cointegration applied to Portfolio Construction & Risk management

Question

There are all sorts of applications of cointegration to generating alpha on mean-reverting timeseries: comparing spot vs. futures, bond spreads, identifying mean-reverting residuals, etc.

But there is not much literature on applying co-integration to portfolio risk. Overwhelmingly, the variance-covariance matrix is used to measure and minimize portfolio risk. Cointegration imposes stricter requirements on the relationship between two time-series than mere correlation. There are also fewer false-but-useful assumptions in the variance-covariance method such as the i.i.d, homoskedasticity, and normal nature of returns.

So are there any citations in the literature that describe portfolio construction procedures for risk minimization using co-integration (or a combination of cointegration and correlation)?

I found this paper - Optimal Hedging Using Cointegration (1999) but it's more of an empirical case-study rather than a framework for thinking about risk thru the lens of cointegration.

Answer 1

The following paper (Identifying Small Mean Reverting) is not directly related to portfolio risk minimization but it provides a method to build tradable mean reverting portfolios based on a multivariate co-integration approach. It has the advantages of providing a theoretical framework along with two algorithms. It also takes into account financial strict financial problems such as transactions costs.

http://www.cmap.polytechnique.fr/~aspremon/PDF/MeanRevVec.pdf

Answer 2

As far as your portfolio is a linear combination of instruments (for non linear portfolios, this is more difficult to explain), the associated risk you would like to monitor is the variation through time of this combination. You stress test your portfolio when you measure its variations when the market conditions are unexpected (in the sense that you can decide for instance to move a market factor) and measure its Value at Risk when you estimate its value-level assciated to a given quantile given usual conditions.

Usual market conditions are difficult to define, but it is often about stationarity of the market context. If you identify a transformation of the market that is stationary, it is reasonnable to test the risk level of your portfolio for any realization of the market in this stationary state space. It is there that you can find a link with cointegration.

Mainly because when two variable are cointegrated, their combination is somehow more stationary than each of them take alone. Of course links between stationarity and cointegration are in practice not easy to deal with (see for instance Kunst, R. M., 2002. Testing for stationarity in a cointegrated system. Tech. rep., Institut für Höhere Studien (IHS)) but from a theoretical viewpoint it should be better to compute VaR using assumptions in a space in which no variable have remaining cointegrated relations.