Figure 1-19 shows a clear-cut relations.h.i.+p between risk and return. Some may object to the magnitude of the risks I've shown for stocks. But as the recent performance in emerging markets and tech investing show, losses in excess of 50% are not unheard of. If you are not prepared to accept risk in pursuit of high returns, you are doomed to fail. shows a clear-cut relations.h.i.+p between risk and return. Some may object to the magnitude of the risks I've shown for stocks. But as the recent performance in emerging markets and tech investing show, losses in excess of 50% are not unheard of. If you are not prepared to accept risk in pursuit of high returns, you are doomed to fail.

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Figure 1-19. Risk and return summary. ( Risk and return summary. (Source: Kenneth French and Jeremy Siegel.) Kenneth French and Jeremy Siegel.)

CHAPTER 1 SUMMARY.

1. The history of the stock and bond markets shows that risk and reward are inextricably intertwined. Do not expect high returns without high risk. Do not expect safety without correspondingly low returns. Further, when the political and economic outlook is the brightest, returns are the lowest. And it is when things look the darkest that returns are the highest.2. The longer a risky a.s.set is held, the less the chance of a loss.3. Be especially wary of data demonstrating the superior long-term performance of U.S. stocks. For most of its history, the U.S. was a very risky place to invest, and its high investment returns reflect that. Now that the U.S. seems to be more of a "sure thing," prices have risen, and future investment returns will necessarily be lower.

The New World Order, circa 1913The tragic events in New York, Was.h.i.+ngton, DC, and Pennsylvania in the fall of 2001 served to underscore the relations.h.i.+p between return and risk. Prior to the bombings, most investors felt that the world had become progressively less risky. This resulted in a dramatic rise in stock prices. When this illusion was shattered, prices reacted equally dramatically.This is not a new story. There is no better ill.u.s.tration of the dangers of living and investing in an apparently stable and prosperous era than this pa.s.sage from Keynes's The Economic Consequences of the Peace The Economic Consequences of the Peace, which chronicles life in Europe just before the lights went out for almost two generations:The inhabitant of London could order by telephone, sipping his morning tea in bed, the various products of the whole earth, in such quant.i.ty as he might see fit, and reasonably expect their early delivery upon his doorstep; he could at the same moment and by the same means adventure his wealth in the natural resources and new enterprises of any quarter of the world, and share, without exertion or even trouble, in their prospective fruits and advantages; or he could decide, to couple the security of his fortunes with the good faith of the townspeople of any substantial munic.i.p.ality in any continent that fancy or information might recommend. He could secure forthwith, if he wished it, cheap and comfortable means of transit to any country or climate without pa.s.sport or other formality, could dispatch his servant to the neighboring office of a bank for such supply of the precious metals as might seem convenient, and could then proceed abroad to foreign quarters, without knowledge of their religion, language, or customs, bearing coined wealth upon his person, and would consider himself greatly aggrieved and much surprised at the least interference. But, most important of all, he regarded this state of affairs as normal, certain, and permanent, except in the direction of further improvement, and any deviation from it as aberrant, scandalous, and avoidable. The projects and politics of militarism and imperialism, of racial and cultural rivalries, of monopolies, restrictions, and exclusion, which were to play the serpent to this paradise, were little more than the amus.e.m.e.nts of his daily newspaper, and appeared to exercise almost no influence at all on the ordinary course of social and economic life, the internationalization of which was nearly complete in practice.

2.

Measuring the Beast Capital value is income capitalized, and nothing else.

Irving Fisher In the history of modern investing, one economist towers above all others in influence on the way we examine stocks and bonds. His name was Irving Fisher: distinguished professor of economics at Yale, advisor to presidents, famous popular financial commentator, and, most importantly, author of the seminal treatise on investment value, The Theory of Interest The Theory of Interest. And it was Fisher, who, a century ago, first attempted to scientifically answer the question, "What is a thing worth?" His career was dazzling, and his precepts are still widely studied today, more than seven decades after the book was written.

Fisher's story is a caution to all great men, because, in spite of his long list of staggering accomplishments, he will be forever remembered for one notorious gaffe. Just before the October 1929 stock market crash, he declared, "Stock prices have reached what looks like a permanently high plateau." Weeks before the start of a bear market that would eventually result in a near 90% decline, the world's most famous economist declared that stocks were a safe investment.

The historical returns we studied in the last chapter are invaluable, but these data can, at times, be misleading. The prudent investor requires a more accurate estimate of future returns for stocks and bonds than simply looking at the past. In this chapter, we're going to explore Fisher's great gift to finance-the so-called "discounted dividend model" (referred to from now on as the DDM), which allows the investor to easily estimate the expected returns of stocks and bonds with far more accuracy than the study of historical returns.1 Bluntly stated, an understanding of the DDM is what separates the amateur investor from the professional; most often, small investors haven't the foggiest notion of how to estimate a reasonable share price for the companies they are buying.

You may find this chapter the most difficult in the book; the concepts we will explore are not intuitively obvious, and, in a few spots, you will have to put the book down and think. But if you can understand the chapter's central point-that the value of a stock or a bond is simply the present present value of its value of its future future income stream-then you will have a better grasp of the investment process than most professionals. income stream-then you will have a better grasp of the investment process than most professionals.

As we've seen, the British enjoy a nearly millennial head start on us in the capital markets. This has allowed them to embed some bits of financial wisdom into their culture that we have yet to absorb. Ask an Englishman how wealthy someone is, and you're likely to hear a response like, "He's worth 20,000 per year."

This sort of answer usually confuses us less sophisticated Yanks, but it's an estimable response, because it says something profound about wealth: it does not consist of inert a.s.sets but, instead, a stream of income a stream of income. In other words, if you own an orchard, its value is defined not by its trees and land but, rather, by the income it produces. The worth of an apartment house is not what it will fetch in the market, but the value of its future cash flow. What about your own house? Its value is the shelter and pleasure it provides you over the years.

The DDM, by the way, is the ultimate answer to the age-old question of how to separate speculation speculation from from investment investment. The acquisition of a rare coin or fine painting for purely financial purposes is clearly a speculation: these a.s.sets produce no income, and your return is dependent on someone else paying yet a higher price for them later. (This is known as the "greater fool" theory of investing. When you purchase a rapidly appreciating a.s.set with little intrinsic value, you are dependent on someone more foolish than you to take it off your hands at a higher price.) There is nothing wrong with purchasing any of these things for the future pleasure they may provide, of course, but this is not the same thing as a financial investment.

Only an income-producing possession, such as a stock, bond, or working piece of real estate is a true investment. The skeptic will point out that many stocks do not have current earnings or produce dividends. True enough, but any stock price above zero reflects the fact that at least some investors consider it possible that the stock will regain its earnings and produce dividends in the future, even if only from the sale of its a.s.sets. And, as Ben Graham pointed out decades ago, a stock purchased with the hope that its price will soon rise independent of its dividend-producing ability is also a speculation, not an investment.

And lest I unnecessarily offend art lovers, it should be pointed out that even an old master, bought from the artist for $100 and sold 350 years later for $10,000,000, has returned only 3.34% per year. Ideally, a fine painting, like a house, is neither a speculation nor an investment; it is a purchase purchase. Its value consists solely of the pleasure and utility it provides now and in the future. The dividend the painting provides is of the non-financial variety.

How, then, do we define a stock's stream of income? Next, how do we determine its actual worth? This is a tricky problem, which we'll tackle in steps. In the next several pages, we'll uncover how the stock market is properly valued and how future stock market returns are estimated. These pages may prove difficult. I recommend that you slow your reading down a bit at this juncture, making sure you have carefully read each sentence before proceeding to the next In the next several pages, we'll uncover how the stock market is properly valued and how future stock market returns are estimated. These pages may prove difficult. I recommend that you slow your reading down a bit at this juncture, making sure you have carefully read each sentence before proceeding to the next.

One of Fisher's favorite investment paradigms was a gold or lead mine that began with a maximum yield in year one, then dwindled to nothing in 10 years: [image]

Now that we've defined the income stream in the above table, how do we value it? At first glance, it appears that the mine's worth is simply the sum of the income for all ten years-in this case, $11,000. But there's a hitch. Human beings prefer present consumption to future consumption. That is, a dollar of income next year next year is worth less to us than a dollar is worth less to us than a dollar today today, and a dollar in thirty years, a great deal less than a dollar today. Thus, the value of future income must be reduced to reflect its true present value. The amount of this reduction must take into account four things: * The number of years you have to wait: The further in the future you receive income, the less it is worth to you now.* The rate of inflation: The higher the rate of inflation, the less value in terms of real spending power you can expect to receive in the future.* The "impatience" of society for future consumption: The more society prefers present to future consumption, the higher are interest rates, and the less future income is worth today. (The second and third factors can be combined into the "real rate of interest.")* Risk itself: The greater the risk that you might not receive the income at all, the less its present value.

The simplest way to look at the problem is to imagine waiting in line to board a plane for a week in Paris. You've been working hard at your job in downtown Cleveland, and you can almost smell the crepes on Rue Saint Germain. But wait! Just as you get to the head of the line, the ticket agent swipes your boarding pa.s.s and says, "Sorry sir, but Hillary Clinton has just arrived, and she needs your seat." (You're flying first cla.s.s, of course.) "It's the last one, and the Secret Service agent demands I give it to her. Don't worry though, because I can offer you another trip in ten years."

What a raw deal! A week in Paris in ten years is not worth nearly as much to you as a trip right now. You balk. Finally, "I'm sorry, but you'll have to make it five weeks in Paris a decade from now to make it worth my while." With a sigh of defeat, the agent accepts.

What you have just done is what financial economists call "discounting to the present." That is, you have decided that a week in Paris in ten years is worth a good deal less to you than a week there right now; you have lowered the value of the future weeks in Paris to account for the fact that you will not be enjoying them for another decade. To wit, you have decided that five weeks in ten years is worth as much as just one week today. In the process of doing so, you have determined that your week-in-Paris discount interest rate is 17.5% per year; 17.5% is the rate at which one week grows to five weeks over ten years.

Here is where things start to get a bit sticky, because the discount rate (referred to from now on as the DR) and the present value are inversely related: the higher the DR, the lower the present value. This is the same as with consols and prest.i.ti, whose values are inversely related to interest rates. For example, if you decide that a week in Paris now is worth ten ten weeks a decade from now, that implies a much higher DR of 25.9%. This is the same as saying that the present value of a week in Paris in a decade has cheapened. Again, an weeks a decade from now, that implies a much higher DR of 25.9%. This is the same as saying that the present value of a week in Paris in a decade has cheapened. Again, an increase increase in the DR means that the present value of a future item has in the DR means that the present value of a future item has decreased; decreased; if the value of one week in Paris now has increased from five to ten weeks in Paris in the future, then the value of those future weeks has just fallen. if the value of one week in Paris now has increased from five to ten weeks in Paris in the future, then the value of those future weeks has just fallen.

Fisher's genius was in describing the factors that affect the DR, or simply, the "interest rate," as he called it. For example, a starving man would be willing to pay much less for a delayed meal than a well-fed person. In other words, a hungry person's DR for food is very high since he has a more immediate need for it than someone who is well nourished. Fisher, in fact, uses the words "impatience" and "interest rate" interchangeably; the wastrel has a higher interest rate (DR) than the tightwad.

Another of Fisher's observations was that societies characterized by highly durable goods have lower interest rates than those that are not. Where the houses are made of bricks and stone, interest rates are low. Where the houses are made of mud and straw, rates are high.

Fisher found that, by far, the single most important factor affecting the DR is risk risk. The one week/five week Paris trip relations.h.i.+p discussed above a.s.sumed that the airline and travel agent were well-established and likely to still be in business in ten years when you return for your vacation. But what if you weren't so sure that they would be there for you in a decade? You would, of course, demand a longer vacation in 10 years-say 10 weeks, instead of five. In which case, you've arrived at the 25.9% DR we mentioned previously. In other words, the riskier the payoff, the higher the return you would demand.

Let's now return to our mine. We have to decide on a discount factor to apply in each successive year to its income. But before I tell you just how to estimate the DR, let's see what a given DR means. Say that we decide on an 8% DR. The table below is the same one we saw a few pages ago, but now we've added two more columns. The column labeled "Discount Factor" is the amount we must reduce the dividend by in a given future year to compute its value in the present day; the first year's income must be divided by 1.08, the second year's by 1.08 1.08, and so on. The last column, labeled "Discounted Income," is the resultant present value: [image]

For example, look at year 8. In this year, the mine earns $600 but, just like your delayed trip to Paris, this future payment of $600 is not worth $600 to you right now. To obtain the current value of this future $600, you must divide it by 1.8509 (1.08 multiplied by itself seven times), to yield a value of $324. This is the present value present value of $600 for which we must wait eight years at an 8% DR. The total present value of the mine-in effect, its "true value"-is the sum of all of the future dividends, of $600 for which we must wait eight years at an 8% DR. The total present value of the mine-in effect, its "true value"-is the sum of all of the future dividends, discounted to the present discounted to the present. This is the sum at the bottom of the table: $8,225.

The next step is to apply this method to stocks. The primary job of the security a.n.a.lyst is to predict the dividend flow of a company so that it may be discounted to obtain the "fair value" of its stock. If the market price is below the calculated fair value, it is bought. If the market price is above the calculated fair value, it is sold. This is no easy task. (In fact, as we'll find out in Chapter 4 Chapter 4, it is an impossible impossible task.) Not infrequently, promising companies with large expected future dividend streams stumble and fall; nearly as often, companies given up for dead recover and provide shareholders with prodigious amounts of future income. task.) Not infrequently, promising companies with large expected future dividend streams stumble and fall; nearly as often, companies given up for dead recover and provide shareholders with prodigious amounts of future income.

On the other hand, when you examine an entire market, consisting of hundreds or thousands of companies, these unexpected events average out. For this reason, the income stream of the market as a whole is a much more reliable calculation.

But at first, even this seems a hopeless task. Because the stock market is expected to produce dividends forever, you have to predict the future income stream for an infinite number of future years, discount the dividends for each year to the present, then add them all up. But with a few mathematical tricks, this nut is easily cracked.

A Stream of Future Dividends, Forever and Ever, Amen To paraphrase the famous Chinese proverb, even a journey of a thousand miles must begin with a single step. Here's our first one. At the end of 2001, the Dow Jones Industrial Average was selling at around 9,000 and yielded 1.55% of that, or about $140 per year in dividends. Further, over the long haul, the Dow's dividends grow at about 5% per year. So in 2002, there should be about $147 of dividends; in 2031, $605. Now take a look at Table 2-1 Table 2-1. In the second column, under "Nominal Dividends" ("nominal" refers to the actual dollar amount, not not adjusted for inflation), I've tabulated the actual dividend for each future year; I've also plotted this rise in dividends in adjusted for inflation), I've tabulated the actual dividend for each future year; I've also plotted this rise in dividends in Figure 2-1 Figure 2-1.

We've just taken the first step in valuing the market: we've defined its future stream of dividends. Next, we must discount the actual dividend in each future year to the present. To do this, we divide the dividend in each future year by the appropriate discount factor, similar to our calculation for the mine. How do we decide on a DR for the entire stock market? Similar to our hypothetically discounted future meal, the DR of the Dow is simply the rate of return we expect from it, taking its risk into consideration the DR of the Dow is simply the rate of return we expect from it, taking its risk into consideration.

Table 2-1. Dow Jones Industrial Average Projected and Discounted Dividends Dow Jones Industrial Average Projected and Discounted Dividends [image]

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Figure 2-1. Dow dividend value. Dow dividend value.

Let's say that we expect an 8% return from stocks. So just like our mine, the market's DR, by definition, is thus 8%. As we've already determined, the Dow's dividend 30 years from now should be about $605. Similar to our mine, to get the present value of those dividends we have to divide that amount by 1.08 for each year in the future. To obtain the present value of the Dow dividend 30 years from now, in 2031, you have to divide $605 by 10.06 (1.08330, that is, 1.08 multiplied by itself 29 times). Dividing the $605 dividend in 2031 by 10.06 yields a present value of $60. If we perceive that economic, political, or market risk has increased, we may decide that the DR should be higher; if we are really frightened about the state of the economy, the nation, or the world, we will decide that 15% is appropriate. In that case, the present value of the year 2031's $605 dividend is reduced even further, to just $9.

Take another look at Table 2-1 Table 2-1. Again, the second column in this table displays the nominal expected dividends, which rise at a 5% annual rate in each future year. The third column is the discount factor at 8% for each year. The fourth column is the value of the dividend in that year, discounted to the present (this is calculated by dividing the actual dividend in the second column by the discount factor in the third). As with prest.i.ti and consols, when the DR rises, prices fall; when the DR falls, prices rise.

I've also plotted these numbers in Figure 2-2 Figure 2-2. The top curve-the same curve plotted in Figure 2-1 Figure 2-1-represents the actual, or "nominal," dividends received in each future year. To reiterate, the top curve represents the actual dividend stream of the Dow received by shareholders before its value has been adjusted down to its present value. The bottom curves are the present value present value of the Dow's income stream, obtained by discounting the nominal dividends at rates of 8% and 15%. of the Dow's income stream, obtained by discounting the nominal dividends at rates of 8% and 15%.

Notice how at the higher discount rate, the discounted value of the dividends decays nearly to zero after a few decades; such is the corrosive effect of high DRs, caused by high risk or high inflation, on stock values.

Better Living Through Mathematics Now we need only perform one more step. To obtain the "true value" of the Dow, you have to add together all of the discounted dividends for each year (excluding the first, because it has already been paid). For example at a DR of 8%, you would add up all of the numbers (except the first) in the fourth column, the one labeled "8% Discount Value." Does this seem like a hopelessly difficult task? It is, if you are doing the computation by what mathematicians call the "brute force" method, i.e., trying to add the infinite column of numbers in column four.

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Figure 2-2. Discounted Dow dividend value. Discounted Dow dividend value.

Fortunately, mathematicians can help us out of this pickle with a simple formula that calculates the sum of all of the desired values in column four. Here it is: Market Value = Present Dividend/(DR Dividend Growth Rate) Using our a.s.sumption of a $140 present dividend, an 8% DR, and 5% earnings growth, we get: Market Value = $140/(0.080.05) = $140/0.03 = $4,667 (Finance types always do their calculations with decimals; 8% becomes 0.08 in the formula.) Oops. This formulation suggests that the Dow, currently priced at around 10,000, is about 100% overvalued compared to the 4,667 value we just computed using the rosy 8% DR return scenario.

And if things get really really rough, investors may decide they require a 15% DR to invest in stocks (as they did in the early 1980s, when Treasury bonds yielded almost 16%). I've shown the relevant figures for a 15% DR in the last two columns of rough, investors may decide they require a 15% DR to invest in stocks (as they did in the early 1980s, when Treasury bonds yielded almost 16%). I've shown the relevant figures for a 15% DR in the last two columns of Table 2-1 Table 2-1. The simplified calculation looks like this: [image]

Figure 2-3. Dow fair value versus discount rate. Dow fair value versus discount rate.

Market Value = $140/(0.15 0.05) = $140/0.10 = $1,400 It is unlikely (but not impossible) that the Dow will drop as far as 1,400 at any point in the future, but recall that at least twice in this century U.S. investors indeed did demand a 15% DR.

This kind of calculation is enormously sensitive to the DR and dividend growth rate. For example, raise earnings growth to 6% and lower the DR to 7%, and you come up with a market value of 14,000. Some of you may be aware of the controversy surrounding a book by James Gla.s.sman and Kevin Ha.s.sett, provocatively t.i.tled Dow 36,000 Dow 36,000, in which they arrive at the t.i.tle's number by fiddling with the above equation in the manner we've described.

In fact, using entirely reasonable a.s.sumptions, you can make the Dow's discounted market value almost anything you want it to be. To show how the DR affects the "fair value" of the Dow via this technique, I've plotted the Dow's "fair value" from the DDM versus the DR in Figure 2-3 Figure 2-3.

Rescued by the Gordon Equation Why have we spent so much time and effort on the DDM when it turns out that it cannot cannot be used to accurately price the stock market? For three reasons. First and foremost, because it provides an intuitive way to think about the value of a security. A stock or bond is not an abstract piece of paper that has a randomly fluctuating value; it is a claim on real future income and a.s.sets. be used to accurately price the stock market? For three reasons. First and foremost, because it provides an intuitive way to think about the value of a security. A stock or bond is not an abstract piece of paper that has a randomly fluctuating value; it is a claim on real future income and a.s.sets.

Second, it enables us to test the growth and return a.s.sumptions of a stock or of the entire market. At the height of the tech madness in April 2000, the entire Nasdaq market sold at approximately 100 times earnings. Applying the DDM to it revealed that this implied either a ridiculously high earnings growth rate or a low expected return. The latter seemed far more plausible to serious observers, and unfortunately, this is eventually what happened.

Third, and most important, the real beauty of the above formulas is that they can be rearranged to calculate the market's expected return, producing an equation that is at once stunningly simple and powerful: DR (Market Return) = Dividend Yield + Dividend Growth This formula, which is known as the "Gordon Equation," provides an accurate way to predict long-term stock market returns. For example, during the twentieth century, the average dividend yield was about 4.5%, and the compounded rate of dividend growth was also about 4.5%. Add the two together and you get 9.0%. The actual return was 9.89%-not too shabby. The approximately 1% difference was due to the fact that stocks had become considerably more expensive (that is, the dividend yield had fallen) during the period.

The Gordon Equation also has an elegant intuitive beauty. If the stock market is simply viewed as a source of dividends, then its price should rise in proportion to those dividends. So if its dividends increase at 4.5% per year, then over the very long term its price should also increase by 4.5% per year. In addition to the price increase, you also receive the actual dividend each year: the annualized total return comes from the combination of the annualized price increase (which is roughly the same as the annualized dividend growth) and the average dividend yield.

The Gordon Equation is as close to being a physical law, like gravity or planetary motion, as we will ever encounter in finance. There are those who say that dividends are quaint and outmoded; in the modern era, return comes from capital gains. Anyone who really believes that might as well be wearing a sandwich board on which is written in large red letters, "I haven't the foggiest notion what I'm talking about."

It is, of course, true that a company never has to pay out a dividend in order to provide capital gains. But even if all of the companies in the U.S. stopped paying out dividends (which they have just about done), in the long term their return would be roughly the same as their aggregate earnings growth. Thus, in a world without dividends, company earnings must grow at an average rate of 10% per year in order to provide the historical 10% long-term return of stocks. And, as we'll soon see, the long-term average rate of corporate earnings and dividend growth is only 5%. Worse, when adjusted for inflation, it has not changed in the past century.

Never forget that in the long run, it is corporate earnings growth that produces stock price increases. If, over the very long term, the annualized earnings growth is about 5%, then the annualized stock price increase must be very close to this number.

One exception to this is the case of companies that are buying back their shares. A company that has grown its earnings by 5% per year and annually buys back 5% of its outstanding shares will appreciate by 10% per year, in the long term. The opposite is true of companies that issue new stock. Averaged over the whole U.S. market, these two factors tend to cancel each other out.

The discounted dividend model is a powerful way of understanding stock and bond behavior. As we've seen, it isn't of much use in accurately predicting the fair value of the market, let alone a stock. Princeton economist Burton Malkiel famously stated that "G.o.d Almighty himself does not know the proper price-earnings multiple for a common stock." In other words, it is impossible to know the intrinsic value of a stock or the market. But the DDM is useful in more subtle, powerful ways. First, it can be used in reverse. That is, instead of entering the estimated dividend growth and DR and getting the price, we can derive these two values from from the price of the market or for a given stock. We've already seen that in 1999, for example, applying the DDM in this manner would have told you that highly unrealistic growth expectations were embedded in the prices of tech stocks. the price of the market or for a given stock. We've already seen that in 1999, for example, applying the DDM in this manner would have told you that highly unrealistic growth expectations were embedded in the prices of tech stocks.

And, of course, the DDM gives us the Gordon Equation, which allows us to estimate stock returns. This raises an important point. Wall Street and the media are constantly obsessed with the question of whether the market is overvalued or undervalued (and by implication, whether it is headed up or down). As we've just seen, this is essentially impossible to determine. But in the process, we've just acquired a much more valuable bit of knowledge: the long-term expected return of the market the long-term expected return of the market. Think about it, which would you rather know: the market return for the next six months, or for the next 30 years? I don't know about you, but I'd much rather know the latter. And, within a reasonable margin of error, you can. But you don't sell newspapers, magazines, and airtime speculating about 30-year returns.

And what does the Gordon Equation tell us today about future stock returns? The news, I'm afraid, is not good. Dividend growth still seems to be about 5%, and the yield, as we've already mentioned, is only 1.55%. These two numbers add up to just 6.55%. Even making some wildly optimistic a.s.sumptions-say a 6% to 7% dividend growth rate-does not get us anywhere near the 10% annualized returns of the past century.

What about bonds? The expected return of a long-term bond is simply its "coupon," that is its interest payments. (For a bond, the second number in the Gordon Equation, dividend growth, is zero. In almost all cases, a bond's interest does not grow.) High-quality corporate bonds currently yield about 6%. This figure provides a reasonably accurate estimate of their future returns. If interest rates rise, their value will fall, but the rate at which the interest is reinvested will rise, and vice versa. So over a 30-year period, the total bond return cannot be very far from the 6% coupon.

What we have now is a very different picture from what transpired in the twentieth century, with its high stock returns and low bond returns. Going forward, it looks like stock and bond returns should both be in the 6% range, not the 10% historical reward. Don't shoot me, I'm only the messenger.

Viewed from an historical perspective, what has happened is that stocks have had an incredible run the past few decades. Their prices have been bid up dramatically, so their future returns will be commensurately lower. The exact opposite has happened to bonds. As we've already seen, bondholders were severely traumatized by the unprecedented monetary s.h.i.+ft in the twentieth century. Their prices have fallen, so their expected returns have commensurately risen.

On an intellectual level, most investors have no trouble understanding the notion that high past returns result in high prices, which, in turn, result in lower future returns. But at the same time, most investors find this almost impossible to accept on an emotional level. By some strange quirk of human nature, financial a.s.sets seem to become more more attractive after their price has risen greatly. But buying stocks and bonds is no different than buying tomatoes. Most folks are sensible enough to load up when the tomatoes are selling at 40 cents per pound and to forgo them at three dollars. But stocks are different. If prices fall drastically enough, they become the lepers of the financial world. Conversely, if prices rise rapidly, everyone wants in on the fun. attractive after their price has risen greatly. But buying stocks and bonds is no different than buying tomatoes. Most folks are sensible enough to load up when the tomatoes are selling at 40 cents per pound and to forgo them at three dollars. But stocks are different. If prices fall drastically enough, they become the lepers of the financial world. Conversely, if prices rise rapidly, everyone wants in on the fun.

Until very recently, there was a great deal of talk about the "new investment paradigm." Briefly stated, this doctrine a.s.serts that Fisher had gotten it all wrong: earnings, dividends, and price no longer matter. The great companies of the New Economy-Amazon, eToys, and Cisco-were going to dominate the nation's business scene, and no price was too high to pay for the certain bonanza these firms would provide their shareholders.

Of course, we've seen this movie before. In 1934, the great investment theorist Benjamin Graham wrote of the pre-1929 stock bubble: Instead of judging the market price by established standards of value, the new era based its standards of value upon the market price. Hence, all upper limits disappeared, not only upon the price at which a stock could could sell, but even upon the price at which it would sell, but even upon the price at which it would deserve deserve to sell. This fantastic reasoning actually led to the purchase for investment at $100 per share of common stocks earning $2.50 per share. The identical reasoning would support the purchase of these same shares at $200, at $1,000, or at any conceivable price. to sell. This fantastic reasoning actually led to the purchase for investment at $100 per share of common stocks earning $2.50 per share. The identical reasoning would support the purchase of these same shares at $200, at $1,000, or at any conceivable price.

Even the most casual investor will see the parallels of Graham's world with the recent tech/Internet bubble. Graham's $100 stock sold at 40 times its $2.50 earnings. At the height of the 2000 bubble, most of the big-name tech favorites, like Cisco, EMC, and Yahoo! sold at much more than 100 times earnings. And, of course, almost all of the dot-coms went bankrupt without ever having had a cent of earnings.

At the end of the day, the Fisher DDM method of discounting interest streams is the only proper way to estimate the value of stocks and bonds. Future long-term returns are quite accurately predicted by the Gordon Equation. As I've already said, these are essentially the laws of gravity and planetary motion of the financial markets. But it seems that once every 30 years or so, investors tire of valuing stocks by these old-fas.h.i.+oned techniques and engage in orgies of unthinking speculation. Invariably, Fisher and Graham's lesson-not to overpay for stocks-is re-learned in excruciating slow motion in the years following the inevitable market crash.

The rub is, the Gordon Equation is useful only in the long term-it tells us nothing about day-to-day, or even year-to-year, returns. And even in the very long term, it is not perfect. As we've already seen above, over the course of the twentieth century, it was off by about 1% of annualized return. This 1% difference can be attributed to the change in the dividend rate, which decreased from 4.5% to 1.4% between 1900 and 2000. In other words, stocks, which in 1900 sold for 22 times their dividends, now sell for 70 times their dividends. The ratio of price to dividends-22 in 1900, 70 in 2000-is called the "dividend multiple." (This is simply the inverse of the dividend yield: 1/.045 = 22, and 1/.014 = 70.) This ratio is the number of dollars you must pay to get one dollar of dividends. It is similar to the more familiar "PE multiple": price divided by earnings. The PE multiple is the most popular measure of how "expensive" the stock market is.

The Gordon Equation does not account for changes in the dividend or PE multiple. The tripling of the dividend multiple between 1900 and 2000 accounts for most of the approximately 1% difference between the 9% predicted by the Gordon Equation and the 9.89% actual return. (Compounding 0.89% over a century produces close to a tripling of the stock market's value.) Stating that there was a "tripling of the dividend multiple" is just another way of saying that an enthusiastic investing public has driven up stock prices relative to earnings and dividends by a factor of three.

Over relatively short periods of time-less than a few decades-this change in the dividend or PE multiple accounts for most of the stock market's return, and over periods of less than a few years, almost 100% of it. John Bogle, founder of the Vanguard Group of mutual funds, provides us with a very useful way of thinking about this. He calls the short-term fluctuations in stock prices due to changes in dividend and PE multiples the "speculative return" of stocks.

On the other hand, the long-term increase in stock market value is entirely the result of the sum of long-term dividend growth and dividend yield calculated from the Gordon Equation, what Bogle calls the "fundamental return" of stocks. In engineering terms, Bogle's fundamental return is the signal-a constant, reliable occurrence. Bogle's speculative return is the noise-distracting and unpredictable. For example, on October 19, 1987, the stock market fell by 23%. Certainly, on that day-Black Monday-there were no significant changes in the dividend payments or dividend growth of common stocks. The market crash of 1987, and the run up which preceded it, were purely speculative events.

The key point, which we'll return to again and again, is that the fundamental return of the stock market-the sum of dividends and dividend growth-is somewhat predictable, but only in the very long term. The short-term return of the market is purely speculative and cannot be predicted. Not by anyone. Not the panelists on Wall Street Week Wall Street Week, not the "market strategists" at the biggest investment houses, not the newsletter writers, and certainly not your stockbroker.

Perhaps somewhere in a dark secret corner of Wall Street, there is one person who knows just where the market is going tomorrow. But if she exists, she would of course not tell a soul for fear of tipping off the market and damaging the enormous profits that are to be hers on the morrow. (Or, as financial economist Rex Sinquefield replies with a straight face when asked about the direction of the stock market, "I know where the market's headed, I just don't want to share that with anyone.") A superb metaphor for the long-term/short-term dichotomy in stock returns comes from Ralph w.a.n.ger, the witty and incisive princ.i.p.al of the Acorn Funds. He likens the market to an excitable dog on a very long leash in New York City, darting randomly in every direction. The dog's owner is walking from Columbus Circle, through Central Park, to the Metropolitan Museum. At any one moment, there is no predicting which way the pooch will lurch. But in the long run, you know he's heading northeast at an average speed of three miles per hour. What is astonis.h.i.+ng is that almost all of the market players, big and small, seem to have their eye on the dog, and not the owner.

As we've already mentioned, the Gordon Equation is not good news for future equity returns. Is there any way out of this gloomy scenario? Yes. There are three possible scenarios in which equity returns could be higher than the predicted 6.4%: * Dividend growth could accelerate. Companies usually only pay part of their dividends out as earnings. At the present time, the market sells at about 25 times its annual earnings. Another way of saying this is that the "earnings yield" of the market is 4% (1/25). So, if these companies are paying out 1.4% as dividends, that leaves 2.6% to pay for growth.The above figures represent an average of the whole market. Many companies earn far more or far less than 4% of their market value, while many, like Microsoft, pay out zero dividends, retaining all their earnings for future growth. It is said that U.S. companies have experienced dramatic increases in productivity in the past few decades, and that this will further accelerate earnings growth beyond the 5% historical figure. This is wishful thinking.In the first place, before 1980, companies kept far more than 2.6% of their capital value in retained earnings. In the second place, there is voluminous evidence that excess corporate cash from "retained earnings" (that is, earnings not paid out to the shareholders, but instead reinvested in the company) tends to be wasted. And finally, it just isn't happening. In Figure 2-4 Figure 2-4, I've plotted the dividends and earnings of the stock market since 1900 (courtesy of Robert s.h.i.+ller at Yale). Figure 2-4 Figure 2-4 is another one of those confusing "semilog" graphs. Their major advantage is that they allow you to estimate the percent rate of increase of earnings and dividends across a wide range of values. This is not true of standard "arithmetic" plots. With a semilog graph, a constant growth rate produces a plot that moves up at a fairly constant angle, called the slope. This is approximately what is seen in is another one of those confusing "semilog" graphs. Their major advantage is that they allow you to estimate the percent rate of increase of earnings and dividends across a wide range of values. This is not true of standard "arithmetic" plots. With a semilog graph, a constant growth rate produces a plot that moves up at a fairly constant angle, called the slope. This is approximately what is seen in Figure 2-4 Figure 2-4.Those of you with an eagle eye will detect that the slope for the first 50 years seems to be ever-so-slightly less than for the last 50. This is because of inflation. In inflation-adjusted terms, dividend growth may actually be slowing. When inflation is factored in, from 1950 to 1975, annualized earnings growth was 2.22%, and from 1975 to 2000 it was 1.90%. Clearly the rapidly accelerating trend of earnings and dividend growth frequently cited by today's New Era enthusiasts is nowhere to be seen. This a.n.a.lysis also demolishes another one of the supposed props of current stock valuations: stock buybacks, which should also increase per-share stock dividends. This is what is actually plotted in Figure 2-4 Figure 2-4.

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Figure 2-4. Nominal earnings and dividends, S&P 500. ( Nominal earnings and dividends, S&P 500. (Source: Robert s.h.i.+ller, Yale University). Robert s.h.i.+ller, Yale University).

* Bogle's speculative return-the growth of the dividend multiple-could continue to provide future stock price increases with further growth of the dividend multiple. Why, you might ask, can't the dividend multiple grow at 3% per year from here, yielding 3% of extra return? Unfortunately, this means that the dividend multiple would have to double every 24 years. While it is possible that this could occur for another decade or two, it is not sustainable in the long term. After all, if the dividend multiple increased at 3% per year for the next century, then stocks in 2102 would sell at 1,350 times dividends, for a yield of 0.07%! In fact, thinking about the future of the speculative return is a scary exercise. The best-case scenario has the dividend multiple remaining at its present inflated level and not affecting returns. It is quite possible, however, that we may see a reduction in this value over time. Let's say, for the sake of argument, that the dividend multiple halves from the current value, raising the dividend from its current 1.4% to 2.8%-still far lower than the 5% historical average-over the next 20 years. In that case, the speculative return will be a negative negative 3.4% per year, for a total annualized market return of 2.8%. Sound far-fetched? Not at all. If inflation stays at the 2% to 3% level of the past decade, this implies a near zero real return over 20 years. This is not an uncommon occurrence. It's happened three times in the twentieth century: from 1900 to 1920, from 1929 to 1949, and from 1964 to 1984. 3.4% per year, for a total annualized market return of 2.8%. Sound far-fetched? Not at all. If inflation stays at the 2% to 3% level of the past decade, this implies a near zero real return over 20 years. This is not an uncommon occurrence. It's happened three times in the twentieth century: from 1900 to 1920, from 1929 to 1949, and from 1964 to 1984.* The stock market could crash. You heard me right. The most sustainable way to get high stock returns is to have a dramatic fall in stock prices. Famed money manager Charles Ellis likes to tease his friends with a clever riddle. He asks them which market scenario they would rather see as long-term investors: stocks rising dramatically and then staying permanently at that high level, or falling dramatically and staying permanently at that low level. The correct answer is the latter, since with permanently low prices you will benefit from permanently high dividends. As the old English ditty says, "Milk from the cows, eggs from the hens. A stock, by G.o.d, for its dividends!"After several decades, the fact that you are reinvesting income at a much higher dividend rate will more than make up the damage from the original price fall. To benefit from this effect, you have to be investing for long enough-typically more than 30 to 50 years. To demonstrate this phenomenon, in Figure 2-5 Figure 2-5, I've plotted three different scenarios: (1) no change in the dividend multiple, with its current 1.4% dividend, (2) a 50% fall, resulting in a 2.8% dividend, and (3) an 80% fall, resulting in a 7% dividend.As you can see, the more drastic 80% fall produces a quicker recovery than the 50% fall. The below table shows why: [image]

After an 80% fall in prices, the higher long-term return eventually compensates for the initial devastation. Even better than having a long time horizon in this situation is having the wherewithal to periodically invest sums regularly at such low levels-this dramatically shortens the "break-even point."

The implications of the last scenario are profound. What this says is that a young person saving for retirement should get down on his knees and pray for a market crash, so that he can purchase his nest egg at fire sale prices. For the young investor, prolonged high stock prices are manifestly a great misfortune, as he will be buying high for many years to invest for retirement. Alternatively, the best-case scenario for a retiree living off of savings is a bull market early in retirement.

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Figure 2-5. Effect of stock declines on final wealth. Effect of stock declines on final wealth.

For the retiree, the worst-case scenario is a bear market in the first few years of retirement, which would result in a very rapid depletion of his savings from the combination of capital losses and withdrawals necessary for living expenses. To summarize: [image]

How to Think about the Discount Rate and Stock Price The relations.h.i.+p between the DR and stock price is the same as the inverse relations.h.i.+p between interest rates and the value of prest.i.ti and consols in the last chapter: when DR goes up, the stock price goes down, and vice versa.

The most useful way of thinking about the DR is that it is the rate of return demanded by investors to compensate for the risk of owning a particular a.s.set. The simplest case is to imagine that you are buying an annuity worth $100 per year, indefinitely, from three different borrowers: The world's safest borrower is the U.S. Treasury. If Uncle Sam comes my way and wants a long-term loan paying me $100 per year in interest, I'll charge him just 5%. At that DR, the annuity is worth $2,000 ($100/0.05). In other words, I'd be willing to loan Uncle Sam $2,000 indefinitely in return for $100 in annual interest payments.

Next through the door is General Motors. Still pretty safe, but a bit more risky than Uncle Sam. I'll charge them 7.5%. At that DR, a perpetual $100 annual payment is worth $1,333 ($100/0.075). That is, for a $100 perpetual payment from GM, I'd be willing to loan them $1,333.

Finally, in struts Trump Casinos. Phew! For the risk of lending this group my money, I'll have to charge 12.5%, which means that The Donald's perpetual $100 payment is worth only an $800 ($100/0.125) loan.

So the DR we apply to the stock market's dividend stream, or that of an individual stock, hinges on just how risky we think the market or the stock is. The riskier the situation, the higher the DR/return we demand, and the less the a.s.set is worth to us. Once more, with feeling: High discount rate = high perceived risk, high returns, depressed stock priceLow discount rate = low perceived risk, low returns, elevated stock price The Discount Rate and Individual Stocks In the case of an individual stock, anything that decreases the reliability of its earnings and dividend streams will increase the DR. For example, consider a food company and a car manufacturer, each of which are expected to have the same average earnings and dividends over the next 20 years. The earnings and dividends of the food company, however, will be much more reliable than that of the car manufacturer-people will need to buy food no matter what the condition of the economy or their employment.

On the other hand, the earnings and dividends of auto manufacturers are notoriously sensitive to economic conditions. Because the purchase of a new car is a discretionary decision, it can easily be put off when times are tough. During recessions, it is not unusual for the earnings of the large automakers to completely disappear. So investors will apply a higher DR to an auto company than to a food company. That is why "cyclical" companies with earnings that fluctuate with business cycles, such as car manufacturers, sell more cheaply than food or drug companies.