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Some Different Looks at the Yield Curve

(Guest Commentary By Bill Rempel – June 5, 2008)

Dear Subscribers and Readers,

For those who had wanted to learn more about individual stocks, the art of stock selection, and model-based trading/investing, it is again time to see what one of our regular guest commentators, Bill Rempel, has to say.  Bill is a prolific writing on the stock market and individual stocks and is the author of a very active market blog at: http://billrempel.com (“The Rempel Report”).

In this commentary, Bill is going to introduce a regression formula that he is experimenting with to predict the shape of the Treasury yield curve going forward.  Essentially, Bill asserts that the Federal Reserve's monetary policy (through the Fed Funds rate mechanism) and the change in the shape of the yield curve over the last six months does have predictive value for the shape of the yield curve over the next six months.  The study (he will be following up with subsequent comments on it) is still in the preliminary stages, but it is already showing a lot of promise.  Without further ado, following is a biography of Bill:

Bill Rempel (aka nodoodahs) is an active poster on the MarketThoughts forum as well as a few others around the web. Bill is a regular, monthly guest commentator on our website (see “A Simple Small-Cap Value Screen” for his last guest commentary). Bill graduated from Caddo Magnet High School (a high school for nerds) back in 1985 and proceeded to learn the hard way when he drank his way out of a scholarship to Tulane later that year. After a few years of sweating for a living, he decided to go back to school, and graduated from LSU-Shreveport in 1995 with a Bachelors in Mathematics - all the while working the overnight shift stocking shelves in a grocery store.

Post-college, Bill has been in the P&C insurance industry as an actuary, product manager, and pricing manager. Bill and his wife Millie are amateur investors with a variety of holdings, but they prefer to buy and hold value investments. In typical "value" style, they live cheap, driving old cars and preferring to save or invest instead of buying fancy "stuff."

Disclaimer: This commentary is solely meant for education purposes and is not intended as investment advice.  Please note that the opinions expressed in this commentary are those of the individual author and do not necessarily represent the opinion of MarketThoughts LLC or its management.


It's hard to mention the "yield curve" without envisioning some esoteric economic forecasting method, and while it's probably pretty useful for that, I've never figured out any way to make money off of economic forecasting that works any better – or easier – than directly dealing with stock market information.  Oh, bother. 

It's also hard to mention the "yield curve" without having someone misunderstand what is meant.  Well, I take that back!  Most people don't pay attention anyhow, so only those that do would potentially misunderstand!  You see, most people throw out the term without defining it, making it less than useful.  For example, is the "yield curve" the basis point spread between the 10-Year Treasury and the 2-Year Treasury?  Between the 10- Year Treasury and the Federal Funds Rate?  Is it a ratio of the 10- Year Treasury to the 2- Year Treasury, rather than a basis point difference?  What about the 30- Year Treasury and its position relative to the 10- Year Treasury?  Etc.

The next question, after the definitional one, is "what good is the yield curve?"

My thought was to examine the yield curve in combination with changes in interest rates, with an eye towards predicting the future shape of the curve, as well as future changes in the Fed's interest rate policy, so that I might use this information to inform a strategy for bond traders.  Ambitious, but what the heck.

Throughout this post, I'm going to use a simple slope definition of the yield curve, in terms of "basis point increase per year."  I will use the Federal Funds Rate (with zero years), the 2-Year Treasury, the 10-Year Treasury, and where available, the 30-Year Treasury, and calculate the slope with a regression formula in Excel.  Data is daily frequency and taken from the St. Louis Fed's data site, FRED II.  I'm looking at the data from September 1982 through the present.

Yield Curve Regression line Slope

The three yield curve "inversions," where the longer-term rates tended to be lower than the shorter-term rates, show pretty clearly.  It's possible the "hump" from Feb 2002 through Feb 2006 was due to the calculation being run without 30-Year Treasury data, but I'm not certain.  Yes, there was a big jump in slope on the date of the removal, but by the time the 30-Year Treasury started trading again, the curve had already started nearing inversion, so one transition had a jump and the other didn't.

These are the average daily statistics for the yield curve over the time covered:

average 0.07
median 0.05
min -0.03
max 0.35
stdev 0.08

The "average" curve of 0.07 means that, on average, each additional year was worth 7 basis points of yield. 

Think of it as the FFR at an average of 5.5% or so over the time period, with the 2-Year Treasury paying 2 x 7 = 14 basis points more (or 5.64%), the 10-Year Treasury paying 10 x 7 = 70 basis points more (or 6.20%), and the 30-Year Treasury paying 30 x 7 = 210 basis points more (or 7.60%).

At its steepest, the curve was averaging 35 basis points a year in change.  Whew! That happened pretty near the bottom for the market in late 2003, and again in early 2004, and during that time, the Federal Funds Rate was running at 1.00% at the end of a loosening cycle.  At its most inverted in 1989, the curve lost 3 basis points a year in duration, with the FFR near 10% and the Fed near the end of a tightening cycle.  It seems intuitive that the curve has a relationship not only with the Federal Funds Target Rate, but also with the recent history of the Target Rate's changes.

To accomplish a look at this, I took the prior changes in both FFR and curve slope (simple subtraction) over the last six months, combined with the current FFR and curve slope, and ran some multivariate linear regressions against the SUBSEQUENT six-month changes in FFR and curve slope.

Summary Output - Subsequent FFR Change

Predicted Vs Subsequent FFR Target Change

Summary Output - Subsequent CRV Change

Predicted Vs Subsequent Curve Steepening

These are statistically significant regression results, but I'm not sure how trade-able the results are yet, as I'm really just starting the investigation.  For what it's worth, the current output suggests that the Fed isn't done yet and the curve will continue to steepen, if only slightly.  If I were forced to be a trader of primarily Treasury bonds, this is the type of analysis that I might use to overweight or underweight specific durations in order to beat a relative benchmark based on the overall Treasury market.

I think I'll get a lot more use and understanding out of analyzing the matrix of situations and subsequent results, but that's a topic for my NEXT column.

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