Roll's Estimator
Market Microstructure glossary · Spread Economics & Liquidity Measurement
Definition
A method of estimating the bid–ask spread from the negative autocovariance of transaction price changes.
Roll's Estimator in plain English
Every stock has two prices at once: a slightly lower price you can sell at and a slightly higher price you can buy at — the gap between them is the "bid-ask spread," basically the dealer's cut. Roll's Estimator is a clever trick for figuring out that hidden spread using only the record of past trade prices, without ever seeing the actual buy/sell quotes. It works because that spread makes prices bounce: a trade at the lower sell price is often followed by one at the higher buy price and back again, creating a see-saw pattern (statisticians call this "negative autocovariance" — consecutive price changes tend to point in opposite directions). By measuring how strong that back-and-forth bounce is, Roll's formula reverse-engineers the size of the spread.
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