Hello everyone, thank you for joining me again. All right, so in this lecture you're going to learn about prospect utility or loss aversion utility. Prospect theory was developed by Dan Kahneman and Amos Tversky. You've been hearing about these guys, right? As a descriptive framework of how we make choices in the face of risk and uncertainty. And their starting point was the role of loss, right? And we've been seeing lots of examples of that. How people respond to the prospect of loss. So here's one of their examples. Suppose you face a choice between, A, a sure loss of $7500. Or B, 75% chance you will lose $10,000 and a 25% chance you will lose nothing. Which one would you choose? Now, notice that the expected loss in either choices, right, the outcome is the same. It's $7500. It's a loss of $7500. But would you deliberately choose the guaranteed loss? Or take a chance, all right? In fact, most people would opt for the latter, why? Well because nobody likes to lose, right? The uncertain outcome holds out the possibility that they may not have to lose, right? And this phenomenon is called loss aversion. And it's not difficult to find real world examples of loss aversion, right? The idea of loss aversion also includes, for example, the finding that investors are typically very reluctant to lock in a loss, right? So consider an investment bought at $1,000, for example, right? And let's say that it quickly rises to 1,500, right? An investor would be tempted to rush to sell it in order to lock in the profit, right? In contrast if the investment had dropped to $500, an investor might tend to hold onto it to avoid the pain of locking in the loss, right? The idea of a loss is so painful, that people tend to delay recognizing it. Now, here is the real example from an individual investor who happened to be invested in Steadman mutual funds. And according to Lipper, between June 30th 1994 and April 15th 1997 Steadman funds did not do well, right?. In fact at least one of them had their worst 10 year returns over this period. Throughout the 1950s, 60s, and 70s Melvin Klahr, a math instructor living in Florida, had $1000 invested in Steadman funds. And his last purchase was at the end of 1974. Now by June 1997 however, his position was down to $434. Had he invested in the average fund, his investment would have grown to $29,000, right? Yet he kept holding onto his Steadman shares. He could not bring himself to sell, right? The idea of realizing the loss, just was too painful to recognize, right? And prospect theory explains all that. So prospect theory has two parts. First, investors find the pain of losses to be greater than the joy from gains, right? So, preferences described by prospect theory or by loss aversion utility allow investors to have different marginal utilities for gains and losses, right? So that very different from typically the many various preferences that we think of. Second, Kahneman and Tversky went even beyond probabilities, not even subjective probabilities. In their formulation, they use decision weights, which did not necessarily obey probability laws, right? They do not, for example, have to some to probabilities. What this allows however, is that they allowed the investors to potentially over weigh low-probability events. Like disasters or winning the lottery, right? Okay, so here is a graph of what a typical loss aversion utility function looks like. All right. So notice that the utility is defined relative to a reference point, right? Now this could be zero or it could be some bench mark return, right? And gains are defined as positive values on the x-axis, right on this side, right? And losses are defined as negative values on this side, right? Now notice that the utility function has a kink, right? Right at the origin. So, there is an asymmetry in how investor's treat gains versus loses, right? Do you feel like the function is concave? Let me change that color. All right, it's concave when it comes to gains, right? So investors are risk-averse on this side when it comes to gains, right? But the utility function is convex over losses. Which captures the fact that people are risk-seeking over losses, right? In other words, they are willing to accept some risks to avoid or avert a certain loss, right? Also notice that the utility function for loses is much steeper than the utility function over gains, right? This implies that investors are much more sensitive to loses than to gains. Now central to prospect theory is also this idea that people would much rather take risk to avoid loses, right? You saw that in the loss region. People are in fact risk seeking. This is what some people might call get-evenitis, right? This explains the behavior of investors with losing positions. Who show a strong desire to just get back to break even. In other words they will take risks and they exhibit risk seeking behavior when facing a loss. But of course some people learn about get-evenitis the hard way. I don't know if you recall the case of Nicholas Leeson, right? Leeson of course became very famous in 1995 for having caused the collapse of Barings, right? A British bank that was more than 200 years old. How? Well, he essentially lost 1.4 billion dollars through trading. So what happened was in 1992 he started trading. A bit rogue, in a rogue way, right? To cover up errors made by subordinates. But it didn't really go his way and soon, right, he incurred additional losses. And he eventually, right, let get-evenitis get better of him, right? In his words, what he said was, he gambled on the stock market to reverse his mistakes and save the bank. He was just trying to recoup, right? Get even, right? But of course, he lost it all. All right, so in this lecture you learned about prospect theory or loss aversion utility, which is based on the idea that people hate to lose. So we treat gains very differently from losses, all right. Prospect theory can explain, for example, why we buy insurance at the same time that we buy lottery tickets. Prospect theory can also help us understand some of the examples we looked at in earlier lectures, right? Why people make different choices in situations with seemingly identical outcomes, right? Prospect theory, in other words, can explain framing effects.
