Hello everyone. Welcome back. In the last several lectures we have been talking about the kinds of errors we make in processing information that naturally stem from the way we think. Now I want to revisit preferences, preferences to describe how we make choices, right? The trade-offs in describing how we balance of risk and reward, right? So you might remember that in the previous course, we talked about mean-variance preferences or mean-variance utility to describe investor preferences. While mean-variance preferences were very convenient to use, they were all so far from reality, right? In fact, preferences are often multidimensional and they are shaped by ethics, psychological tendencies, peer decisions, or other social backings, right? So in the next few lectures, you will learn about other types of more realistic ways of describing preferences. But first, what are some shortcomings of the mean-variance utility? Well, for starters remember that mean-variance preferences treat upside or downside fluctuations relative to the mean-variance completely the same. But we just saw lots and lots of evidence that, in fact, investors feel losses much more powerfully than any equivalent gain, right? We're going to see prospect theory that describes how people actually make decisions in this way. Second, remember that mean-variance preferences centered on the first two moments, right? The mean and the variance. And the assumption was that, that's all investors care about, but of course, we know that given the chance of a large lottery payoff, for example, investors like positive skewness and at the same time they shy away from negative skewness, all right? A huge downside risk. Third, in maximizing expected utility, right, we assume that rational investors are able to use objective probabilities. However again, right, we saw less and less of examples where this is not necessarily true. Given complex problems, people perceive probabilities very differently than actual probabilities, right? In particular, they tend to overestimate the probability of disasters. Finally, perhaps utility is not absolute but it's relative, right? It could be relative. In other words, what might be considered bad times for an investor, need not necessarily be defining absolute terms. What I mean by that is, maybe being rich or poor, right? Feeling richer or poor in absolute terms does not matter as much as whether you feel rich or poor relative to a neighbor or perhaps a relative to what you felt in the past., right? So it could be good, all right? So in the next few lectures we take a look at some more realistic utility functions that incorporate all of these considerations.