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Like The Roaring 2000s and The Long Boom this is a disappointing book. Originally written as a long magazine article that is a much better size for the amount of information that the authors had available.
So what did I do? I just read the magazine article. I just found it on the internet, a brief search should bring it up.
So what did the book (magazine article) have to say? Basically that every single person has misjudged the price of shares for the last couple of hundred years.
The crux of the book is some simple mathematics, so I will now include some equations. Those of you who don't like equations just go to the bottom of this article and buy the book.
The basis of their work is the dividend discount model. This is a way of estimating how much a share (or a collection of shares such as the Dow Jones Industrial Average) is worth. The theory is that an investment (any investment, Shares, property, lottery tickets) is worth the sum total of money that you will be paid for owning it. For shares the money you are paid is called dividends.
You can't just add up all the dividends you will ever be paid however. There is also the time value of money to take into account. In lay terms this means that a dollar paid to you in the future is worth less than money paid right now. A bird in the hand is worth two in the bush and all that.
The question remains of how much less money to be paid in the future is worth. For reasons that I won't go into, this is generally considered to be equal to the long term bond rate. I.e. if Long term bonds are paying 5% then the present value of a sum of money decreases 5% for each year into the future it is to be paid.
So now we can calculate how much a share is worth. You just get each prospective dividend that the company is likely to pay in the future, reduce the value of that dividend by the bond rate compounded for how far into the future that dividend is to be paid. And add them all together. You can do this on a spread sheet but for a constant rate of dividend growth you can use the formula:
Perfectly Reasonable Price(PRP) = dividend /(bond rate-dividend growth rate)
So for example if a share is paying $1.00 dividend, and the dividends are growing at 4%/year, and the bond rate is 5%/year you get PRP = 1.00/(0.05-0.04) = $100.00.
So in this book the authors took the dividend yield of the Dow ($150) the long term dividend growth rate (5.1%) and the bond yield at the time (5.5%) and low and behold, a Dow of 36 000.
So what's wrong with that? Well it turns out that the equation is very unstable. If you change the expected bond yield or dividend growth by only a tiny amount the answer can plumet by 80% or rocket up to infinity. Eg. if the bond yield drops to 5.1% then dividend /(bond rate-dividend growth rate) = dividend/0 which is infinity. If the bond yield drops BELOW the dividend growth rate then the value is more than infinity, which is obviously more that what anyone will actually pay for it.
So the equation is obviously wrong. But how can such a widely accepted piece of simple mathematics be wrong? It pays to take a look at the St. Petersburg's Paradox.
This is a mathematical paradox that can be explained as a bet. (A great deal of finance comes down to concepts that can be explained as a bet. Try to explain insurance in any other way.) The bet goes: Bob and Sue have a game. Bob will pay Sue a sum of money, and then Sue will start flipping a coin. If the coin lands heads on the first flip, she pays Bob $1. If tails she flips again. If it lands heads on the second flip, she pays Bob $2. If tails she flips again. The third flip pays $4, the forth $8 and so on.
The question is, how much money should Bob pay Sue in the first place to make it a fair bet?
Mathematically the calculation is simple. There is a 50% chance of Bob getting $1 on the 1st flip, so that is worth 50 cents. Then there is a 25% chance he'll get $2, so that is worth another 50 cents. There is a 12.5% chance of $4, so that is another 50 cents and so on. You add all the 50 cents until you get to a total of 100%, and that is the fair value of the bet. The problem is that that is an infinite number of 50 cent pieces, or an infinite amount of money.
Is this right? Mathematically it is, in reality no-one will pay more than about $15 or $20 for the game. So what is wrong? The secret is that in reality, once you have flipped the coin about 30 times, you are up to 2^30 or a billion dollars. After 40 flips you have a trillion dollars. Now the mathematics assumes that a trillion dollars is worth 1000 times as much as a billion dollars, but in fact it isn't. <0>"What's that? Of course it is" I hear you think. But consider this. If your mate offered you a bet in which he would pay you a billion dollars, or a trillion dollars, is one bet any different from the other? Of course not! Because he doesn't have a billion dollars OR a trillion dollars. No-one has a trillion dollars. Even the United States government can't give you a trillion dollars. So any bet in which you stand to win a trillion dollars is meaningless.
It gets worse. Say you DID win a trillion dollars. Say the 100 richest billionaires in the world got together and gave you a trillion dollars. Now what. What could you do with a trillion dollars that you couldn't do with $500 billion. What can't you do with one trillion that you could do if only you had 2 trillion? It doesn't make any difference at that point. So, the basic premise of the game, that 2 trillion is worth twice as much as 1 trillion isn't true. The number theory we use for our mathematics doesn't apply to money once you reach very large amounts. Hence the St. Petersberg's Paradox. Once you reach about 30 or 40 flips the whole thing becomes meaningless. So the maximum value of the game is about 30 or 40 flips, multiplied by 50 cents/flip. I.e. about $15-20.
Now exactly the same thing happens to our share price equation. When we are calculating the amount of money we'll recieve after 5 or 10 years of 5% growth then it all works out. But once we start including the million dollar dividends we'll recieve in 150 years then it all becomes silly. The maths is right, but the maths doesn't apply to very large amounts of money or to long periods of time. Do you care what the company does 100 years after you die?
Which brings up a second problem. How do you know what is going to happen in 150 years? No-one can tell what is going to happen in 20 years. Lot's of people are very wrong about what will happen next year. The share price calculations in this book assume that you can fortell company returns for decades and centuries in advance. Yeah right. How many investors in the year 1800 could tell what companies were going to do well for the next few centuries. If they could, they would all have sold British and Dutch East India comporations and piled into Bank of England and ... well I don't know, there are probably a couple of others that have done well for all that time.
There are even more problems wrong with the analysis in this book, but if I keep writing about them I'll end up with a book of my own.
In short, just read the magazine article, but if you must: Dow 36,000: The New Strategy for Profiting From the Coming Rise in the Stock Market
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