Free lesson · Execution & microstructure

Measure implementation shortfall

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Start with the idea

Execution quality should be evaluated against a price known when the decision was made. Including the unfilled portion prevents a strategy from looking good simply because it avoids filling difficult orders.

Symbols, units & horizon

IS: implementation shortfall in currency, positive means worse than decision price
d: +1 buy, −1 sell
Q: positive desired quantity
qⱼ: positive filled quantity of fill j
Pⱼ: fill price
P₀: decision price
P_T: end-of-horizon opportunity-cost price
Fees: currency expenses
VWAP: volume-weighted average price
Vⱼ: nonnegative volume at price Pⱼ
Σⱼ: sum across fills or sampled trades

When and why to use this

Use implementation shortfall to compare routing and urgency choices; use a clearly defined VWAP window when that is the mandate’s benchmark.

I S = d [\sum_{j} q_{j} (P_{j} - P_{0}) + (Q - \sum_{j} q_{j}) (P_{T} - P_{0})] + fees

Algebra and arithmetic

Compare the ideal order with the realised outcome

An ideal buy fills all Q at decision price P₀. Filled quantity qⱼ incurs qⱼ(Pⱼ−P₀). Value the unfilled remainder at Pₜ to account for missed opportunity.
Sum the two pieces, multiply price differences by d=+1 for buys or −1 for sells and add fees. Divide by QP₀ and multiply by 10,000 for shortfall bp.

Work it by hand

Buy 1,000 at reference 50; fill 600 at 50.03, end price 50.10, fee 2 → 18+40+2=$60, or 12 bp.

For a parent order of Q positive units, d is +1 for a buy and −1 for a sell, P₀ is the decision price, fills have quantities q and prices P, and P_T values any unfilled remainder at the end of the evaluation window. Positive shortfall is a cost. The unfilled term measures opportunity cost and can be negative.

V W A P = \frac{\sum_{j} P_{j} V_{j}}{\sum_{j} V_{j}}

Algebra and arithmetic

Derive a volume-weighted price

Total transacted notional is $\sum_{j} P_{j} V_{j}$ and total units are $\sum_{j} V_{j}$ . The single price that reproduces that notional satisfies $V W A P \sum V = \sum P V$ .
Divide by positive volume. For an incremental update, add the new price×volume to cumulative notional and new volume to cumulative volume.

Work it by hand

100 shares at $10 and 300 at $11 give VWAP=(1000+3300)/400=$10.75.

VWAP weights observed trades by volume; TWAP weights intervals equally. A benchmark is only useful if the window, venues, and eligible prints are specified. Beating VWAP can coexist with poor decision-price performance if the market moved before the execution window began.

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

def implementation_shortfall(side, desired_quantity, fills, decision_price, end_price, fees):
    """fills is [(positive_quantity, price), ...]. Includes unfilled opportunity cost."""
    filled = sum(q for q,p in fills)
    if side not in (-1,1) or filled > desired_quantity or any(q<0 for q,p in fills):
        raise ValueError("Invalid side or fill quantities")
    execution = sum(q*(p-decision_price) for q,p in fills)
    opportunity = (desired_quantity-filled)*(end_price-decision_price)
    return side*(execution+opportunity)+fees

def vwap(price_volume):
    volume = sum(v for p,v in price_volume)
    if volume <= 0 or any(v<0 for p,v in price_volume):
        raise ValueError("Positive aggregate volume required")
    return sum(p*v for p,v in price_volume)/volume

print(implementation_shortfall(1,100,[(60,100.1)],100,100.5,2))

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