Schwarze Null

The Treasury Yield Curve

By Steven J. Grisafi, PhD.

In our previous blog post Modern Monetary Theory I sought to explain how Modern Monetary Theory (MMT) helps us recognize that central banks are redundant for fiat currency issuing entities possessing a treasury. Theorists of the MMT persuasion wish to seek government policies tending to drive short term interest rates to zero. They view the capacity of commercial banks to grant credit, thereby creating money, as detrimental to society when short term interest rates are non-zero. It is their contention that a treasury sells its government debentures in a effort to drive short term interest rates to zero. Assuming this capacity to do so would imply an understanding regarding the mechanisms causing deviation of the debenture interest rate yield curve from linearity. While a currency issuing treasury, or central bank, can assert the overnight zero interest rate it pays upon reserves held in its accounts, the capacity of any sale of long term debentures to drive interest rates to zero at maturities longer than overnight requires knowledge of some mechanism of which we are not yet cognizant. However, empirical data has long ago made apparent that bond prices fluctuate as in a random walk. While we cannot yet identify what expectations motivate the bids that investors place at treasury auctions, we are assured that the bond prices ultimately achieved follow a random walk. Recognizing that, in a gross average fashion, bond prices vary inversely proportional to their interest rates, allows us to treat the time progression of interest rates as following a random walk. As such we may then treat the time progression of debenture interest rate as an exercise in the dynamics of diffusion.

Our ability to analyze the time progression of interest rates with diffusion dynamics may provide us with one important clue. While we may never know what lurks within the mind of investors who place bids at the auctions of treasury debentures, we can know the time scales that are reflected in those bids which act upon the expectations. When considered alone, the relaxation time for the diffusion dynamics of bond prices, or their respective interest rates, is of no value for assessing a mechanism that can cause deviation of the interest rate yield curve from linearity. But if compared to other relevant time scales it may help indicate why longer term interest rates do not increase monotonically from shorter term interest rates. While it may never explain why investors hold the sentiments that they do, it may help make those sentiments more apparent.

When pondering a comparison of dynamical systems similar to that which we expect the yield curve for United States Treasury securities to possess, the most pertinent variable would seem to be the relaxation time for the money supply managed by the Federal Reserve Bank (FRB). When doing so one must understand that this relaxation time does not possess a constant value. Its value varies over time because the monetary system of the United States is not closed: Americans trade with other nations throughout the world and in doing so often sell to them their treasury securities. The greater an imbalance of trade that a nation has with the United States the greater its effect upon America’s monetary system. Over the course of the past six years, during which we have evaluated the relaxation time for America’s money supply, the relaxation time has climbed from approximately four months to more than six months during Quantitative Easing. It then began to decrease from over two hundred days to approximately 180 days after Quantitative Easing ended. At the time of this writing the relaxation time is about 187 days and is increasing again now that the FRB has signaled that it will delay any further interest rate hikes. Hence we take for comparison a relaxation time of approximately six months to compare with any estimate for a relaxation time we may obtain for the yield curve of United States Treasury debentures.

After evaluating one week of data we find a relaxation time of zero. This is a curious result, especially while pondering the estimate for the money supply relaxation time. It can have several interpretations. A graphical summary of the analysis is posted here. A relaxation time of zero means that the dynamical system returns immediately to its original configuration after having been perturbed. It may also mean that the dynamical system cannot be perturbed from its configuration. One week of data is hardly sufficient for a reliable estimate so this analysis continues. Interestingly enough, of all the analyses conducted on central bank money supply relaxation times there was a time when a relaxation time of zero was observed. It was for the money supply of the European Central Bank (ECB) before the time when the bank began its program of Quantitative Easing. The relaxation time for the ECB then increased quickly to exceed that of the FRB and is now approximately 282 days. Its ascent continues!

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