Research disclosure.
Monotonicity test — does decile rank predict return?
A working long-only-ranked factor produces a monotone decile ladder
(return falls as score rank rises). We test this two ways: a Spearman
rank correlation between decile index and annualised return, and an
OLS trend regression β of return on decile index. Negative β with a
small p-value would indicate factor efficacy; near-zero β or positive
β indicates noise or factor inversion respectively.
Equity curves — Decile 1, Decile 10, Benchmark
Equal-weight monthly rebalance inside each decile. Curve starts at
1.00 on the first evaluable rebalance date.
Per-decile metrics with inference (HAC, block bootstrap)
α vs benchmark, t-statistic and p-value use Newey-West HAC standard
errors with a Bartlett kernel and automatic lag selection
L = ⌊4·(T/100)2/9⌋. Annualised-return 95 % CIs come from
a circular block bootstrap on the monthly series.
| Decile |
Ann Return % |
95 % CI |
Ann Vol % |
Sharpe |
α vs BM % |
t (HAC) |
p |
Max DD % |
Avg Hold |
Limitations
- Hypothetical backtest — no live capital, no managed accounts, no client portfolios.
- Single-factor study — interaction with other risk factors not isolated; multi-factor attribution lives on the same page below (Factor Attribution).
- Small per-decile holdings (~9–10 names per decile) — decile statistics are noisy; CIs from block bootstrap quantify this.
- Transaction costs and turnover not modelled; the spread Sharpe is a gross-of-cost upper bound.
- Universe survivorship — current S&P-500-ish list; a point-in-time universe loader (capacity / sentiment screens not retroactively applied). Direction of bias: survivors are more homogeneous, compressing cross-sectional dispersion — this pulls the measured D1−D10 spread toward zero, so an INCONCLUSIVE verdict is conservative on this axis. (The classic upward level bias applies to absolute decile returns, not to the long-short spread.)
- Multiple testing — with ten deciles, the strongest decile will outperform by chance; the factor-attributable return is the D1−D10 spread, not D1 alone.
- Risk-free rate is a flat constant; a time-varying T-bill series is the institutional default for production GIPS reporting.
Factor Attribution — FF-5 + Carhart MOM (HAC, Newey-West)
—
Loadings (β) and t-statistics under Newey-West HAC with
Bartlett kernel and automatic lag L = ⌊4·(T/100)2/9⌋.
Two-sided asymptotic p-values.
| Portfolio |
Factor |
β |
SE (HAC) |
t (HAC) |
p |
Contrib (ann) |
Capacity Analysis (Top-Decile holdings)
—
ADV-cap rule: per-position USD ≤ adv_cap_pct × median 21d ADV USD.
IS estimate uses the square-root market-impact model
(Almgren-Chriss style, k≈100 calibration).