As of June 3, 2008, the interpolated yield was dropped as a yield curve input and the on-the-run 52-week bill was added as an input knot point in the quasi-cubic hermite spline algorithm and resulting yield curve.

Treasury does not provide the computer formulation of our quasi-cubic hermite spline yield curve derivation program. However, we have found that most researchers have been able to reasonably match our results using alternative cubic spline formulas.

http://www.ustreas.gov/offices/ d…ieldmethod.html

Assessing the Effects of Variability in Interest RateDerivative Pricing
http://www.lib.ncsu.edu/theses/a…tricted/ etd.pdf

a knot is a point that divides two such sectionsof the data. Between knot points, a smooth curve is fit to the data, and conditionsare met so that the curves in each section of the data connect at each knot point.Generally, derivative conditions must be met at the knot points to ensure smoothnessin the spline. The result is a smooth curve that fits the data according to a criteriondefined by the spline method itself.

The Hull-White model also improved upon the Ho-Lee modelby incorporating mean-reversion, which the Ho-Lee model lacks. Both of these modelstake the initial zero curve as an input, but neither model requires that the zero curvebe differentiable. Some no-arbitrage models can be implemented in a discrete-timesense through the use of trees. Section 1.3.1 details the construction of a trinomial treein the case of the Hull-White model.

Hull (2003) notes that one negative aspect of the HJM model framework is thedifficulty of calibrating the model to the prices of actively traded instruments. Yan(2001) also points out that since HJM models use continuous compounding of theinstantaneous forward rate curve, specifying a lognormal process in the HJM frameworkis no longer possible.

This result implies that there exists a convenience premium for Treasury instru-ments due to their liquidity (among other factors). The implication for the currentresearch is that the interest rate being used in the Hull-White trinomial tree to dis-count future payments might not be as close to the true riskless rate as one woulddesire. An extension to this work could involve an adjustment to the discount rates inthe tree so that they are closer to the riskless rate….

1. “the standard deviation of the change in yield to maturity in a given time span is
the square root of the time span times the annualized standard deviation of
the change in yield to maturity”

2. Since by definition an estimate is only an ap-
proximation to reality, the distribution at the investment horizon cannot be
precise. In fact, the farther in the future the investment horizon, the larger
the effect of the estimation error. We discuss estimation risk and how to cope
with it extensively in the third part of the book.

Propagation of uncertainty

http://en.wikipedia.org/wiki/Error_propagation

Most commonly the error on a quantity, Δx, is given as the standard deviation, σ. Standard deviation is the positive square root of variance, σ2. The value of a quantity and its error are often expressed as . If the statistical probability distribution of the variable is known or can be assumed, it is possible to derive confidence limits to describe the region within which the true value of the variable may be found.

In the special case of the inverse 1 / B where B = N(0,1), the distribution is a Cauchy distribution and there is no definable variance. For such ratio distributions, there can be defined probabilities for intervals which can be defined either by Monte Carlo simulation, or, in some cases, by using the Geary-Hinkley transformation…. and that about wraps that shit up … (today).

Estimating a Latent Trait Model by Factor Analysis of Tetrachoric Correlations

http://ourworld.compuserve.com/homepages/jsuebersax/irt.htm

We consider here estimation of a fully Gaussian latent trait model. “Fully Gaussian” means that both the latent trait and measurement error are assumed to be normally distributed. This model, equivalent to what Item Response Theory (IRT) terms a two-parameter normal (2PN) model with a normally distributed latent trait, is often used in educational testing, social science research, and, increasingly, in health research. It is also useful–perhaps one of the best methods–for binary data factor analysis.

Here we are again with the short-term stuff at zero:

http://finance.yahoo.com/q/bc?s=%5EIRX

As I thought about the stuff I posted last night, it seems probable that there is an overvaluation problem with money. Can that be placed into the mold of deflation or is it related to my concern that there has been fraud overstating GDP, and are those two possibilities related, i.e, if there was fraud or mistakes made to over value GDP for years, has that resulted in triggering deflation?

That seems like a good question to me, and what I’m looking at is gamma and the factor by which money has been overvalued, e.g, if the yield curve has been a model that has been increased by a factor of 1/2, what does that mean?

In terms of GDP, which used to be around $13 Trillion, how could that be related to money being overvalued.

This is over my head, but what the hell:

Tikhonov regularization is the most commonly used method of regularization of ill-posed problems. In statistics, the method is also known as ridge regression. It is related to the Levenberg-Marquardt algorithm for non-linear least squares problems.

So, the trick here is to see if this overvaluation is recent or if it has been building up ever since:

The Cox-Ingersoll-Ross model in finance is a mathematical model describing the evolution of interest rates. It is a type of “one factor model” (Short rate model) as describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives. It was introduced in 1985 by John C. Cox, Jonathan E. Ingersoll and Stephen A. Ross as an extension of the Vasicek model.

Re: What is the big picture meaning of short-term treasuries at .0005?

IMHO, the future value of money is decreasing, depreciating and decaying in relation to current value. I’m trying to understand this as well, so this is just a bunch of thinking out loud and some background info. I’m also thinking about how a 3-month period acts as a discount factor, but there are lots of directions to go on this, so this info may or may not be accurate, but maybe something to improve later.

The Treasury Curve is a depiction of money value across a time spectrum, spanning between 13-week Treasuries and 30 year Bonds. The short-term drop to zero probably represents deflation and is not something in any model or represented in standard curves for valuation.

Here is some background from Wiki related to yield curves: The main disadvantage is that, under Vasicek's model, it is theoretically possible for the interest rate to become negative, an undesirable feature. This shortcoming was fixed in the Cox-Ingersoll-Ross model. The Vasicek model was further extended in the Hull-White model.

http://en.wikipedia.org/wiki/Vasicek_model

The standard deviation factor corrects the main drawback of Vasicek's model, ensuring that the interest rate cannot become negative. Thus, at low values of the interest rate, the standard deviation becomes close to zero, cancelling the effect of the random shock on the interest rate. Consequently, when the interest rate gets close to zero, its evolution becomes dominated by the drift factor, which pushes the rate upwards (towards equilibrium).
http://en.wikipedia.org/wiki/Cox-Ingersoll-Ross_model

>> So then, why did the standard deviation correction factor fail to correct the plunge to zero and why have we returned to .0005 (today)??

The Vasicek model apparently implies that interest remains constant in the absence of shocks, but then, The Cox-Ingersoll-Ross model “apparently” fixed that potential glitch by adding in a standard deviation factor, which cancels the effect of random shocks on interest rates that are close to zero, because the evolution of the rate becomes dominated by the drift factor, which pushes the rate upwards (towards equilibrium).

In terms of factor shocks, they seem to be referring to supply and demand relating to inventory exchanged from auctions of new issues and maturity and expiration things. The assumption about the gamma term is different for each one-factor model. It is assumed zero in Vasicek (1977) and ½ in Cox, Ingersol, and Ross (1985) models. Chan, Karolyi, Longstaff, and Sanders (1992)’ estimate of gamma is 1.5. According to the results of ordinary regressions, constants associated with the quantity shocks of 13-week and 26-week bills are always significant. A very big concern now has to do with failed auctions.

See: Treasury Market Practices Group Endorses Several Measures to 
Address Widespread Settlement Fails 
November 12, 2008 
http://www.ny.frb.org/tmpg/PR081112.pdf

Special collateral repo rates cannot exceed the Treasury general collateral repo rate. As a 
result, settlement fails across a variety of CUSIPS can similarly become widespread and persistent when the Treasury general collateral repo rate is near zero – as is currently the case. 

The underlying problem is the Treasury market contracting convention that a seller can deliver securities after the originally scheduled 
settlement date at an unchanged invoice price, i.e., without incurring any penalty. Introduction of a dynamic fails penalty with a finite cap 
rate would remedy this problem.

Also See: The 2-yr yield just dropped below 1% for the first time

Back to Wiki: A positively sloped yield curve has not always been the norm. Through much of the 19th century and early 20th century the US economy experienced trend growth with persistent deflation, not inflation. During this period the yield curve was typically inverted, reflecting the fact that deflation made current cash flows less valuable than future cash flows. During this period of persistent deflation, a 'normal' yield curve was negatively sloped.

>> However, IMHO, the current yield curve is adjusted and factored in a way to not accommodate a deflationary model. I have also posted in the past that I think GDP has been over-stated and manipulated and adjusted to falsify economic growth and thus distort the valuation of money. Thus, when you look at the yield curve today, it looks like the economy is ready to go into a huge growth spurt, but obviously that doesn’t make sense if the short-term Treasuries are crashing to zero.

The actual reason as to why yields are falling is because there is a wide spread money hoarding by banks and financial institutions, who are bailing out of over-valued equities that have dividends that are out-of-step with the current deflation. Obviously the majority of Joe The Plumbers are doing the same thing too, because no one in the world has any confidence for the future. Hence, everyone at the same time is jumping into short-term bills and crashing the system by taking money out of longer-term future investments.

This is also a self-fulfilling catch-22 feedback loop that is fueled by more and more expensive Treasuries, which yield less and less. We are well beyond the point of bubble-like overvaluation with Treasuries, and this is now the equivalent of buying a share of dotcom garbage with a P/E of over 2000. Valuation and fundamental reason are no longer priced into the reality of this chaos, because it is panic, and the models are broken!

This situation is like taking $1000 to a bank and getting nothing for your investment, for three months. The only thing you can do is to accept zero for 3 months, or move into longer-term bills and then freeze your cash. This is somewhat like a liquidity trap, but in reality the money isn't trapped, it just will have less and less value in the future.

I’m working on it and that is on my mind too. It’s about the decrease in the future value of money… but I need to make some cookies first…..

Be back soon

I cordially invite you to display your understanding of molecular absorption in the infrared through the near UV, how differential absorption over this spectrum interacts with the thermal photon blackbody spectrum of far-out-of-equilibrium heat sources, and your clear understanding of the extent to which the greenhouse metaphor is or is not appropriate to said scientific issues.

Once you have displayed that, maybe we can judge your competence to declare global warming “junk science.”

The drop of money supply due to a drop in velocity will take out perfectly viable businesses.

What the new administration needs to do is print, not borrow, money to re-capitalize the banking system after it is purged through an FDR style Bank Holiday.

Without direct intervention by the Federal Government through a truly Public central bank the entire economy is put at risk.

I would consider myself a “layman” in every sense of the word when it comes to finance and economics.

However, I do feel that I have a tremendous amount of common sense and this is why I religiously read this blog as well as the RGE Monitor….the postings from Yves and readers as yourself make A LOT of sense to me (they are the main reason I pulled completely out of stocks back in July of 2007).

Anyway, to my question…..

What is the big picture meaning of short term treasuries at .0005?

Also, if the return is so small, why would an investor purchase these? Is it because of the “safety” of these?

Thank you in advance for your insight.