- 2001: Volume 10, No. 3 Yield Curve: Steepen Faster Than Flatten?

Someone recently mentioned that he was working with the yield curve and noticed that it appeared to steepen faster than it flattens. We decided to do some research to see if that is true.

We defined the yield curve as the yield spread between the 30-year Treasury bond and the 2-year note. The curve steepens when the spread rises, and the curve flattens when the spread falls.

First, we recorded the level of the spread on the starting day of the entire test period. Then we tracked the spread, moving forward one day at a time. We ended the period the day the spread had risen (or fallen) at least 20 bps above (below) the starting level. That day we recorded the change of the spread over the period and the number of days between the starting day and the ending day of the period.

Second, we calculated the average daily rate of change (ROC) of the period. That is equal to the change of the spread over the period divided by the number of days in the period.

Third, we marched forward again. The day the spread had risen (fallen) at least 20 bps above (below) period two’s starting level, we ended

that period. Again, we calculated the daily ROC of the period.

For example, on Jan 12 1996 the yield spread started at the 98 bps level (see chart at left). It then took 16 days for the spread to change at least 20 bps. On February 2 the spread closed at 125.5, so the curve was 27.5 bps steeper. The average daily ROC that period equaled +1.78 bps. The following 19 days the spread flattened to 104.5 or by 21 bps. The average daily ROC was -1.11 bps. We repeated this process, examining a period at a time until we reached the end of the entire test period. In the end we identified all the periods the spread changed at least ±20 bps.

Figure 1:

Fourth, we calculated the average ROC all the times the yield curve steepened, and compared it with the avg. ROC the times the curve flattened.

Fifth, to capture periods of large changes in the spread we employed steps one to four using ±40 bps and ±60 bps thresholds.

Test & Results
We employed this approach using daily yield data of three different test periods—1995 to present, 1990 to present and 1987 to present. The results are listed below. For example, since 1990, the times the curve steepened by 40 bps, it did so at an average daily rate of 1.79 bps per day. The times the curve flattened by 40 bps, it did so at an average rate of 1.44 bps per day.

1990 ~ Present	Curve Steepen	Curve Flatten
Avg. ROC (20 bps) Avg. ROC (40 bps) Avg. ROC (60 bps)	+2.01 bps +1.79 bps +1.10 bps	-1.69 bps -1.44 bps -0.94 bps
1995 ~ Present	Curve Steepen	Curve Flatten
Avg. ROC (20 bps) Avg. ROC (40 bps) Avg. ROC (60 bps)	+2.48 bps +1.43 bps +1.82 bps	-1.31 bps -1.08 bps -0.49 bps
1987 ~ Present	Curve Steepen	Curve Flatten
Avg. ROC (20 bps) Avg. ROC (40 bps) Avg. ROC (60 bps)	+1.81 bps +1.41 bps +0.72 bps	-1.70 bps -0.96 bps -0.64 bps

Comment
Does the curve steepen faster than it flattens? Yes. The tendency has been the strongest the past few years. Examining Greenspan’s entire reign (1987 to present), the tendency is there as well. When speculating on the yield curve, you have to consider more than the direction of the spread. Often it costs money to carry the trade, and that cost depends on whether you are buying or selling the spread, the level of the spread, the hedge ratio and financing rates. When there is a carrying charge, not only do you have to get the direction right, but the spread must move your way quickly.

Yield curve traders: keep the curve’s tendency to steepen faster than it flattens in mind.

Alex Saitta is a vice president and Yuxin Li is a research assistant in the New York office of Salomon Smith Barney. Alex can be reached at alex.saitta@ssmb.com