Modigliani Transcript

Relationship Between the Stock & Bond Market

Franco Modigliani

October 29, 1997

Well, I guess that with the help of the stock market shenanigans I have attracted a good crowd...

Well, the topic for tonight really was conceived not at a time of so much action in the market and was in response to a question I heard very frequently, or to a view that is so frequently heard, and that is the view that the stock market and the bond market should move together. This is a view that has not been usually quantified, but it is certainly a general view. It comes from a very simplistic model that essentially the value of a stock is its earnings, its stream of earnings. A stock is a perpetuity in principle, that is it will give you an income forever (it is an indebted stream?). Then, you take the current value of that stream and you capitalize it by dividing it by the interest rate. So that you have a stream of $20 and you capitalize it with an interest rate of 10%. That means you divide by .1 or multiply by 10, so it's worth $200. Now, the value for a bond is the same because the bond is a stream; let's think for a moment it's perpetual. In this country most bonds are not perpetual.

Fortunately we can make an appeal to the British who always provide you with good examples. The British do have so called consults and the consult is a perpetuity, that is the common issue is a promise to pay one pound per year forever. Now, with the case of perpetuity, the value is precisely the amount divided by the long term interest rate. So, both things are very similar, the earnings divided by the interest rate which may be somewhat variable, fixed earning divided by the interest rate is a very similar thing. Whenever interest rates rise, both fall in value, that is well known in the bond market and it's also a great source of confusion because the newspapers usually quote interest rates and not bond prices, and when they do it is very easy to confuse. Bond prices went up...that means interest rates went down and visa versa. And so you have this very simple notion, that essentially the two move together. When the interest rate comes down, stock market and bond market move up; when interest rates move up, both move down. Now, it turns out that this view is a very simplistic view. That is valid sometimes, not valid other times, and the funniest part is that it is more valid than it should be.

I will explain that very carefully. What I mean is the following thing: that if investors knew how to handle inflation properly, if they understood the distinction between nominal and real rates, the association between the bond market and the stock market would not be very large. But because investors confuse the two, and discount at the nominal rate instead of the real rate, you get more movement in the same direction than there really should be. I'll show you some examples of that. So, let me do the following things. I happen to be an economist who believes that economics does not just consist in deriving nice theories, but in seeing whether the theories fit the facts. I think that that is an important function. Every one of my theories has been tested. If it isn't successful then I shelve the theory and try again, or try to change the facts.

So, let's look at the facts. Do the two move together? Well, I've done the simplest thing you could do, which is to compare the movement of stock prices and interest rates, but you have to be a little careful because interest rates are essentially trendless. Over a long history we have had periods of relatively high interest rates, periods of relatively low interest rates, but it's not the case that interest rates keep rising forever. So, interest rates are trendless. If you think of the post-war period we have quite a few waves of ups and downs. On the other hand, stock prices tend to grow in time simply because the firm tends to grow. As the economy grows, the firm that issued the stock tends to grow, and therefore the price of stocks is rising. So, rather than looking at the price itself, what I'm doing is to look at the Price Earnings Ratio. As earnings rise, the price should rise at the same time, so the price earnings ratio should behave like the reciprocal of the interest rate. So this graph then, is a graph of the price earnings ratio. The price earning ratio is this thinner line and the reciprocal of the interest rate is the heavy line. Now, as you look at this graph, I think you will see that, particularly if you're not a sophisticated practitioner of statistics, you'll say "Well, they do look like they move together," right? By and large they do seem to move together. Here they are high, and then they come down, then they don't move, and then they rise, etc. At the end, this is by the way, a 47, this is the 22 where we had been before the crash. This is the middle of 1997. And of course a lot of the similarity is due to this decline in here, and rise in there. However, if you are used to looking at time series graphs, you know better than to just look at it and say, "Ha, it looks similar." You know that you have to see for every point whether the points are high at the same time or low at the same time. That's quite different from "generally" behaving the same way. I mean, you can see for instance here this is very high and this is very low. So they don't move together here. And you have other times in which the reverse is true. Like here, this is high and this is low. It turns out that if you actually compute the correlation, which is a measure of movement together, it's a very standard measure, you find it is only .45: positive; significant. Significant means that it could not be due to mere chance from random drawings, but it's not a large number. Particularly with time series economists are able to produce correlations of .99 very easily. So, there is some (correlation), but not that much.

The question then is, what are the things that move each? Why don't they move together? What is wrong with the simple view that they simply have to move together? Well, to answer that question, I provide you with a set of equations which you don't have to, if you don't like mathematics, you don't have to look at them very much. I will explain what they mean. It can be explained in simple words; it's just easier to write it down in symbols. The first two equations are the fundamental ones for us. The first is what determines the price of stocks? The second is what determines the price of bonds? The second equation is very easy: it says that the price of bonds is the reciprocal of the interest rate. Capital R is the interest rate, but you have to be careful for future consumption. Once you have inflation you have to distinguish between something called the interest rate, or the nominal interest rate which is what is quoted in the New York Times financial column, and what is the real rate which is not quoted, but which takes into account the fact that when you have inflation and you lend money you need to be paid more because every year you're losing purchasing power through the inflation. Therefore, you have a very simple rule which is [attributed] to the great American economist Irving Fisher, which is stated here: the nominal rate is equal to the real rate which is the small (r) plus the rate of inflation. In other words, to a first approximation, it's not an exact formula, but it's a good approximation. The exact formula is 1 plus (p) times 1 plus (r) minus 1. Which is not quite the same as (p) plus (r). Anyway, it's a good approximation. The real rate is the nominal rate minus inflation. The nominal rate is what you read in the newspaper; the real rate you don't. So you see, the real rate I can compute by taking what I find in the proper column of the New York Times then subtracting the rate of inflation.

That relation itself has slight complications because strictly speaking the inflation should be the expected one. Strictly speaking, if you're lending for a year then you should take the nominal one-year rate and subtract the one-year inflation, but if you're lending for a quarter, you should subtract the one-quarter inflation. So, it's essential you have to be careful, but for present purposes it's a good approximation. In addition to the distinction between nominal and real I have to make this distinction: that R and r are long-term interest rates. Because you're dealing with a perpetuity-- a bond or a stock-- therefore, you need to discount it by the longest rate you can think of. Now, it actually doesn't make too much difference if you use the 20-year rate or 30-year rate or 50, because these rates are very similar. Usually there isn't much difference. So, even though conceptually you want a 50-year rate, if you have a 20-year rate which is more easy to find, you can use that as a good approximation.

So the bond price index is very simple. Let's look at the stock price index, and that's of course where perhaps the formula is not necessarily known to everybody or agreed to by everybody. It says that you take the earnings and you capitalize them not simply at the interest rate but at something which is more complex. First of all, we know that you capitalize the equity stream at the higher rate than the bond stream because the bond stream is sure, the equity rate is uncertain. Because people don't like uncertainty, they will usually be persuaded to buy the risky thing only if they get a premium for buying it. That premium is called the risk premium: it's the difference between the required return on an equity stream and on a bond. Just for rough size, if you think of discounting, tabulations have been made over the long run to try to see a relation between them, but for very rough approximation, say that the equity stream is about 10%, the interest rate about 4%, and the risk premium about 6%. At the present time the interest rate is higher, but just as a rough order of magnitude, the risk premium is in the order of 6%. That is, people are, on the whole, pretty risk averse. In order to shed the risk, they accept a substantially lower return. And this can vary over time, and I'll come back to that. But in principle, that's the order of magnitude.

The first thing is that you mustn't use (r), you must use ?(rho). ?(rho) is the [inaudible] to determine the interest rate. And the difference between the two is here, the difference between this rate and this rate, is precisely the risk premium. The risk premium is that difference. So, the first thing is that we use ?(rho). The last term is better understood, and it says that you subtract something related to the rate of growth of the stream. In other words, you buy your stock-- now the simplest case is where the stock gives you a stream that is expected forever to be constant. Then, you just use ?(rho). But suppose that the stream is rising 3% per year, and suppose for a moment that's forever. What do you do then? Well, you can demonstrate that if indeed there is good reason to expect it will rise at 3% forever, then instead of discounting it at the rate ?(rho), you take the rate ?(rho) minus growth. So, let's say that ?(rho) is 10%, and the company has a 3% growth, then you discount the stream not at 10%, you don't multiply it by 10, but you discount it at 7, (that is you multiply it by 16). It's worth a lot more because it's growing and it's understandable that you have something that gives you more and more every year. I have written (ge) to indicate two things. First of all, that the growth is not the past. You don't care [about the past], what you want to know is [expected growth], growth from now on. This is all forward looking. Secondly, that it is [the subtraction of (g), is the limiting case of sure growth forever.?] Sure growth forever is very rare. Most of the forecasts of analysts show growth for five years, sometimes ten years. So, you certainly don't have perpetuity. And if you have a very fast growth over the next five years, you can be pretty sure that the next five years is going be less. It's not a law, it's just very likely because you cannot keep up a very fast growth. For one thing, the market gets exhausted. If you read (g) from the recent growth, then you cannot take it, but you have to take some fraction of it and just how much a fraction is something that we may discuss in a moment.

The next term is due to the so-called Modigliani/Miller Theorem. The Modigliani/Miller Theorem is a very radical proposition that was set out by me and Merton Miller in the middle of the 1950's, and essentially asserted and proved, under proper conditions, that the whole of the so-called science of finance was bogus. The typical role of the science of finance before our time was to tell you what was the best structure of your liabilities. Should you have equity? Should you have some debt? How about some convertible bonds? What about some preferred stock? What of these things would give you the maximum valuation [inaudible]? You have some assets here, and here are these instruments which are sold in the market. Which would make the combination give you the highest value? The Modigliani/Miller Theorem says in the absence of corporate taxes, and that's an important exception, it makes no difference how you finance the firm. It would work exactly the same. Namely the value of the assets which you bought, essentially, you cannot lever them in any way. It doesn't make any difference because it is true that leverage increases the earnings of the levered stock, but that increase is obtainable by anybody by levering on his own. That is, you buy a stock, borrowing from the broker, and then you will find that on the money you put in you make more money because in addition to the stock you get the difference between the interest rate--that is, you earn the risk premium on top of that, times the amount of debt. That's what you can earn, you can earn the ?(rho) rate plus the amount of debt, the proportion of debt, times the risk premium. And this proposition, of course, has caused a lot of consternation because it put a lot of people out of a job and the next two decades were spent showing that Modigliani/Miller were very clever but they were all wrong, of course.

There were many reasons why Modigliani and Miller were all wrong and very few of those reasons are, in fact, valid. There are limiting cases where you may have some problems [with the Modigliani/Miller Theorem], but fundamentally the proposition is logically valid--if people make the best use of their resources. Then they would not hold a levered company if it was worth more than the value of its assets. So, another way to say it is that a levered company is worth as much as the unlevered company, all the assets minus the debt. So, the levered company is worth the total assets minus the debt. This proposition has irritated many people. One of the things is that it is sort of difficult to prove empirically because in this country, which is the best source of information, there is a corporate tax. With a corporate tax the situation is different, because with a corporate tax, debt increases the total income that the firm pays out because it reduces the tax burden. Therefore, given the total earnings before tax, if you have debt, you can pay out more money between stockholders and bondholders then if you don't have debt. That is worth something. Cheating the government (legally, of course), is worth something. Therefore a levered company would sell for more, but because of the taxes not because of the old idea that leverage is good because that is cheaper than equity.

That was the old idea. That's not a good reason, but taxes are a good reason; although, I should tell you that on this issue Modigliani and Miller have split. Miller maintains that even in a world of taxes it makes no difference, and I think he's wrong. I think it does make a difference in a world of taxes.

Now I was going to tell you this, that recently I have found that I can give you an empirical proof of the Modigliani/Miller Theorem that you can go and see for yourself. A good sample is the company of which I am director. It is a closed-end fund, investing bonds (that's minor). What is important is that it is levered. That is, the closed-end fund borrows 1/3 of the capital. So we have $300 million of assets; $200 are held against the equity and $100 against the debt. Now, it happens that when you're dealing with a closed-end fund there is no tax advantage in debt because a fund is just a vehicle that passes out the income in debts. It does not pay a tax on its income before it is passed out. So, from that point of view, the composition of the liability has no effect on total income produced, therefore, the Modigliani/Miller Theorem should apply. And you can verify that it does. In what sense? You take my fund, the equity of my fund is worth exactly the total value of the shares minus the debt. Even though the income yield is higher than an unlevered funds because it's levered. So, we yield a couple percentage points more than other funds, but the price is exactly as the Modigliani/Miller Theorem says. It is essentially, it's discounted at a higher rate because it has leverage which a person could do on his own. Of course, because it is levered it is more risky. In fact, it is, in that class, it is close to the riskiest. Since the leverage exists, then Modigliani/Miller Theorem proves that you have, for levered stock, you have to add to ?(rho) the debt, the ratio of debt to equity, times the risk premium. That's the Modigliani/Miller Theorem. Which is what you get by personal leverage, precisely that. So, that's the formula.

First it may be sort of interesting to use this formula to explain why I told the reporter of the Colorado Springs Gazette that I thought the market was over-valued. Let's use this formula, by putting in some of the numbers which we roughly know. With the interest rate at 6% and a risk premium around 6%, ?(rho) is around 12%. The leverage is about 1/3 in the United States and the risk premium 6, so you add 2% to 12%, and you get to 14%. Now from that you have to subtract the growth. If you are very naive, you say the growth over the last three years has been 10%. You take 14, subtract 10, you get 4 and the reciprocal of 4 is 25. So, a P/E of 25 is 5. However, first of all, 10% is nominal and what you need is the real growth. So you have to take 10%, subtract 3% and that gives you 7. And then from 7 that is the perpetual growth. I certainly don't believe that stock will keep growing at 7% real for a long time. So let's be very bullish and say, 5%, which is very high. So, now you've got, I think we had gotten to 12, and 2 is 14, and if you subtract something like 5, that would give you 9. The reciprocal of which 11. Now, I am actually prepared to make the growth somewhat larger, and so let's believe that it's somewhat larger and perhaps the risk premium a little lower. I get to something like the nominal rate, about 7, the reciprocal of which is 15. My conclusion is that the market, the fundamentals, justify a price earnings ratio, an average price earnings ratio of 15. Being higher for companies which have much growth, and 15 for those who don't essentially. That is the basis of the 15.

If the fundamentals say that the P/E should be 15, why is it 22? There must be something wrong with your formula because your formula should reproduce the world. Well, I'll come back to that at the end by essentially saying that the difference is, what I call the current bubble. We now have a bubble which has inflated stock values above fundamentals and the sharp decline is the bubble that is being deflated. The bubble that has been pricked, and since it was under tension as you prick it comes down quickly, people, once they realize that the stock market is not such a wonderful thing they want to get out and at that moment the high price can no longer be supported. And I'll come back to that at the end.

Let's then, instead, move on to the question: given this formula, should I expect things (stocks and bonds) to move together? And the answer is given in a table which you have, which tries to look at what things make interest rates and risk premium...what are the things that cause changes in these two, in these two valuations? Some of them are very simple. Take the case of a rise in expected earnings, such as might have been justified recently because corporate earnings have been pretty good, aside from the rise, a pretty good level, and you may lift your expectations of earnings, and that should raise the price in proportion. In general, it should really have no effect on interest rates. So, that's a situation where the market should go up, but interest rates should not go up. So they should not move together. There is a possibility that interest rates might actually rise, but let me leave that for a moment. We can come back to that later.

Now we come to a very important issue, which is inflation. In a world of rational behavior, the interest rate that matters, that is the interest rate that people should compare with stock returns. Stock returns are 10%. The risk premium is 6. That difference should be the difference between the real and the nominal. What I mean is this: that the rate that is used to capitalize the stock should be the real interest rate plus the risk premium. In reality, there is strong evidence that people don't understand the difference between these two; therefore, they use the nominal interest rate to capitalize the stock. Now what does that mean? That when you have inflation, with a small inflation rate it doesn't make that much of a difference, but when you have as through the 70's, inflation rising and getting to two-digit levels, nominal interest rates went from 4% or 5% up to 13%, long term rate, 13% or 14%. You can imagine what that does to the stock. It just makes them very depressed. And now if you will put again the picture of the two [time] series, you will see this most markedly. All of this dip in interest rates is due to inflation. From 1970, see here, interest rates were fairly steady, through the beginning of the Vietnam War, 1969-1970. Then by 1972 the inflation began to really kick in and inflation and interest rates began to rise. The nominal rates began to rise and you have this nominal rate here from 1972, this great dip in the reciprocal of interest rates. Interest rates sort of doubled or more and the price, the value of the bond declined enormously.

The stock should not have responded. The stock should have depended on the real rate. It should not have come down, but it did, because people used the nominal rate. And this has been demonstrated. I wrote an article on this in the 1970's in which I had the guts, again, of saying that the market was half as high as it should be. Written in 1978, I think, at a time when economists were infatuated with the notion of the [random walk?] whatever the market did was right. There could not be irrationality, everybody was perfectly rational, everything was fine, everything was unexpected because news came along, but there was no error ever. And I had the guts to say, no, there is an error, people don't know how to calculate. And it's a very simple technique I used, very easy to understand. I looked at the price, and then used as a variable the real rate, and then added on the rate of inflation, which should have no effect in a rational model. It turns out that the rate of inflation explains a great deal of what happens. The higher the inflation, the lower the market. And I went on, well, in that article we said, as the market, when you say it's half as much, we mean not some abstract thing but something very concrete. That as inflation abates, the market will double. And that's what happened between 1977 and the early 1980's when the market did an enormous rise which is represented here.

And later on I went on to say in another article that I thought that that rapid rise, due to the decline of inflation, which happened in a few years, would generate such a rise in prices that it would cause a bubble. I predicted the '87 bubble before it came-- a year before. Then, see what happens here...BANG!! If you go back to the chart that says do they move together or not, you find that with the rational valuation inflation reduces the value of bonds. But that should not affect the value of the stock. With irrational valuations they both will come down. So, here is one case in which things move together, and it is important because, in fact, a lot of the subsequent history are simultaneous movements of the two variables. Because the market is convinced, wrongly, that the nominal rate is what matters and so when the nominal rate declines, and the stocks and bonds suffer, the market has typically suffered, and you read continuously [statements such as this:]

"The market declined last week, because people are very much concerned that inflation is lurking in the back. And if there is inflation, interest rates will rise and then the stock will decline." Without saying that if the rise in interest rate is due only to inflation that should have no affect on the market. But as long as people believe it, it does. In fact, one of the best lines in my paper was to explain that believing irrational behavior I had not sold my stock in the early 1970's because I thought that inflation would not affect it. I have lost money that way. I ended the article by saying to my fellow economists, if you are so smart, why aren't you poor? Of course, since I stayed in the stock, I recovered when the stock doubled, I made it up again, but initially I did lose. So, here is one case of movement in the same direction.

There is another movement which is of some interest. What happens if ?(rho) rises? What does it mean that ?(rho) rises? What it is essentially means is that capital is more productive, so the rate that can be paid, or the required rate of return, goes up because the opportunities are higher. That rise in ?(rho), if the earnings are constant, you just see from now on I expect it to be more productive. Then if earnings are constant and ?(rho) rises, the stock should decline. At the same time if the risk premium is the same, the rise in ?(rho) drags into the [inaudible], the thing fundamentally, and that's perhaps an important concept. Interest rates are not a primitive thing. The primitive is ?(rho), the return to capital, that's the economics. The interest rate reflects that return and risk aversion. It is the result of these two things. Interest rates don't exist in nature. Nature only produces risky streams. The sure streams, due to debt, are the creation of people, where I assume more risk and I give you certainty. Then I earn more on the average or I go bankrupt. In this case, if there is an increased return and earnings were the same, then stock market and bond market would both decline. However, when you have an expectation that the return of capital is higher, it is very likely that earnings are also rising. That is, you think the capital is more productive because to begin with, the capital earns more. In that case, since earnings and ?(rho) rise together, by and large you wouldn't expect much to happen in the stock market. The interest rate will still go up and the bond market will go down. In this case, essentially, you have no effect on one side and a negative effect on the other.

One important source of movements is the possibility that the degree of risk aversion changes. You can put it several ways. One way is to say that people require less of a premium to take risks, or accept a smaller cost of shedding risk. When the risk premium rises, then the interest rate will decline because you have to induce people, you have to pay more because they're more risk averse, you have to offer them more to take the risk or people accept a smaller return to shed risk. So, essentially an increase in risk aversion will reduce interest rates. People become more cautious and then you accept a smaller payment for a sure thing. At the same time, because of the Modigliani/Miller Theorem-- which we have lost in the mean time-- in the evaluation equation there was a Modigliani/Miller Theorem, which had debt times the risk premium. Because the risk premium rises, the stock, the value of stock, should decline. If you have a rise in the risk premium alone, you should expect the stock market and the bond market to move in opposite directions. Bonds get more valuable because people shed risk, and stock gets less valuable, if it's levered, essentially because with the higher risk premium you have a larger opportunity to increase your earnings by levering. The risk premium tells you how much more you can earn, more by giving up the safety of the bonds and accepting the risk of the stock. By the way, the increase in risk aversion may have two sources. It may be that people become less tolerant of risk. The other is that the risk itself has increased. For instance, the uncertainty of outcomes is increased. That also has the effect of increasing the risk premium.

I think this is an interesting case because I think it has something to do with what happened just now. As the market shrunk, as the market came down, why did it come down? Well, I think the main reason is, you can say, is the consciousness that the price was too high, but I think more concretely that the expectation that stock prices would keep rising disappeared. Now, you understand I haven't talked about the bubble, but the essence of the bubble is that the price is kept up by the fact that (g) is not the growth of earnings; (g) is the growth of prices. So if the stock prices keep rising, then you can justify a very high price because the denominator is small. That high price depends on the very fast growth. The problem is that's what we call the rational bubble. As long as the rise in the stock market continues, it's OK, it's a good buy. The problem is that as this happens the price rises faster than earnings. The price/earning ratio gets more and more distorted and has no longer any relation to the interest rate which it should have. So it becomes unrealistically high, and we sometimes say that you are in a balloon and the earth gets smaller and smaller and at some point you think you had better come back. When people realize that, then they begin to understand that it's not very likely that they will find somebody who will buy at an even higher price, which is the essence of the growth. I buy at a very high price, it's OK as long as I can sell it 15% higher. At some point you begin to doubt that you will find somebody stupid enough to buy it at that point. Then, you decide it's better to get out. The moment you do that, there is no more rise and the moment there is no more rise, the high price cannot be maintained. Therefore, you come down and you come down slamming because nobody wants to hold stocks while they are declining. People who keep holding stock do it because they think the end has come. But that's the only reason they do that. Because essentially no one wants to hold stocks when they are declining in price because you have a negative return. I think a large part of that is the fact of growth expectation, but also I think the fact that such a big movement could occur made people realize how risky stocks are, and made them inclined to increase the risk premium, which you would expect would lead to higher interest rates.

We have observed through this period, that on the whole interest rates have declined. The newspapers have said that people try to buy bonds and sell stock, and the effect of that is to essentially reduce interest rates. I think that that is the kind of mechanism that's in here, where the change in risk preference is due mostly to an increased perception of risk. On the other hand, I think you have to say that in the long run risk aversion has tended to decline in this country. There is no question that the movement to investment funds has reduced the risk for many holders and that per s� has made stock less risky. Also, I think it has given the idea that you have a vehicle for investment, which is as liquid as a bond, and yet gives you a higher return. And I think it has essentially given some assurance and thereby reduced the risk premium. I think this is a long run trend.

The last thing is the effect of the growth rate, and that obvious. If you have a more bullish expectation about the growth rate, that will increase the stock. And then, of course, while in the initial formula I wrote down (g) as the growth rate of earnings, once you allow for bubbles you will make that the real growth of prices. Which gives you this vicious circle sort of thing. That is, if for some reason you get a spurt of a rise in price as you did with the decline of inflation, prices rose, and they rose year after year, people began to think that stocks had large returns, because on top of the yield you got the capital gain. Everybody wanted to buy them and that bids them up and that is how you inflate the bubble. Then at some point the bubble crashes. This is known from other areas. This is a tendency that economists are aware of, these so-called mini-bubbles. One of the most interesting ones, which reminds me most of the stock market is the so-called Tulip Bubble. When in Holland in one of the few months in between crops when bulbs could not be produced, people began to bid up the price of bulbs and as they rose in price, people thought that this was a fantastic investment. They could get a 50% return in a week, and they all rushed in and rose the price of tulips to incredibly absurd levels, and then some smart people decided it was too high and then it came down crashing very, very quickly. That is, I think the special feature of bubbles. In every case you have to look for some mechanism that for awhile produces a relatively fast rise either in earnings or in price or both. Which in the case of 1987 was, in my view, the declining inflation, which produced a rise in value, wrongly, but it did. And in the present case I think it had to do with essentially the fact that interest rates began to decline (inverse rises) and on top of that there was a first pretty fast rise of earnings. The combination of the two made prices rise very fast for several years and then you get this phenomenon of the bubble.

I have only to tell you one thing. This chart is misleading in one sense, that is, it is not the chart that you want to pay too much attention to for the following reason: you do have in addition to the 1987 very high value preceding the crash, you do have a very high value there which also appears to proceed the crash. That turns out to be all fake, and is due to the fact that the price earning ratio, I think I've said it, but I certainly said it in the paper that was passed out, the earnings are not current earnings, but the earning capacity of the firm. That is, cleaned up of any temporary things. What happened is that we had some horrible years in 1991, 92, 93, where the earnings were quite depressed. The reason, I'll tell you a way of looking at measuring earnings which is very good in the short run, and that is to take dividends. Why? Because it is well known that companies like to keep their dividends stable. They choose a number, which they can maintain in the light of what they expect their earnings to be. Dividends, in general, are a good measure of expected earnings.

Using dividends would be perfectly good if the payout was stable over an average of two years. Unfortunately, this is not true. Recently the payout has declined and the main reason the dividend has declined is we wrongly measure cash dividends but firms have now learned that a much better way of paying their income is by buying shares. Then you avoid the tax on dividends. There is more and more a tendency of paying out dividends in that way since that is not counted in the official data of Standard and Poor's. It appears that dividends are really small. So if you take, instead of the earnings, you put the dividends, then the graph doesn't have this peak at all. This is all smoothed out and the end is very high, and you can see the bubble, which you cannot here because of the high peak before. But that is really due to the poor measurement of earnings.

I think that just about completes what I wanted to say. The discussion of bubbles has been not systematic, but I think you understand the basic view. The reason that there is a difference between the formula and what happens is because this formula is a formula about fundamentals and the fundamental is earnings. When there are no bubbles, earnings and price move together. The price earnings ratio is stable, therefore the two move together and it makes no difference whether you use one or the other. When you have the bubble, prices are rising faster than earnings and what really matters is the return, which is dividends plus capital gains. Then you must use the rate of growth of prices. From a technical point of view, it is a very hard thing to fit a model in which things get out of equilibrium and then at some point they crash. This is extremely hard to model from a statistical point of view. I think the facts are fairly clear-- there have been some other studies which point at the same direction--and the existence of bubbles is supported by the work of several of my students, independently actually. One at the University of New York presented recently a paper in which he tries to estimate the bubbles, and where they are and how they came about. And it is the work of my student, very well known student, maybe sometime a Nobel Prize, I don't know, Robert Schiller at Yale, who essentially has shown that the market fluctuates more than is justified by fundamentals.

Franco Modigliani won the Nobel prize in economics in 1985, in part for his research on the life-cycle hypothesis which asserts that individuals plan their spending activities based on their expectations of their lifetime or permanent income.