#### Introduction

Lead-lag strategies are very well-known in the literature, and effects of this type can still be found across many timeframes. There are a few tricks of the trade when it comes to lead-lag that I’d like to explore + a bit of detail on the popular models behind lead-lag strategies.

#### Simplest Method

Simple is often best, and especially when working with noisy financial data, it pays to have a robust method. That’s where our linear regression comes in; there’s nothing fancy here, just standard linear regression.

We take a regression between the returns of one asset and the returns of another asset to model our lead-lag relationship. The only difference is the timeframe of the returns since we need to shift our returns based on the lead-lag interval we are modeling.

This does create an awkward issue of needing to estimate the delay between them, but we can find this using statistical tests or simply plotting the returns.

Once we have our regression, we can predict how much a lagging asset will move based on the move in the leading asset.

#### Cheap Convergence Trading vs. Event Driven

Lead-lag strategies can be thought of in two ways: either as a cheaper method for executing a relative value trade where you would normally put on a spread but instead have opted to take the more mispriced leg (and reduce trading costs) OR as an event-driven trade.

The event could simply be a large price shock, but the key differentiator here is that we expect to realize our alpha in discrete vs. continuous time. With an event, we see a sudden move in the leading asset and a sudden move in the lagging asset - this tends to be more of an HFT trade, and because our alpha decays extremely fast, we probably need to execute as a taker.

For a relative value trade, we will not have such a sudden realization of our edge and instead can look into smarter forms of execution without worrying about missing the trade. This is the mid-frequency to low-frequency version of lead lag and is a bit more statistically driven because causality is harder to establish. Sudden moves are rare; one following another is a clear causal relationship, but smaller moves are common, and thus, gradual convergence is noisier.