The leading normative theory in economics – expected utility theory – postulates that individuals should evaluate the options they face based only on these choices’ qualities. The decision to sell a stock, for example, should be based only on the stock’s current price and expectations about the future – not on its historical prices. For many, however, selling a stock for €1,800 that just a few weeks ago was trading at €2,000 feels like a loss, and they are reluctant to realise this loss by selling the stock. People tend not to evaluate their current situation based solely on its own qualities.
There is ample evidence that our willingness to take risks is influenced by prior gains and losses (Grinblatt and Keloharju 2000, Weber and Camerer 1998, Gneezy and Potters 1997, Haigh and List 2005). The leading theoretical model that explains such behaviour is Kahneman and Tversky’s prospect theory (1979). At the heart of prospect theory stand the assumptions that we:
- Evaluate outcomes relative to a reference point (prior expectations, our status quo, etc.), and that everything above is a gain, everything below is a loss;
- Dislike losses more than we appreciate gains of equal size; and
- Dislike losses so much that it makes us willing to take greater risk to avoid them.
Just what determines the reference point that is such an important driver of behaviour is a question for which Kahneman and Tversky (and related research in the 35 years since the publication of their seminal article) offer only partial answers.
In a recent study, we explore – both theoretically and experimentally – how people behave when their reference level is equal to the best offer they received in the past (Viefers and Strack 2014); that is, a model where your felicity from selling for €1,800 is lowered by the regret associated with not having sold at a higher price. While regret theory is not new to economics (Loomes and Sugden 1982, Wald 1945, Savage 1951), it has been predominantly applied to static now-or-never decisions. Note that this theory not only specifies what the reference price is, but also points that it is not a fixed level. It is a path- or context-dependent theory where reference points can change with every history of past offers. Depending on how the world plays out, regret leads to different preferences.
Towards a theory of dynamic regret
We first incorporate an aversion to regret into a simple model in which a decision-maker observes a series of random offers. The decision-maker can always waive or accept the current offer, but cannot reconsider past offers. Once an offer is accepted, no changes are allowed. This setting captures the fundamental trade-off of sequential decisions – the trade-off between the immediate gains with the loss of the ability to act in the future.
Regret and its anticipation affect this trade-off for three reasons.
- A higher offer in the past lowers the reward from acting today.
- The risk that even lower offers might be coming also affects the expected reward from waiting; and
- Continuing to gamble for future offers also includes the possibility of making up for current regret, which makes gambling more attractive.
In our paper, we demonstrate that for someone who feels regret, the optimal strategy is as depicted in Figure 1. The graph shows all possible combinations of prices (vertical axis) and past maximal prices (horizontal axis). All points below the 45° line are points where the current price is below its historical peak. For all points on the 45° line, the current price equals the past price. We have also shaded the regions where it is optimal to reject an offer (light grey) and where it is optimal to accept it (dark grey). For all offers larger than B, the price is high enough to warrant acceptance irrespective of the past peak. Note, however, the section of the acceptance region that stretches along the 45° line. For any price between A and B, acceptance is never optimal below the past peak.
Figure 1. Combinations of prices and past maximal prices
Hence, a theoretical prediction of the regret model is that for offers between A and B, decision-makers will gamble until they receive a payoff matching the best offer. We also demonstrate that this prediction sets the regret model apart from expected utility and prospect theory, which both predict that decision-makers have a reservation price that only conditions on the current price.
Regret and gambling for resurrection in the laboratory
Armed with this insight, we replicated our theoretical backdrop in an experiment. Participants took part in a computer-based experiment where they repeatedly played an asset-selling game. They observed a stock price over time – like on a ticker tape – and could decide to either sell at the current price or to hold out for a better one.
The behaviour of the participants over multiple rounds of the same task was fairly erratic. Contrary to the predictions made by expected utility and prospect theory, the price at which they sold clearly wasn’t stable over rounds. Instead, participants were generally reluctant to stop anywhere appreciably below the historical peak of the price series. Since the historical peak that subjects saw was different over the rounds, this helps explain the way they changed their mind between rounds. Data analysis confirms that the price at which stock was sold is systematically related to the past peak. Our estimates suggest that this makes subjects willing to gamble, on average, for prices up to 24% higher than initially planned.
We are clearly a long way from fully understanding how people behave in dynamic contexts. But our experimental data and that of earlier studies (Lohrenz 2007) suggest that regret is a part of the decision process and should not be overlooked. From a theoretical perspective, our work shows that regret aversion and counterfactual thinking make subtle predictions about behaviour in settings where past events serve as benchmarks. They are most vividly illustrated in the investment context.
Our theoretical findings show that if regret is anticipated, investors may keep their hands off risky investments, such as stocks, and not enter the market in the first place. Thus, anticipated regret aversion acts like a surrogate for higher risk aversion.
In contrast, once people have invested, they become very attached to their investment. Moreover, the better past performance was, the higher their commitment, because losses loom larger. This leads the investor to ‘gamble for resurrection’. In our experimental data, we very often observe exactly this pattern.
This dichotomy between ex ante and ex post risk appetites can be harmful for investors. It leads investors and businesses to escalate their commitment because of the sunk costs in their investments. For example, many investors missed out on the 2009 stock market rally while buckling down in the crash in 2007/2008, reluctant to sell early. Similarly, people who quit their jobs and invested their savings into their own business, often cannot with a cold, clear eye cut their losses and admit their business has failed.
Therefore, a better understanding of what motivates people to save and invest could enable us to help them avoid such mistakes, e.g. through educating people to set up clear budgets a priori or to impose a drop dead level for their losses. Such simple measures may help mitigate the effects of harmful emotional attachment and support individuals in making better decisions.
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