Wednesday, April 23, 2014

The Yield Curve and Rate Movements

I was taking a look at interest rates during the Great Moderation period.  Here is a graph of rate changes over time.  This probably requires some explanation.

First, this is based on data from treasury rates and the fed funds rate.  I probably should have used 3 month treasuries, but I don't think it affects the general analysis.  It is based on a monthly forward yield curve that I produced with a combination of bootstrapping and curve fitting.  So, again, these aren't exact numbers, but they are close enough for some basic analysis.

The red line is the expected change in short term rates, given by the yield curve.  In other words, if two years ago, the 2 year forward rate was 2.5% and the fed funds rate was .25%, then the yield curve was predicting a 2.25% increase in the fed funds rate over the intervening two years.

The green line is the raw change in the Fed Funds rate over two years.  If 2 years ago, the Fed Funds rate was .25% and today it is .5%, then the Fed Funds rate has increased by .25%.

The blue line is the difference between the forward 2 year rate from two years ago and the Fed Funds rate today.  So, if the 2 year forward rate two years ago was 2.5% and the FF rate today is .5%, then, today's rate has decreased by 2% over two years.

The dates are the end date of the two-year period.  One way to read the graph is that the Green line is the sum of the red and blue lines.  The Green line is the total change in the interest rate.  The red line is the portion of the change that was predicted by the yield curve and the blue line is the portion of the change that wasn't predicted by the yield curve, and therefore could have been captured by taking a forward position on the yield curve two years ago.

Here are correlations between the yield curve slope (red line) and the subsequent change in the short term rate (green line), and between the yield curve slope (red line) and the subsequent change in future short term rate compared to the starting 2 year forward rate (blue line).

The yield curve has been a very unbiased predictor of the subsequent change in short term rates (Future rate minus current rate) during this period (the first graph).  If the yield curve slope increases by 1%, then you better darn well expect future rates to be 1% higher.  It's not a good forecaster - there is a lot of noise around this correlation - but it is unbiased.

If we look at the second graph, this is the subsequent change over two years, starting with the 2 year forward rate and ending with the eventual short term rate after two years have passed (future rate minus forward rate).  There is no persistent correlation.  In other words, if you take naïve positions on two year forward rates, based on the slope of the yield curve at the time, there is no systematic profit available.

The y-intercept for both of these correlations is -1.85% over 2 years.  It would be possible for there to be some bias in the yield curve, reflecting maturity premiums or skewed risk profiles.  But, here, I believe this is simply a product of the decline in interest rates across the curve over the past 30 years.  This decline cannot continue, since we are at the zero bound.  So, forward rates should have a neutral or positive bias.  First, because the zero bound will limit the negative outcomes.  Eventually, rates might trend up again, although I suspect this will not happen soon.  The combination of a hawkish Fed and demographic pressures will probably keep a lid on rates for some time.

But, I think there is a pattern here that might be exploitable.  In cases where the yield curve is negative, the future short term rates are almost always lower than the initial forward rates would have predicted.  There are a few outcomes where future rates are higher, coming from the episode in 1998 where the yield curve flattened and then the economy recovered.  But, in all the other cases where the yield curve inverted (including all the cases that triggered the Federal Reserve yield curve inversion recession indicator), yields had much more negative movement than the yield curve would have predicted.

If the Fed gets scared by rising home prices, I suspect this might happen again.  If the yield curve has a bias, it might be an inability to signal a money-supply-related recession when the Fed is inclined to impose one.

Of course, if we remove the points where the yield curve is inverted, then the yield curve at positive levels stops correlating so well to future rate movements.  At positive slopes, it overstates the future rate by about double, so that there appear to be persistent profits from positioning against the yield slope, but with a tremendous amount of variance.

Looking back at the initial graph, in the recoveries after the previous two recessions, there were brief periods where rates increased by more than the yield curve had predicted (the green line is above the red line).  I have been positioning for this movement again.

If expected yields remain where they are, the 2 year forward rate when short term rates start to climb will be slightly over 2% more than the spot rate.  But, with interest on reserves, tremendous excess reserves which can be unwound, etc., there are a number of mitigating factors in play.  I don't have as much confidence in the expectation that rates will move more than that as I once did.

But, I do believe that there will be a point where a long position on Eurodollar futures (which gains when rates decline) should have a decent likelihood of profit.  This will be the case when the curve flattens, and maybe even when it is still positive.  I also believe that the combination of demographic factors and a hawkish Fed that has taken very little blame for the 2008 fiasco, and faces public pressure for disinflation because of broad misunderstanding of the role of housing in financial markets, eliminates much of the risk of having an unexpected interest rate bump (either in real rates or in the inflation premium) go against that position.

I wish that wasn't the case, but I'm afraid it is.

 In general, although the scatterplot of interest rate changes shows a large amount of unpredicted changes, there does appear to be a decent amount of serial correlation in the error.  Generally, if the yield curve has been sloped too steeply, and is beginning to show a decline in the error for the two year periods coming to an end, it seems likely that it will continue to decline until it begins to under-predict the actual coming changes in rates.  There might be a somewhat regular tendency for the error to move in waves through the business cycle.  This pattern would suggest that contracts expiring around 2017 or so will predict the 2017 interest rates fairly well, possibly being a bit low, and by 2019 or 2020, long positions might tend to be profitable, with interest rates in 2019 and 2020 coming in below the original expectations.

That's probably the optimistic case.  The bad scenario would be if the economy starts to falter before short term rates ever get off the ground.

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