Comparing Effective Spreads After Adjusting for Volatility and Trading Activity
Summary
The document cautions that comparing effective bid-ask spreads across assets can be misleading when volatility and trading activity differ. It gives a qualitative relationship for small-tick securities: spreads tend to rise with volatility and fall as the number of daily trades increases. Greater volatility raises the risk borne by liquidity providers, while more frequent trades give them more chances to unwind inventory. For large-tick securities, it says an additional bid-ask bound term is needed.
To compare securities more fairly, the proposed method regresses observed effective spreads on volatility divided by the square root of trade count. The residual for each security then represents the spread left after accounting for those factors, offering a basis for relative comparison. This is a suggested analytical approach, not an empirical result: the document provides no sample, fitted coefficients, or validation. Its stated relationship is qualified by tick size, and the residual comparison depends on how the regression is specified and estimated.
Key ideas
- Raw effective spread comparisons can confound liquidity with volatility and trading frequency.
- For small-tick securities, the described spread relationship increases with volatility and decreases with the square root of daily trade count.
- Higher volatility raises liquidity providers' risk, while frequent trading can create more inventory-unwinding opportunities.
- Large-tick securities require an additional bid-ask bound adjustment.
- Regressing spreads on the proposed volatility and activity measure allows comparisons using residuals.
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Full text
# Comparison between Effective Bid-Ask spreads
# Comparison between Effective Bid-Ask spreads
I understood that given two listed assets, the one with the lower effective spread is more liquid, and if one has effective spread lower than the quoted one, it means there has been a price improvement. Which other conclusions could be figured by comparing one asset’s effective spread with another?
## Answer by lehalle (score 1)
https://quant.stackexchange.com/a/70499
in general, the bid-ask spread is proportional to the volatility and inverse proportional to the number of trades per day: $$\psi\propto \frac{\sigma}{\sqrt{N}}.$$
This is true for small tick securities, for large tick securities you need to introduce a "bid-ask bound term" (the Rosenbaum's $\eta$). For details see Section 2.2 p143 of Market Microstructure in Practice (L and Laruelle, 2nd edition).
Qualitatively
- the larger the volatility $\sigma$, the more risk to bare for liquidity providers, hence the larger the BA-spread to get more money in front of this risk
- the more trade per day, the more occasions to unwind your inventory per day, hence the more market makers can afford to offer an attractive spread.
Hence you can check the consistency of this formula for your different assets, what is interesting is to
- perform a linear regression over all your securities to obtain $$\psi=a + b\frac{\sigma}{\sqrt{N}} + \epsilon.$$
- for each security $i$, computes the residuals $$\epsilon_i := \psi_i-\left(a + b\frac{\sigma_i}{\sqrt{N_i}}\right).$$
- now you can compare the $\epsilon_i$ that are the effective bid-ask spread corrected from the volatility and liquidity of each security.
Otherwise you can think that one security is more attractive than another, but indeed it has a smaller volatility of more trades per day.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.