What do ex post alpha and the Treynor measure primarily compare?

Ex post alpha and the Treynor measure are both aimed at evaluating performance in terms of risk-adjusted returns. Ex post alpha represents the measured excess return of an investment relative to the return predicted by the Capital Asset Pricing Model (CAPM), which essentially gauges how much additional return an investment has generated over and above its expected return based on its systematic risk, as measured by beta.

Similarly, the Treynor measure assesses performance by looking at excess returns, but it does so specifically in relation to systematic risk, which is the risk that cannot be eliminated through diversification. It uses the portfolio's return over the risk-free rate divided by its beta to measure how much excess return was achieved per unit of systematic risk.

Since both metrics focus on the relationship between excess returns and the level of systematic risk associated with those returns, the comparison indicates how effectively an investment has performed relative to the risk taken. This understanding underscores why the relationship between excess returns and systematic risk is the core focus of both measures.