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In the beginning, commodity prices and yields were one.

Or at least as far back as 1730 and up until the 1910s, consumer and producer prices were highly correlated with equity and bond yields. That is to say, it was not the rate of inflation that was correlated with yields but the absolute level of prices that moved with yields.

When one considers the tremendous technological, ideological, demographic, scientific, and geopolitical changes that occurred over those centuries in contrast with the stability of this relationship, this suggests that we are confronted with something like a natural law of markets and economics. And, yet laws were made to be broken, it seems.

(click to enlarge)

(Note: All data in this article comes from Robert Shiller, except corporate bond data in the chart above, which is from the St Louis Fed).

Nowadays of course, nobody cares what the absolute level of CPI or PPI is. We only wish to know the rate of change, but it was not always so.

Recently, while in the process of writing a synoptic history of how the relationship between yields and inflation had changed in the 1910s and then again in the 1960s, I almost inadvertently came up with a kind of back-of-the-envelope equation for describing the behavior of the one-year Treasury yield prior to the establishment of the Federal Reserve.

As I went over the various permutations of that equation and then extended it out over the entire period from 1871 to today, it struck me that as clumsy, naive, and unlikely as the equation was, it seemed to point to an equilibrium within the yield complex that endured in somewhat aloof fashion from inflation and yet adjusted to changes in the nature and behavior of inflation, as well.

I think this equation confirms that a) since the 1960s, the yield complex has come to a new "understanding" with the inflation complex, b) that the period between the establishment of the Fed and the implosion of Bretton Woods in the 1960s was a chaotic period of transition from one price regime under the gold standard to the new, more inflationary price regime under the dollar standard, and c) that the behavior of yields since the 1960s show increasing signs that the post-Bretton Woods equilibrium is unsustainable.

In that vein, although many people have complained that Treasury yields, for example, are being held down to unnatural levels by the Fed, history suggests that they are behaving more or less as they have always behaved in great crises. It does not say anything in and of itself about causation, but it does seem to suggest that we may either be in the midst of a normal, once-in-a-half-century-or-so systemic crisis or that we may be on the cusp of a transformation in the global financial regime.

Coming to a fuller understanding of how interest rates, inflation, and P/E ratios interact would likely permit us to prepare more fully as investors and citizens for whatever the future might hold.

In future articles, I would like to describe in greater detail how the behavior of particular yields (and types of inflation) and their relationships with one another have changed over the last 140 years, but in this article, I would simply like to present the original equation I found and point to the initial questions that it raises.

In the following charts, you can see how it models the S&P earnings and dividend yields and the ten- and one-year Treasury yields, as well as the relationship with CPI prior to the establishment of the Fed.

I have no grand theories to back them up, only observation of the phenomena. In the original variation of the model, which I have termed "boe1" ("boe" as in "back of envelope"), the critical period to pay attention to is the gold standard period when yields matched the price level, although as I said, it does seem to hold up fairly well over time.

(click to enlarge)Earnings yield model boe1 1871-2011

(click to enlarge)Dividend yield model boe1 1871-2011

(click to enlarge)One-year Treasury yield model boe1

(click to enlarge)Ten-year Treasury yield model boe1

Correlations by time period, yield, and model
Correlations1872-19121913-19601960-20111872-2011
EY vs CPI0.50.07-0.39-0.30
EY vs boe10.390.510.340.5

DY vs CPI

0.80-0.21-0.60-0.69
DY vs boe10.350.680.800.69
10y vs CPI0.85-0.19-0.240.40
10y vs boe10.400.470.830.76
1y vs CPI0.59-0.04-0.390.1
1y vs boe10.360.350.570.58

The table of correlations suggests that as the relationship between yields and prices deteriorated, the model's correlations grew stronger.

A problem emerges though as we go into the equation, however. As you can see from the charts above, the levels predicted by the model are fairly random.

The equation is EY - DY = 10y - 1y.

As you can see right off the bat, it has something to say about the spread between the yield curve, but before I get to that, I want to get the so-called "Fed model" out of the way. The Fed model equation can be expressed as EY - 10y = DY - 1y.

(click to enlarge)Fed model boe1 model

In recent years, the spread between the earnings yield and the ten-year Treasury, treated as an equity valuation tool, has been ridiculed on the basis of a lack of historical correlations between the two yields, and perhaps a narrow or absolutist application of it has been unwarranted, but it does not appear to be wholly random. If the earnings and ten-year yields have been uncorrelated, perhaps it points to a deeper imbalance in the system. In any case, the equation for the Fed model appears to hold up fairly well, with a correlation of 0.72.

So that takes us to the much dicier problem of the yield curve, which should be equivalent to the spread between equity yields.

(click to enlarge)yield curve boe1 model

During the gold standard, the correlation between these two sides of the equation was only 0.18. During the 1961-2011 period, it had fallen to -0.23. What is more, even during the gold standard period, the 10y-1y spread was almost always negative, while the EY-DY spread was (and has remained) almost always positive.

Indeed, from 1871-1950 or thereabouts, every instance of the Treasury yield spread going positive coincided with a bottoming and sudden reversal in the EY-DY spread (which would tend to make the correlation negative). After 1950, however, an upward sloping yield curve seemed to have no such effect and perhaps even the opposite effect.

In my next article (in this series), I intend to make amends for this fault in the model by introducing a second variation of this equation (boe2, if you will) that takes into account inflation. For the period of 1961-2011, this second equation will solve virtually every problem manifest in boe1, but it leaves or accentuates the question as to why and how the relationship between equity yields and the Treasury curve seem so tied to one another, in harmony or in combat, depending on the perspective one uses.

In any case, as this series unfolds, I think we will find that the behavior of the EY-DY spread is and always has been an under-appreciated aspect of the yield complex.

Source: Inflation And Yields: Towards A Unified Field Theory

Additional disclosure: I am short December S&P 500 futures.