Using Python to Decode Market Panic: S&P 500 Return Distribution Since 1995
A deep dive into return distributions, crash rebounds, and rare market extremes visualized through data , that’s what i keep telling myself before i thought about writing this article.
It’s funny how a simple discussion can trigger a full-blown article — especially one that’s relevant to our current U.S. tariff madness, which has impacted global markets and led to one of the most volatile weekends in history since 2008.
I had an interesting conversation with some friends and investors about the current state of the market. Many of them are scared and uncertain about their positions. So I thought — why not bring some statistical methods into play and analyze the historical daily returns of the S&P 500 index using return distribution models.
Before diving in, let’s clarify something: the stock market’s historical trajectory, returns, and performance cannot be fully captured using a normal distribution model. That’s because the market doesn’t behave in a statistically “normal” way when it comes to daily movements. And no one has a magical crystal ball to predict what the market will do tomorrow — especially with unprecedented events like tariffs shaking things up.
However, there’s one thing that’s consistently true: how the market behaves after a major drop is remarkably predictable. And only a handful of experienced investors truly take advantage of that.
So that night, I went home and started developing a quick data review to explore the best and worst market days since 1995. What I discovered reinforced my hunch — you shouldn’t fear market downturns. In fact, history proves time and again that stock markets are wealth creators — if you play your cards right.
The model is simple: I extracted historical closing prices for the S&P 500 from 1995 to the present and calculated daily returns, focusing on return density. Then, I ranked every single daily return from worst to best.
To keep things engaging, I zoomed in on just the top 3 best and bottom 3 worst days over the last 30 years — and the results were eye-opening.
Libraries used and technologies
Yfinance : yfinance is a python library that helps us to fetch stock information directly from Yahoo Finance
Pandas : I believe we all know what is pandas library is , we use it for data manipulation and analysis , also it offers data structures and operations for manipulating numerical tables and time series .
Matplotlib and Seaborn: we will use both of these libraries for creating static, animated, and interactive visualizations.
Code
import yfinance as yf
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
# Load S&P 500 index data from 1995
sp500 = yf.Ticker("^GSPC")
sp500_data = sp500.history(start="1995-01-01")
sp500_data = sp500_data[["Close"]]
# Calculate Daily Returns (%)
sp500_data["Daily Return %"] = sp500_data["Close"].pct_change() * 100
sp500_data.dropna(inplace=True)
# Identify Top 3 Worst and Best Days
worst_days = sp500_data["Daily Return %"].nsmallest(3)
best_days = sp500_data["Daily Return %"].nlargest(3)
# Helper: Get next day return info
def get_next_day_returns(index_list, data):
results = []
for dt in index_list:
try:
next_idx = data.index.get_loc(dt) + 1
next_day = data.index[next_idx]
next_return = data.iloc[next_idx]["Daily Return %"]
results.append((dt, data.loc[dt, "Daily Return %"], next_day, next_return))
except IndexError:
results.append((dt, data.loc[dt, "Daily Return %"], None, None))
return results
worst_info = get_next_day_returns(worst_days.index, sp500_data)
best_info = get_next_day_returns(best_days.index, sp500_data)
# --------------------------------------------
# 📊 Chart 1: Distribution of Daily Returns
plt.figure(figsize=(15, 6))
sns.kdeplot(sp500_data["Daily Return %"], shade=True, color="skyblue")
# Add vertical lines for worst and best 3 days
for dt, val, _, _ in worst_info:
plt.axvline(val, color="red", linestyle="--", linewidth=1.2, label="Worst Day" if dt == worst_info[0][0] else "")
for dt, val, _, _ in best_info:
plt.axvline(val, color="green", linestyle="--", linewidth=1.2, label="Best Day" if dt == best_info[0][0] else "")
# Title and labels
plt.title("S&P 500 Historical Daily Return Distribution (1995–Present)", fontsize=14)
plt.xlabel("Daily Return (%)")
plt.ylabel("Density")
plt.legend()
plt.grid(True)
plt.show()
# --------------------------------------------
# Chart 2: Ranked 1-Day Return Plot
returns_sorted = sp500_data["Daily Return %"].sort_values().reset_index()
returns_sorted["Rank"] = returns_sorted.index + 1
plt.figure(figsize=(15, 6))
plt.plot(returns_sorted["Rank"], returns_sorted["Daily Return %"], color="orange", linewidth=1)
# Annotate worst 3 and best 3 days
for dt, val, next_dt, next_val in worst_info:
rank = returns_sorted[returns_sorted["Daily Return %"] == val]["Rank"].values[0]
label = f"Worst: {dt.date()} ({val:.2f}%) - nNext: {next_dt.date() if next_dt else 'N/A'} ({next_val:.2f}%)"
plt.scatter(rank, val, color="red", s=60)
plt.text(rank + 50, val, label, fontsize=9, verticalalignment='bottom', color="black")
for dt, val, next_dt, next_val in best_info:
rank = returns_sorted[returns_sorted["Daily Return %"] == val]["Rank"].values[0]
label = f"Best: {dt.date()} ({val:.2f}%) - nNext: {next_dt.date() if next_dt else 'N/A'} ({next_val:.2f}%)"
plt.scatter(rank, val, color="green", s=60)
plt.text(rank - 150, val, label, fontsize=9, verticalalignment='bottom', color="black")
plt.title("Ranking of 1-Day S&P 500 Performance (Worst to Best)", fontsize=14)
plt.xlabel("Rank (from Worst to Best)")
plt.ylabel("1-Day Return (%)")
plt.grid(True)
plt.tight_layout()
plt.show()Charts
Comprehensive Analysis and discussion
So what do we gather from both charts , well the first chart titled “S&P500 Historical daily return distribution” looks a bit intimidating but I believe you will like what you seeing once you understood it .
Here , we can see return density represented in Y-axis shows how frequently certain percentage changes in price occur. As for the X-axis we have daily return % , how much the S&P 500 went up or down in one day. Both of these form a histogram, but smoothed out to represent a probability distribution of daily returns. Hence, the higher peaks on the graph mean that type of daily return happened more often.
The second chart, titled “Ranking of 1-Day S&P 500 Performance (Worst to Best)”, visualizes the top 3 worst and best performances over the same period. It provides a clearer perspective than the first chart and reinforces the comparison between each worst day and its following day’s performance.
Example of a Worst Day:
As you see from the chart that the worst daily returns was on March 16, 2020, during the COVID-19 crash
- Return were: -11.98%
- This was a very rare event.
- On the density chart, it appears on the far left tail, where returns are very negative and very rare.
- Its density is low, meaning this kind of drop hardly ever happens or let’s see a rare event.
Text interpretation of my model:
On March 16, 2020, the S&P 500 dropped nearly 12% , one of the worst days since 1995. This kind of extreme negative return has a very low density on the chart, highlighting how unusual it is. However , the next day the market rebounded back by 6%.
Example of a Best Day:
Now let’s flip this to the best day , the best daily returns was on March 24, 2020 — just days after the big crash.
- Return: +9.38%
- Appears on the far right tail of the density chart.
- Again, low density — rare event.
Text interpretation:
On March 24, 2020, the S&P 500 rebounded with a gain of over 9%. Such strong positive moves are also rare, and appear on the far-right side of the distribution.
Summary Table
Key takeaway
Based on all of these information we gathered , you can see that right after a major drop ,the next day a noticeable recovery and a rebound happen and the market goes back up.
Equity market returns do not and I repeat again DO NOT follow a normal distribution. They exhibit fat tails, skewness, and volatility clustering, leading to more frequent extreme events than the normal curve predicts.
If you tried to time the market and bailed during the back-to-back sell-offs on April 3 and April 4 due to the Tariff , you likely missed one of the best single-day gains in history just days later. Of course you can always cash out or trim some of your winners , and that’s the smart way to reach to a portfolio equilibrium.
Strategy implication
Always Stay invested and diversified. Don’t try to predict the unpredictable ,however you can always take a hunch based on similar historical events and be on the right side of equation.
If you’re playing binary events, use non-directional strategies instead of betting one way.
Because when the market decides to break the rules, it really breaks them.
I always like this term “intelligent restraint investor” , as being an intelligent restraint in this market is a vital trait you should nurture where you won’t sway out of fear in these market conditions.
Please if you have any questions or if you need to reach me , Leave me a message on : Medium or comment below, you can also take your time to view my list of research published papers at ResearchGate.
IEEE Member: 98768904
ResearchGate: https://www.researchgate.net/profile/Abdalla-Mahgoub
