Acquired bid ask spread

What Is Acquired Bid-Ask Spread?

The acquired bid-ask spread is a concept in market microstructure that represents the portion of the quoted bid-ask spread effectively captured by a liquidity provider over a specific transaction or period. It is essentially the actual revenue earned by market makers or other liquidity suppliers after accounting for potential adverse price movements that occur between the time a quote is made and a trade is executed. This metric falls under the broader category of transaction costs in financial markets.

The bid-ask spread itself is the difference between the highest price a buyer is willing to pay (bid price) and the lowest price a seller is willing to accept (ask price) for a security²⁶. Market makers facilitate trading by simultaneously quoting both a bid and an ask, profiting from the spread. The acquired bid-ask spread, also known as the realized spread, refines this by considering how much of that initial spread is truly realized by the liquidity provider after subsequent price changes.

History and Origin

The concept of decomposing the bid-ask spread into its various components, including the portion attributable to liquidity provision, has evolved with the study of market microstructure. Early models of the bid-ask spread often focused on its role as a measure of liquidity costs and how it covered the market maker's expenses, such as order processing, inventory holding, and adverse selection²⁴, ²⁵.

With the rapid advancements in technology and the rise of electronic trading in the late 1990s, the dynamics of price formation and transaction costs became a subject of deeper scrutiny²², ²³. Researchers began to develop more sophisticated models to empirically measure and decompose the bid-ask spread, recognizing that the quoted spread didn't always reflect the true profit for market makers due to price movements driven by new information or order imbalances²¹. The acquired bid-ask spread, or realized spread, emerged as a way to quantify the profit that a liquidity provider actually "acquires" from facilitating a trade, taking into account the post-trade price adjustments. This more nuanced view allows for a better understanding of the profitability of market making and the true cost of liquidity.

Key Takeaways

• The acquired bid-ask spread, also known as the realized spread, measures the actual revenue captured by a liquidity provider from a transaction.
• It accounts for adverse price movements that may occur after a trade is executed, which can erode the initial quoted spread profit.
• This metric is a component of overall transaction costs and provides insight into the profitability of market making activities.
• A higher acquired bid-ask spread indicates more profit captured by the liquidity provider per unit of volume traded.
• It contrasts with the simpler quoted spread, which is the immediate difference between the bid and ask prices at a given moment.

Formula and Calculation

The acquired bid-ask spread (often referred to as the "realized spread" in academic literature) quantifies the profit a liquidity provider gains from a round-trip transaction, adjusted for the price movement after the trade. It is typically calculated as twice the difference between the transaction price and a future reference price (often the midpoint of the bid and ask quotes a short time after the trade).

The formula for the acquired bid-ask spread, also known as the realized spread, for a single trade is:

For a buyer-initiated trade:

For a seller-initiated trade:

Alternatively, it can be defined relative to the effective spread:

Where:

• Transaction Price ((P_t)): The actual price at which the trade was executed.
• Midpoint Price before trade ((M_t)): The average of the best bid and ask prices just before the trade.
• Midpoint Price after trade ((M_{t+\Delta})): The average of the best bid and ask prices at a short interval (e.g., 5 minutes or 10 minutes) after the trade¹⁹, ²⁰. This later midpoint is considered a proxy for the security's fundamental value after any immediate price impact of the trade has dissipated¹⁷, ¹⁸.
• Effective Spread: A measure of the transaction cost from the perspective of the liquidity demander, calculated as twice the absolute difference between the transaction price and the midpoint price at the time of the order submission¹⁶.

The difference between the acquired bid-ask spread and the effective spread reflects the impact of adverse selection costs and inventory holding costs on the market maker's profitability¹⁴, ¹⁵.

Interpreting the Acquired Bid-Ask Spread

The acquired bid-ask spread provides crucial insight into the profitability of providing liquidity in a financial market. A positive acquired bid-ask spread indicates that the liquidity provider (e.g., a market maker) successfully captured a profit from facilitating the trade, even after accounting for any price movements. This profit is essentially the compensation for taking on the risk of providing immediacy and holding inventory¹², ¹³.

Conversely, an acquired bid-ask spread close to zero or negative suggests that the liquidity provider either broke even or incurred a loss on the transaction. This can occur due to significant adverse price movements that erase the initial quoted spread or due to informed trading, where the market maker trades with someone who has superior information, leading to the market moving against their position¹¹.

Analyzing the acquired bid-ask spread helps assess market quality and the efficiency of price discovery. In highly liquid and efficient markets with low adverse selection, the acquired bid-ask spread tends to be a significant portion of the total quoted spread, reflecting healthy profitability for liquidity providers. However, in less liquid markets or during periods of high market volatility, the acquired bid-ask spread can be lower or more volatile, indicating higher risks and potentially lower profitability for market makers¹⁰.

Hypothetical Example

Consider a hypothetical stock, "DiversiCo Inc." (DCSI), with the following market data:

• Initial Bid Price: $50.00
• Initial Ask Price: $50.05
• Initial Midpoint Price: ($50.00 + $50.05) / 2 = $50.025

Scenario 1: Buyer-Initiated Trade

An investor places a market order to buy 100 shares of DCSI. The trade executes at the ask price:

• Transaction Price: $50.05

Five minutes after the trade, new quotes appear:

• New Bid Price: $50.01
• New Ask Price: $50.06
• New Midpoint Price (after trade): ($50.01 + $50.06) / 2 = $50.035

To calculate the acquired bid-ask spread for this buyer-initiated trade:

Acquired Bid-Ask Spread = (2 \times (\text{Transaction Price} - \text{Midpoint Price after trade}))
Acquired Bid-Ask Spread = (2 \times ($50.05 - $50.035))
Acquired Bid-Ask Spread = (2 \times $0.015)
Acquired Bid-Ask Spread = $0.03

In this case, the market maker acquired $0.03 per share from this transaction, meaning they captured a portion of the initial spread.

Scenario 2: Seller-Initiated Trade

An investor places a market order to sell 100 shares of DCSI. The trade executes at the bid price:

• Transaction Price: $50.00

Five minutes after the trade, new quotes appear:

• New Bid Price: $49.98
• New Ask Price: $50.03
• New Midpoint Price (after trade): ($49.98 + $50.03) / 2 = $50.005

To calculate the acquired bid-ask spread for this seller-initiated trade:

Acquired Bid-Ask Spread = (2 \times (\text{Midpoint Price after trade} - \text{Transaction Price}))
Acquired Bid-Ask Spread = (2 \times ($50.005 - $50.00))
Acquired Bid-Ask Spread = (2 \times $0.005)
Acquired Bid-Ask Spread = $0.01

Here, the market maker acquired $0.01 per share, reflecting a smaller realized profit due to the slight downward movement of the market after the sell order. This example illustrates how the acquired bid-ask spread considers the impact of subsequent price movements on the market maker's actual profitability. This is distinct from the initial order book spread.

Practical Applications

The acquired bid-ask spread is a crucial metric with several practical applications across various facets of financial markets:

• Market Maker Profitability Analysis: For liquidity providers and market-making firms, the acquired bid-ask spread is a direct measure of their profitability on individual trades. By tracking this metric, they can assess the effectiveness of their quoting strategies, manage inventory risk, and optimize their trading algorithms. A consistently low or negative acquired bid-ask spread might signal issues such as aggressive competition or significant adverse selection.
• Transaction Cost Analysis for Investors: While primarily a market maker's perspective, understanding the acquired bid-ask spread indirectly benefits institutional investors and portfolio managers. High acquired spreads for market makers can imply higher implicit costs for investors "crossing the spread." Analyzing how the acquired bid-ask spread behaves across different securities and market conditions can inform order execution strategies, helping investors minimize their overall trading costs⁹.
• Market Quality Assessment: Regulators and exchanges use metrics related to bid-ask spreads, including the acquired bid-ask spread, to assess market quality. A healthy acquired bid-ask spread environment, where market makers are adequately compensated for providing liquidity, encourages their participation, leading to more robust and liquid markets. Conversely, consistently narrow or negative acquired spreads might signal a lack of incentive for liquidity provision, potentially leading to wider quoted spreads and reduced market depth. Historical data on bid-ask spreads, available through various financial databases, can be used for such analysis⁸.
• Academic Research and Model Validation: The acquired bid-ask spread is a fundamental concept in academic research within market microstructure. Researchers use it to empirically test theories related to the components of the bid-ask spread, such as adverse selection and inventory costs⁷. This helps refine theoretical models of price formation and market behavior.

Limitations and Criticisms

While the acquired bid-ask spread offers valuable insights into the profitability of liquidity provision, it comes with certain limitations and criticisms:

• Proxy for Fundamental Value: A primary criticism is its reliance on a "post-trade midpoint price" as a proxy for the underlying fundamental value of a security after a trade⁶. This assumes that a short period after the trade, the market price has fully adjusted to any new information conveyed by the trade and that this adjusted midpoint accurately reflects the true value. However, in highly volatile markets or for illiquid securities, the market may not fully absorb information or stabilize quickly, leading to an imperfect proxy⁵.
• Arbitrary Time Horizon: The choice of the time interval ((\Delta)) for determining the post-trade midpoint is often arbitrary (e.g., 5 minutes or 10 minutes)⁴. Different time horizons can yield different acquired bid-ask spread values, potentially affecting the interpretation of market maker profitability or transaction costs. There is no universally agreed-upon optimal time window, and the appropriate interval may vary depending on the asset class and market characteristics.
• Bias in Discrete Markets: In markets with discrete price increments (e.g., penny increments for stocks), the effective bid-ask spread measured relative to the midpoint can overstate the true effective spread. This bias can be significant, especially for low-priced stocks. This issue also impacts the acquired bid-ask spread, as it is derived from these spread measures³.
• Doesn't Capture All Market Maker Costs: The acquired bid-ask spread primarily focuses on the direct profit from crossing the spread. It does not explicitly account for all the operational costs, technological investments, or regulatory burdens that market makers face. These indirect costs can significantly impact the overall profitability of a market-making operation, even if the acquired bid-ask spread appears healthy.
• Impact of High-Frequency Trading: The prevalence of high-frequency trading (HFT) and algorithmic strategies has altered market dynamics². These participants can quickly react to information, potentially eroding the acquired bid-ask spread for traditional market makers or making it more challenging to capture consistent profits from providing liquidity.

Acquired Bid-Ask Spread vs. Effective Bid-Ask Spread

The acquired bid-ask spread and the effective bid-ask spread are both critical measures in market microstructure, but they offer distinct perspectives on transaction costs and liquidity. The key difference lies in the reference point used to evaluate the trade's price.

While the effective bid-ask spread tells an investor what they paid for immediacy, the acquired bid-ask spread tells the market maker what they earned after the dust settled. Both are essential for a comprehensive understanding of market efficiency and the true costs associated with trading.

FAQs

What does "acquired" mean in the context of a bid-ask spread?

"Acquired" in this context refers to the portion of the bid-ask spread that a liquidity provider, such as a market maker, actually earns or "acquires" as profit after accounting for any price changes that occur shortly after a trade is executed. It's a measure of their realized revenue from facilitating a transaction.

How is the acquired bid-ask spread different from the "quoted spread"?

The quoted spread is the simple difference between the current bid and ask prices at any given moment. The acquired bid-ask spread, also known as the realized spread, is a more refined measure that considers the actual transaction price and how the market's midpoint price moves after the trade. It accounts for potential losses due to new information entering the market or inventory imbalances, giving a truer picture of the market maker's profit¹.

Why is the acquired bid-ask spread important for market makers?

For market makers, the acquired bid-ask spread is a crucial metric for evaluating the profitability of their trading strategies. It helps them understand how much they truly earn from providing liquidity and whether they are effectively managing risks like adverse selection. Monitoring this allows them to adjust their pricing models and inventory management to optimize returns.

Can the acquired bid-ask spread be negative?

Yes, the acquired bid-ask spread can be negative. This occurs when the market moves significantly against the market maker's position after a trade, causing them to lose more on the subsequent price adjustment than they initially gained from the bid-ask spread. This often happens when trading with informed investors or during periods of high information asymmetry.

How does the acquired bid-ask spread relate to transaction costs?

The acquired bid-ask spread is a key component of the overall transaction costs from the perspective of the liquidity provider. While investors incur transaction costs when they cross the spread, the acquired bid-ask spread measures the revenue collected by those supplying the liquidity. A healthy acquired bid-ask spread is necessary to incentivize market makers to provide liquidity, which in turn helps keep overall trading costs lower for investors in the long run.