Multi Scale Analysis of Nifty 50 Return Characteristics Valuation Dynamics and Market Complexity 1990 to 2024 (2509.00697v1)

Abstract: This study presents a unified, distribution-aware, and complexity-informed framework for understanding equity return dynamics in the Indian market, using 34 years (1990 to 2024) of Nifty 50 index data. Addressing a key gap in the literature, we demonstrate that the price to earnings ratio, as a valuation metric, may probabilistically map return distributions across investment horizons spanning from days to decades. Return profiles exhibit strong asymmetry. One-year returns show a 74 percent probability of gain, with a modal return of 10.67 percent and a reward-to-risk ratio exceeding 5. Over long horizons, modal CAGRs surpass 13 percent, while worst-case returns remain negative for up to ten years, defining a historical trapping period. This horizon shortens to six years in the post-1999 period, reflecting growing market resilience. Conditional analysis of the P/E ratio reveals regime-dependent outcomes. Low valuations (P/E less than 13) historically show zero probability of loss across all horizons, while high valuations (P/E greater than 27) correspond to unstable returns and extended breakeven periods. To uncover deeper structure, we apply tools from complexity science. Entropy, Hurst exponents, and Lyapunov indicators reveal weak persistence, long memory, and low-dimensional chaos. Information-theoretic metrics, including mutual information and transfer entropy, confirm a directional and predictive influence of valuation on future returns. These findings offer actionable insights for asset allocation, downside risk management, and long-term investment strategy in emerging markets. Our framework bridges valuation, conditional distributions, and nonlinear dynamics in a rigorous and practically relevant manner.