Freeze the inputs before the return interval
The universe consists of SYN-01 through SYN-06, two invented securities in each of Technology, Healthcare and Infrastructure. Their membership is marked available on 15 December 2023; the teaching policy is frozen on 20 December. The first scores are available on 29 December, before formation at 00:00 UTC on 1 January 2024. These are fictional accounting boundaries, not claims about exchange hours or executable prices.
Descending score determines selection, with ascending synthetic ID breaking exact ties. The first scores are 90, 80, 70, 60, 50 and 40, so the selected names are SYN-01, SYN-02 and SYN-03. Returns are not used to form or rank entries. Kenneth French's portfolio descriptions provide a primary-source example of explicitly stating formation dates and lagged inputs; this toy rule does not replicate his portfolios or factors.
Track the portfolio, including its cash
With three selections and a 40% single-security ceiling, each selected security receives one third and cash receives zero. The initial weights are 20%, 20%, 20%, 20%, 10%, 0%, plus 10% cash. The absolute equity changes sum to 70% and the cash change is 10%, giving one-way policy turnover of (70% + 10%)/2 = 40%. Equity traded notional is a different quantity from one-way turnover. The first portfolio has 66.6667% Technology exposure; the security ceiling does not impose sector neutrality.
At 10 basis points per equity buy or sell, the formation fee c satisfies c = 0.001 * (0.7 - c), giving c = 7/10010 of beginning capital. Fees shrink the capital allocated, so the first-period net return is (1-c)*1.04-1 = 3.9272727%. The 4% gross return comes from (10% + 4% - 2%)/3, with the losing selected security retained.
Carry drift forward and compound
The first period ends with normalized weights 55/156, 1/3 and 49/156 in the three held securities. Those drifted weights, not fresh one-third weights, become the next period's prior holdings. The 40% ceiling applies at formation only. Choosing a 25% ceiling instead would leave 25% in zero-return cash; it would not redistribute that residual above the ceiling.
Gross returns of 4%, 2% and 1% compound to 1.04*1.02*1.01-1 = 7.1408%, not 7%. With the stated costs the synthetic net change is 6.7806527%; a notional 100,000 starting units becomes 106,780.65. Fees are paid at each formation and no terminal liquidation is assumed. A period's currency fee equals that period's beginning net wealth multiplied by its cost fraction.
What the sample labels cannot establish
Development, validation and holdout are consecutive labels demonstrating where a frozen protocol would divide observations. All three periods were authored together, and no training occurred. Neither these labels nor passing software tests establish independent investment evidence. The dossier has no estimated factor premium, realistic capacity estimate, annualized statistic or actual provider performance record.
Inspect the example
| Period / teaching split | Selected synthetic IDs | Gross return | Net return | One-way turnover | Formation cost / beginning NAV |
|---|---|---|---|---|---|
| 2024-01 / development | SYN-01, SYN-02, SYN-03 | 4.0000000% | 3.9272727% | 40.0000000% | 0.0699301% |
| 2024-02 / validation | SYN-02, SYN-04, SYN-05 | 2.0000000% | 1.8640453% | 66.6666667% | 0.1332889% |
| 2024-03 / holdout | SYN-01, SYN-04, SYN-06 | 1.0000000% | 0.8653782% | 66.6666667% | 0.1332889% |
Sources & reproduction
Primary references support the definitions and method. Numerical examples are illustrative unless a source record is explicitly identified.