3
$\begingroup$

Currently studying on techniques to estimate the bid-ask spread. Perhaps the most widely known model is the Roll model (1984). Let $P_t$ indicate log prices

$\begin{cases} Bid_t=P_t-c, \\ Ask_t=P_t+c, \end{cases}$

Where $c=\sqrt{-Cov(\Delta P_t, \Delta P_{t-1})}$.

My question comes down to the interpretation of autocovariance. My intuition is that positive autocorrelation in returns, imply presence of informed traders (Probability of having a trade in the same direction after a buy\sell is higher), and dealer sets a higher spread due to adverse selection. On the other, with negative autocorrelation, a trade is likely to be followed by a trade in the opposite direction (Sell after a Buy and vice versa) and dealer does not have adverse selection risk, so he\she should set a low spread. In the literature, some researchers take the absolute autocovariance to deal with undefined spread. Does this imply overestimation bias ("Expensive" spread when there is negative autocorrelation)?

$\endgroup$
3
$\begingroup$

This does not imply overestimation bias. We expect a negative autocorrelation in high- and ultra-high-frequency (every trade) data due to bid-ask bounce. Bounce occurs when buy and sell orders trading at the offer and bid are interspersed; that yields what seems to be returns even when the bid, ask, and midpoint do not change.

The Roll (1984) model examines this bounce in a theoretical market and determines that the negative autocovariance can be used to estimate the bid-ask spread.

What if ultra-high-frequency returns do not exhibit a negative autocovariance? That is rare and suggestive of very strong trending behavior. In that case, the best estimate of the bid-ask spread would be the minimum tick size -- since the Roll model offers you no useful information.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.