# Statistical Arbitrage¶

Here we investigate whether 5-year generic KO bonds and 5-year generic PEP bonds are a good candidate for pair trading. Intuition suggests that (some) shocks to the spread between those two yields should be temporary hence potentially exploitable. The first step in evaluating that potential typically employed by quantitative shops is to ask if those yields are co-integrated, i.e. if a linear combination of them is stationary.

We wil investigate this in two ways. We will perform a standard co-inegration test on spreads along the lines of Engle and Granger (1987.) We will also ask more directly if spreads $\{S_t\}$ have a tendency to mean-revert by estimating:

$$S_{t}=\gamma S^* + (1-\gamma) S_{t-1} + \epsilon_t$$

where $S^*$ is the long-term tendency of the spread, $\gamma$ is the speed of convergence to it, and $\epsilon$ is noise. Rejecting $H_0: \gamma=0$ via an augmented Dickey Fuller test would be finding evidence that spreads do in fact mean-revert.

All told then, we end up with weak evidence in favor of co-integration, at best.