Thread by @christinaqi

#HFT strategy time, part 2: Examples of features.
- Skew: The simplest type of book feature is called the skew, which is the imbalance between resting bid depth (v₂) and resting ask depth (v₁) at the top of the book.

So we can formulate this as some sort of difference between v₂ and v₁. It’s convenient to scale these by their order of magnitude, so we take their log differences instead:
skew = log(v₂)−log(v₁) = log v₂ / v₁

Notice that it doesn’t matter whether it’s log (v₂) − log (v₁) or log (v₁) − log(v₂). It’s just nice to formulate signals in a way that (+) values imply that we expect prices to 📈 & (-) values imply that we expect prices to 📉, so it’s easy to debug your strategy & models.

I picked this ordering because intuitively, we expect higher bid depth to mean higher buy demand and hence higher prices. Anyway on to the next feature.

- Book imbalance: A variation of the skew is called a book imbalance:
imbalance = (v₂ − v₁) / (v₂ + v₁)

This works on the same microstructural principle except we’re scaling the signal differently. The imbalance is more sensitive to changes whereas a larger magnitude of change is needed to effect the same marginal change in the skew.

We won’t use the book imbalance this time but I thought to bring it up because it is similar and there is plenty of financial literature and econometric research on the book imbalance.

Last post in this thread: Next week I'll put these into a strategy. I'll also explain why I chose skew rather than a billion other feature examples. I should probably also put a bunch of disclaimers in place (one-in-a-million examples, not investment advice, etc).