Specify the denominator before quoting a rate
A basis point here is 0.0001 of the equity notional bought or sold. Both equity legs incur the stated rate once. Cash transfers incur no extra fee, and the rate is not a round-trip quote. One-way policy turnover is half the absolute change across normalized target and prior weights, including cash. Multiplying that turnover blindly by twice the cost rate can give the wrong answer when cash weight changes.
The flat rate is a chosen teaching assumption, not a calibrated liquidity or execution model. AQR's practical cost-analysis discussion is a useful primary-source reminder that implementation analysis requires more than an unqualified single fee number. Nothing in this example estimates spread, impact, commissions, taxes or capacity for a real security.
Fund the fee without borrowing
Let p be prior weights, w post-fee normalized target weights, k the per-leg rate and c the fee fraction of pre-trade NAV. The engine solves c = k * sum_equities(abs((1-c)*w-p)). Post-fee holdings are (1-c)*w. This distinction keeps a fully invested target self-financing: paying a cost does not create negative cash or a hidden external contribution.
In the separate 1,000,000-unit workbench, move SYN-01/SYN-02/SYN-03/cash from 40/30/20/10% to 30/40/30/0%. One-way turnover is 20%, while pre-fee equity traded notional is 300,000. At 20 bps, c = 0.002*(0.3-0.4c) = 3/5004. Actual equity traded notional is 299,760.19 and the fee is 599.52. The simple 600 estimate is explicitly the pre-fee approximation, not the exact result. The prior cash plus sale proceeds funds purchases and this fee.
Compare the same exposure under different assumptions
In the three-period dossier below, the universe, signals, selected securities and normalized target weights are unchanged across cost scenarios. Because each formation fee is a common capital scale, normalized end-of-period drift weights also remain unchanged. Gross returns therefore stay fixed while net wealth falls as the assumed rate increases.
The net period formula is (1-c)*(1+g)-1, where g is the gross return. It is not simply g-c: the fee is paid before the period's return is earned. The gross-to-net gap includes that timing effect, and the compounded gap is not the sum of period fee fractions. All amounts exclude terminal liquidation and non-trading account charges.
Do not turn a sensitivity table into model selection
The table answers how a declared assumption changes the same invented ledger. It does not justify choosing securities or tuning entry scores using net performance. There is no empirical case for any row's cost rate. An actual research decision would need timestamped data, execution evidence and independent samples beyond this educational fixture.
Inspect the example
| Cost bps per equity leg | Compounded gross return | Compounded net return |
|---|---|---|
| 0 | 7.1408000% | 7.1408000% |
| 10 | 7.1408000% | 6.7806527% |
| 50 | 7.1408000% | 5.3512020% |
| 200 | 7.1408000% | 0.1459680% |
Sources & reproduction
Primary references support the definitions and method. Numerical examples are illustrative unless a source record is explicitly identified.