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 (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{E(x) = 1,200\ € \cdot 50 \% - 2 \cdot 1,000\ € \cdot 50 \% = -400\ €} } Even though the lottery seems profitable from a rational point of view (expected value without loss aversion: 100 €), the individual would turn down the offered lottery due to the underlying loss aversion (Yang 2019, pp. 1-5). Due to observations like the above, Kahnemann and Tversky propose that people demand a substantial premium to be willing to make a risky decision (Kahnemann, Tversky 1979, p. 279). The assumed parameter 𝜆 can be interpreted as the multiplicator by which the possible gain has to exceed the possible loss to be attractive for a loss-averse investor. In the example above, the possible win has to be above 2,000 € (possible loss 1,000 € x 2 [𝜆]) to be attractive.

An empirical study by Gächter, Johnson, and Hermann (2021) investigated the loss aversion in riskless as well as risky choices in a wide sample of customers of a car manufacturer (non-students). Their results show on the one hand that 82 % of the participants displayed loss aversion by refusing to take part in a riskless lottery. On the other hand, they show that 71 % of people also declined the risky choice by not participating in a lottery with a positive expected return. On top of that, the results emphasize that the loss aversion of each individual varies due to the respective situation as well as the different socio-demographic characteristics of each person (Gächter, Johnson, Hermann 2021, pp. 617-619).

Practical implications of loss aversion

Loss aversion helps to understand the following practical occurrences:

• Motivation to buy insurance to prevent potential losses, as loss aversion relates to prevention focus (van Raaij 2016, pp. 63-68),
• Stop-loss orders to avoid losses in trading on financial markets (Schulmerich, Leporcjer, Eu 2014, p. 408),
• Hesitation of companies to stop projects with poor financial performance (Yang 2019, p. 3),
• The tendency of investors to rather sell overperforming stocks than underperforming stocks, i.e., to sit out losses and realize gains too early which is also called the dispositions effect,
• Reluctance of investors to invest in risky assets or to possess any risky investments (van Raaij 2016, pp. 94-95),
• The nonparticipation of private individuals in stock markets due to fear of losses (Yang 2019, pp. 7-9),
• In asset pricing, it helps to understand the (too) high average return on stocks – the so-called ‘Equity premium puzzle’ (Yang 2019, p. 3).

Critical appraisal

As with every concept or theory, loss aversion also has its (possible) downside or points of criticism, which will be addressed below:

• It’s hard to actually define gains and losses, therefore, a lot of assumptions are required. On the one hand, regarding the reference point. On the other regarding the realization of gains and losses, they usually have to be realized in order to be counted.
• Evaluation frequency is another important point to mention. How often do investors evaluate their investments (Yang 2019, pp. 5-7)?
• Not all investors are fully loss-averse (Yang 2019, pp. 18-19).
• Loss aversion is highly individual; hence it can’t be generalized as it highly depends on an individual’s socio-demographic (e.g., age and education) background as well as financial preferences (Gächter, Johnson, Hermann 2021, pp. 617-619).

References

• Gal, D., Rucker, D. D. (2018). The Loss of Loss Aversion: Will It Loom Larger Than Its Gain?, J Consum Psychol 28 (3), S. 497–516.
• Gächter, S, Johnson, E. J., Herrmann, A. (2021). Individual-level loss aversion in riskless and risky choices, Theory Decis 92 (3-4), S. 599–624.
• Kahneman, D., Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk, Econometrica 47 (2), S. 263.
• Ōgaki, M., Tanaka, S. (2017). Behavioral economics. Toward a new economics by integration with traditional economics, Singapore: Springer (Springer texts in business and economics).
• Schulmerich, M., Eu, C.-H., Leporcher, Y.-M. (2014). Applied asset and risk management. A guide to modern portfolio management and behavior-driven markets, Heidelberg: Springer (Management for Professionals Ser).
• van Raaij, W. F. (2016). Understanding Consumer Financial Behavior. Money Management in an Age of Financial Illiteracy, New York: Palgrave Macmillan (Springer eBook Collection Economics and Finance).
• Yang, L. (2019). Loss Aversion in Financial Markets, Journal of Mechanism and Institution Design, 4(1), 119 –137.

Author: Robin Jungert