Testing Multi-Asset Cointegration and Trading Yield Curve Spreads
Summary
The document discusses cointegration among more than two assets, using yield curve rates as its main example. It describes principal component analysis of yields: the first components represent level, slope, and curvature, while a later component can capture a relationship involving multiple instruments. It also identifies the Johansen test for testing cointegration across an arbitrary number of assets and contrasts it with a state-space approach to stochastic common trends.
A historical rates example compares the 2s–30s slope with the 5s–10s slope, describing a pre-crisis trade called a condor. The answer says direct regression of individual yields in levels was not robust, while regressing one slope on another performed better out of sample. It cautions that hedge ratios can shift and transaction costs may make the trade unattractive. The response is based on the author’s experience and does not establish that similar relationships work for equities or remain viable today.
Key ideas
- The Johansen test can assess cointegration among multiple asset series.
- Yield curve principal components represent common movements such as level, slope, and curvature.
- Slope-on-slope relationships can offer a more robust specification than regressing individual yields in levels.
- Cointegrating relationships can shift, and trading costs can erode the appeal of a rates spread strategy.
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# Are there any papers about cointegration consisting of time series of more than two assets? # Are there any papers about cointegration consisting of time series of more than two assets? Are there any papers about cointegration consisting of time series of more than two assets ? I wonder if there could be any trading strategy for three assets case. ## Answer by NBF (score 4) https://quant.stackexchange.com/a/36858 Technically, if you do PCA on the yield curve (live dangerously!, do it in levels), the first two PCAs are nonstationary. The third is questionable. Note that this is a perfectly valid way of looking for stochastic common trends (see Madalla-Kim, Unit Roots, Cointegration and Structural Change for refs). The fourth principal component is stationary by most measures. FYI, stochastic common trends is the state-space analog of Cointegration. In cointegration, we use Johansen for testing. In Stoch-common trends, one uses Nyberg, which switches H0 and H1, just like for unit root testing one uses ADF, but for mean-reversion testing, one uses KPSS. The fourth principal component requires the use of four assets to replicate it. Since PCs are ordered by their modes (first PC=level=no zeros, second PC=slope=one zero, third PC=curvature=two zeros,..) the fourth PC=three zeros and best corresponds to the relationship between one slope on another. A proxy we used to use for this was 2s-30s slope vs 5s-10s slope. These slopes are generally cointegrated although as with most relationships, the beta can shift. We used to call this the condor back when we covered this trade pre-crisis. It turns out, that finding the cointegrating relationship is not very robust. Doing the regression of say 2s on 5s,10s and 30s in levels is not robust. The stderrs are too high. Regressing 2s30s slopes on 5s10s slope performs much better OOS. This was traded pre-crisis, but I don't think it's a very viable trade for most given that there are too many transaction costs. A similar slope vs slope, well-behaved, trade would be close-maturity futures slopes, so EDH8-EDM8 vs ERH8-ERM8). It is pretty straightforward to come up with multi-asset portfolios in rates which one can make sense of, because each product is only modestly different from other products. In fact, the factor mimicking portfolio for levels or for slope or for curvature are all multi-asset portfolios. You might be asking about equities, however, and, unlike rates, I do not personally know whether it makes sense for a triplet of assets to be mean-reverting, since it is a little less intuitive. ## Answer by RRG (score 2) https://quant.stackexchange.com/a/36860 The Johansen test can be used to test for cointegration among $n$ assets. https://en.wikipedia.org/wiki/Johansen_test The original paper: Johansen, Søren (1991). "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models". Econometrica. 59 (6): 1551–1580
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.