# Bonferroni Correction

In trading, this counter-bias technique is often used in backtesting (emulating strategies against historical data) and risk management. The Bonferroni Correction can be applied as a penalty when more than one factor is being backtested at once, such as dividing the CAGR (compounded annual rate of return) by the number of factors being tested at once.

The ideal situation is when there is a large data set and a few tested rules. Even after applying these rules, it is prudent to apply a bias correcting method. The simplest is the Bonferroni Correction. This scales any statistical significance number by dividing by the number of rules tested… This test is simple but not powerful. It will be overly conservative and skeptical of good rules. When used for developing trading strategies this is a strength. (Sinclair, 2020, p. 23)

This correction can also be used with some form of penalty based on the number of tests performed, such as a genetic algorithm that keeps looking for better-performing combinations of parameters. A correction here would guard against excessively changing parameters in a strategy until strong-enough results are found. The idea is to avoid inflating the actual value of the strategy being tested. After all, it is the truth we are seeking when backtesting, and we want to know if a strategy is not as good as we would like it to be.

Either application would help to reduce the likelihood of overfitting, which leads to overconfidence in a strategy from undeserved success on a conveniently suitable segment of historical data.