Implementation shortfall and unfilled orders

Compare an intended whole order with actual fills, separate missed trading from paid costs, and audit arrival-reference attribution.

34 minutes · intermediate · Original Poker4Quant lesson

What you will learn

Derive paper-minus-actual implementation shortfall for a partially filled intention, prove arrival-attribution invariance and construct a completion-versus-average-price counterexample.

Prerequisites: Quotes, spreads and reference prices · Book depth and execution curves · Inventory, cash and marked wealth · Net payoff and sunk costs

Fix the intended order before seeing its fills

A good average execution price can hide a failure to complete an intended trade. Imagine planning to acquire six units, receiving three cheaply, and watching the reference value rise before the deadline. A report containing only completed trades discards the very units whose absence matters. Implementation shortfall starts with the intention and compares two portfolios at one common horizon. CFA Institute introduces the paper-versus-actual comparison and separates costs of delay, execution and missed trading. We will construct those accounts directly rather than infer success from a favorable price statistic.

Assume a fictional asset, chips as currency, multiplier one and a fixed intention Q=6 at decision reference D=100. The arrival reference A=101 is recorded when execution begins; terminal reference H=106 is recorded at a prespecified deadline. Actual fills are two units at 99 and one at 102; three units remain unfilled. Each executed unit pays a half-chip fee. The paper account obtains all six instantly at D without fees. There are no funding costs, dividends, taxes, deposits, position changes or terminal liquidation trades. Reference marks are valuations. The paper trade is a comparison assumption, not evidence that six units really were available at 100. Keep that caveat attached to the result.

Build the paper and actual gains separately

For a buy, the paper gain at the deadline is Q(H−D)=6×6=36. Actual purchase spending is 2×99+102=300 and paid fees total 3/2. The three purchased units are valued at 3×106=318. Actual marked gain is therefore 318−300−3/2=33/2, or 16.5. Unspent cash does not vanish: using the same starting cash in both portfolios makes their wealth difference equal this difference in gains. Shortfall is paper gain minus actual gain: 36−33/2=39/2. Positive shortfall means the implementation trails its paper comparison. It does not mean the actual account lost money.

Let d=+1 for a buy and d=−1 for a sale. For sales, assume six units are already owned; measure gain relative to retaining those units until H. Selling q units at p gives incremental gain d q(H−p)=q(p−H). The paper sale uses D in place of p. No borrowing or short selling is needed. For either direction, paper gain is dQ(H−D), actual gain is d times the sum of q(H−p), minus paid fees F. This common orientation makes a lower sale price adverse and a higher purchase price adverse. Fees reduce actual gain in both directions, so their contribution to shortfall is always positive.

Derive the missing-quantity term without inventing a cash bill

Write n for total filled quantity and r=Q−n for the remainder. Subtract actual gain from paper gain: IS=d[Q(H−D)−sum q(H−p)]+F. Replace Q by n+r and collect terms. The nH terms cancel, leaving IS=d sum q(p−D)+d r(H−D)+F. Each filled unit contributes its signed price displacement from the decision reference. Each missing unit contributes the signed reference movement it did not capture. This missed-trade term is a counterfactual difference, not a commission charged by an exchange. It can be negative when not trading avoids an unfavorable move.

Our filled displacement is 2(99−100)+(102−100)=−2+2=0. The remainder contributes 3(106−100)=18. Add fees 3/2 to recover 39/2 independently of the two-portfolio calculation. If H falls to 96 with the same fills, the remainder term becomes −12 and shortfall becomes −21/2. Actual marked gain is then 3×96−300−3/2=−27/2, while paper gain is −24. Actual implementation loses chips yet outperforms paper by 10.5. A negative shortfall is relative outperformance, not a certificate of absolute profitability or a forecast that delaying orders is wise.

Move the arrival reference and preserve the identity

Insert A into every filled displacement: p−D=(A−D)+(p−A). Our chosen attribution convention is delay=d n(A−D), execution=d sum q(p−A), missed=d r(H−D), and explicit fees=F. The delay term applies to filled quantity only; the missed term already measures the entire decision-to-horizon movement for unfilled quantity. Multiplying delay by Q while leaving missed unchanged counts the unfilled decision-to-arrival movement twice. Other attribution conventions can be valid if all their terms are defined consistently. Derive the identity before importing a label from another report.

At A=101, delay is 3, execution is 2(99−101)+(102−101)=−3, missed is 18 and fees are 1.5. These sum to 19.5. Move only the attribution reference to A=104: delay becomes 12 and execution becomes −12. Their sum stays zero and total shortfall stays 19.5. Generally, raising A by a changes delay by d n a and execution by −d n a. This telescoping cancellation is an audit tool. Changing the decision reference D instead changes the paper portfolio itself: raising D by a changes shortfall by −d Q a. Arrival attribution and the original decision benchmark have fundamentally different roles.

Construct a whole-order comparison and state its limits

Compare a second stipulated execution plan that fills all six at 102, paying the same fee per unit. Its average fill price is 102, worse for a buyer than the starting plan’s 100. Yet actual gain is 6(106−102)−3=21, so shortfall is 36−21=15, lower than 19.5. Direct attribution gives filled displacement 12, no remainder and fees three. The extra completion captures enough of the stated terminal increase to outweigh the higher prices and fees. This is a deterministic comparison under supplied executions. It does not establish that a trader could choose either tape in a real market or that its prices would survive a larger order.

In the workshop cycle each intended unit between unfilled, executed at 99 and executed at 102. Freeze a plan, change its completion pattern, then reconcile both gains and all four shortfall components. Move the arrival reference without changing fills to test attribution invariance. Change direction or the deadline mark to see why the same completion pattern can help one objective and hurt another. With zero fills, the average fill price is undefined, actual incremental gain is zero and shortfall equals paper gain. With all units filled, terminal reference changes cancel from shortfall. Never divide by zero or treat the terminal mark as an executable exit. Single-order shortfall also mixes trading effects with unrelated market movement; it does not identify the causal impact of the trader.

Worked example

Intend to buy six at decision reference 100. Fill two at 99 and one at 102; fee 1/2 per fill, arrival 101 and horizon reference 106. Reconcile shortfall.

Paper gain: 6(106−100)=36. Actual gain: 2(106−99)+(106−102)−3/2=33/2.
Subtract: IS=36−33/2=39/2. Independent cash check: spend 300+3/2, value the three units at 318.
Filled displacement: 2(99−100)+(102−100)=0; missed: 3(106−100)=18; fees=3/2. Total=39/2.
Arrival split: delay=3(101−100)=3; execution=2(99−101)+(102−101)=−3. Thus 3−3+18+3/2=39/2.
Move A to 104: delay twelve and execution minus twelve leave total fixed.
Alternative six fills at 102: actual gain=24−3=21; shortfall=15. Its higher average price accompanies lower total shortfall.

Fix the intention, benchmark and horizon before comparing implementation. Price averages omit missing units.

Hands-on: Build a whole-order shortfall ledger

Construct unit-level completion plans, freeze a comparison and move arrival attribution while reconciling paper and actual gains.

Build a whole-order shortfall ledger

Intend six units at decision reference 100. Buy from cash, or sell already-owned units relative to holding. Cycle each intended unit: unfilled → executed at 99 → executed at 102 → unfilled. These are stipulated alternative tapes, not promised liquidity. Fee is 1/2 per fill, no funding or liquidation; terminal reference values both portfolios. Draft is visit-only and earns no credit.

Construct completion

Direction buy; arrival 101; terminal 106; decision 100. Filled 3 of six; average fill 100; execution total 300.

Move references and compare plans

Challenge: freeze the starting buy plan, then construct six fills at 102. Can the worse average fill price accompany lower shortfall? Move arrival alone and explain which two components offset. Direction or terminal changes invalidate comparisons.

Construct a plan and reconcile its ledger.

Common mistakes

Dropping the intended units that did not execute.
Interpreting missed opportunity cost as a cash debit.
Applying full intended quantity to delay while keeping the full missed term.
Changing the paper benchmark when merely moving arrival attribution.
Calling negative shortfall absolute profit.
Reporting a zero average price for an empty fill set.

Keep these ideas

Shortfall is paper gain minus actual gain at a common horizon.
Filled displacement, missed trading and fees reconstruct that difference.
In our convention delay uses filled quantity; arrival shifts cancel against execution.
Completion and average fill price can rank plans differently.