econ-252-08: Financial Markets (2008)
Lecture 6 - Efficient Markets vs. Excess Volatility [February 1, 2008]
Chapter 1. Last Thoughts on Insurance and Catastrophe Bonds [00:00:00]
Professor Robert Shiller: I want to talk today about the efficient markets hypothesis. Let me just first say, last lecture was about insurance and I was telling you about the theory of insurance and how it has evolved over the years and how it has produced some real benefits. Is that better? It says, "Mike volume." I wanted to just tie this in — the advantages of insurance that we have to some big events that occurred and that will, I think, point out the strengths and weaknesses of our institutions. We had a terrible hurricane a couple of years ago in Los Angeles; Hurricane Katrina damaged the city of — I'm sorry did I say Los Angeles? You have to stop me when I say things that are obviously wrong. My mind lapses sometimes — New Orleans — and Los Angeles doesn't have to worry about hurricanes as far as I know, unless there's some major change. In New Orleans there was a Hurricane Katrina; it broke the levies that were surrounding the city and caused the flooding of the city.
What saved the people of the city, mostly? I would say it was actually the insurance institutions because the city was heavily damaged but homes were generally insured. There were some conflicts when this huge disaster came. Some people had wind insurance and some people had flood insurance and it became difficult whether this was a wind or a flood problem, because the wind caused the flood. So, if you had only wind insurance are you covered? There was a lot bickering and arguments afterwards but I think it worked out well. There were surveys of customer satisfaction after the event and I think, generally, people were happy with their insurance companies. Of course, there were some that were not, who may have found out that they weren't covered; but on the whole, the experience worked well.
The other thing I want to say about the last lecture is that as financial progress moves on, the distinction between insurance and other forms of risk management may get blurred. One very interesting thing that's been happening is that we are starting to see development of another institution called the catastrophe bond, which is another way that people have for protecting themselves against catastrophes and it's not insurance. A catastrophe bond is a bond that the issuer doesn't have to pay off if there's a catastrophe. You could have hurricanes — the City of New Orleans could raise money with catastrophe bonds that they have to pay back if there's no hurricane but they don't have to pay back if there is a hurricane. Or it could be some mixture: they'd pay back part of it if there is a hurricane. That's like insurance, isn't it? But it doesn't operate through an insurance company, it operates through a securities market.
A good example of that is a couple of years ago the Government of Mexico issued catastrophe bonds against earthquakes. Mexico City was hit by a terrible earthquake about twenty years ago and it's vulnerable to being hit again. So, what does Mexico do about this? Mexico could wait until there is a hurricane (sic) and hope that there's some international relief effort, but that's not a very good way to proceed. We want to arrange it in advance. What Mexico did was issue cat bonds that have to be repaid in the absence of a hurricane and have a lower repayment if there is — I'm sorry, I'm not on my best form today — earthquake. Mexico City does not have to worry about hurricanes either. Every area is different and they have their own individual characteristics.
Right now, the insurance industry is a bit challenged because — in terms of some risks — because the risks seem to be changing through time and, notably, it looks like hurricane risk is increasing. So people who are insured in — it seems to be increasing because of global warming, although I don't know if all scientists are agreed on that. If you live in a coastal area of Florida it does appear that your risk is increasing through time. So insurance companies want to raise your rates and this is a huge issue down in Florida. Well, the government has kind of taken over for the time being — insurance in Florida — because we have problems. People are having problems paying the increased insurance premium. I don't think we've figured out finally how insurance will ultimately look in a matter of years. But, I think that the important thing is that it's protecting against us already, maybe imperfectly, but it's already protecting us against some of our worst fears, like hurricanes and earthquakes. I think the system is evolving and we're getting new developments like cat bonds that are changing the way we're doing things. In the future, I think these will develop more and make us even better able to handle catastrophe risks.
Chapter 2. Information Access and the Efficient Markets Hypothesis [00:06:28]
Anyway, that's the last lecture. Today I wanted to talk about — back to securities markets or actually, more general, asset markets. I want to talk today about the efficient markets hypothesis, which is a very important intellectual construct that has guided a lot of theory in finance. I want to talk first about the history of the hypothesis — I haven't defined it yet for you but maybe you already have heard of this — but history of the hypothesis, the arguments for it, and then the arguments against it. I want to talk about technical analysis and empirical evidence in the literature — about technical analysis — and other schools of thought that doubt the market efficiency, talk somewhat about behavioral economics. Then, finally, we have a homework assignment; actually, it's coming up. I'll start talking about it now so you — it will be an assignment for you to try to forecast the stock market using statistical methods. You don't have to look at the screen yet; I'll come back to that.
What is the efficient markets hypothesis? The term actually is a fairly recent origin — that is, a few decades ago — but the idea goes back much further. The idea is that in asset markets that have good regulations and market makers and developed markets that have a lot of depth and liquidity — in these markets, the prices that you see are perfect indicators of true value. In other words, efficient market says that the market efficiently incorporates all information and the prices are like the best information about the value of something. In other words, efficient markets hypothesis tells you: trust markets, don't trust people, trust markets.
I've been trying to find out who said that first. The earliest statement of the efficient markets hypothesis, although it doesn't call it the efficient markets hypothesis — the earliest statement that I could find comes from a book written in 1889 by George Gibson and it's called The Stock Exchanges of London, Paris, and New York. I'll quote him, he said, "When shares become publicly-known in an open market, the value, which they acquire there, may be regarded as the judgment of the best intelligence concerning them." I was kind of interested to see this book. I found it in the Mudd Library, actually by accident, looking through old stock market books.
The book had some interesting observations. One observation, which took my interest, was that he points out that in this modern electronic age information speeds around the globe at the speed of electricity — or the speed of light. When I first read that I thought for a minute, wait a minute, 1889? That sounds like 1989 or something. Just a moment. We found the microphone. Oh, it was right there? Now I am free from my tether. In 1889, they had already invented the telegraph. In fact, that goes back decades earlier. The telephone was starting to appear, so it really was true that information would speed around the globe. Information that became publicly-known would be entered into market price almost immediately. The conclusion that Gibson had was that there's no hope in trying to beat the price or beat the market because the price already has all of the information in it.
Let me elaborate on that theme a little bit. Actually, it goes back before telegraph, there was a famous story of Mr. Reuters, who had an information service before the telegraph was invented. He wanted to help his clients get the information first so that they could trade on it and he had the idea of using what you call carrier pigeons. What you do is you get these birds and you raise them — you know what I'm talking about, right? You raise them in one place and then they're going to want to go back there. Then you take them away in a cage to another city and when you need to get a message across, you tie the message to the pigeon's foot and release it. Then it will fly back and it will beat any other method of message transmission. Incidentally, Reuter's information service is still in business today and now they use computers the way everyone else does, but the whole principle precedes the invention of computers.
The idea is that the only way you can beat the market is to get information that nobody else has. The way it works today is that the — we can't actually improve on the speed from 1889 because they were already going at virtually the speed of light with their information; but, we can improve on our access to it. Now, many people have beepers or something like this in their pocket that wakes up and tells them when news is announced.
What happens where there's news about a stock? Let's say it's a drug company that just makes an announcement that it has a new drug — let's say good news — or it has gotten FDA approval to market some new drug. Well, it would put that out over the network of information and some people would have their things beep on them and alert them immediately. There are analysts who try to keep up with news about stocks. So, these analysts then would jump to action when they hear news like that. That's because they know that markets move really fast to important new information and they've got to be there first. What happens when the drug company announces that they have some news — important news? Well, the guys who are with their beepers immediately spring to action and try to figure out what the news is. Within seconds they're trading because you know you've got to be there first; otherwise, you can't benefit from the news.
What happens? They say they've announced — they've got approval for this new drug. Then maybe do a quick call to their drug company expert and say, quick how much should I change the valuation of this stock? The guy will give a quick guess — this is now twenty seconds after the announcement — and then immediately you place a big trade for a million shares or plus or minus. Then the guy calls back thirty seconds later and says, "Oh no, I wasn't exactly right on that. I've had thirty more seconds to think about this, so let me change it again." Over the next few minutes, the price — a lot of people are trading like that so the price is jumping around rapidly. Then, after maybe five minutes, these people have had time to assimilate it and think about it and check their thinking and the price starts to settle down. Maybe I'm exaggerating how fast it settles down. Maybe an hour later you have a committee meeting and the experts are arguing about what this really means and trying to assimilate other information and coordinate with it; but, after two hours it started to really settle down.
Suppose you then, the next day, read in The Wall Street Journal about this new announcement. Do you think you have any chance of beating the market by trading on it? I mean, you're like twenty-four hours late, but I hear people tell me — I hear, "I read in Business Week that there was a new announcement, so I'm thinking of buying." I say, "Well, Business Week — that information is probably a week old." Even other people will talk about trading on information that's years old, so you kind of think that maybe these people are naïve. First of all, you're not a drug company expert or whatever it is that's needed. Secondly, you don't know the math — you don't know how to calculate present values, probably. Thirdly, you're a month late. You get the impression that a lot of people shouldn't be trying to beat the market. You might say, to a first approximation, the market has it all right so don't even try.
The efficient markets hypothesis is a hypothesis that one should respect financial markets very much. Your textbook by Fabozzi, et al. mentions — I looked it up in the index to see what they say about efficient markets hypothesis. They define it. I'm quoting the textbook Fabozzi, "Publicly-available, relevant information about the issuers will lead to correct pricing of freely-traded securities in properly-functioning markets." That's their definition of the efficient markets hypothesis. They didn't say it was right; they just said that's the hypothesis. What Fabozzi, et al. said is that the hypothesis has informed a lot of regulation. The Securities and Exchange Commission and other agencies that regulate financial markets have shown some faith in the efficient markets hypothesis. Therefore, they feel that their — maybe their primary mission is to regulate the flow of information to make sure that it's an even playing field so that everyone has access to information at the same time. For example, the Securities and Exchange Commission requires that when a corporation publishes information that's relevant to the value of their stock, they have to put it out to everyone at once or there's rules about what that means. Typically, they'll have a webcast or something like that and it's announced in advance, so everyone who is really interested can listen in. I don't find a whole lot of enthusiasm in the Fabozzi book for the efficient markets hypothesis and maybe that's because it's not exactly right, which is my view. It's a half truth; I'll come back to that.
I want to quote another best-selling textbook, not your own, but there's another textbook, Brealey and Myers, which is a textbook of corporate finance. They are much more enthusiastic about efficient markets hypothesis. At the end of their textbook, they have a concluding chapter and the concluding chapter is built around what they call the "seven most important ideas in finance." One of those seven ideas to them is efficient markets. They don't call it a hypothesis, they just say "efficient markets," which they define as the theory that — I'm quoting them, "Security prices accurately reflect available information and respond rapidly to new information as soon as it becomes available." Then they have a little qualifier — I think this is interesting — they say, "Don't misunderstand the efficient market idea, it doesn't say that there are no taxes or costs. It doesn't say that there aren't some clever people and some stupid ones. It merely implies that competition in capital markets is very tough. There are no money machines and security prices reflect the true underlying value of assets." That's a pretty enthusiastic endorsement of efficient markets.
Chapter 3. Varying Degrees of Efficient Markets and No Dividends: The Case of First Federal Financial [00:20:00]
I said I have some doubts about it. I guess I don't — I guess what I don't like is their concluding statement, "Security prices reflect the true underlying value of assets." I don't think that's really true but I guess I agree, it's tough to make money reliably and quickly in financial markets. So, if that's what efficient markets means, they're right. "Efficient markets" is not so easy to define. We can go back to — the term really goes back to 1967 and it was Professor Harry Roberts at University of Chicago who defined three different efficient markets hypotheses. There's the weak form, the semi-strong form, and then the strong form. The weak form — these differ only in terms of the amount of information that is assumed to be efficiently incorporated into prices. The weak form says that information of past prices is already in the — incorporated into price, but only past prices. What it means "only" is that you can't predict stock prices by noting that, say, if it goes up today, it'll probably go up tomorrow or it goes up today, it'll probably go down tomorrow. That would be relying only on past prices. Harry Roberts felt most confident that this form of the hypothesis was good, so he called it the weak form; it's the least criticizable form of efficient markets.
Semi-strong form says that market prices incorporate all public information. Anything that's known to the public is already incorporated into price, so don't bother to trade on it. The strong form says all information, whether public or not, is incorporated into price. This is a really strong — it's the least likely to be true because every time you increase the information set — what strong form says is that no information is private, really, it all gets out into price. Companies keep secrets, so that's not public information. The Securities and Exchange Commission insists that companies keep secrets because they have to disseminate information in an orderly way. So, there has to be a secret until a certain hour in which it's announced to everybody. But the strong form efficient markets hypothesis is cynical about that and says, you know, nobody keeps secrets, it all leaks out.
I think that when we refer to the efficient markets hypothesis, it's the semi-strong form that we're usually referring to because the strong form is a bit strong. The definitions of efficient markets that I gave you are intuitive but not very precise. Then you have to ask, well what does it mean to say that price incorporates all information? What does it mean to incorporate information? Unfortunately, there's not one answer to that question, so I'm going to give the simplest answer. What does efficient markets mean? I might — I'll have to — this is the simplest version but it's often the one that is referred to most. That is that price is the expected value — the expected present value — of future dividends paid on a stock.
The efficient markets hypothesis says, the true value of a stock comes from the dividends that it pays — that's a cash flow that is valued by the market and the market values it as the present value of the optimally-forecasted future dividends. The theory that's most often referred to is the simple — I've already talked in the second lecture about present value formulas; we had a growing-perpetuity model. Remember that I said that the present value — the present discounted value of a growing perpetuity that pays an amount D — well, if it pays Degt or D0egt is the dividend, so it's growing at rate, g. Then, the formula we had for the present value was D/(r-g). Remember that? This assumes, of course, that the growth of dividends has to be less than the discount rate, r.
The simplest version of the efficient markets hypothesis says, price is equal to the dividend all over the discount rate minus the growth rate of dividends, where g, the growth rate of dividends, is an optimally-forecasted growth rate of dividend. That gives us a value — a model for the price. Another way of writing, more generally — if I don't assume the constant growth rate of dividends — is to write just a present value formula. It's another less strong form of writing down the efficient markets hypothesis because it doesn't say how dividends are thought to grow. But you can write: price is equal to the summation of E(Dt+k)]/(1 + r)k; k = 1 to infinity. This is another — that's just the present value formula. I have the price — I'm sorry, this should be expectation at time, t — the price at t is the expectation of the dividend, at time t plus k, discounted by a discount factor r. That's just the present value formula where I've substituted an expectation for the future dividend. That's the efficient markets theory in this incarnation.
There are other ways to envision the efficient markets — what it means — but let's consider this simple story. What this means then is that the price is a forecast of future dividends to be paid on the stock. This would be — of the present value of future dividends to be paid on the stock — and this means then that price, relative to dividend, is related to expected future growth rates of dividends. If you expect dividends to grow a lot, if g is high, then price will be high, relative to dividends, because this is subtracted off the denominator. It makes the denominator smaller and it makes the price higher. On the other hand, if you expect dividends to do poorly in the future, then price will be low relative to dividends; that's what the efficient markets hypothesis would say.
I would give you an example of that. I talked last year about a company that I read in Business Week — that I read about in Business Week, so this is a year old story in Business Week. There was a company called First Federal Financial, which was a company that issues mortgages. This was in January of 2007, actually the Business Week story was in December of 2006, but I was still reacting to it a year ago, in January of 2007. The Business Week story — this is First Federal Financial — was referring to the fact that the price-dividend ratio — actually they talked about price-earnings ratio, but the price-earnings ratio for this company was very low. It was only 8.5 in December 2006. Typically, price-earnings ratios of the companies are very high, much higher than that — typically like fifteen. The price of First Federal Financial, relative to its earnings, was very low, so some people might be inclined to think well that looks cheap. I can buy — by buying First Federal Financial, I can buy the stock at a low price relative to its earnings. But, if you believe in efficient markets you wouldn't think that this is any reason to buy the company because efficient markets would say that if the price is low relative to either dividends or earnings, it must mean that people think that bad things are going to come to the dividends or earnings. In other words, the First Federal Financial has a low expected growth rate of dividends in the future. So, I was interested in this particular story because Business Week wrote an article about them and noted the low price-earnings ratio and said, what does this mean? What Business Week presented a year ago was an argument why g was likely to be low. Yes?
Professor Robert Shiller: If they don't pay dividends you can't use this formula. I'm not sure what the dividends were at First Federal Financial. I only know the price-earnings ratio at that time. You're right, you cannot use this formula if they're not paying a dividend today because this formula — I erased it, but it was up here — assumes that dividends are following a growth path. If they're not paying a dividend, then we're very clearly — that's not an appropriate assumption.
Student: So how would the efficient market theory explain prices of companies that do not pay dividends?
Professor Robert Shiller: Right. So for–incidentally, if you know, Berkshire Hathaway is the company Warren Buffett owns and it's a very famous company because it's done extremely well. Warren Buffett is regarded as, by many people, as the financial genius. If Berkshire Hathaway is not paying a dividend, we have to revert to this formula. The efficient market theory would say, well they're going to pay a dividend eventually, so the price reflects these future terms. If you spell this out, this is the expected dividend next year plus the dividend in two years — this is divided by (1 + r)2 — the expected dividend in three years divided by (1 + r)3, etc.
This theory would say that the dividend — that Berkshire Hathaway has value only because they — investors expect them to pay dividends in the future. That sounds right because if Berkshire Hathaway is never going to pay dividends, why would you hold it? You might say, I'll hold it because I could sell to someone else at a higher price. But then you say, well why would anyone else buy it? Look, if they're never going to pay a dividend, what good is it? It's just a piece of paper, unless I can sell to a greater fool. But anyone who buys it is either — would be buying it either on the assumption that there's some greater fool coming or they would be a fool themselves. This theory says that the value — if Warren Buffett — of course, he can't even say this, but let's somehow say the company could say, we will never pay a dividend. This company is going to give itself away to charity someday and you won't get a penny as a stockholder. Well, if that happened the price should be zero. It would convert into a non-profit, like Yale University. So what's the price of a share in Yale University? I mean, it's undefined — I its guess zero, right? Because Yale is not paying — I'll write a piece of paper for you and say this is a share. On my authority, this is a share in Yale University. It might just as well be that because it also says in my fine print, you will never get a dividend on this. So what's the point, right? Incidentally, Microsoft for many years never paid a dividend. It's often common for young companies not to pay dividends; but they did start paying a dividend.
The whole theory — efficient markets theory — says that that's what people are looking for. That's why the value of a company is related to its activities; otherwise, if the company never paid a dividend, then what would you care what the company is doing? You only care about it because someday they're going to give you money. A lot of investors forget that; that's a very naïve attitude. They think that somehow stocks generate capital gains — prices go up — but you have to realize and efficient markets theory is saying this: prices only go up because there's new information about future dividends. First Financial anyway — this is an efficient markets story — First Financial had a low P/E, so people were wondering, is this a bargain? This is a cheap stock — P/E means price-earnings ratio. The Business Week article pointed out that 40% of First Federal had been sold short — 40% of their stock had been sold short; this is a very high level of shortage. You know what means? That means a lot of investors said, "I don't like First Federal Financial, I don't want to invest in it. Worse than that, I want to go and short them." That means you borrow shares and sell them and hope that the price goes down. When you have 40% of the shares sold short that means that there were a lot of people who didn't believe in First Federal Financial.
Business Week, in its article, pointed out that this — First Federal Financial was a small mortgage lender — this is before the mortgage crisis that we have started — in Santa Monica, California. And it was particularly innovative, in a sense, in its lending. Notably, 80%, according to the Business Week article, 80% of the mortgages it's issued were no-doc mortgages. Do you know what a no-doc mortgage is? It's something that appeared recently in the housing frenzy. A no-doc mortgage is a mortgage where you walk in and say, "I want to borrow money to buy this house." The company says, "Fine we'll give you a mortgage. We won't even ask you to have your employer send a letter saying that you have a job. We won't even ask you to prove that you own anything or have — we'll just give you the mortgage." That's considered by many people risky behavior but it was done during the housing boom.
Also, they issued an unusually high proportion of what are called "option ARMs." These are mortgages that are adjustable-rate, but the person doesn't have to pay the full payment every time. You have the option of paying and if you don't want to pay, you can delay it for a while. These are also controversial because it thought they would attract borrowers who were unreliable. Borrowers who thought that they could afford the house because they didn't have to pay now; but of course, it's all going to come later and then they might default.
Business Week thought that the low price-earnings ratio was because the market expected earnings to go down and dividends to go down. A year later, that is this morning, I wanted to see what First Federal Financial was doing. Actually, it's still in business; everything is all right. It has positive earnings but the price was $70 in beginning of 2007 and now it's down to about $40 in 2008. This is a testimony to efficient markets. The market was expecting the price-earnings ratio — they gave it a low P/E because they were worried about — they had information that there was something going badly in this company and indeed, they were right. It's not as bad as you might have thought with the Business Week story but it is bad. I guess the lesson — are you following what I'm talking — what happened was they did get into trouble. The low P/E was indeed a forecaster of bad performance later.
Now, I guess this isn't exactly — efficient markets wouldn't — in this case, the people who sold First Federal Financial short made a lot of money when the price went down so much. That's not really consistent with efficient markets because it makes it sound like — as a matter of fact, I could have — Reading the Business Week article at the beginning of 2007, I could have called my broker and I could have told my broker, short–please, I want to short First Federal Financial. I could have done that and it looks like I would have made a lot of money by shorting it because the price went down a lot. Efficient markets theory would have to say that that was an anomaly — that that was just good luck. Those people who shorted First Federal Financial did make a lot of money but, hey, they were just lucky this time. In other words, efficient markets theory would say that the price was already down as far as it would — basically as far as it would go in 2007 and that earnings would fall and dividends would fall later and that would explain why the price was low. But, it wouldn't allow you to predict the price. This anomaly of — the fact that it worked out so well is really not — to short investors — is really not testimony to efficient markets.
Efficient markets — in some sense I think I'm sympathetic to efficient markets. You have to be sympathetic to some extent. If I were trying — I actually did not short First Federal Financial when I read this last year and it was because, I guess, I had my doubt; I had my feeling. You read a Business Week article and it's — everyone in the world knows it now that a lot people doubt First Federal Financial. If I come in late as a short seller, am I going to do well? I start to doubt it myself because there are so many people looking at it and so many people who are more knowledgeable about First Federal Financial than I am; so, maybe I won't try shorting it. That's what efficient markets is all about.
Chapter 4. The Random Walk Theory [00:41:44]
The efficient markets theory became very popular in finance around 1970 and it became a prominent theory in finance. It has a particular incarnation that I wanted to emphasize called "random walk." The random walk theory, which follows loosely from this formula, though I have to qualify it — but let me talk about random walk as a theory in itself. The random walk theory says that under efficient markets, stock prices and other speculative asset prices are random walks. That term goes back to Karl Pearson in an article in Nature in 1905. This idea is about a hundred years old.
What Pearson wrote about was–well, the example he gave was a drunk. Imagine a person who is so drunk that every step that person takes is random and independent of the preceding step. Suppose we — this is a 1905 story — suppose we had a lamppost and we had a drunk standing at the lamppost — I've drawn a picture, that's a lamp post and that's a drunk. This person is so intoxicated that steps are completely random and your objective is to predict where will this person be in a minute, in ten minutes, and twenty minutes. Well, Pearson wrote about this and said that the optimal prediction is to assume that the person in ten minutes — the best forecast is the person will be here. In twenty minutes, what's the best forecast? The person will be here. Of course, they probably won't because they're randomly staggering around but the point is that if it's a true random walk, there's no bias. It's equally likely to go this way or this way. The most likely place for the person is right where that person is now.
So Pearson and other people following him thought that speculative prices are like that. That sounds like the markets are crazy — they're drunk — but they're not drunk. It's because they respond only to new information. New information is, by its essence, unforecastable. So, it has to look like the market is driven by a drunk when, in fact, it's very precise and responding optimally to new information. That's one of the paradoxes that confuses people.
Statisticians developed the theory of a random walk and let me define that for you. A random walk occurs when you have a variable, x, at time, t, equal to x at time (t – 1) + et where et is noise — unforecastable noise. This is the random walk; x would be here — how far the person is from the lamppost. Here's 0, let's say, and x is the distance from the lamppost. At every time interval we have xt which is how far the drunk has deviated from the lamppost. This is the random step; this is where the drunk was last period and this is where the drunk is this period. So that's a random walk.
In the heyday of efficient markets theory, people said that efficient markets is working very well. In other words, the random walk hypothesis describes stock prices very well. Let me go to my spreadsheet, which I have up here, and I'll put this spreadsheet up on the web for you. What I have here is shown — there are two lines shown, one is a blue line, which is the — the blue line is the actual Standard & Poor's composite stock price index going back to 1871. This is a series that I–well, actually I got this series from Standard & Poor's and I emphasize it a lot in my book. It's a 130-year long stock price series; it's monthly for the United States. It's now called the S&P 500 because, starting in 1957, Standard & Poor's kind of reorganized the index and they kept it at 500 stocks. This is the second most famous stock price index after the Dow Jones Industrial Average. I think it's better than the Dow Jones Industrial Average because the Dow has only 30 stocks and this has 500 and it's representative of most of the market. That's history; that blue line there is history.
What I did on Excel was I generated a random walk, because there's a random number generator on Excel. I used the random number generator and plugged it into this formula: xt = xt-1 + et That pink line is a true random walk. It was generated by a random number generator. The point here is — don't they look kind of similar? When you look at — when people look at stock prices they get a — it's an illusion. This is a psychological illusion. They get the sense that there are bull markets when the market is going up and there are bear markets when the market is going down. There must be some force pushing it up for a while. You can see, for example — I'm looking at the blue line — there was a bull market in the 1920s, a famous bull market, the Roaring 20s. You would say, that just can't be a random walk; it was just going up all the time. Then, this is the 1929 peak and there's the crash from 1929 to 1932; a big crash. That can't be a random walk, right? That's what people think. They have this intuitive idea. But, if you look, this random walk seems to do the same thing.
The pink line has a — look there's a nice bull market there — there's another crash. Look at this whole period here; this was really strong and then it leveled out. We had bad — in fact, they kind of look similar, don't they? This is pure chance because that random walk that I generated was pure random walk. There's the bull — the actual bull market of the 1950s and 60s and my random walk comes out pretty close to that. The random walk theory says that people are operating under illusions; that there really are no trends or there's no way to predict the market. It is just completely unforecastable. Now incidentally, a nice thing about Excel is I can generate a new random walk for you on the spot by pressing F9 — if you know that key on Excel. So, I will press F9 and history is going to stay the same — the blue line is going to stay the same — but the pink line is going to change. I can generate whole hundred-year history — pseudo histories — with a press of a button.
Let's see if this works, we just got — what is that saying? I put an upward trend to the random walk there because I think there's an up trend to the stock market. It's a little different than this, I just added a time trend; otherwise, it's exactly the random walk formula that I used. Okay, that looks pretty much like history too except we would be in a bear market for quite a while, right? We have quite a bear market in the pink line but I can correct that by pressing F9 again. This is bad luck, the stock market crashed in the — it went off the chart here; that's bad luck but I can try again. Look at that one, isn't that a beauty? That almost — it really looks like the market we've had. So, I can just go — it's just amazing how fast this thing generates. I should stop. Tell me when one looks really interesting. That's an interesting one. That's — if that was the history that we randomly had, Jeremy Siegel would write not just Stocks for the Long Run. He would be jubilant if the returns on stocks — he would say for a hundred years — this is 130 years — for 130 years stocks have wonderfully outperformed the market — outperformed other things. That is looking pretty good, isn't it? Now, I just press the button and get — I'm not getting many bad ones. That probably has an uptrend in it. They all look similar, right?
Chapter 5. The First Order Auto-regressive Model [00:51:30]
The other thing I wanted to talk about was another thing called an AR-1, which is a different story. The AR-1 — this is the random walk, here. The other idea is that — let me do it intuitively first. I'm going to tie an elastic cord around the ankle of the drunk and tie it to the lamppost. You see my elastic cord? It's very loose at the beginning so the drunk can move freely but if it starts to get stretchy, when the drunk makes it all the way over here, then its really hard for — it's pulling the drunk back. That means it biases the drunk back towards the starting point. That's called an AR-1 or a first order auto-regressive model. That means that there's something — the random walk has no center; it just has a starting point. It doesn't tend to go back anywhere, but here we have a center. What do I call that? I'll call it — x-bar is this point here, not necessarily 0. It says that (xt - x-bar) = x-bar + ρ (xt – 1 - x-bar) + et. ρ lies between minus one and positive one; usually it's positive. You see that? So ρ — the smaller ρ is, the tighter the elastic cord is. It gets pulled back by 1- ρ of the way back to the x-bar in every time period. But then there's new noise that adds onto it. If there were no new noise, then the drunk would just be gradually pulled back; but there's new noise, so the drunk is not so predictable. That's another model of the stock market but it's not an efficient markets model.
The random walk is the efficient markets model that says, you can't profit by trading because you just cannot predict the changing price. But with the first order auto-regressive, you can predict the change of price, at least a little bit. Well when it's — what goes up comes down. If the drunk is over here, it tends to get pulled back here; if the drunk is over here, it tends to get pulled back up. So, that's the random walk model. I programmed into this program an AR-1. I go down here and click on it. That looks very different, doesn't it? Maybe I didn't get the parameters exactly right, but let me just hit F9; I'll get it so it looks better. Well, it looks a little different; you can see a difference in this? That's because I chose ρ = .95 for that diagram so it's kind of getting tugged back to the trend. Sometimes it's hard to tell. I thought — can you tell the difference between a random walk and an AR-1? It seems to be coming back faster, so that looks different. Well, with ρ = .95 I guess it does look noticeably different because it's coming back pretty fast. I have 130 years of observations and it's coming back 5% of the way every year, so in five years it's 25% of the way back. I've got the cord too tight so it's not fooling you, right?
You can see a difference between this AR-1 and the true stock market. The stock — so this is revealing some truth to the efficient markets hypothesis. What if I made ρ = .99? Then I think — I should have done that instead of .95; then it gets harder for you to see the difference. If I make ρ = 1 in this — what happens if I plug ρ = 1 into this expression? It comes back to the random walk because the x-bars drop out — because you've got 1*x-bar and you've got minus x-bar over here so they drop out of the equation and you come back up here. A random walk is just an AR-1 with a coefficient — of ρof 1. Now, the point is then that we can easily see that the stock market is not strongly mean-reverting or trend-reverting. It's somewhat — it may be somewhat trend-revering; it's very hard to tell whether its ρ is 1 or .99. So, that's the point of my little analysis here, of random walk versus AR-1.
Chapter 6. Challenges in Forecasting the Market [00:56:59]
Now, the homework — the problem set that you will have next time — now you still haven't turned in your second problem set, but I want to work ahead now to the third one. What I want you to do is to try forecasting the stock market. So, let me show you what I did here and I want you to do something. You could use this spreadsheet but I'm also encouraging you to find your own data. Here's my spreadsheet, which has stock prices back to 1871. Can you see all this? I have this on my website all the time; I've had it on my website how long? It must be twenty years. I give it away because I'm the person who updates S&P data for 1871 to the present. I now have a relationship with S&P because they're publishing our indices, but they still don't provide updates of this hundred year-long series. So, here it is all the way back to 1871.
What do I have here? I have in column one is the Standard & Poor composite stock price index — today called the S&P 500. This is the dividend on the S&P 500. They've been paying a dividend consistently; it has never missed a year. Maybe some companies have missed a year, like Berkshire Hathaway or Microsoft, but the whole aggregate has never missed a year. This is the earnings report on the company. It's all per share so this is per share earnings. I have here the Consumer Price Index in this column and then I've got long-term interest rates and I can convert it into a real price by dividing by the Consumer Price Index. This is the change in the real price. I don't — it's between this year and the next year. What I wanted to do is — this is your homework assignment and maybe I'll come back to this or maybe your T.A.'s will come back to it as well. I want you to try to forecast the stock market. What that means — remember what you're trying to forecast. You're trying to forecast e; you're not trying to forecast x. We already know x, it's easy to forecast; it's close to what it was last period. The hard thing is to predict where the next change will be. So, I had to generate a column of data here, which is the change in the price. You see, up here it says J10 minus J9 is the change in the price; that's what you want to try to forecast. I've created this column going all the way back to 1871, showing for each year how much the S&P composite index, in real terms, changed. I did it in logs. I took the change in the logs of real price. That's essentially the percentage change.
That is going to be hard to forecast. Obviously, it's going to be hard to forecast because there's some truth to the efficient markets hypothesis. If that were easy to forecast, you could have been rich over this period — somebody could have been rich. It can't be that easy. Nonetheless, the problem set for you is to try to do that — to try to forecast it. What you have to do is go to regression analysis. You don't have to use Excel but that's just what I'm suggesting here because that's the easiest thing. To run a regression, you go up to Tools and — let me see — Data Analysis is down here — and then you go to Regression. I guess I have to say "okay." Then it asks you to fill in your "x range" and your "y range." The x-variable is the — remember the regression model is — it's y = α +βx + some error term, e or u — I'll call it u so we don't get it mixed up. It's asking you to say where your y-variable is and I've got that that my y variable is in column K, because that's what I've generated. That's the change — where is K? I've lost it; it's not column K, it's — I'm trying to find it here — it's column I, isn't it? That's the change in price. Then the x-variable — I can pick some variable to forecast. What I did is I just took column A, which is time — it's just the year — and I ran the regression since 1950 and I got the results here.
I'm just going to show you the results from what regression I ran. That's how Excel prints out regression results. The α, which is the intercept, is shown here — so the intercept was .05. The βis the coefficient of the variable is -2 times 10-5. You can see now I've struck out; it doesn't like time as a forecaster — it's a very small coefficient. The t-statistic is a measure of statistical significance and the t-statistic should probably be over two for a statistical significance. I've got insignificant t-statistics for both α and for β. The R2 is a measure of what fraction of the dependent variable y's variance I have predicted. It comes out with a fraction of .000147 — this is a not a success. This is not a get rich quick story because I'm explaining 1/10,000th of the variance of the stock market; so I struck out. I wasn't really trying that hard, I just regressed the returns on time.
The problem set for you is to think about seeing if you can forecast the market. You don't have to use my data set, you can use others and you can go online and find them. For example, finance.yahoo.com has a lot of indices, but you can find them on other sites. If you find some other data, you can try to see if you can beat me. I'm not setting up a very high standard for success. If it were this bad, efficient markets — well, this looks good for efficient markets theory.
What I thought you might do for the problem set is to try to think creatively about how to forecast the market. Let me say this: I'm not — I'm going to have to continue with my doubts about efficient markets in another lecture, but I think that the story has a good element of truth to it. It has to be hard to beat the market but it's oversold as well, especially in academic circles — I think us professors, who are poor are — it's kind of a wishful thinking bias. We're not making much money and you can't anyway and so we kind of tend to overstate efficient markets hypothesis. On the other hand, relative to your expectations as naïve young people, it may be a good thing to do to overstate efficient markets hypothesis. It seems to be a lifecycle effect where young people think, I can surely predict the market and then they get beaten down.
Brad Barber and Terry O'Dean were professors at UC — at different campuses of California — teamed up with some economists from Taiwan and looked at data of — they got really good data from Taiwan about day traders and their actual returns. Day traders are people who trade everyday in the markets and they found that there was a really predictable pattern. The young people — they start in as a day trader and they quickly lose everything; they lose badly because they're trading too much and they really can't predict the market. There's like 1% of them, though, who seem like they can actually beat the market. This looks like really good for efficient markets. They found that there are some Taiwanese people who know how to beat the market — 1% survives and stays in. Is that contrary to efficient markets? Well, it does seem contrary because they found that a small number of people did find some forecasting rule and succeeded. On the other hand, none of the — hardly any of them got really rich and so it's very rare — Warren Buffett is an extremely rare outcome. So it's — I guess, when I talk about efficient markets I want to help prevent you from suffering under any delusions about your forecasting ability. I don't mean that Warren Buffett can't do it or that you can't do it if you develop yourself into a Warren Buffett.
The next problem set, number three, asks you to think creatively about how you would forecast the market and to take a stab at it by running a regression. I expect you all to fail — or almost all of you to fail. Your grade will not depend on your success in forecasting; it may even depend inversely because if you show a big success in forecasting, your teaching assistant will look at it very carefully and try to find some mistake you made because, if you do succeed, it's probably a mistake. On the other hand, I don't want to tell you that you can't because, as I said — we're going to come back to this — I have doubts about efficient markets and I think that you just might be able to do it if you're smart about it.
[end of transcript]