Hello, welcome back. In this lecture, you're going to learn about one of the most important puzzles in finance, the equity premium puzzle, and how we might understand this puzzle based on behavioral finance. Specifically, through a specific behavior that we call myopic loss aversion. So, first of all, what is the equity premium puzzle? Well, the equity premium puzzle refers to the empirical fact that stocks have outperformed bonds over the last century by a surprisingly large margin. So estimates of the historical equity premium, whether you look at the data since 1928, or the more recent data from 1966, or even the most recent ten years, all of these estimates show that the equity premium has been around 6 to 7%. So what does this mean? Well, it means that investors have required 6 to 7% over the risk-free rate to hold stocks. So, what is the puzzle, you might ask? Well, the puzzle is why is the equity premium so large? Right? Or is it consistent with rational expected utility maximization models of economic behavior? Well, it would be consistent if investors were very, very, very, very risk averse, right? In fact, researches have estimated that it would take a risk aversion coefficient as high as 30 to justify such a large equity premium, when in fact, as we saw in the previous course, typically, investors' risk aversion coefficient is typically around one. So then why is the equity premium so large? Or put alternatively, why is anyone even willing to hold bonds then, right? Well, [COUGH] instead of looking at rational models, we can use behavioral models to understand this puzzle. In particular, we're going to look at specific type of behavior, what we call myopic loss aversion, to explain this phenomenon. So myopic loss aversion is based on two concepts. The first is, loss aversion, recall that loss aversion refers to people's tendency to be more sensitive to losses or reductions, than to increases or gains. Right? So we saw this in the previous lectures as prospect theory. And the second part or the second component of myopic loss aversion, is mental accounting. Again, recall that mental accounting refers to the implicit methods that we use to organize in our minds, for example, in evaluating financial outcomes like transactions or investments or gambles. To understand how myopic loss aversion works, consider the problem first posed by the economist Samuelson. So Samuelson asked the colleague whether he would be willing to accept the bet that has 50% chance of winning $200 and a 50% chance of losing $100. Well, his colleague turned it down, saying that he would feel the loss of $100 much more than the $200 gain, but he also added that he would willing to take the bet, 100 times, as long as he did not have to watch the bets being played out. Now of course, this provoked Samuelson into writing a theorem that shows that his colleague was completely irrational, his behavior being inconsistent with what we'd expect from expected utility theory, but let's dissect his colleague's response a little bit more. That he doesn't accept the bet, of course illustrates loss aversion, right, the concept of loss aversion. But in addition, right, mental accounting is, the role of mental accounting is illustrated by noting that he is willing to except more such bets, as long as he doesn't have to watch them, right? Even though, the single bet by itself is unattractive to him, right? So, what this example illustrates, is that when decision-makers are loss averse, they will be more willing to take risks if they evaluate their performance infrequently. And this combination is what we call myopic loss aversion. So, how is this related the equity premium puzzle? Well, consider for an example an investor who has to choose between a risky asset, let's say with an expected return of 7%, right, and a volatility of 20%, risky asset, right? Well, that's just like the equity market, and a risk free asset, right, a safe asset that pays for sure, 1% return, right? Now, the attractiveness of the risky asset will depend on the time horizon of the investor, right? So two factors contribute to the investor being unwilling to bear the risks associated with holding equities, and therefore require large risk premium. One is loss of aversion, and the other one is the fact that investors typically have short horizons, right? Short evaluation periods. So yeah, I mean it's It's a plausible idea, right? So, can myopic loss erosion explain the magnitude of the equity premium puzzle? Well, you might ask for example, how often would investors have to be evaluating their portfolios, right, to explain the observed equity premium of, let's say 6.5%, right, according to this theory? Well, it turns out that the answer is in the neighborhood of about one year, right, which is what we observe, very plausible and not far from what we observe, okay? Now, in fact, it can be shown that if the evaluation period were longer, right, let's say it was two years, the required premium would fall to 4.65%. And if you even considered longer evaluation periods, let's say, five, ten, and twenty-year evaluation periods, the premium, the corresponding premium would be 3%, 2%, or 1.4%, right? So it's like as if, right, for someone with a 20 year investment horizon is as if there's a psychic cost of evaluating the portfolio annually of about 5.1%, right, per year. Where does that come from? Well, if you're evaluating every year, right, the required risk premium is 6.5, if we didn't evaluate at all, the required risk premium falls down to 1.4%, so it's like a psychic cost, right, we can't not look at the performance, of about 5.1%. It's pretty amazing. Well, you might say, well, but the bulk of the financial assets are held by institutions, right? So, they should not be subject to myopic loss aversion. But yes they are, right? Yes, they too are subject to myopic loss aversion. Think of pension funds, right? A typical asset allocation for pension funds is 60% stocks and 40% bonds, and treasury bills. Now, given the historical equity premium, and the fact that pension funds have essentially an infinite time horizon, right, why wouldn't they invest in higher proportions in stocks? Well, think about it. The pension fund is indeed likely to exist as long as the company remains in business, right? But what about the fund manager, right? The pension fund manager reports on the performance of the pension plan and the returns on the funds' assets pretty regularly, right, probably on a much shorter period, right? And he must account for any losses not to get fired, right? So, his shorter horizon induces myopic loss aversion. So, in this lecture you learned about the equity premium puzzle, the idea that high rates of returns on stocks is difficult to reconcile with low risk aversion within the standard expected utility paradigm. Myopic loss aversion offers one possible explanation for why we observe such high equity premium.