What causes bid-ask bounce?

Successive trades can alternate between the bid and ask as the initiating side changes. The transaction price moves even when the midpoint changes less.

Does bid-ask bounce mean the market is inefficient?

No. It can arise from the mechanics of trading across a spread. The classic Roll model assumes efficient fundamental-price changes while transaction costs create the observed negative dependence.

What if the Roll covariance is positive?

The square-root expression is not real. Report the estimator as unavailable for that sample rather than converting the result to a zero spread.

Can Pine Script calculate the true effective spread?

Not from OHLC bars alone. It can implement a price-only proxy. Direct effective-spread analysis needs suitable quote and trade data plus a documented trade-direction method.

Bid-ask bounce: why transaction prices can alternate

Bid-ask bounce occurs when successive transactions alternate between prices near the bid and ask even if the underlying value changes little. That alternation can create negative first-order covariance in price changes and inflate volatility measured from very short return intervals.

Observed input: Successive transaction prices
Classic signature: Negative lag-one covariance of price changes
Main limit: Price movement also reflects information and inventory

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Key Takeaways

Transaction prices can move between bid and ask without the midpoint moving by the same amount.
Roll's estimator infers an effective spread from negative serial covariance.
The estimator relies on market-efficiency and stationarity assumptions.
Quoted bid and ask data is preferable when the actual spread is available.

The bounce mechanism

A buyer-initiated marketable order often trades near the ask. A seller-initiated marketable order often trades near the bid. If the next trade switches side while the midpoint is stable, the observed transaction-price change reverses. Repeated switching can look like short-horizon mean reversion.

The Roll price-only estimator

Richard Roll derived an implicit spread estimate from the first-order covariance of transaction-price changes. The real-valued expression requires a negative covariance. A non-negative sample covariance is not evidence of a zero spread; it means the simple estimator does not produce a valid estimate under that sample.

Roll estimator

effectiveSpread = 2 × sqrt(-Cov(ΔPₜ, ΔPₜ₋₁))
condition: Cov(ΔPₜ, ΔPₜ₋₁) < 0

Assumptions and competing effects

The original model assumes an informationally efficient market and a stationary distribution over the estimation window. Price discreteness, clustered trades, changing spreads, serially correlated fundamental returns, stale prices, and different market regimes can bias the result.

A Pine Script proxy has a narrow claim

Pine Script can calculate lagged covariance from the price series available on the chart and display when the Roll condition holds. Bar closes are not transaction ticks, so the output is a price-series proxy rather than a direct bid-ask measurement. Pineify can generate that code, but it cannot add missing quote history.

Generate a clearly labeled Roll proxy

Define the price field, covariance window, missing-value behavior, and the non-negative covariance state. Pineify can generate editable Pine Script that plots the proxy and its validity flag. Review the calculation against your data source.

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Sources and verification

Last verified: 2026-08-17

Roll 1984, A Simple Implicit Measure of the Effective Bid-Ask Spread

This page is educational and does not provide investment advice. The methods described are diagnostics or estimates, not trading signals. Results depend on data quality, sampling, market structure, and model assumptions.