Which yield curve to measure?

27 August 2018

The US yield curve has been attracting quite a bit of attention recently, especially now the gap between 2 year Treasury bonds and 10 year Treasury bonds is so small.  The reason for this attention lies in the reliability of a negative spread as a predictor of US recessions since the 1950s.

FOMC minutes through 2018 indicate the slope of the yield curve has been regularly discussed in recent months. Some Federal Reserve members have even gone so far as to state publicly they would oppose any rate rise which would invert the yield curve. Bank of Atlanta President Raphael Bostic said he “will not vote for anything that will knowingly invert the curve…” despite his belief an inverted curve does not necessarily always precede a recession.Just what is an inverted or inverse yield curve? Put simply, a yield curve is inverted if long-term yields are less than short-term yields. If a bond’s yield is plotted against its time to maturity and then this process is repeated for bonds from the same issuer with various times to maturity, most of the time it looks like an uphill slope from left to right. In mathematical terms, the gradient is positive. However, sometimes the curve slopes downhill and the gradient is negative, thus producing a yield curve which is then described as “negative” or “inverse”.

The slope or gradient of a curve can be calculated mathematically by measuring between two points, usually one at the very beginning or a curve and one at the very end. In the case of the US government yield curve, this suggests taking the yield on a 3-month Treasury bill and comparing it to a 30-year Treasury bond yield.

However, convention in US markets often ignores these two points and, instead, the difference between 2-year bonds and 10-year bonds is the traditionally-calculated spread. In academic circles, the 3-month/10-year spread is widely used. There is even another measure which uses the gap between the current implied forward rate (on 3-month Treasury bills) six quarters from now and the current yield on a 3-month Treasury bill. Is one of these measures “better”?

Michael Bauer and Thomas Mertens are research advisors in the Economic Research Department of the Federal Reserve Bank of San Francisco. In a paper they produced just this week, they looked at these three measures and came to the conclusion one measure is superior to others. “The difference between 10-year and 3-month Treasury rates is the most useful term spread for forecasting recessions…” Term spread is another way of referring to the difference in yields of two securities with different terms to maturity.

Their paper will probably not cause a dramatic shift in usage towards their measure, simply because traditions change slowly and the relationship between 3-month bills and 2-year bonds is reasonably stable.

However, their paper is another reminder of the slimness of the gap between short-term and long-term yields no matter which measure is used.