Hi, everyone, welcome back. In this lecture, you're going to learn about another very important puzzle, what is known as the volatility puzzle, or the question of whether stock prices move around too much. And, again, we're going to look at how behavioral theories may be able to shed light on this puzzle. So to understand the volatility puzzle, or the question of whether stock prices move around too much, let's think about what should determine a stock's price, all right? So, for example, suppose you're going to buy a share of stock today and hold it forever, right. You can't leave it to your kids or whatever, right, so you're never going to sell the stock. So the only money you're going to receive from it are the expected future dividends that you will receive over time, all right. And as we saw in the very first course of our series, the value of the stock today, right, should be equal to the present value of all the expected dividends that you will be collecting going forward for forever, right, discounted at the appropriate discount rate. Of course, we don't know what the future dividends will be. But the stock price, right, is at best a forecast, or the market's expectation, of the present value of all those future expected dividend payments. Now, an important property of a rational forecast, as a stock price is supposed to be, right, is that it should not or can not vary more than the thing that we're trying to forecast, right. So let me give you an example. Imagine that you're trying to forecast the daily temperature in Singapore, right. I've never been there myself, but I am told the weather doesn't vary all that much over there, right. Typically, the temperature is around 90 degrees Fahrenheit or 32 degrees Celsius, right. So maybe on a hot day it goes up to 95 degrees, right. And maybe on a coolish day, maybe it drops down to 85 degrees, right. So if you were to predict 90 degrees every day, you wouldn't be that far off. But if you predicted 50 degrees on one day, right, that is colder than it actually ever gets, and then 110 degrees, right, 110 degrees on another day, much hotter than it actually gets, you would be clearly off the mark, ight. And you would be violating that a rational forecast should not vary more than the thing that we're trying to predict, right. You get the idea. So now enters into the picture, Bob Shiller. Bob Shiller, of course, of Yale University. Right, I'm talking about Bob Shiller of Yale University who won the Nobel Prize in Economics jointly with Fama and Hansen just a few years back, right. What he did is, he applied, basically, this principle to the stock market, all right. He collected data on stock prices and dividends all the way going back to 1871. And then for each year, he computed the present value of the dividends that would accrue to someone who bought portfolio stocks that existed at the time, all right. Essentially, kind of an ex post forecast of the dividends since he took the actual dividends that did get paid out and discount them back, all right. So he found that, indeed, the present value of dividends is pretty stable. But stock prices, which we should be interpreting as a forecast of the present value of those dividends, are all over the place. They're highly variable, right. So, in fact, you can see these findings in this graph, right. The dark flattish line. Let me. Right, the dark flattish line is the present value of the dividends, right. While the other line that's all over the place is the level of the stock prices, right. And he called his paper, Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends? And based on this picture, the answer appears to be yes. Now, the lesson here, is that stock prices can move away from fundamental value for long periods. But then they eventually revert back. And, in fact, in 1996 Shiller, along with his co-author, John Campbell, gave a talk to the Federal Reserve Board warning that stock prices in the US seemed dangerously high. And they appear to have had an influence because just two days later after their talk, the then Chairman of the Fed, Alan Greenspan, famously used the term "irrational exuberance," right, to describe the state of the US stock market at the time. So what did Shiller and Campbell tell the Federal Reserve Board at that time? To understand this think back to our discussion of value stocks, all right, stocks with very low prices relative to Their earnings. All right, value stocks. All right, low P/E ratios, basically, all right. Low P/E ratios or extremely low prices. Right, these stocks predictably outperformed the market. Well, we could do the same thing for the overall marked. We could compute a price-earnings ratio for the overall market. Does the same principle apply? Can you beat the market by buying stocks when they are relatively cheap and avoiding them when they are relatively expensive? Well, the answer is yes, but, right, and I'll tell you what the but is in a minute. So here I have a graph of the long-term market P/E ratio, right? And the way Shiller computes this is to divide the market price of an index, say there's 7,500, by a measure of the earnings average over the past ten years. Right, so this is what we call the long-term P/E ratio. Right, and this way it kind of smooths out the temporary fluctuation over the business cycles. Now, of course, this is with the benefit of hindsight. But you can see, right, what an investor would have liked to do, right, looking at this P/E ratio, right. Notice that whenever the market pulls away from historical trends, right, sorry. Right, there's a peak in the P/E ratio, right, and then it reverts back to the mean. So, for example, stocks looked relatively cheap in the 70s, right. They eventually recovered and then they looked relatively expensive, right, in the 1990s until they eventually crashed, right. So what I'm trying to say here is that there seems to be some predictive power of this long-term price-earnings ratio, right. It does have some predictive power, but the predictive power is not very precise. Why? And this is why I have to say but, right. Now, was Shiller right or wrong in his warning at the time in 1996, right? Well, at the very best he was four years early, right, before the market actually peaked. So he was wrong for a long time before he was actually right, all right. And this lack of precision, yes we have predictability, but it's not really precise, means that the long-term price-earnings ratio is not exactly a sure way to make money, right. So if you followed this warning and had bet against the market in 1996, you probably would have gone broke by the time it peaked. So the question, of course, is can behavioral theories help us explain these patterns? Well, it's possible that it may be, right, maybe that it's investors biases that generate these patterns. So one possible story is based on the representative of this bias that we talked about, right. It's the idea of law of small numbers, right, where people tend to expect, right, even short samples to be informative. If the investor, for example, sees many periods of good earnings, right, the law of small numbers leads him to believe that earnings growth has gone up, right, and that earnings will be high in the future, right. Similarly, investors may extrapolate past returns too far into the future when forming expectations of future returns. Another possible explanation, or another story, relies on overconfidence, right. So suppose an investor has seen some public information about the economy, right, formed an opinion about the future cash flow growth. And then he goes and does his own research and becomes overconfident about the information he gathered, all right. He overestimates the accuracy and puts too much weight on that information relative to his pride, right. And if the private information that he gathered is positive, he will push up prices too high relative to the current dividends. Finally, right, another possible explanation is based on the house-money effect. Think about the house-money effect that we talked about before. The idea that after prior gains, right, people tend to be more willing to take on gambles that they would normally refuse, all right. A model of this kind could also explain the volatility puzzle. So suppose there is some good cash flow news. This pushes up the stock market, right, generating prior gains, gains for investors, who are now less scared of stocks, right, because any losses will be cushioned by the prior gains, right. And then they therefore discount future cash flows at a lower rate, pushing prices up relative to current dividends. All right, so in this lecture, we discussed the puzzle that has been the subject of many debates. Whether stock prices move too much to be rationally justified by subsequent changes in dividends. We saw that long-term price-earnings ratio has some predictive power for future returns, but it is far from perfect, right. And we also looked at some behavioral theories that might explain these patterns.