Validation · #359491 · Equities
Reward-risk parity
Diversified reward-risk parity in portfolio construction, 2021
The rule
Each month, score every Dow member on its trailing-6-month Calmar ratio (return over drawdown), weight proportionally to the score — losers floored to zero — and hold for six months, replacing one-sixth of the book monthly.
Overstated
+48bp vs equal weight→t = 0.69 — noise
the claim → what we measured
10.98%
Headline reproducesclaimed 10.32% · EW 9.96 vs 9.84
0.69
t-stat of the edge22 years of data — the +102bp is noise
0.18
Momentum in disguiseβ(Mom), t = 4.0 · residual α t = 0.4
AssetUS equities
StrategyCalmar-parity long-only
UniverseDow 30 (point-in-time)
Period1999–2020
CostsNone in paper
UniverseAAPL MSFT JPM KO PG IBM GE XOM C AIGThe paper's own point-in-time Dow table, replicated verbatim — including its holes: GM and Kraft were never servable from Yahoo (the paper's own source), and Chevron, Kodak, Sears and SBC are missing from the table entirely.
The exact rules
| Month-end, for each Dow member | → | Compute 6-month Calmar: cumulative return ÷ max drawdown over the window |
| Calmar positive | → | Weight proportional to the ratio (raw ρ rule) |
| Calmar negative (in a net drawdown) | → | Weight = 0 — the name is dropped entirely |
| Normalise + hold | → | Weights sum to 1, long-only; sleeve held 6 months, ⅙ of the book re-formed each month |
The backtest, re-run
Inside the model
- Position mix
- long-only; on average 17 of ~30 names at zero weight (negative-Calmar names are dropped)
- Concentration
- effective N 13.5 avg, 3.0 min — up to 54% in a single name, under a 'diversified parity' title
- Win rate
- 54% of days · 62% of months · vs EW: 50.4% of months — a coin flip
- Skew / kurtosis
- −0.1 / 12.5 daily — Dow-like, no tail transformation
- Best / worst day
- +10.7% / −12.3%
- Best / worst month
- +12.2% / −12.6%
- Annual actives
- avg +102bp hides −1441bp (2000) to +1845bp (2008); 2020 +1481bp
- Tabled 'Sharpe' caveat
- the paper's Sharpe column is return ÷ vol with NO risk-free — flatters every row by ~0.08
The validation ladder
| C0 | Replicate | Tight: 10.98% vs claimed 10.32 (EW 9.96 vs 9.84); vol, drawdown and turnover conventions all reproduce row-by-row across the 46-config grid. |
| C1 | Honesty | The paper applies zero costs at 66% turnover. At an honest 10bp one-way the spread only drops +102 → +91bp — costs are not the problem here. |
| C2 | Deflate | The claimed outperformance fails everything: best active t = 0.69 across all 45 configs, Deflated Sharpe 0.43 (needs 0.95), PBO 0.61 — the winner is more likely than not to underperform out-of-sample. |
| C3 | Crisis | Long-only Dow book: −13%/yr dot-com, −19%/yr GFC absolute. The drawdown improvement is real (−38.5% vs EW −57.6%) but the paper's universe ran the GFC without GM's collapse. |
| C5 | Frictions | Breakeven one-way cost 89bp vs 5–10bp reality for Dow megacaps — survives costs comfortably. It dies of insignificance, not friction. |
| C6 | Decay | True post-publication OOS (2021–2026): active +209bp/yr — but at a ~6%/yr tracking error, 5½ years says nothing. Annual actives swing −1441bp to +1845bp. |
| C7 | Originality | The active tilt is momentum: β(Mom) = 0.18 (t = 4.0), residual α 0.7%/yr (t = 0.4). Scoring by trailing Calmar = buying recent winners with shallow drawdowns. |
ReproducesStatistically realOriginal vs factorsCost-robustCrisis-robustOverfit (PBO)
How we rebuilt it
- Data
- Yahoo Finance adjusted daily prices — the paper's own disclosed source, replicated like-for-like (^IRX as risk-free).
- Method
- Trailing-6-month reward-risk scores → proportional weights (4 allocation rules × 20 measures); 6-sleeve overlapping tranches, ⅙ replaced monthly.
- Universe
- Paper Table 1 point-in-time Dow membership, verbatim — with its documented holes (GM, KRFT unservable; CVX, EK, S, UK, SBC omitted).
- Regime stated
- None — 1999–2020 treated as one sample; the claimed edge concentrates in three years (2008, 2009, 2020).
Deviations from the paper
- Model-based measure rows (Sharpe/STAR/Rachev/VaR/CVaR under ARMA-GARCH tempered-stable models) → historical estimates; the headline Calmar row is model-free by the paper's own construction and replicates exactly as specified.
- WBA (member 2018–2020) excluded — went private in 2025 and its public data disappeared; 1 of ~30 names for 2.5 of 22 years, impact under 5bp/yr.
- UTX served via the RTX price lineage (2020 rename).
- Undisclosed → estimated: daily risk-free convention, construction-score units (calibrated so the paper's near-EW rows reproduce), sleeve warm-up, costs in C1 (10bp).
- 2026 vs 2021 Yahoo vintage moves 22-year annualised returns by tens of bp — the measured +102bp vs claimed +48bp spread sits inside this sensitivity, which is itself evidence of the effect's fragility.
ProvenanceBeta
- Engine
- v1
- Blocks
- 4 new (daily equity adapter, reward-risk measures, score-parity rules, overlapping-tranche backtest), 7 reused (Ken French factors + Mom, metrics, G1/G2/G3, regime, spanning)
- Data
- yahoo daily adjusted · 1999–2020 paper window + 2021–2026 frontier · run_id 6
- Source
- arXiv 2106.09055 ↗ · Ken French Data Library ↗
- Tests
- 30/30 passing · known-value (Calmar/VaR/CVaR/STAR/Rachev, no-lookahead, turnover/cost) + multi-seed negative control + independent EW cross-check
- Reproduce
- view code ↗
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