Yield Curve Slope Correlations

When looking at bond yields, one should keep in mind that the entire yield curve is a mathematical object. A venerable research approach is to attempt to use time series econometrics to either isolated tenors or slopes. This approach leads to misleading degrees of freedom in bond yield dynamics.

In this article, I will do the simplest step towards modelling the yield curve -- looking at the relationships between selected slopes. We see that slopes move together, which pins down how disjointed various parts of the curve can get. Digging further would require access to a fitted curve.

Short End

Figure: Front-end slopes

We will first look at the front end of the yield curve (beyond the money market maturities). The top panel shows the 2-/5-year and 5-/10-year U.S. Treasury slopes. Summed together, they form the 2-/10-year slope, which is one of the most commonly looked at slopes. We see that the slopes are highly correlated, with the two slopes often being roughly equal.

The main deviation in the post-1999 period is around 2012 when the hawks finally capitulated on their belief that the Fed would rapidly normalize rates. The 2-/5-year slope was suppressed, while the 5-/10-year slope was at relatively "normal" levels for an expansion. (The current curve is perhaps moving towards this configuration.)

The bottom panel shows the average change in the slope per year of maturity. E.g., if the value of the series at a time point is 20, that means that the slope changes by 20 basis points per year. (For the 2-/5-year slope, that implies a slope of 60 basis points, for the 5-/10-year it implies a slope of 100 basis points.) The change in slope between the 2- and 5-year maturity is normally much greater -- yield changes are gradual.

The lower magnitude of yield changes is not surprising when we consider what par coupon yields represent. (Link to primer on par and zero curves.) The zero curve can be viewed as the average of the instantaneous forward curve, and since the instantaneous forward curve is smooth in practice, the zero curve gets smoothed out as maturities lengthen. The par coupon curve is even smoother since the coupons are discounted at the zero rate of shorter maturities.

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Disclaimer: This article contains general discussions of economic and financial market trends for a general audience. These are not investment recommendations tailored to the particular needs of an ...

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