An explanation for the distribution characteristics of stock returns

ArXiv ID: 2312.02472 “View on arXiv”

Authors: Unknown

Abstract

Observations indicate that the distributions of stock returns in financial markets usually do not conform to normal distributions, but rather exhibit characteristics of high peaks, fat tails and biases. In this work, we assume that the effects of events or information on prices obey normal distribution, while financial markets often overreact or underreact to events or information, resulting in non normal distributions of stock returns. Based on the above assumptions, we propose a reaction function for a financial market reacting to events or information, and a model based on it to describe the distribution of real stock returns. Our analysis of the returns of China Securities Index 300 (CSI 300), the Standard & Poor’s 500 Index (SPX or S&P 500) and the Nikkei 225 Index (N225) at different time scales shows that financial markets often underreact to events or information with minor impacts, overreact to events or information with relatively significant impacts, and react slightly stronger to positive events or information than to negative ones. In addition, differences in financial markets and time scales of returns can also affect the shapes of the reaction functions.

Keywords: Market microstructure, Return distribution modeling, Reaction functions, Fat tails, Behavioral finance, Equities (General)

Complexity vs Empirical Score

• Math Complexity: 4.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Street Traders
• Why: The paper uses established statistical models and behavioral finance concepts rather than cutting-edge mathematics, but it applies its model to real market data (CSI 300, S&P 500, Nikkei 225) across multiple time scales, demonstrating empirical testing and calibration.

  flowchart TD
    A["Research Goal<br>Explain non-normal stock return distributions<br>characterized by high peaks & fat tails"] --> B["Assumption<br>Market reaction to info/events is the driver<br>Information impact normally distributed"]
    B --> C["Key Methodology<br>Propose a Market Reaction Function<br>Model real return distribution based on it"]
    C --> D["Data & Inputs<br>High-frequency returns from major indices:<br>CSI 300, S&P 500, Nikkei 225"]
    D --> E["Computational Process<br>Fit Reaction Function to empirical data<br>Analyze across varying time scales"]
    E --> F["Key Findings & Outcomes<br>1. Underreaction to minor info<br>2. Overreaction to major info<br>3. Asymmetric response (positive > negative)<br>4. Reaction shape varies by market/time scale"]