Validation · #363172 · Equities

Risk-model diversification

Quantitative Investment Diversification Strategies via Various Risk Models, 2024

Maysam Khodayari Gharanchaei, Prabhu Prasad Panda & Xilin Chen · arXiv q-fin

The rule

Each month, weight 49 industry portfolios to maximise the diversification ratio under a constant-correlation covariance estimate — long-only, 10% cap, 60-month lookback.

Overstated 1.04→0.60 claimed → measured Sharpe

1.04

Claimed Sharpepaper headline

0.60

Measured Sharpenet, survivorship-clean

≈2×

Overstatedt = 4.16 — still real

AssetEquities

StrategyMax-diversification

Universe49 industries

Period1970–2023

Costs10 bps/side

UniverseAll 49 Ken French value-weighted industry portfolios (Agric, Food, Beer … Banks, Insur, RlEst) — the survivorship-clean stand-in for the paper's undisclosed 1,000-stock CRSP screen.

The exact rules

Each month, from a 60-month lookback	→	Estimate the covariance of the 49 industries (constant-correlation)
Optimise	→	Solve max-diversification weights — long-only, 10% per-name cap
Rebalance	→	Hold to next month (turnover ~0.01–0.06/mo)

The backtest, re-run

Inside the model

The validation ladder

C0	Replicate	Claimed 1.04 → measured 0.60 net on survivorship-free data.
C1	Honesty	Survivorship-clean data + 10 bps/side — immaterial (turnover ~0.01–0.06/mo).
C2	Deflate	Survives BHY multiple-testing across 9 configs and the Deflated Sharpe — statistically real.
C3	Crisis	Negative Sharpe in all four crisis windows — no downside protection.
C6	Decay	Edge erodes in-sample → out-of-sample, consistent with published anomaly decay.
C7	Originality	FF3 α ≈ 0, R² ≈ 0.95, market β ≈ 1 — a factor-tilt, spanned by known factors.

Reproduces magnitudeStatistically realCrisis-robustOriginal vs factorsCosts survivable

How we rebuilt it

Data: Ken French 49-industry value-weighted portfolios (free, survivorship-clean).
Method: Max-diversification optimiser × constant-correlation covariance; CVXPY open solvers.
Universe: Paper's stock screen undisclosed → 49 industries (the correct survivorship control).
Regime stated: None disclosed — the paper never says which regime it was fit in.

Deviations from the paper

Universe: paper's stock selection undisclosed (1000 constant names, no delisting handling → survivorship-suspected) → Ken French 49-industry.
Solver: GUROBI → CVXPY open solvers (numerically equivalent).
Weight cap undisclosed → 0.10; shrinkage target undisclosed → Ledoit-Wolf.

ProvenanceBeta

Engine: v1
Blocks: 11 typed blocks (covariance · optimizers · backtest · metrics · gates)
Data: ken_french/49_industry_vw · 1970–2023 monthly
Source: Ken French Data Library ↗
Tests: 14/14 passing · statistical + cross-engine QA