Risk Management from First Principles

Most investors focus on finding good trades. Professional investors focus on sizing them correctly. The difference between amateur and professional is often not in the quality of ideas, but in the management of risk.

The Kelly Criterion and Its Limits

The Kelly criterion provides a mathematical framework for optimal position sizing: bet in proportion to your edge divided by the odds. In practice, full Kelly is too aggressive—most practitioners use fractional Kelly to account for estimation error and the psychological difficulty of large drawdowns.

Correlation: The Hidden Risk

A portfolio of uncorrelated positions is safer than a portfolio of correlated ones, even if individual position sizes are identical. Correlation often increases during market stress—precisely when you need diversification most. Risk management must account for this regime-dependent behavior.

Tail Risk: Expect the Unexpected

Market returns are not normally distributed. Extreme events occur more frequently than standard models predict. Position sizes must account for the possibility of moves that have never occurred in the historical sample.

The Ruin Constraint

The first rule of compounding is to never interrupt it. Position sizes should be set such that even a worst-case scenario does not result in catastrophic loss. Living to trade another day is worth more than any single opportunity.

Risk management is not a constraint on returns—it is the foundation that makes returns sustainable.