Walk-forward testing: does the model hold up?

L’idée en termes simples

Any model looks good on the data it was fitted to. The honest test is to fit it on one period and judge it on the next, as you would have lived it. A model whose out-of-sample results stay close to its in-sample ones is robust; one whose results collapse was memorising noise.

Mode de calcul

The study splits the daily returns at 75%. Each model is fitted on the first part only; its weights are then held through the last part, and the same figures are measured there: return, volatility, Sharpe, drawdown, total return.

Fit:   w* = model(r₁ … r_{0.75T})
Test:  metrics(w*, r_{0.75T+1} … r_T)

Comment l’utiliser

• Sort the study by OOS Sharpe as well as Sharpe; prefer models that rank well on both.
• Use a longer history (3–5 years) so the test part is long enough to mean something.
• Treat a model that wins in-sample and loses out-of-sample with suspicion, however good its headline numbers are.

Tirer des conclusions

• Return-chasing models (Kelly, Maximum Sharpe, Markowitz) usually lose the most out of sample, because expected returns are the hardest input to estimate.
• Risk-based models (risk parity, ERC, HRP, minimum variance) usually keep their character out of sample.

Points de vigilance

• One split is one test: a single good OOS period can be luck too.
• The test part is short with little data; treat small differences as ties.

Un peu d’histoire

Walk-forward analysis was popularised for trading systems by Robert Pardo (1992). In portfolio research, DeMiguel, Garlappi and Uppal (2009, "Optimal Versus Naive Diversification") found that out of sample, many optimised portfolios fail to beat simple equal weights, a result that shaped how models are judged since.