Short Term Control Established

By Steven J. Grisafi, PhD.

The impulse that caused the New York branch of the United States Federal Reserve Bank to lose control of its overnight lending rate has passed. The relaxation time for the United States Treasury debentures yield curve has stabilized at thirty-two days. Having stabilized at a non-zero value implies that the interest rate yield can be controlled. While the current value of thirty-two days can change, it does indicate that the central bank can indeed control the shape of the yield curve. However, the magnitude of thirty-two days implies control that may not be robust for long term debentures.

If we knew the form of the relaxation time decay we could speak with greater certainty. However, we cannot know the functional form of the decay because we do not know of any governing probability distribution that could be associated with the interest rate yield curve. Most likely, there cannot be a governing probability distribution because the time series data is non-stationary. In lieu of any knowledge of a governing probability distribution, Finance Rheology substitutes our knowledge of an associated money potential, and its related functions, its integrals and its gradient. If we could assume the relaxation time decay to be Gaussian, which strictly speaking, we cannot, because that would require stationary time series data, then we would expect approximately 62% of the decay to vanish within one relaxation time of thirty-two days. After three relaxation time periods, we would expect virtually all of the decay, approximately 99%, to occur. With non-stationary time series data we would need to fit the empirical data of each and every relaxation time decay that we observe to some functional form to know exactly what has occurred. A relaxation time value of thirty-two days suggests that the central bank should be able to use its overnight lending and deposit interest rates to manipulate prices and yields for debentures of at least three months maturity. For maturities beyond this, market participants decide what the yields must be.

I have provided an additional graph of the relaxation time evaluation that displays the time evolution for this determination. I have also included this graph for the central banks relaxation times evaluations. However, in the case for the treasury yields, I am keeping all data points within the graph until one year of data is acquired. Even though data beyond the rolling period of 22 weeks is not used in the evaluation. After obtaining a year’s data, I will attempt to roll the relaxation time evaluation on an annual basis. If no singularities occur, and the relaxation time remains non-zero, then we can confirm that the efforts of central banks to control an economy by manipulating interest rates is not futile.