backtesting

Probability of Backtest Overfitting (PBO)

The estimated probability that the best in-sample strategy will underperform the median out-of-sample, using combinatorial cross-validation.

The Probability of Backtest Overfitting (PBO), introduced by Bailey and López de Prado (2014), uses Combinatorial Symmetric Cross-Validation (CSCV) to estimate the probability that a strategy selected for maximum in-sample performance will underperform the median strategy out-of-sample.

The CSCV procedure

  1. Divide the track record into S equal sub-periods
  2. For each possible combination of S/2 sub-periods as the training set, evaluate all strategy variants on the training set and select the best performer
  3. Test whether the best training-set strategy also outperforms the median strategy on the complementary S/2 test sub-periods
  4. PBO = the fraction of all combinations where it does not

A PBO of 0.5 means the best IS strategy underperforms the median OOS half the time — i.e., the research process is producing no more signal than random selection. A PBO near 0 indicates genuine IS-to-OOS predictive stability.

PBO is complementary to the Deflated Sharpe Ratio: both address the inflation from multiple testing, from different methodological angles.

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