Roll Spread

Calculate the Roll (1984) implied bid-ask spread, per asset.

Roll’s model shows that, under a stylized microstructure model in which the true (efficient) price follows a random walk and observed trade prices randomly bounce between the bid and the ask, the effective spread can be backed out purely from the serial covariance of consecutive price changes, without needing any actual quote data. If the estimated covariance is zero or positive, no valid estimate can be backed out and NaN is returned instead.

The Roll measure is used when no quote data is available, typically for less liquid stocks or historical studies. On daily closes of liquid large caps it mostly picks up price noise rather than the bid-ask bounce, and in trending periods the autocovariance is positive and no estimate exists, so treat it as a rough, relative measure.

For more information about the method, see the following paper:

• Roll, R. (1984). “A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market.” The Journal of Finance, 39(4), 1127-1139.

The formula is as follows:

Where P is the Close price, ΔP_t = P_t - P_(t-1) and Cov the sample autocovariance (ddof=1) of consecutive price changes; a covariance of zero or above gives NaN.

Also known as: Roll’s implied spread, Roll measure.

Roll Spread in Python or via the MCP

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_roll_spread as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["KO", "PEP", "PG"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2021-01-01",
    end_date="2025-12-31",
)

toolkit.risk.get_roll_spread()

Or, after setting up the Finance Toolkit MCP, ask:

Which returns:

Parameters

get_roll_spread accepts the following parameters.

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