## The Prospect Theory

The prospect theory was developed by Daniel Kahneman and Amos Tversky between 1979 and 1992. They showed how human decisions depart from those predicted by standard economic theory in decision-making under uncertainty. The prospect theory better accounts for observed behavior, taking into account heuristic shortcuts. Contrary to the expected utility theory, which gives a mathematical optimization model, the prospect theory describes people’s real behavior.

The curve shown above compares the psychological value we give to wins and losses to their actual value. We can clearly see that the curve is not symmetrical: it is steeper on the side of the losses than that of the wins. This is what we call “loss aversion”. As an approximation, losing money is nearly twice as painful as gaining money is satisfying.

Similarly, people do not make the same decisions when it comes to choosing between a certain win/loss and a potential benefit. When people are proposed a certain gain ($1,000), they prefer to keep it rather than taking the risk to gain more (if this $1,000 becomes uncertain). Conversely, when people are submitted a certain loss, they prefer to take the risk of losing more if they have a chance to avoid the initial loss.

However, as always, things are not as simple as an equation or a tradeoff between two situations. That is where behavioral finance intervenes. The influences of the decision are greater than what we would expect in standard economic theory.

Suppose a client has invested €60,000 in a stock, and that this stock is entering a downtrend.

2 strategies are proposed to preserve our client’s capital.

If strategy A is adopted, our client will conserve €20,000.

If strategy B is adopted, there is 1 chance out of 3 that the €60,000 are conserved, and 2 chances out of 3 that everything is lost.

Which strategy will you choose?

Empiric studies show that 65 % choose A, 35 % choose B.

Suppose a client has invested €60,000 in a stock, and that this stock is entering a downtrend.

2 strategies are proposed to preserve our client’s capital.

If strategy A is adopted, our client will lose €40,000.

If strategy B is adopted, there is 1 out of 3 chance that nothing is lost, and 2 out of 3 chance that the €60,000 are lost.

Which strategy will you choose?

Empirics studies show that 32 % choose A, 68 % choose B.

We observe that the answers related to the two situations are diametrically opposed: while 65 % chose the first solution in the first case, 68 % chose the second solution in the other one. Yet, taking a closer look at the two situations, we realize that these are exactly the same.

Again, the concept of loss aversion comes into play. We usually make decisions to avoid losing: that is what we do in the second situation, when the first proposition makes us lose €40,000. In the first situation, when the first solution was presented as a win of €20,000, we were unwilling to take more risk and the majority of people were content with this.

Besides the loss aversion, we can also clearly observe the diminishing sensitivity of the curve, known as “diminishing marginal utility”. The levelling off of the curve represents that we’ll enjoy winning €100 if we only have €100, much more than we would enjoy winning €100 if we had €900. In fact, behavioral finance shows that our decisions are almost always taken from a reference point, rather than from absolute values.