Realized Spread

The realized spread is formally defined as 2 * d * (P_exec - P_future) for a round-trip trade, where d is the trade direction (+1 for a buy, -1 for a sell).

• P_exec: The price at which the market maker's quote was hit or lifted.
• P_future: The midpoint price at a specified future time horizon (typically 5 minutes).
• A positive realized spread indicates the market maker earned revenue after the price moved back toward the fundamental value.
• A negative realized spread signals adverse selection—the price moved against the market maker and did not revert.

The realized spread decomposes the total effective spread into a revenue component and a loss component.

• Effective Spread: The total double-sided cost paid by a liquidity taker, calculated as 2 * d * (P_exec - P_midpoint).
• Adverse Selection Cost: The portion of the effective spread lost to informed traders, calculated as Effective Spread - Realized Spread.
• A wide effective spread is meaningless if the realized spread is near zero; it implies all potential revenue is being lost to toxic flow.
• Market makers optimize for a high ratio of realized spread to effective spread.

The choice of the future time horizon for measuring P_future is critical and non-trivial.

• 5-Minute Horizon: The industry standard. It balances capturing mean reversion against introducing noise from new information events.
• 1-Minute Horizon: Captures very fast mean reversion but may miss slower inventory effects.
• Trade-Time Horizon: Uses the midpoint at the time of the next trade, linking the realized spread directly to the next market event.
• Selecting a horizon that is too long introduces fundamental risk, contaminating the realized spread with price moves unrelated to the original trade's information content.

The realized spread is not a pure measure of information asymmetry; it is entangled with inventory risk compensation.

• After executing a trade, a market maker holds a non-zero inventory position that is exposed to price volatility.
• A portion of the realized spread compensates the market maker for bearing this inventory risk until the position is unwound.
• To isolate pure adverse selection, researchers often control for inventory risk using a cross-sectional regression of realized spreads against inventory holding periods and volatility.
• In highly volatile markets, a positive realized spread may reflect inventory risk premiums rather than a lack of informed trading.

Realized spreads vary systematically across market capitalization and trading volume.

• Large-Cap Stocks: Typically exhibit small but consistently positive realized spreads due to high competition and low information asymmetry.
• Small-Cap Stocks: Often have wider effective spreads but a lower percentage realized, as informed trading is more prevalent.
• Exchange-Traded Funds (ETFs): Generally show high realized spreads relative to effective spreads because the underlying basket arbitrage mechanism rapidly corrects pricing errors.
• Academic studies (e.g., Hendershott, Jones, and Menkveld, 2011) show that algorithmic trading tightens effective spreads but can compress realized spreads by competing away the revenue.

The realized spread is the empirical counterpart to the theoretical Roll (1984) model of the bid-ask bounce.

• The Roll model implies that under pure transaction costs with no information asymmetry, the effective spread equals the realized spread.
• Serial covariance of price changes is used in the Roll model to estimate the implied spread; the realized spread directly measures it.
• A divergence where Effective Spread > Realized Spread empirically validates the Glosten-Milgrom (1985) model of adverse selection.
• This relationship allows researchers to quantify the breakdown of the pure transaction cost assumption in real markets.

The primary risk that defines the realized spread. Adverse selection occurs when a market maker trades with a counterparty possessing superior information about the asset's future price direction. The market maker buys from an informed seller just before the price falls, or sells to an informed buyer just before the price rises. The realized spread captures this cost by measuring the difference between the trade price and the future midpoint price (often 5 minutes post-trade). A negative realized spread indicates the market maker was adversely selected and lost money on the round-trip transaction.

A measure of execution quality that compares the trade price to the prevailing midpoint at the time of order arrival. Unlike the realized spread, the effective spread does not account for post-trade price movement. The relationship between the two is critical:

• Effective Spread = 2 × |Trade Price - Midpoint at Trade|
• Realized Spread = Effective Spread - Adverse Selection Cost A wide effective spread that collapses into a negative realized spread signals toxic order flow and unsustainable market making.

Order flow from a counterparty that is likely to be informed, meaning it will move adversely against a market maker's position shortly after the trade. Toxic flow is the mechanism through which adverse selection manifests. Market makers use the realized spread as a real-time diagnostic to detect toxic flow:

• Consistently negative realized spreads indicate the market maker is trading with informed counterparties
• This triggers defensive actions: widening quotes, reducing size, or withdrawing from the market entirely
• VPIN (Volume-Synchronized Probability of Informed Trading) is a related metric for quantifying toxicity

The dominant order matching rule in electronic limit order books that determines who trades first. Orders are ranked first by price (best bid or offer wins) and then by time of entry (earliest order at that price wins). This rule directly impacts the realized spread because:

• Market makers compete for queue position to capture the spread
• The realized spread must compensate for the risk of being picked off by faster traders who react to new information before the market maker can cancel stale quotes
• In a price-time priority market, speed is a defense against adverse selection

A pricing structure where exchanges provide a rebate to liquidity makers (limit orders that rest on the book) and charge a fee to liquidity takers (market orders that execute immediately). The realized spread calculation must be adjusted for these fees to reflect true economic profit:

• Net Realized Spread = Realized Spread + Maker Rebate - Taker Fee
• In inverted venues, makers pay a fee and takers receive a rebate, flipping the incentive structure
• Fee arbitrage across venues with different maker-taker schedules is a core HFT strategy that compresses realized spreads

The difference between the theoretical decision price of a trade and the actual execution price achieved, including all costs. For institutional investors executing large orders, the realized spread is a component of implementation shortfall:

• Implementation Shortfall = Commissions + Fees + Market Impact + Delay Cost + Opportunity Cost
• The realized spread represents the liquidity cost embedded in the bid-ask spread
• Minimizing implementation shortfall requires understanding when realized spreads are wide (high cost) versus narrow (low cost) across different venues and times of day