CFA Level III · Level III Core

Trading Costs and Electronic Markets: formula sheet

Full chapter guide

Key formulas

Quoted bid-ask spread: Spread = Ask − Bid; Percentage spread = (Ask − Bid) ÷ Midpoint. Midpoint = (Ask + Bid) ÷ 2.
Effective spread: Effective spread = 2 × |Trade price − Midpoint|; Midpoint is taken at the time of the trade. Use the full-spread version to compare with the quoted spread. Half-spread is |Trade price − Midpoint|.
Implementation shortfall (total): IS = Paper portfolio return − Actual portfolio return; This is the return-based form, so the result is a return (percentage or basis points). The component sum below is in currency: explicit costs + realized (execution) cost + delay cost + missed trade opportunity cost. To convert the currency total to basis points, divide by the order value at the decision price and multiply by 10,000.
Delay cost (total): Delay cost = Shares executed × (Arrival price − Decision price) for a buy; For a sell, reverse the sign so that a falling price is a cost. Arrival price is the price when the order reaches the market. For a per-share figure, drop the share count.
Realized (execution) cost: Realized cost = Shares executed × (Average execution price − Arrival price) for a buy; Includes market impact and spread. For a sell use (Arrival price − Average execution price).
Missed trade opportunity cost: Opportunity cost = Unexecuted shares × (Cancel price − Decision price) for a buy; Cost is positive if the price rose for a buy, or fell for a sell. Cancel price is the price when the order is cancelled.
Explicit costs: Explicit = Commissions + Fees + Taxes; Add these to the other components to reach total implementation shortfall.
Implementation shortfall (total): IS = Explicit costs + Realized profit/loss (price cost on filled shares vs decision price) + Delayed-trade (opportunity) cost on unfilled shares; Paper portfolio assumes the full order trades at the decision price with no costs. IS is the gap between the paper and actual portfolios. Express IS as a positive cost, in money or as % of the paper trade value. The realized price cost on filled shares includes the delay cost and market impact. For a buy, paying more than the decision price is a cost. Direction reverses for a sell.
Delay cost (buy): Delay cost = Shares executed × (Arrival price − Decision price); Use the sign that makes adverse moves a cost. For a sell, use (Decision price − Arrival price).
Market impact (buy): Market impact = Shares executed × (Average execution price − Arrival price); Measures the cost of your own trading after the order reached the market.
Opportunity cost (unfilled, buy): Opportunity cost = Unexecuted shares × (Closing/cancel price − Decision price); Positive when the price rose, so the missed shares gained value. Use the same price convention as the question.
VWAP: VWAP = Σ(Price × Volume) ÷ Σ(Volume); Market-wide VWAP over the period is the usual benchmark. Compare the average fill price with it.
Cost vs benchmark in basis points: Cost (bps) = (Execution price − Benchmark price) ÷ Benchmark price × 10,000 for a buy; Flip the sign for a sell so that a worse price is a positive cost.
Order-driven matching priority: Price priority first, then time priority (often then size or display rules); Typical rule. Exact priority rules vary by venue, so use the rule given in the vignette.
Quoted bid-ask spread: Spread = Ask − Bid; This is the dealer's gross compensation per round trip and a measure of implicit cost.
Half-spread cost of a market order: Cost per share ≈ (Ask − Bid) ÷ 2; Approximates the cost of crossing the spread against the midpoint. Valid when the trade executes at the quote.
Midpoint: Midpoint = (Bid + Ask) ÷ 2; Many dark pools price trades at the midpoint of the lit market quote, which saves the half-spread.
Venue trade-off rule: Less pre-trade transparency → lower information leakage but higher non-execution risk; A qualitative rule to use when recommending dark versus lit venues.
TWAP slice size: Slice per interval = Total order size ÷ Number of equal time intervals; TWAP ignores volume patterns. Use it when volume is hard to predict or you want a simple, even schedule.
VWAP: VWAP = Σ(price × volume) ÷ Σ(volume); A VWAP algorithm targets this benchmark by trading in proportion to expected volume in each interval.
VWAP slice size: Slice in interval = Total order × (Expected volume in interval ÷ Expected total volume); Uses the forecast volume profile, so accuracy depends on the forecast.
Percentage of volume: Order size traded = Participation rate × Market volume; Finishing time depends on actual volume, so completion is not guaranteed.
Implementation shortfall (buy): Shortfall per share = Execution price − Decision (arrival) price; For a sell, reverse the sign. Include delay, impact, fees and unexecuted portions when the question asks for total shortfall.
Total trading cost: Total cost = Explicit costs + Implicit costs; Explicit: commissions, fees, taxes. Implicit: spread, market impact, delay (opportunity) cost.
Market vs limit order trade-off: Market order: execution certain, price uncertain. Limit order: price controlled, execution uncertain.; Use this one line to justify most order choices.
Urgency rule: Higher urgency, larger information value, or higher price risk → trade faster and accept more impact. Lower urgency, high liquidity needs, or high impact → trade slower.; A guide, not a fixed law. Always apply it to the facts given.
Half-spread cost of a market order: Cost per share ≈ (Ask − Bid) ÷ 2, measured against the midpoint; A buy at the ask pays about half the spread above the midpoint.

Quick revision

Explicit costs are visible, such as commissions and fees; implicit costs are not, such as spread, market impact and delay.
Wider spreads and thinner depth signal lower liquidity and higher cost.
Implementation shortfall compares the actual portfolio result with a paper portfolio traded at the decision price.
Its parts include explicit costs, realised profit or loss, delay cost, and missed trade opportunity cost.
Check the sign and the basis of each component before adding them up.
Transaction cost analysis compares execution with benchmarks, so the benchmark you choose affects the conclusion.
Electronic markets match orders using rules, and the order book shows resting buy and sell interest.
Algorithmic trading uses rules to split and time orders to cut impact.
High-frequency trading relies on speed and tiny price gaps, and it raises questions about fairness and stability.
Urgent or information-based trades favour speed and accept higher impact; patient trades favour lower-cost, passive execution.
Market orders give certainty of execution but not price; limit orders give price control but not certainty of execution.
Best execution is a client-focused duty, so link trade choices to the client's objectives.

Common mistakes

Applying opportunity cost to all shares instead of only the unexecuted shares. Fix: Split the order first. Executed shares go to delay and realized cost. Unexecuted shares go to opportunity cost.
Using the quoted spread as the effective spread. Fix: Effective spread uses the actual trade price against the midpoint at trade time, doubled. Quoted spread uses only bid and ask.
Ignoring unfilled shares and omitting opportunity cost Fix: Always compute ordered minus filled. If shares were not traded, price them at the final or cancel price against the decision price.
Using the wrong sign for sell orders Fix: Ask whether the price move hurt the client. For a sell, a lower execution price than the benchmark is a cost.
Saying dark pools always give better execution. Fix: Always state both sides: less leakage and impact, but non-execution risk and reduced transparency.
Treating ECNs and dark pools as the same thing. Fix: An ECN is a type of ATS that displays and matches orders. A dark pool hides orders before the trade. Some venues can be one and not the other.
Treating TWAP and VWAP as the same thing. Fix: TWAP slices by equal time. VWAP slices by expected volume. Say which input each uses.
Recommending VWAP for an urgent, information-driven order. Fix: VWAP spreads trades across the day and leaves the order exposed to drift. Choose arrival price or a faster approach when urgency is high.
Saying a limit order guarantees a better price and fills. Fix: Say a limit order guarantees only the price limit, not that it will execute. It may miss the market.
Recommending a market order for a large order in an illiquid stock. Fix: Check size versus depth. Large orders in thin markets need slicing, hiding, algorithms or a block unless urgency is extreme.

Exam tips

Read the command word. If it says calculate, show each component line and type the number clearly. If it says discuss, link the cost to the trade urgency or liquidity given.
Always write the side (buy or sell) before any arithmetic. Sign errors are the most common lost marks.
When asked to recommend a trading approach, tie it to the cost trade-off: faster trading raises impact but cuts delay and opportunity cost.
In essay sets, answer only the number of responses asked for. Extra items are not marked.
Label prices as decision, arrival, execution and cancel on your working so a partial error can still earn credit.
Read the command word: calculate means show the number, explain or justify means give the reason in a short sentence tied to the vignette.
Write the decision, arrival and execution prices on your scratch sheet first. Most errors come from using the wrong price.
Always check whether the order is a buy or a sell before you set signs.