Gordon Equation Revisited

Back on December 16, 2009, I wrote the following over on the old blog.

Market Return = Dividend Yield + Dividend Growth Rate is known as the Gordon Equation. This simple equation provides a way to predict long-term stock market returns, and we need to emphasize long-term.  Quoting Bernstein from his “Four Pillars of Investing” book, page 57, “…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.”

Dr. Bernstein seems to contradict himself on the prior page (#56) with this paragraph.  “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%. [It seems a stretch to include three significant figures.] These two numbers add up to just 6.55%.  Even making some wildly optimistic assumptions–say a 6% to 7% dividend growth rate–does not get us anywhere near the 10% annualized returns of the past century.”

Keep in mind that “Four Pillars” has a copyright of 2002 and Dr. Bernstein likely wrote some of this material near a market high.  The market certainly did not look good in the latter part of 2000.  If we include the market returns over the last decade, that 10% annualized figure is not quite so high.

Now move forward to Bernstein’s third book, “Investor’s Manifesto,” with a copyright date of 2010.  Assume most of it was written in late 2008 and early 2009.  Quoting from this book (page 35), “The Gordon Equation currently suggests that there are better returns to be earned in both stocks and corporate bonds for the first time in more than a decade, perhaps in the range of 4 to 8 percent real returns for stocks of various kinds, and 2 percent real returns for bonds.  Both of these, in my opinion, are high enough to compensate for the risks of owning them.”

While the extensive quotes do not align with his argument that the Gordon Equation is not useful for short-term projections, Bernstein was right on with both calls as the NASDAQ fell off the cliff after the first quarter of 2000 and we have witnessed a roaring bull market since March of 2009.

What brought the Gordon Equation to mind was a reference I picked up this morning, and here is the article.

No Margin of Safety, No Room for Error

While it is important to read the entire article, let me extract some cogent information.

"Prior to the mid-1990's, the median dividend yield on the S&P 500 had been about 4.1%. Then, the market launched into what would ultimately become a valuation bubble, followed by a decade of dismal returns for investors. Since then, the dividend yield on the S&P 500 has regularly dipped below 2.65%, and as of last week, had dropped to just 2%.

It is not a theory, but simple algebra, that the total return on the S&P 500 over any period of time can be accurately written in terms of its original yield, its terminal yield, and the growth rate of dividends. Specifically,

Total annual return = (1+g)(Yoriginal/Yterminal)^(1/T) – 1 + (Yoriginal+Yterminal)/2

As it happens, the long-term growth rates of S&P 500 dividends, earnings (measured peak-to-peak across economic cycles) and other fundamentals have been remarkably stable for more than 70 years, at about 6% annually, with very little variation even during the inflationary 1970's. Even if one includes the depressed yields of the bubble period, and restrict history to the post-war period, the median dividend yield is 3.7%. Thus, a reasonably good estimate of future 7-year total returns for the S&P 500 is simply:

Total annual return = (1.06)(Yoriginal/.037)^(1/7) – 1 + (Yoriginal + .037)/2

At a 2% dividend yield, this estimate is currently -0.07%."

Substituting 0.02 for Yoriginal   I came up with -0.08%, likely due to a rounding error. Checking this morning, the yield for VFINX is 2.0% and for VTSMX it is 1.9%. Such a low yield does not bode well for the market over the next few years. This projected low yield over the next few years is why we are focusing on conservative portfolios and hedging the portfolios using SDS when deemed appropriate.


Photograph: Image captured in the middle of the afternoon outside a pub in London. I have no idea why these folks were not in the office.