A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market
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What they found
Roll showed that you can estimate a stock's effective spread from its price changes alone, without quote data. Because trades bounce between bid and ask, consecutive price changes are negatively autocorrelated, and the spread equals twice the square root of the negative of that covariance. He applied the measure to NYSE stocks and found spreads were larger for smaller firms. The paper also explains why measured short-term reversals partly reflect bid-ask bounce rather than genuine mean reversion.
See it drawn
Original diagrams for the ideas on this page. Illustrative, not real market data.
What you can use
- Bid-ask bounce creates fake mean reversion in transaction prices; be skeptical of short-term reversal backtests on trade data.
- You can estimate trading costs for any market from price data alone using Roll's formula.
- Effective spreads are much larger in small stocks, which is where most 'anomaly' returns live.
Caveats
The estimator fails (produces an imaginary spread) when autocorrelation is positive, which happens often in practice. Based on 1963 to 1982 data when spreads were far wider than today.
Tags: microstructure, bid-ask-spread, transaction-costs, estimation
Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.