetary and non-monetary outcomes. Professional investors in Mauritius prefer prospects which are certain to risky one. This phenomenon could be explained by the fact that investors may prefer to win a prospect even if its payoff is smaller instead of losing both opportunities (risk aversion). However, when the probability of winning decreases, the fact that both prospects are risky, the investors prefer the one offering the higher payoff even if it is riskier. Thus, it can be deduced that when a gain is certain, individuals are risk averse as opposed to when the gain is probable where investors are risk seekers. The risk profile of an investor changes in accordance with the circumstances he or she faces, thus, violating the axioms of EUT.

Reflection Effect

In the situations described below, the participants are awarded Rs20000 to participate in a survey whereby they are required to choose one option out of each pair.

In option 1, two choices are given, either a 30% chance to lose Rs1000 and losing Rs600 with certainty. The chart given below depicts that 86% of the respondents opted for the first choice and 13% opted for the second choice. This phenomenon is known as the reflection effect. As described by Kanhneman and Tversky (1979), reflection effect occurs when the preference of participants are reversed as the prospect changes from a positive prospect (gain) to a negative one (loss). In the current study, the preference for the certain gain of Rs1000 is reversed when it becomes a certain loss of Rs1000. It is important to note that in situation of losses, the respondents preferred the risky prospect (50% chance to lose R1000) over the riskless one (losing Rs600 with certainty). This phenomenon, that is individuals being attracted to risk when having to choose between negative prospects, was discovered by Markowitz (1952).

In option 2, investors are given a choice between 20% chance to lose Rs4000 and 80% chance to lose nothing and 25% chance to lose R3000 and 75% chance to lose nothing. The data collected show that 34.4% opted for the first choice while the remaining 65.6% opted for the second choice. It is important to note that when the probability of losing changes from 50% to 20% and from certain to 25%, so does the risk profile of the investors (from risk seeking to risk aversion). In Option 2, participants prefer to lose Rs3000 since it is a lower amount and has a higher expected value (-750 v/s -800) than losing Rs4000.

General Comment

Comparing option 1 and option 2

According to the research carried out, it has been found that investors tend to be risk seeking when faced with a situation where loss is certain. However, when the probability of losing changes from certain to probable, investors are averse to risk. Thus, once again, the risk profile of an individual changes as the circumstances he or she faces change, thereby, violates the properties of EUT.

Positive prospect v/s Negative prospect

When analyzing Game 1 and Option 1, it can be seen that for Game 1 participants preferred winning Rs600 with certainty while in option 1 they opted for 50% chance to lose Rs1000. Therefore, it can be said that "preferences between negative prospects is the mirror image of preferences between positive prospects." Kanhneman and Tversky (1979). Another observation made is that when having to choose between positive prospects, respondents are risk averse as found in the case of Game 1, 2 and 5 as opposed to when they have to choose between negative prospects where they tend to be attracted to risk. When outcomes change from positive to negative, a drastic shift from risk aversion to risk seeking can be observed [Williams (1966)]. Therefore, the certainty effect has an influence in the domain of gains as well as in the domain of losses. In the domain of gains, participants tend to overweight risk-free outcome while in the domain of losses they tend to overweight risky outcomes. As such, whether an individual will prefer an outcome which is certain will depend on whether the outcome is a gain or a loss, thus, defeating the principles of EUT.

Isolation Effect

Below is described a two stage game. In the first stage, there is a probability of 0.75 to end the game without winning anything and a probability of 0.25 to move into the second stage. Once a participant has reached the second stage, he or she has the choice between 80% chance to win Rs4000 and 20% to win nothing and winning Rs3000 with certainty. In this game, the final outcome depends on whether the participant has successfully completed the first stage.

Taking this fact into account, option A offers 0.25* 0.8= 0.2 probability of winning Rs4000 and 0.25 probability of winning Rs3000. Thus, the participants have a choice between (4000, 0.2) and (3000, 0.25), similar to the final outcome in Game 3.

However, as depicted in the chart, 45.9% chose option A while more than half of the sample population chose option B. The rationale behind this choice is that although this game is similar to Game 3 in terms of final outcome and probability, the participants "ignored the first stage of the game" Kanhneman and Tversky (1979) and considered this game similar to Game 2 whereby a choice between (4000,0.8) and (3000) was given. This finding is inconsistent with the rationality axioms of EUT where it states that participants should view the two stage game and Game 3 as similar since its expected value are the same. Therefore, the results obtained are in line with the findings of Kanhneman and Tversky (1979), with two notable differences. First, the proportion of investors choosing B is much lesser than that of Kanhneman and Tversky (1979) (78%).

Secondly, when stratifying the sample population into male and female, it can be seen from the table below that men are more influenced by the isolation effect than women. Out of 33men, 24 of them chose option B as opposed to only 9 out of 28 women choosing option B.

To confirm this result, a Chi-Square test was conducted. A P-value of less than 0.05 (0.02) implies that the null hypothesis (there is no significant difference between men and women) is rejected. Therefore, the P-value indicates that there is a greater tendency for men to ignore the first stage than women.