Quoted spread
spread = a - bThe spread is the round-trip price gap faced by an immediate buyer and seller.
Foundations
Bid–Ask Spread
The gap between what the market will pay you and what it will charge you — your immediate cost of trading.
Mental model
Every immediate trade crosses a spread that measures the market's price of immediacy.
Quotes come in pairs: the bid is the best price you can sell at; the ask is the best price you can buy at. The mid is just their average and is usually not tradable.
If you buy at the ask and immediately sell at the bid, you lock in a loss equal to the spread — this is the friction every trade must overcome.
Explore the mechanism
How much value is lost when a position must be entered and exited immediately?
Quotes come as a bid–ask pair: bid is where you can sell, ask is where you can buy. The dashed line is the mid price (average of bid and ask), a reference level you almost never trade at. The coloured band is the friction zone.
Per-unit spread metrics
Half-spread (one side) ≈ 0.500 (0.500% ≈ 50.0 bps)
Round-trip spread cost (buy then sell) ≈ 1.000 per unit
Position notional ≈ 10000.00
Round-trip cost on this size ≈ 100.00
One-day σ move ≈ 1.500 per unit. Spread is 0.67× that.
Interpretation
If you buy at the ask, value is marked to the mid: you are instantly down by roughly half the spread. If you sell at the bid, it is the same story in the other direction. A full round-trip (buy then sell) burns roughly one full spread.
The sliders show how this friction scales with position size and typical daily volatility. If the spread is a big fraction of a one-day σ move, small price moves are mostly eaten by costs: you need a meaningful move just to break even.
In control-system language, the spread is a deadband around the setpoint: inside this band, small “signals” (price wiggles) cannot be turned into actionable profit because friction dominates. Tight spreads mean a thin deadband and high effective liquidity; wide spreads are thick friction zones.
UNDERSTAND
What to notice
Spreads widen when liquidity is low or uncertainty is high, and they can explode in stressed markets.
Ignoring spreads (and other costs) makes backtests structurally over-optimistic, especially for high-turnover strategies.
The quantitative structure
Notation
b- best bid
a- best ask
m- quoted midpoint
Midpoint
m = (a + b) / 2The midpoint is a reference between executable quotes, not a guaranteed trade price.
A small example
Buying at 100.10 and selling immediately at 99.90
The best bid is 99.90 and the best ask is 100.10.
- Compute the spread: 100.10 - 99.90 = 0.20.
- Compute the midpoint: (100.10 + 99.90) / 2 = 100.00.
- An immediate round trip loses 0.20 per unit before fees.
ResultThe quoted round-trip cost is 0.20 per unit, or 20 basis points of the 100.00 midpoint.
Where it appears
- estimating transaction costs in a backtest
- measuring market liquidity
- choosing between passive and aggressive execution
Where the intuition breaks
What this view leaves out
- The quoted spread does not capture market impact, hidden liquidity, fees, or the price movement caused by a large order.
Common mistakes
“The midpoint is a price at which you can always trade.”
Not quite.The midpoint is a reference value; executable prices are normally the bid or ask and depend on available depth.
Where this concept sits
Follow the strongest prerequisites, applications, extensions, and contrasts.
Connections for Bid–Ask Spread
Bid–Ask SpreadYOU ARE HERE
Used byOptimal Execution as Stochastic ControlExecution strategies trade off urgency and market impact against spread and liquidity costs.
Used byOrder Types (Market, Limit, Stop)Market and limit orders interact directly with quoted bid–ask prices and available liquidity.
MeasuresLiquidity vs Solvency RiskBid–ask spread is one observable indicator of market liquidity and transaction friction.
Used by · Optimal Execution as Stochastic Control
Execution strategies trade off urgency and market impact against spread and liquidity costs.
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