Loss aversion

Loss aversion is a psychological phenomenon first brought to light by Kahnemann and Tversky (1979) as part of their concept of prospect theory, which is the fundamental approach to explaining human decision making in the context of behavioral finance (Kahnemann, Tversky 1979, pp. 263-291). Therefore, it is a counter-theory of the expected utility theory that was founded by Morgenstern and von Neumann, which was the stepping stone of modern game theory (Ogaki, Tanaka 2017, p. 33).

The most important observation in loss aversion is that humans perceive losses with a greater psychological impact than gains of a similar magnitude. This means that a loss of €50 has a greater negative impact than a gain of €50 has a positive impact. These respective gains and losses are assessed as changes from a neutral reference point, which is often seen as the status quo. The current scientific consensus assumes, on the one hand, that it is a fundamental and generalizable psychological principle. On the other hand, it considers it as an atypical principle that has no specific psychological processing and merely describes behavior rather than explaining it. (Gal, Rucker 2018, p. 498).

This psychological effect has a variety of implications for an individual’s investment behavior and is in line with a wide range of other empirical findings in this study field, such as the endowment effect (Ogaki, Tanaka 2017, p. 56) and the disposition effect (Schulmerich, Leporcjer, Eu 2014, p. 401). This phenomenon is often referred to as the reason why human beings reject lotteries such as 50:50 beats, or even lotteries that are slightly advantageous (Yang 2019, p. 2).

Evaluation of gains and losses

Within prospect theory, it is stated that people use the following value function to evaluate their gains and losses based on their respective reference points. This value function can be denoted as follows:

Failed to parse (unknown function "\begin{cases}"): {\displaystyle \mathrm{V(x) =} \mathrm{\begin{cases} \mathrm{x}, & \mbox{if }\mbox{x ≥ 0} \\ \mathrm{𝜆x}, & \mbox{if }\mbox{x < 0} \end{cases}} } In which x < 0 represents the losses and x > 0 represents the gains. The parameter 𝜆 denotes the risk aversion of the individual person, which’s empirical value is close to 2. Hence, a risk-averse investor has a parameter 𝜆 > 0, a risky investor has the parameter 𝜆 < 0, and a completely risk-neutral investor would have a parameter 𝜆 = 1. In order to evaluate the attractivity of a lottery, a person applies the above-stated value function to each possible outcome (possible gains and losses) and multiplies it which the underlying probability to receive the individual expected value of the respective lottery.

Example: A person faces a 50:50 lottery to either win 1,200 € or lose 1,000 €. Assuming the person has a risk aversion that correlates with the empirical value of 2, the lottery would have the following expected value:

Failed to parse (syntax error): {\displaystyle E(x) = 1,200 € \cdot 50 % - 2 \cdot 1,000 € \cdot 50 % = -400 € }