Formulated in 1979 by Amos Tversky and Daniel Kahneman, the prospect theory, also known as the loss-aversion theory, posits that people do not relate the same levels of pleasure and pain with equal effects in which an individual tends to be more sensitive to loss compared to the same amount of gain. When deciding between multiple options, people avoid losses and optimize for certain wins since the agony of losing outweighs the satisfaction of an equivalent gain. The theory outlines how people choose between different “prospects” and how they gauge the perceived probability of each option, commonly in a biased or inaccurate manner. For example, the utility of a trader gaining USD100 is not the same as gaining USD200 and then losing USD100, even though the net amount of gain is USD100 because people are more emotional about losses, as shown in the below graph where the psychological value of the loss is larger than that of the gain.
The theory also explains one of the biases that people commit when making decisions. People are willing to take big risks to escape losses. A famous example is an incident that happened in the Barings Bank which is one of the oldest merchant banks in England that has defunct after 233 years of operations. The story begins by hiring Nick Leeson, a trader in the bank, who has covered losses in an error account worth more than GBP 23 million. Leeson used the doubling strategy to escape losses by betting double the lost amount to recover the losses. However, in 1995, the Great Hanshin Earthquake sent his trading positions into complete disarray with a total loss of around GBP 827 million, and his willingness to take a bigger risk to escape losses cost the collapse of a 233 old bank to be sold for GBP 1.
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It is important for investors to guard against loss aversion by reframing losses as gains and setting conservative stop-losses to lessen realized losses. Remembering all of the intricacies of each option causes cognitive strain, so focusing on the differentiators makes sense. Leaving out similar aspects reduces the burden of comparing different options, but it can also result in inaccurate choices depending on how those choices are presented. Kahneman and Tversky did an experiment; they gave participants 2 different cases.
In Case 1, they gave people USD 1000 and gave them two options:
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Gaining another USD 1000 with a likelihood of 50% and gaining nothing with a likelihood of 50%
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Gaining USD 500 with a likelihood of 100%.
In Case 2, participants are given USD 2000, and they are given two options:
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Losing USD 1000 with a likelihood of 50% or not losing at all with a likelihood of 50%
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Gaining another USD500 with a likelihood of 100%.
Because the starting sums in the two situations were different, it turned out that the two scenarios were essentially equivalent: if they chose option B in the first scenario or option D in the second scenario, they would have the same amount of money in the end. (Options A and C are also interchangeable.) People, however, made opposite choices in the two scenarios: in case 1, the majority chose the risk-averse option B, whereas in case 2, the majority chose the loss-averse option C. And as implied by the example, changing the problem framing by modifying the initial amount and choices correspondingly led to a different decision.
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