⊕ See here for a link to purchase Joel’s book. It’s a good one.

Today was the first day of the empirical session with Albert Menkveld . We covered the first couple chapters of Joel Hasbrouck’s excellent book.

⊕ Roll, Richard, 1984, A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market, The Journal of Finance 39, 1127–1139.

We started with the general Roll (1984) model, which is a really straightforward way to think about how order processing costs make it into the bid-ask spread. Basically, it is assumed that trade prices $p^t$ have a random walk with drift evolution, such that

$$ p_t = p_{t-1} + \mu + u_t $$

Hasbrouck notes that the drift term $\mu$ is largely unnessecary, especially since at micro-scale it’s hard to have any notion of expected return.

The model above is expanded upon by including an efficient price (fundamental value) $m_t$, which is a martingale:

$$ m_t = m_{t-1} + u_t $$

Prices are then a noisy proxy of the true value, as a function of a cost that market makers need to recoup for processing orders

$$ p_t = m_t + q_tc $$

where $c$ is a fixed per-trade cost incurred by the dealer and $q_t$ is an indicator for a buy or sell ($+1$ for a buy and $-1$ for a sell).

⊕ Hasbrouck, Joel, 2009, Trading Costs and Returns for U.S. Equities: Estimating Effective Costs from Daily Data, The Journal of Finance 64, 1445–1477.

It’s a good model. I’m particularly interested in how Hasbrouck (2009) approaches trying to approximate the $c$ variable, as he uses a Gibbs sampler to run a Bayesian linear regression. Given my association with Turing.jl, I can’t help but feel that there is a hierarchical model that would provide a better structural estimate of things like adverse selection cost and order processing cost. That’d need a more sophisticated model than the Roll model, however, and I’m not quite sure I’m up to the task (yet).