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Validation: DeMiguel, Garlappi & Uppal (2009)

Status: planned for v0.2

This reproduction is on the roadmap. The walk-forward backtest infrastructure is implemented (markowitz.backtest.WalkForward), but full reproduction of DeMiguel-Garlappi-Uppal (2009) on Fama-French datasets is deferred to v0.2.

DeMiguel, Garlappi, and Uppal [@demiguel2009] ran a large horse race of fourteen portfolio strategies against the naive \(1/N\) rule on seven empirical datasets. Their controversial conclusion: out of sample, \(1/N\) was hard to beat. This page sketches the planned reproduction protocol; see the warning above for current status.

Protocol (planned)

For each strategy and dataset:

  1. Use a rolling estimation window of \(M = 120\) months.
  2. At each rebalance, fit moments on the trailing window.
  3. Form portfolio weights and hold for one month.
  4. Record realized return.
  5. After the full backtest, compute:
  6. out-of-sample Sharpe ratio,
  7. certainty-equivalent return at \(\gamma = 1\),
  8. portfolio turnover.

The relevant out-of-sample metrics in the paper are Tables 3-5.

Strategies to cover

The reproduction will target the strategies most relevant to mean-variance research:

strategy building block
Equally-weighted \(1/N\) markowitz.backtest.OneOverN
Plug-in mean-variance MeanVariance + SampleMean / SampleCovariance
Mean-variance with Ledoit-Wolf \(\hat\Sigma\) MeanVariance + LedoitWolfShrinkage
Minimum-variance, sample covariance MeanVariance(risk_aversion=large) + SampleCovariance
Minimum-variance, Ledoit-Wolf MeanVariance(risk_aversion=large) + LedoitWolfShrinkage
Black-Litterman with equilibrium prior BlackLitterman + MeanVariance

Planned reproduction sketch

Once shipped, the reproduction will look approximately like:

# Sketch only - not yet implemented in v0.1
from markowitz.backtest import WalkForward
# Plus a Fama-French data loader (deferred to v0.2)

wf = WalkForward(
    window=120,
    rebalance="monthly",
    strategy=...,  # any callable returning weights from a returns DataFrame
)
result = wf.run(returns_df)
print(result.sharpe(), result.turnover())

The walk-forward engine already exists; what is deferred to v0.2 is (a) the bundled Fama-French dataset loaders and (b) the comparison harness that runs all six strategies over all seven datasets and produces the paper's tables.

Expected qualitative findings

The reproduction is expected to confirm the paper's headline results:

  • The plug-in mean-variance strategy underperforms \(1/N\) on Sharpe and has extreme turnover.
  • Ledoit-Wolf shrinkage closes most (not all) of the Sharpe gap and reduces turnover by an order of magnitude.
  • Minimum-variance with Ledoit-Wolf is the most consistent positive-edge strategy across datasets.

References

[@demiguel2009]; [@ledoit2004]. See Citations.