Bond Market Gymnastics: The Science of Yield Curves

Economics is what I would describe as a “semi-science”. It has some attributes of the scientific method – empirical observations, leading to analytical models underpinned by tight logical reasoning that possess some degree of predictability. However, unlike physics, where mathematics is the natural language for nature’s immutable laws, economic forces are far more capricious and slippery to be captured by equations, no matter how impressive they look on paper. Nevertheless, there are some rare corners of economics where the astounding happens: the reasoning is intuitive and elegant and the analytics are powerful and predictive. The bond market – the world’s largest financial asset market – is one such domain. In this post, I will describe a peculiar regularity in the highly influential US Treasury Bond market – the so-called “inverted yield curve” and show why it’s ability to predict the trajectory of the economy lends it great scientific respectability.

The Concept of Bond Yield

One way governments and corporates can raise money is by issuing bonds, paying investors interest in the form of coupons. Once these bonds are traded in markets, information about the coupon rate, the current bond price, and the bond’s maturity can be used to back out the bond’s yield-to-maturity, or simply, the yield. The slope of the Treasury yield curve reflects the difference between the yield for long-term treasury (or government) bonds and the yield for short-term treasury bonds. For example, if the 10-year Treasury bond yield is currently 5% and the 2-yrar Treasury bond yield is 2%, the slope of the Treasury yield curve is 3%. This is a highly important number. Many studies have documented the predictive power of the slope of the Treasury yield curve for forecasting recessions.  They produce results such as those depicted in Figure 1, which shows the term-structure slope, measured by the spread between the yields on 10-year and 2-year U.S. Treasury securities. The shaded bars in the plot denote U.S. recessions (dated by the National Bureau of Economic Research). Spare a few moments looking at this chart and see if you can spot interesting patterns.

The plot shows the time series of the term-structure slope, measured by the spread between the yields on ten-year and two-year U.S. Treasury securities. The shaded areas denote official periods of recession as identified by the National Bureau of Economic Research.
Source: Federal Reserve Bank of Chicago.

Figure 1 shows that the yield-curve slope becomes negative before each economic recession since the 1970s. In other words, US recessions are always preceded by an “inversion” of the yield curve.  This impressive evidence, using something as simple as the spread between the 10-year and 2-year Treasury yield, is to me, one of the most elegant and powerful regularity in all of economics. Think of the yield spread as an analytical tool, albeit a very simple one. Then couple it with the amazing predictability of an inverted yield curve for recessions, and we have the attributes that make this area of economics very much like the hard sciences. Indeed, economists have exploited this empirical regularity to estimate recession probabilities using quantitative (probability-based) models such as probit specifications. An example is the probit analysis in Figure 2, which shows the fitted probability that a recession will occur over the next year when the explanatory variable is the 10-to-2-year yield-curve spread. The fitted probability peaks before the beginning of each recession, with the exception of a false positive in the mid-1960s.

The plot shows the probability that the U.S. economy will enter a recession in the next year, estimated with a probit model in which the explanatory variable is the ten-to-two-year yield-curve spread. The shaded areas denote official periods of recession as identified by the National Bureau of Economic Research. Source: Calculations by Luca Benzoni , Olena Chyruk and David Kelley.

The Economics of Bond Yield Spreads

Why is an inverted yield curve such a reliable predictor of recessions? In a nutshell, the yield spread quantifies investors’ expectations of the short and long-term trends in the economy and interest rates. In normal (non-recessionary) times, investors demand that yield on long-term bonds to be higher than yields on short-term bonds. It is only logical. Why would any rational investors sock away his money for the long-term unless he or she is compensated with higher yields? Hence, in a normal economy, the yield curve is positively-sloped. This has been the case for the last couple of decades until this year. Firstly, liquidity was abundant, and credit was cheap. So short-term yields were especially low (almost zero in some countries like Japan), while long-term yields were high because investors were not in favor of buying long-term bonds that pay fixed nominal coupons knowing that the real value of these coupons are far less due to a growing economy and the attendant inflationary pressures. Low bond prices translate to high bond yields. So in short, a positively-sloped yield curve reflects investors’ expectations that the economy is rolling along quite well with no recessions in sight.

An inverted yield curve, on the other hand, is a warning that a recession is likely in the months to come. Given this expectation, investors who previously avoid long-term bonds, now don’t mind buying them. After all, a recession ultimately chases away inflation (and might even lead to deflation). So, demand for long-term bonds go up, pushing their yields down. What can lead to this? The short answer: an over-zealous Federal Reserve that is hell-bent on taming inflation, like what Jerome Powell is doing this year, by aggressively raising the Fed Fund rate (a short-term borrowing rate) multiple times (twice this year up to late July and another possible hike in September). So, right now, the Treasury yield curve is inverted due to a combination of high short-term rates and relatively low long-term rates. If the yield curve stays this way, the chances of a near-term recession is high, if the past is any guide.

Economics has been dismissed as the “dismal science” for its lack of predictability. Not always, as the analytics of the Treasury bond yield curve clearly show.

Leave a Reply