Trade Strategy and Execution: formula sheet

Key formulas

Bid-ask spread

Spread = Ask − Bid; Percentage spread = (Ask − Bid) ÷ Midpoint

A market order buying and then selling pays roughly the full spread. Midpoint = (Ask + Bid) ÷ 2.

Limit order execution rule

Buy limit fills at limit price or lower; sell limit fills at limit price or higher

A limit order never fills at a worse price than the limit.

Stop order trigger

Sell stop is placed below the current price; buy stop is placed above it

Once triggered, a stop becomes a market order; a stop-limit becomes a limit order.

Order priority in an order book

Price priority first, then time priority (often then display or size)

Best-priced orders trade first; ties go to the earlier order.

Order choice trade-off

Market order: certainty of execution high, price control low. Limit order: price control high, certainty low

Use this to justify any order-type recommendation.

Implementation shortfall (total)

IS = Explicit costs + Delay cost + Market impact + Opportunity cost

Express per share, in currency, or as a percent of the paper trade value. Keep the same basis for every part.

Delay cost (buy order)

Delay cost = Shares executed × (Arrival price − Decision price)

Some texts apply delay to the full order including unfilled shares and treat unfilled shares under opportunity cost. Follow the vignette's definition. For a sell, reverse the sign: (Decision price − Arrival price).

Market impact (buy order)

Market impact = Shares executed × (Average execution price − Arrival price)

For a sell, use (Arrival price − Average execution price).

Opportunity cost (buy order)

Opportunity cost = Unfilled shares × (Final price − Decision price)

Final price is the close or the price when the order was cancelled. For a sell, use (Decision price − Final price).

Explicit costs

Explicit costs = Commissions + Fees + Taxes

Add them as a cost. Do not include the spread here; spread is implicit.

Implementation shortfall as a percent

IS % = Total IS ÷ (Shares in full order × Decision price)

The base is the paper portfolio value of the full intended order.

Implementation shortfall (buy)

IS = (Average execution price − Decision price) ÷ Decision price

For a sell, reverse the sign. The full measure also includes missed-trade opportunity cost and explicit costs.

VWAP benchmark

VWAP = Σ(Price × Volume) ÷ Σ(Volume)

Computed over the trading period. Buying below VWAP is favourable; selling above is favourable.

TWAP benchmark

TWAP = average of prices at equal time intervals

Each interval gets equal weight regardless of volume.

Participation rate

Participation rate = Order shares traded ÷ Total market volume in the period

Higher participation means faster completion and more market impact.

Urgency rule

Higher urgency / alpha decay / risk aversion → faster, front-loaded, more aggressive

Lower urgency → slower, passive, schedule-based (VWAP, TWAP).

Implementation shortfall (per share, buy)

IS = (Execution price − Decision price) per share, plus explicit costs; for a sell the sign reverses

Total IS = delay + trading (impact) + opportunity cost + explicit costs. Express in currency or basis points of the paper value.

Cost versus arrival price in basis points (buy)

Cost (bp) = (Average execution price − Arrival price) ÷ Arrival price × 10,000

For a sell use (Arrival − Execution) ÷ Arrival × 10,000. Positive means cost.

VWAP

VWAP = Σ(price × volume) ÷ Σ(volume)

Computed over the trading interval, normally on market volume. Slippage to VWAP for a buy = (Execution − VWAP) ÷ VWAP.

Opportunity cost of unfilled shares (buy)

(Unfilled shares) × (Closing or end price − Decision price)

Only unfilled shares count. A rising price on an unfilled buy is a loss.

Benchmark rule

Decision price (IS) → full cost incl. delay before arrival; Arrival price → impact and trading cost from desk arrival, excludes pre-arrival delay; VWAP → intraday execution vs market; Close → can be gamed

Match the benchmark to the manager's intent and urgency.

Quick revision

• Order choice trades off certainty of execution against price control: market orders favour speed, limit orders favour price.
• Liquidity is judged by spread, depth and resilience; low liquidity raises impact cost.
• Implementation shortfall compares the actual portfolio result with a paper portfolio traded at the decision price.
• Shortfall components: explicit costs, realised profit or loss (which includes the market impact element), delay cost and missed trade opportunity cost.
• Market impact is not a separate fourth component; it is captured within realised profit or loss.
• Delay cost comes from price movement between decision and order placement or execution.
• Unfilled shares create opportunity cost measured against the benchmark price at the end of the period.
• Fast trading raises market impact and lowers price-drift risk; slow trading does the opposite.
• Informed, urgent and alpha-decaying trades usually call for faster, more aggressive execution.
• Uninformed or low-urgency trades can be spread over time to reduce impact.
• Algorithms such as VWAP and TWAP follow a schedule; implementation shortfall algorithms balance impact and risk.
• Best execution is about the whole process and total cost for the client, not just the lowest commission.
• Judge execution against a benchmark that matches the trade's goal, and show every calculation step.

Common mistakes

• Saying a limit order guarantees execution at the limit price. Fix: Remember: limit means price certainty if filled, but no certainty of a fill.
• Thinking a stop order guarantees the stop price. Fix: A stop becomes a market order when triggered, so it can fill at a worse price in a fast market. Only a stop-limit controls price.
• Getting the sign wrong on a sell order Fix: Ask whether the price moved against you. For a sell, a falling price is a cost, so reverse the subtraction.
• Measuring market impact from the decision price Fix: Impact uses arrival price to average execution price. Delay uses decision price to arrival price.
• Recommending VWAP for an urgent, information-driven trade. Fix: VWAP spreads trading across the day, so alpha may decay. Use arrival price when urgency is high.
• Saying TWAP follows the volume pattern. Fix: TWAP uses equal time slices. VWAP follows expected volume.
• Treating best execution as the lowest commission or the best price on every trade. Fix: State that best execution is a process to get the most favourable overall outcome for the client, considering all costs and circumstances.
• Getting the sign wrong for sells. Fix: For a sell, cost is benchmark minus execution. Write the sign rule before calculating.

Exam tips

• For recommendation questions, always name urgency, information and liquidity, then choose. A bare order name earns few points.
• Read the command word in bold: 'identify' needs a name, 'justify' needs a reason, 'calculate' needs a number shown clearly.
• Give only the number of reasons asked for; extra responses are not evaluated, and order matters.
• Link the order to the client: an index manager is patient, an alpha-driven manager is urgent.
• Write the trade-off in both directions when asked to compare orders: what you gain and what you give up.
• Read the command word. If it says calculate, show each component and the sum. A correct number alone can earn full credit, but written steps protect you if a slip occurs.
• In item sets, check how the vignette defines delay cost. Some apply it to executed shares only, others to the full order. Use the stated definition.
• For explain or discuss questions, link the cost to a cause: urgency raises market impact, slow trading raises delay and opportunity cost.