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A Second Look at the Yield Curve

(Guest Commentary By Bill Rempel – July 24, 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”). 

As we discussed in our mid-week commentary last week, Bill's schedule earlier this month did not allow him to pen his usual commentary during the first Thursday of this month – fortunately, Bill found some time to share some of his thoughts with us today.  In this commentary, Bill is going to follow up with more of his thoughts on yield curve prediction techniques that he started discussing in his last guest commentary.  Specifically, Bill comes up with four distinct variables (as defined by the level of the Fed Funds rate, the slope of the yield curve, the first derivative of the Fed Funds rate over the prior six months, and the first derivative of the yield curve over the prior six months) and discusses the implications of the 14 most common combinations of these variables.  Take the time to understand this study – all the analysts and economists who got it wrong last year when they predicted the Fed would not cut aggressively (that means the vast majority of these folks) would've changed their minds if they had read the results of Bill's study 12 months ago!  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 “Some Different Looks at the Yield Curve” 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.


In my previous column, I took a few different looks at the yield curve.  With this column, I'll expand on some of those basic definitional points and add some fresh analysis. 

My first take on objectively defining the slope of the yield curve was to use the slope of a regression line, with the Federal Funds Target Rate as "0" or overnight, and the 2-year, 10-year, and 30-year constant maturity yields forming the four points for each day's "slope" measurement.  I mentioned one problem with that approach at the time, which is that period where there was no 30-year Treasury in the market.  There's another problem with that approach, however, and that is that the yield curve isn't linear.  Generally speaking, it's a lot steeper from zero (FFR Target) to 10-year yield than it is from the 10-year to the 30-year yield.

Here are the min, max, and average yields for the entire time since 1982 that all four data points existed.

Year Min Max Average
FFR 1.75 11.50 6.05
2-yr 1.35 13.17 6.55
10-yr 3.34 13.99 7.32
30-yr 4.17 13.94 7.55

The "average" curve slope is about 1 basis point/year from 10 years to 30 years, but about 12 basis points/year from overnight to 10 years.  That's a big difference in steepness.

Because of that, I made the decision to work on the zero (FFR Target) to 10-year slope as definitional from here to the conclusion of the article.

Another oddity (at least to me) of the yield curve is that, even for the 0-10 year range, the 2-yr showed much more yield volatility (relatively speaking) than the 10-yr did.  Here is the data for the entire 1982-present time period.

Year Min Max Avg StDev Range StDev/Avg
FFR 1.00 11.50 5.41 2.45 10.50 0.45
2-yr 1.10 13.17 5.95 2.51 12.07 0.42
10-yr 3.13 13.99 6.85 2.30 10.86 0.34

In the last update, 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.  This time, in addition to calculating slope using exclusive the 0-10 year durations, I will look at combinations of relative values in the independent variables, with an eye towards what might be predictive of subsequent changes to the FFR and curve slope.

Since I've got four independent variables (current FFR and slope, last six months change in FFR and slope), I need to simplify the relative values.  To do this, I split the 6204 daily data points (where I have the change over both previous and subsequent six months) into thirds, where each variable was either in the lower third, the middle third, and the upper third.  That way, with four variables, I will have only 3^4 = 81 potential combinations.

Variable FFR Slope L6FFR L6Slope
Minimum 1.000 -0.111 -3.250 -0.216
LowMiddle 4.750 0.065 -0.250 -0.039
HighMiddle 6.000 0.202 0.250 0.029
Maximum 11.500 0.373 2.125 0.272

Over the time period, the FFR Target ranged from 1.00% to 11.50%, and the middle range was from 4.75% to 6.00%.  I will call anything below 4.75% LOW, anything above 6.00% HIGH, and everything else (about 1/3 of the data) MIDRANGE.

Over the time period, the slope of the 0-10 yield curve ranged from -.111 percent per year to +0.373 points per year, and the middle range was from +0.065 to +0.202 points per year, defining FLAT (or inverted), STEEP, and MIDRANGE.

Over the time period, the Fed made changes to the FFR Target rate which ranged from dropping it 3.25% in a six month period (L6FFR) to raising it 2.125% in a six month period, with the midrange changes being from -0.25% to +0.25% in a six month period (many of those being "no change").  I will call any L6FFR between -0.25% and +0.25% a STEADY FFR, and define the others as either FALLING or RISING FFRs.

Over the time period, the slope of the yield curve would change in any given six-month period (L6Slope), with a maximum decrease of -0.216 and a maximum increase of +0.272.  About one-third of the time, however, the change in slope was between -0.039 and +0.029, which I shall call a STEADY slope, and I shall define the others as either FLATTENING or STEEPENING slopes.

Just because there are 3^4 = 81 potential combinations doesn't mean there are 81 ACTUAL combinations.  Matter of fact, there are only 63 valid combinations, and 14 of them account for more than half of the data!

For example, you just don't see a LOW FFR with a FLAT curve, when rates have been STEADY.  It doesn't happen that way.  Historically, if the FFR is LOW and the curve is FLAT, the Fed has either been rapidly lowering into that situation, or they've just started raising rates out of that situation.

Another combination that doesn't get seen very often is a MIDRANGE FFR that has been STEADY, combined with a STEEP curve.  Generally speaking (64% of the time), if the FFR is midrange and steady, the yield curve is FLAT.  Interestingly, the tendency in those cases is for the FFR to fall rather rapidly, and the curve to steepen, over the next six months, especially if that curve had been flat for some time before the measurement (i.e. a STEADY slope).

NOW we're getting somewhere!  These combinations of events, and their subsequent changes, each represent points in the Fed's "management" of the economic cycle – or as the Austrian economists would state, in the Fed's "creation" of the economic cycle.  I run through the 14 most common combinations (representing more than half the data), with some (tongue in cheek) situational analysis and subsequent statistical *tendencies*, below.  The ranges I refer to are listed above.

  1. HIGH and RISING FFR, curve is FLAT and has been FLATTENING.  368 of 6204 observations.  Statistically speaking, the FFR will FALL in the next six months.  Situation: the Fed has raised rates until they broke it.

  2. LOW and FALLING FFR, curve is STEEP and has been STEEPENING.  348 of 6204 observations.  Statistically speaking, the FFR will continue to FALL in the next six months.  Situation: this is after the Fed has broken it, and they're cutting for "damage control."

  3. MIDRANGE and STEADY FFR, curve is FLAT and has been STEADY.  292 of 6204 observations.  Statistically speaking, the FFR will FALL like a bloody rock in the next six months.  Situation: sounds like not too long ago, the Fed took one raise too far or held steady too long, and they've got some catching up to do.

  4. LOW and STEADY FFR, curve is STEEP but has been FLATTENING.  277 of 6204 observations.  Unclear statistical result following this configuration.

  5. MIDRANGE and STEADY FFR, curve is FLAT and FLATTENING.  276 of 6204 observations.  Tendency is for rates to fall in the subsequent six months.  This is a lot like 3., above, where perhaps the Fed has "been steady too long" and will wind up playing catchup.

  6. LOW and STEADY FFR, curve is STEEP and STEADY.  264 of 6204 observations. Very strong statistical tendency for the FFR to RISE over the next six months.  Situation: the Fed is done lowering and must now "fight inflation" by raising rates.

  7. MIDRANGE and FALLING FFR, curve is MIDRANGE and STEEPENING.  200 of 6204 observations, note the falloff in frequency from the top six groupings.  No clear statistical tendencies following this.  Situation is a loosening cycle, but apparently a calm one.

  8. LOW and FALLING FFR, curve is STEEP and STEADY.  192 of 6204 observations. There is a slight tendency towards rates continuing to fall.  Situation: near the end of a loosening cycle.

  9. MIDRANGE and RISING FFR, curve is FLAT and STEADY.  182 of 6204 observations. Very clear statistical tendencies for the FFR to continue to RISE, probably rapidly, and the slope of the curve to flatten considerably.  Situation: this is the Fed in the middle of a deliberate attempt to "slow the economy."

  10. LOW and RISING FFR, curve is MIDRANGE and FLATTENING.  179 of 6204 observations.  Very clear statistical tendencies here, the average increase in the FFR after this situation is humongous, and the curve has a very strong flattening tendency. Situationally, this is perhaps a historical forerunner of 9., above, where the Fed is not only "taking away the punchbowl," but putting antifreeze in it.

  11. HIGH and RISING FFR, curve is MIDRANGE and STEADY.  178 of 6204 observations. There is a slight tendency for the FFR to be rising, but it's not incredibly strong. Situationally, this looks like it's near the end of a tightening cycle.

  12. HIGH and RISING FFR, curve is MIDRANGE and FLATTENING.  163 of 6204 observations. The tendency here is a falling FFR, but it's not a huge tendency. Situationally, this is where the Fed "breaks the economy," similar to 1., above, but not as severe a break (curve is midrange not flat) and hence not as big a reaction.

  13. LOW and STEADY FFR, curve is STEEP and STEEPENING.  152 of 6204 observations.  There is no strong statistical tendency here.  This is near the end of a loosening cycle.

  14. LOW and RISING FFR, curve is STEEP and STEADY.  149 of 6204 observations.  Very strong tendencies here, the FFR rises dramatically and the curve tends to normalize. 

By keeping an eye on the historical tendencies of subsequent Fed action and curve movement, following certain situations, we can get some solid clues as to what might happen next, given today's situation.  We can also wait for "fat pitches."

For example, situations 10. and 14., above, are very fat pitches for rising FFR with a curve that's flattening.  Looking at ALL the situational analyses, not just the top 14, we can make the general statement that when the FFR is LOW and RISING, it's a trend worth following – rising rates and a flattening curve.  How do you play that?  Any way you like, but "don't fight the Fed."

Flipside "don't fight the Fed" fat pitches occur at the other side, when the FFR is HIGH and FALLING.  There's no need to call the turning point, just recognize that the train is leaving the station, the Fed's gonna be on a roll, and the curve will probably steepen a bit, too.

The fattest pitch on the yield curve changes occur when the FFR is HIGH and the Fed hasn't raised rates overly much in the last six months.  Here, the tendency is for the curve to normalize, if it's currently on either extreme.  That is, if the curve is either FLAT or STEEP, look for it to revert to normal rather rapidly following this situation.  If the curve is FLAT, the Fed will probably be cutting rates soon, to boot.  How do you play that?  "Don't fight the Fed."

The key takeaway from this post, and the previous one, is that when dealing with an interaction like the yield curve, interest rates, and Fed policy, we can use a combination of any variety of statistical techniques (regression in the previous episode, groupings in this one) with a situational analysis based on some historical understanding, to come away with actionable planes that present high odds of success. 

Today's situation: LOW and FALLING FFR, curve is MIDRANGE (borderline steep) and has been STEEPENING.  Statistically the bet is for continuing lowering of the FFR and continuing steepening of the curve.  Although this is consistent with June's analysis based on regression output, it seems counterintuitive to what I'd gather from watching CNBC.  Oh, bother.

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