This article aims to analyse the yield curve of the US Treasury bond form 1962 until now. The analysis has been carried forward with monthly data from FRED (Federal Reserve Economic Database provided by the FED of Saint Louis). The final goal is to spot possible fixed income strategies from the expected fed decision of raising the fed fund rate.

The graph shows the level of the Fed Fund rate and the yield of the Treasury bonds, respectively at the following maturities 1 and 10 years. In order to model the data and make accurate forecasts, we need a basic econometric analysis. Looking at the graph, we see that the series suffer a lack of stationarity. For this reason, the following step is to spot some long-term relationship between the series through a Cointegration test. Thanks to the Johansen test we decide that the right model is the following:

deltaYt≈a*(cointegration relation) + beta*deltaYt-1 + eR2 = [ 0.34 0.14 0.11 ] 

Where Y is a vector containing the level of our series [FF_Rate; 1YR; 10YR], ϵ is a vector of white noise variables and by definition a cointegrating relation is a stationary linear combination of non-stationary series.

In our case cointegrating relation = FF_Ratet-1 + theta*1YRt-1 + delta*10YRt-1

Looking at the results of the model: is the FED decision to influence the market or vice versa? 

  1.  The first graph shows, according to our model, how much of the total variance (in percentage) of the Fed Fund Rate is explained by the 1 Year and 10 Year yield to maturity (red line and yellow line respectively) in 24 month (X – axis). We see that, with a time horizons of 2 months, more than 90% of the total change in the Fed Fund rate is due to the Fed Fund Rate itself. It means that for this model the fed moves interest rate independently by the fixed income market, or we could say that the Fed Fund Rate is an exogenous variable in our model.
  2.  Instead, the second graph shows the variance decomposition of the 10 year yield to maturity and we see that for the first month the 1 year yield to maturity explains the most of the variance of the 10 year yield.

Looking at the following 2 charts, which show the impulse response functions (by definition: these show the effects of shocks on the adjustment path of the variables), we observe that on average a movement in the 1 year yield shows a positive relation to a movement in the FF rate (first chart). Although the positive link between the 10 year yield and the FF rate, we spot a negative relation between the 10 year and 1 year yield to maturity (second chart). The strong assumption behind this IRF is that a shock in one variable is independent to the others.

This historical feature of the yield curve tells us that, on average, a flattening of the curve will follow an increase of the Fed Fund Rate. The best strategy in order to exploit this expectation is a long/short strategy for going long on the 10-year Treasury bond while going short on the short-term part of the curve.

Riccardo Aimone

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