One of my assertions about William Bernstein is that it is difficult to determine where his actual numbers come from, as supported by something better than rules of thumb and plausibility arguments. Here is an example from page 52, when he discusses the Dividend Discount Model.

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 assumption of a $140 present dividend, an 8% DR, and 5% earnings growth, we get:..[Emphasis added]

The earnings growth rate replaced the dividend growth rate, but without an explanation.

This paragraph from page 54 has been quoted frequently on these boards.

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 form 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."

From page 56:

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 assets seem to become more attractive after their price has risen greatly..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.

From page 61:

In that case, the speculative return will be a 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.

From pages 56, 59, 68, 71 and 72:

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% [nominal]...

There are three possible scenarios in which equity returns could be higher than the predicted 6.4% [nominal]:..

For starters, the DDM [Dividend Discount Model] tells us to expect cash to yield a zero real return, bonds to have approximately 3% real return, and stocks in general to have about a 3.5% real return..

In Table 2-2, I've summarized reasonable expected real returns, derived from the DDM..

Large U.S. Stocks 3.5%

Treasury Bills and Notes 0-2%

These last few numbers are similar, but not the same.

Have fun,

John R.