The Adjusted PNP Index: Benchmark-Integrated Performance Measurement

This paper presents the Adjusted Positive-Negative Probability (PNP) Index, an enhanced framework for evaluating investment performance. Building upon the foundational PNP metric, the Adjusted PNP incorporates a periodic benchmark interest rate (rf), enabling a more rigorous and economically meaningful analysis of financial returns. By comparing excess returns relative to this benchmark and measuring their proportion against total deviations, the Adjusted PNP provides a robust and intuitive probabilistic indicator of performance. Unlike traditional measures such as the Sharpe, Sortino, or Omega ratios, which rely on mean and variance assumptions, this metric evaluates full distributional behavior with respect to a defined benchmark. The adjusted model seamlessly integrates into algorithmic trading, machine learning models, and backtesting environments, where directional bias, volatility scaling, and benchmark-relative returns play a critical role. Several examples illustrate how the Adjusted PNP dynamically adapts to changes in interest rates, revealing when high-volatility assets outperform low-volatility ones depending on the economic environment. This flexibility and interpretability make the Adjusted PNP Index an essential tool for modern quantitative finance.