We know that market returns are hardly i.i.d. Still, after the market turmoil following "Liberation Day" the markets finally started to recover and starting on 2025-04-17 the SPX went on a 9-day winning streak. Let's see how rare this has been historically.
I ran a simple using the historical SPX data from 1928 to date to count the number of consecutive up and down days. One important model choice is to make sure we don't count overlapping streaks, e.g. a 4-day streak counts only as a 4-day streak, and not toward 2 or 3-day streaks.
Overall Market Direction
- The market unsurprisingly shows a slight upward bias, with 52.4% of days being positive
- This translates to approximately 5.24 up days for every 4.76 down days
Maximum Streaks
- The longest observed up streak was 14 consecutive days (1971-04-15).
- The longest observed down streak was 12 consecutive days (1966-05-09).
- Interestingly both streaks occurred a decade known for its high volatility and wacky monetary policy.
Historical Streaks
Here's the complete breakdown of consecutive days in the S&P 500:
| Length | Up Days | Down Days |
|---|---|---|
| 2 | 1,490 | 1,498 |
| 3 | 866 | 804 |
| 4 | 441 | 352 |
| 5 | 213 | 181 |
| 6 | 125 | 82 |
| 7 | 65 | 40 |
| 8 | 36 | 13 |
| 9 | 14 | 8 |
| 10 | 8 | 3 |
| 11 | 3 | 3 |
| 12 | 5 | 2 |
| 13 | 0 | 0 |
| 14 | 1 | 0 |
Conclusion
The analysis reveals that while the market can maintain momentum in either direction, there's a natural limit to how long these streaks can persist. This is not surprising, as we know that equity markets show both volatility clustering and mean-reversion around trend. It is also worth nothing that conditional probability of continuing the streak one more day is basically the same as the unconditional probability of the market going up or down.
Code Snippet
SPX Historical Returns since 1928 (courtesy of Yahoo Finance) can be found here.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
# Read the data
df = pd.read_csv('SPX_historical_data.csv')
# Calculate daily returns and direction
df['Return'] = df['Close'].pct_change()
df['Direction'] = np.where(df['Return'] > 0, 1, -1) # 1 for up, -1 for down
# Calculate consecutive days
df['Consecutive_Days'] = df['Direction'] # Initialize with direction (1 or -1)
for i in range(1, len(df)):
if df.loc[i, 'Direction'] == df.loc[i-1, 'Direction']:
# If same direction, increment/decrement based on direction
df.loc[i, 'Consecutive_Days'] = df.loc[i-1, 'Consecutive_Days'] + df.loc[i, 'Direction']
else:
# If direction changes, reset to new direction
df.loc[i, 'Consecutive_Days'] = df.loc[i, 'Direction']
# Calculate unconditional probabilities
total_days = len(df)
up_days = (df['Direction'] == 1).sum()
down_days = (df['Direction'] == -1).sum()
p_up = up_days / total_days
p_down = down_days / total_days
# Find maximum observed consecutive days
max_up_streak = df[df['Direction'] == 1]['Consecutive_Days'].max()
max_down_streak = abs(df[df['Direction'] == -1]['Consecutive_Days'].min())
max_consecutive = max(max_up_streak, max_down_streak)
print(f"\nUnconditional Probabilities:")
print(f"Probability of Up Day: {p_up:.4f}")
print(f"Probability of Down Day: {p_down:.4f}")
print(f"\nMaximum Observed Streaks:")
print(f"Longest Up Streak: {max_up_streak} days")
print(f"Longest Down Streak: {max_down_streak} days")
# Function to find maximal streaks
def find_maximal_streaks(series, direction):
streaks = []
current_streak = 1
for i in range(1, len(series)):
if series.iloc[i] == direction and series.iloc[i-1] == direction:
current_streak += 1
else:
if current_streak > 1:
streaks.append(current_streak)
current_streak = 1
if current_streak > 1:
streaks.append(current_streak)
return streaks
# Get all maximal streaks
up_streaks = find_maximal_streaks(df['Direction'], 1)
down_streaks = find_maximal_streaks(df['Direction'], -1)
# Analyze patterns for different lengths
results = []
for n in range(2, max_consecutive + 1):
# Count streaks of exactly length n
up_count = up_streaks.count(n)
down_count = down_streaks.count(n)
results.append({
'n': n,
'up_count': up_count,
'down_count': down_count
})
# Print results
print("\nConsecutive Days Analysis:")
print("=" * 50)
print(f"{'Length':^6} | {'Up Days':^10} | {'Down Days':^10}")
print("-" * 50)
for r in results:
print(f"{r['n']:^6} | {r['up_count']:^10.0f} | {r['down_count']:^10.0f}")
# Create visualization
plt.figure(figsize=(12, 6))
n_values = [r['n'] for r in results]
up_actual = [r['up_count'] for r in results]
down_actual = [r['down_count'] for r in results]
plt.plot(n_values, up_actual, 'b-', label='Up Days', linewidth=2)
plt.plot(n_values, down_actual, 'r-', label='Down Days', linewidth=2)
plt.xlabel('Number of Consecutive Days')
plt.ylabel('Count')
plt.title('Historical Occurrences of Consecutive Days')
plt.legend()
plt.grid(True)
plt.savefig('consecutive_days_analysis.png')
plt.close()