S&P 500 Historical Log Return Analysis

Overview

This repository contains a Python script for conducting a statistical analysis of the S&P 500 index's historical log returns over a 10-year period from January 1, 2010, to December 31, 2020. The analysis includes data retrieval, computation of log returns, statistical measurements, data visualization, and probability estimation of negative returns.

Features

1. Data Retrieval: Fetch S&P 500 historical data using the yfinance library.
2. Log Return Calculation: Compute daily log returns for consecutive trading days.
3. Statistical Analysis: Calculate mean and standard deviation of daily log returns.
4. Data Visualization: Plot a histogram of log returns and a normal distribution curve for comparison.
5. Probability Estimation:
   • Calculate the daily probability of the index dropping by 1% to 5%.
   • Estimate the probability of the index dropping over 5% in a 30-day period.

Usage

To run the script, navigate to the script's directory and execute the python notebook

Requirements

• Python 3
• pandas
• numpy
• matplotlib
• scipy
• yfinance

Make sure to install all required libraries using pip before running the script.