Yield Curve Indicator

 

The yield curve indicator was designed to anticipate a crisis using the theory of the business cycle as a deterioration of liquidity. A crisis can be anticipated when the yield curve begins to flatten, or is flat. Under normal market conditions, the yield curve behaves like this: as the maturity of a financial asset becomes greater, the yield increases. The indicator has two components: first, the percentage change in the slope (upwards or downwards) during the previous period; second, the calculated difference between the compounded slope of the entire interest rate and the continuous compound interest rate1 It is important to note that the slopes of the yield curves were calculated using a semi-logarithmic model. The compound interest rate is a geometric average that equalizes the starting and end points passing through intermediate points.

The indicator was defined with a priori probabilities with a specific weight of 50% each, in time we hope to modify the a priori probabilities with additional information with a Bayesian probability model.

We have designed a traffic signal indicating risk levels: 1 is low risk (green), 2 is medium risk (yellow), and 3 is high risk (red). We put it together with the change tables from the indicators previously mentioned and a priori elements, hoping to modify them over time with the Bayesian probability model.

Risk Scoring
Risk value	Slope reduction
1.00	Increases
2.00	Decreases up to 50%
3.00	Decreases more than 50%
Difference continuous compound and compound rates

50%	Difference compound and continuous compound rates
1.00	> 0.1
2.00	> 0.05 <0.1
3.00	<0.05

Figure 1

 

Figure 2

Table 1

Date	1 Mo	3 Mo	6 Mo	1 Yr	2 Yr	3 Yr	5 Yr	7 Yr	10 Yr	20 Yr	30 Yr	Continuous compound slope (Short term proxy)	Compound slope (Long-term proxy)	Gap Short or long term	Slope reduction	GAP rate	Slope reduction rate	Risk Level
Dec 2001	1.68	1.74	1.83	2.17	3.07	3.59	4.38	4.84	5.07	5.74	5.48	0.17	0.18	0.01
Dec 2002	1.2	1.22	1.23	1.32	1.61	1.99	2.78	3.36	3.83	4.83		0.19	0.21	0.02	15%	3.0	1.0	2.0
Dec 2003	0.9	0.95	1.02	1.26	1.84	2.37	3.25	3.77	4.27	5.1		0.24	0.27	0.03	27%	3.0	1.0	2.0
Dec 2004	1.89	2.22	2.59	2.75	3.08	3.25	3.63	3.94	4.24	4.85		0.11	0.12	0.01	-57%	3.0	3.0	3.0
Dec 2005	4.01	4.08	4.37	4.38	4.41	4.37	4.35	4.36	4.39	4.61		0.01	0.01	0.00	-89%	3.0	3.0	3.0
Dec 2006	4.75	5.02	5.09	5	4.82	4.74	4.7	4.7	4.71	4.91	4.81	-0.00	-0.00	0.00	-127%	3.0	3.0	3.0
Dec 2007	2.76	3.36	3.49	3.34	3.05	3.07	3.45	3.7	4.04	4.5	4.45	0.05	0.05	0.00	-1501%	3.0	3.0	3.0
Dec 2008	0.11	0.11	0.27	0.37	0.76	1	1.55	1.87	2.25	3.05	2.69	0.44	0.55	0.11	1036%	1.0	1.0	1.0
Dec 2009	0.04	0.06	0.2	0.47	1.14	1.7	2.69	3.39	3.85	4.58	4.63	0.60	0.83	0.23	51%	1.0	1.0	1.0
Dec 2010	0.07	0.12	0.19	0.29	0.61	1.02	2.01	2.71	3.3	4.13	4.34	0.53	0.70	0.17	-15%	1.0	2.0	1.5
Dec 2011	0.01	0.02	0.06	0.12	0.25	0.36	0.83	1.35	1.89	2.57	2.89	0.70	1.01	0.31	44%	1.0	1.0	1.0
Dec 2012	0.02	0.05	0.11	0.16	0.25	0.36	0.72	1.18	1.78	2.54	2.95	0.59	0.80	0.21	-21%	1.0	2.0	1.5
Dec 2013	0.01	0.07	0.1	0.13	0.38	0.78	1.75	2.45	3.04	3.72	3.96	0.71	1.03	0.32	29%	1.0	1.0	1.0
Dec 2014	0.03	0.04	0.12	0.25	0.67	1.1	1.65	1.97	2.17	2.47	2.75	0.58	0.78	0.20	-24%	1.0	2.0	1.5
Jan 2015	0.01	0.02	0.07	0.18	0.47	0.77	1.18	1.49	1.68	2.04	2.25	0.55	0.73	0.18	-7%	1.0	2.0	1.5
Feb 2015	0.02	0.02	0.07	0.22	0.63	1.01	1.5	1.82	2	2.38	2.6	0.53	0.70	0.17	-4%	1.0	2.0	1.5
Mar2015	0.05	0.03	0.14	0.26	0.56	0.89	1.37	1.71	1.94	2.31	2.54	0.45	0.57	0.12	-19%	1.0	2.0	1.5
Apr 2015	0.00	0.01	0.06	0.24	0.58	0.91	1.43	1.79	2.05	2.49	2.75	0.55	0.74	0.19	0.30	1.00	1.00	1.00

Source: Author, from Treasury Department data available at http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/Historic-Yield-Data-Visualization.aspx.

As we can see in figure 1, when the short-term slope is less than the long-term slope it is clear that the interest rate curve is in normal market conditions. The long-term in normal market conditions would imply greater interest rates than those in maturity periods of short-term investments. During crises, the two slopes are equal or tend to be equal, an undeniable sign that the curve is flattening. In figure 2, we clearly see how the risk indicator increases as the slopes equalize and the difference between them is reduced.

Table 1 shows the calculations for each of the periods (annually) from 2001 and monthly up to April 2015.

During the crisis years, we clearly see how the indicator reaches level 3 (alert) and how the two slopes (continuous compound and compound) tend to have no difference. In practical terms, this implies a deterioration of the system’s liquidity and a potential crisis.