Return distribution

This chart compares the theoretical normal distribution (outlined circles) with actual weekly market returns (filled circles) over the past 10 years. Each circle represents one week, stacked vertically within 0.5% return bins. The normal distribution assumes returns follow a bell curve based on observed mean and standard deviation. Circles colored blue fall within the theoretical distribution; red circles represent weeks that exceed what a normal distribution would predict, revealing in particular the market's fat tails corresponding to extreme events. 

Data: Weekly S&P 500 returns from August 2015 to August 2025 (522 weeks). Returns binned at 0.5% intervals spanning -14.5% to +12.4%. Normal distribution fitted to observed parameters.