The paper ‘Prospect Theory: An Analysis of Decision Under Risk’ was published by Daniel Kahneman and Amos Tversky in March 1979.

What is Prospect Theory?

Kahneman and Tversky published what is now considered to be the seminal paper describing how we make decisions. Prospect Theory replaced the ‘Expected Utility Theory’ which hitherto had dominated the discussion of decision-making under risk. The word ‘prospect’ refers to a gamble. After Kahneman and Tversky published the Prospect Theory in 1979 the work attracted a lot of attention, comment and criticism. It wasn’t immediately accepted by the economists. As a result, in 1992 they published a modified version of their Original work and called it the Cumulative Prospect Theory and it is this theory that is now widely used in academia.

Prospect Theory highlighted the fact that we don’t make decisions based on an analysis of the probabilities of the outcomes. We use heuristics instead of using probabilities and expected values. Their work has gone a long way in improving the ‘efficiency’ of the global markets. Ergo, we are moving from a comparatively inefficient market to one that is becoming efficient with every passing day. The five elements of the Prospect Theory are:

  • Certainty Effect
  • Reference Point Dependence
  • Loss Aversion
  • Diminishing Sensitivity
  • Probability Weighting

Let us consider each of these separately:

Certainty Effect

Under the earlier theory which was the ‘Expected Utility’ theory, it was assumed that our preferences are weighted by the probabilities. In other words, we weigh the probabilities of occurrence and then make decisions according greater weight to those outcomes that are more probable. Kahneman and Tversky showed that we don’t actually do that. We prefer to take decisions according to the certainty, in the process ignoring probabilities altogether. They called this the certainty effect; we have a strong preference for outcomes that are defined as a ‘sure thing’. To illustrate, given the choice between (a) a guaranteed win of Rs. 100 and (b) an 80 per cent chance of winning Rs. 150, we tend to opt for (a). This is despite the fact that the expected value of option (b) above, is the higher of the two.

Reference Point Dependence

Kahneman and Tversky highlighted the fact that people derive utility from gains and losses, measured in relation to some reference point. In other words, we don’t measure our gains and losses in absolute terms, but use comparison metrics for assessing them. It seems that we tend to perceive changes in attributes such as brightness, loudness and temperature rather than their absolute levels. While investing outcomes that are better than our reference point are perceived as gains and outcomes that are worse than their reference points are perceived as losses. If for example, your usual birthday gift from your parents is the equivalent of Rs. 1000 and on your next birthday they hand out Rs. 800, you feel we have lost something. If they hand out Rs. 1200, we fell that we have gained. Kahneman and Tversky called this feature of human behaviour ‘reference point dependence’.

Olympic Athletes Might be Happier Winning Bronze Medals than Silver

This phenomenon has been described as ‘counterfactual thinking’ because the silver medalist is the first one who lost! Psychologists have studied this extensively and they came to the conclusion that a person’s achievements matter less than how that person subjectively perceives their achievements. If the silver medalist compares up, he is unhappy. But if he compares down, he ought not to be so. Its because of our Refence Point DSependence.

Rule of Three

A related concept is called Trade Off contrast or Extremeness Aversion. Consider the following example.

There are two groups of participants, say Group A and Group B.

Group A is offered two choices. they have to decide between buying (a) a smartphone manufactured by Xiaomi model I costing Rs. 10000 for sale at a discount of 35 per cent and (b) a smartphone manufactured by Samsung model I costing Rs. 20000 at a discount of 35 per cent. It’s a simple choice and 60 percent chose the Xiaomi over the Samsung.

Group B is not only offered the same choices as Group A but also an additional third choice as well – another smartphone manufactured by Samsung model II that costs Rs. 30000 and is available at a discount of 10 per cent. What do you think happens? Psychologists conducting similar experiments found that now the choices flipped. Nearly 60 per cent chose the Samsung I, 30 per cent chose the Xiaomi and 10 per cent chose the Samsung II.

This is called a trade-off contrast or an Extremeness Aversion, whereby we move higher in the value chain, just because we have a choice. Here is how it works: when customers are offered three products (rule of three), one high-priced, one mid-priced and the third low-priced, they tend to gravitate upward from the low-priced one to the one that is mid-priced. The justification that we give ourselves is that we are ‘saving money’ and that we are getting a ‘good deal’ with the ‘compromise product’. It is used in car dealerships, restaurants, coffee shops and at a host of other places that are trying to sell us something. Whenever you see the Rule of Three being employed, you know what is happening and maybe, you might now end up making a rational choice.

Loss Aversion

The idea that we are much more sensitive to losses (even small losses) than to gains of the same magnitude. The reason Loss Aversion as a concept has gained importance is because it highlights a fundamental truth about all of us, which is the fact that we are motivated to act when we are fearful. In practical terms, the pain of losing Rs. 100 is far higher than the joy of gaining the same (or even a slightly higher) amount. If you consider the world of sports, a defeat in a cricket match causes fans more pain than victories bring them comfort. In fact, emotionally the ‘pain v/s comfort ratio’ is estimated at 2:1.

Implications of Loss Aversion

Diminishing Sensitivity

Under the Prospect Theory, our sensitivity to things becomes smaller and smaller. The first spoonful of ice-cream on a hot day has a greater utility for us than the last one. It is similar to the law of diminishing returns that economics teaxhes us.

Probability Weighting

Concave v/s Convex: A concave surface is one that curves inwards and a convex surface is one that curves outwards. In investing, a concave strategy is one that has less upside potential and more downside risk. A convex strategy has more upside potential and less downside risk. There is nothing universally correct about either of the strategies. In fact, the more people that use one of the strategies (concave or convex)., the better the other strategy works. A recent example is the Great Financial Crisis (GFC) of 2008-09. In January 2008, most institutional investors used concave strategies i.e. ones which had unlimited downside potential as compared to the downside risks. To restate the concave v/s convex conundrum in probabilistic terms, in January 2008 the markets were at All-Time Highs and the probability that they would move higher was lower than the probability that they would move lower. In October 2008, the probabilities switched sides. However, many money managers were caught wrong-footed twice in the same calendar year.

What Kahneman and Tversky highlighted was the fact that we tend not to weight our decisions according to their objective probabilities. Instead, we transform the objective probabilities and we end up overweighting low probability events and underweighting high probability events. A rational person should, in fact, be doing the reverse of the above. In other words, when we stand to gain something we are risk-averse, but when we stand too lose something, we inadvertently tend to be risk-seeking and taking low probability bets.

How we frame the problem matters. If we frame the problem in terms of a loss, we become risk-seekers and if we frame the problem in terms of a profit, we become risk averse. Loss Aversion differs from Risk Aversion. Risk Aversion is when we choose between gambles. Loss Aversion is when deciding whether to play. If we decide not to play at all, we are Loss Averse. Having decided to play, if we choose the safer option, we are risk-averse.

Consider the following example. Two investors bought shares in Infy. One purchased them at Rs. 800, the other purchased at Rs. 900. The current share price of Infy is Rs. 850. The investor who is “in the black”, showing Rs. 50 as a notional profit, is inclined to sell and realise his or her gains. The other investor who is “in the red” with an Rs.50 loss is inclined to hold onto the shares in the hope that they will go back up.

Another Example:

  • Suppose we have bought stock A for Rs. 40 and the current price is Rs. 80. We are afraid that the stock will come down and hence we want to book our profits – we are risk-averse, even though the probability of the stock moving higher is more than that of it moving lower.
  • Contrarily if we were to have bought a stock for Rs. 40 and it sinks to Rs. 20, we feel it is safe to buy more of the same since it has halved in price. Inadvertently, we are taking a low probability bet and the risk is higher since doubling down on a losing bet increases the absolute loss that we might incur in the event that the price continues to fall. Most investors misinterpret this as a safe bet

In other words, we are risk-seeking when we are losing money and risk-averse when we are making money. This risk-averse v/s risk-seeking behaviour is called the reflection effect. In the example above, what we are doing, almost unknowingly, is that for profit-making positions, we prefer to book a gain and for loss-making positions, we increase the absolute amount of the loss. We should, in fact, be more patient with winning trades and impatient with losing trades. Kahneman and Tversky called this phenomenon as a demonstration of ‘inverted risk preferences’ for uncertain choices.

Daniel Kahneman – Talks at Google – System 1 v/s System 2