Simulating stock market returns using Monte Carlo › 6. Creating Meaningful Visualizations

# Portfolio Value Distribution Histogram
fig, ax = plt.subplots(figsize=(12, 8))

# Filter out values over $600 to focus on the main distribution
filtered_values = final_portfolio_values[final_portfolio_values <= 600]

# Creating histogram with modern aesthetics
n, bins, patches = ax.hist(filtered_values, bins=60, alpha=0.7, 
                          edgecolor='white', linewidth=0.5, color='#3498db')

# Adding vertical lines for key percentiles with better positioning
percentiles = [5, 25, 50, 75, 95]
percentile_values = np.percentile(final_portfolio_values, percentiles)
colors = ['#e74c3c', '#f39c12', '#27ae60', '#f39c12', '#e74c3c']
labels = ['5th%', '25th%', 'Median', '75th%', '95th%']

max_height = n.max()
for i, (perc, val, color, label) in enumerate(zip(percentiles, percentile_values, colors, labels)):
    if val <= 600:
        ax.axvline(val, color=color, linestyle='-', linewidth=2, alpha=0.8)
        ax.text(val, max_height * (0.85 - i * 0.1), f'{label}\n${val:.0f}', 
                ha='center', va='top', fontweight='600', fontsize=10,
                bbox=dict(boxstyle="round,pad=0.4", facecolor='white', alpha=0.9, edgecolor=color, linewidth=1.5),
                color='#2c3e50')

# Adding initial investment line for reference
ax.axvline(INITIAL_INVESTMENT, color='#2c3e50', linestyle='-', linewidth=2)
ax.text(INITIAL_INVESTMENT, max_height * 0.95, f'Initial\n${INITIAL_INVESTMENT:.0f}', 
        ha='center', va='top', fontweight='600', fontsize=10,
        bbox=dict(boxstyle="round,pad=0.4", facecolor='white', alpha=0.9, edgecolor='#2c3e50', linewidth=1.5),
        color='#2c3e50')

# Calculate excluded scenarios
excluded_count = len(final_portfolio_values) - len(filtered_values)
excluded_pct = (excluded_count / len(final_portfolio_values)) * 100

ax.set_title(f"Portfolio Value Distribution After {YEARS} Years\n"
             f"Expected Return: {MU:.1%} • Volatility: {SIGMA:.1%} • {N_ITER:,} Simulations",
             fontsize=16, fontweight='600', pad=20, color='#2c3e50')
ax.set_xlabel("Final Portfolio Value ($)", fontsize=13, fontweight='500', color='#2c3e50')
ax.set_ylabel("Number of Simulations", fontsize=13, fontweight='500', color='#2c3e50')

# Adding summary statistics in a cleaner box
stats_text = f"Expected Value: ${final_portfolio_values.mean():.0f}\n" \
            f"Median: ${np.median(final_portfolio_values):.0f}\n" \
            f"Loss Probability: {prob_loss:.1f}%\n" \
            f"Double Probability: {prob_double:.1f}%"

ax.text(0.97, 0.97, stats_text, transform=ax.transAxes, fontsize=11, fontweight='600',
        va='top', ha='right', color='#2c3e50',
        bbox=dict(boxstyle="round,pad=0.5", facecolor='white', alpha=0.95, 
                  edgecolor='#bdc3c7', linewidth=1))

# Clean up the plot
ax.grid(True, alpha=0.3, color='#ecf0f1')
ax.set_axisbelow(True)

plt.tight_layout()
plt.show()

# Box Plot showing percentile ranges with modern styling
fig, ax = plt.subplots(figsize=(10, 8))

box_data = [final_portfolio_values]
bp = ax.boxplot(box_data, patch_artist=True, tick_labels=['Portfolio Values'],
               medianprops=dict(color='#27ae60', linewidth=2.5),
               boxprops=dict(facecolor='#3498db', alpha=0.6, edgecolor='#2980b9', linewidth=1.5),
               whiskerprops=dict(color='#34495e', linewidth=1.5),
               capprops=dict(color='#34495e', linewidth=1.5),
               flierprops=dict(marker='o', markerfacecolor='#e74c3c', alpha=0.5, markersize=4))

# Adding percentile annotations with cleaner styling
percentiles_to_show = [5, 25, 50, 75, 95]
perc_values = np.percentile(final_portfolio_values, percentiles_to_show)
colors = ['#e74c3c', '#f39c12', '#27ae60', '#f39c12', '#e74c3c']

for i, (perc, val, color) in enumerate(zip(percentiles_to_show, perc_values, colors)):
    ax.annotate(f'{perc}th: ${val:.0f}', 
                xy=(1, val), xytext=(1.15, val),
                fontsize=11, ha='left', va='center', fontweight='600',
                color=color,
                arrowprops=dict(arrowstyle='->', color=color, alpha=0.7, lw=1.2))

ax.set_title('Portfolio Value Distribution Summary', 
             fontweight='600', fontsize=16, color='#2c3e50', pad=20)
ax.set_ylabel('Portfolio Value ($)', fontweight='500', fontsize=13, color='#2c3e50')
ax.grid(True, alpha=0.3, color='#ecf0f1', axis='y')
ax.set_axisbelow(True)

# Remove top and right spines for cleaner look
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['left'].set_color('#bdc3c7')
ax.spines['bottom'].set_color('#bdc3c7')

plt.tight_layout()
plt.show()

# Cumulative Distribution Function (CDF) with modern styling
fig, ax = plt.subplots(figsize=(12, 8))

sorted_values = np.sort(final_portfolio_values)
cumulative_prob = np.arange(1, len(sorted_values) + 1) / len(sorted_values)

# Main CDF line with gradient-like effect
ax.plot(sorted_values, cumulative_prob * 100, linewidth=3, color='#3498db', 
        label='Cumulative Probability', alpha=0.9)

# Reference lines
ax.axvline(INITIAL_INVESTMENT, color='#e74c3c', linestyle='--', alpha=0.8, 
          linewidth=2, label='Break-even ($100)')
ax.axhline(50, color='#95a5a6', linestyle=':', alpha=0.7, 
          linewidth=2, label='50% Probability')

# Key probability markers with modern styling
key_values = [150, 200, 250, 300]
marker_colors = ['#e67e22', '#f39c12', '#27ae60', '#8e44ad']

for val, color in zip(key_values, marker_colors):
    prob = (final_portfolio_values <= val).mean() * 100
    ax.plot(val, prob, 'o', markersize=8, color=color, 
           markeredgecolor='white', markeredgewidth=2, zorder=5)
    ax.annotate(f'${val}: {prob:.0f}%', 
               xy=(val, prob), xytext=(val+25, prob+8),
               fontsize=11, ha='left', fontweight='600', color=color,
               bbox=dict(boxstyle="round,pad=0.3", facecolor=color, alpha=0.15, 
                        edgecolor=color, linewidth=1),
               arrowprops=dict(arrowstyle='->', color=color, alpha=0.7, lw=1.2))

ax.set_title('Cumulative Probability Distribution', 
             fontweight='600', fontsize=16, color='#2c3e50', pad=20)
ax.set_xlabel('Portfolio Value ($)', fontweight='500', fontsize=13, color='#2c3e50')
ax.set_ylabel('Probability (%)', fontweight='500', fontsize=13, color='#2c3e50')

# Modern legend styling
ax.legend(fontsize=11, frameon=True, fancybox=True, shadow=False,
         facecolor='white', edgecolor='#bdc3c7', framealpha=0.9)

# Clean grid and spines
ax.grid(True, alpha=0.3, color='#ecf0f1')
ax.set_axisbelow(True)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['left'].set_color('#bdc3c7')
ax.spines['bottom'].set_color('#bdc3c7')

plt.tight_layout()
plt.show()

# Portfolio growth over time with modern styling
fig, ax = plt.subplots(figsize=(12, 8))

# Calculate portfolio values for each year for sample scenarios
sample_scenarios = annual_returns[:100, :]  # First 100 scenarios
portfolio_evolution = np.zeros((100, YEARS + 1))  # +1 for initial value
portfolio_evolution[:, 0] = INITIAL_INVESTMENT

for year in range(YEARS):
    portfolio_evolution[:, year + 1] = portfolio_evolution[:, year] * (1 + sample_scenarios[:, year])

# Plot sample paths (very light gray lines)
for i in range(20):
    ax.plot(np.arange(YEARS + 1), portfolio_evolution[i, :], 
           alpha=0.15, color='#95a5a6', linewidth=0.8, zorder=1)

# Calculate evolution for all scenarios for confidence bands
all_portfolio_evolution = np.zeros((N_ITER, YEARS + 1))
all_portfolio_evolution[:, 0] = INITIAL_INVESTMENT

for year in range(YEARS):
    all_portfolio_evolution[:, year + 1] = all_portfolio_evolution[:, year] * (1 + annual_returns[:, year])

# Add confidence bands with gradient-like colors
percentile_5 = np.percentile(all_portfolio_evolution, 5, axis=0)
percentile_95 = np.percentile(all_portfolio_evolution, 95, axis=0)
percentile_25 = np.percentile(all_portfolio_evolution, 25, axis=0)
percentile_75 = np.percentile(all_portfolio_evolution, 75, axis=0)

# Fill confidence bands with different opacities
ax.fill_between(np.arange(YEARS + 1), percentile_5, percentile_95, 
               alpha=0.15, color='#3498db', label='90% Confidence Band', zorder=2)
ax.fill_between(np.arange(YEARS + 1), percentile_25, percentile_75, 
               alpha=0.25, color='#3498db', label='50% Confidence Band', zorder=3)

# Plot median line
median_evolution = np.percentile(all_portfolio_evolution, 50, axis=0)
ax.plot(np.arange(YEARS + 1), median_evolution, linewidth=3, color='#27ae60', 
        linestyle='--', label='Median Growth Path', zorder=4)

# Plot average evolution
mean_evolution = all_portfolio_evolution.mean(axis=0)
ax.plot(np.arange(YEARS + 1), mean_evolution, linewidth=3, color='#e74c3c', 
        label='Expected Growth Path', zorder=5)

# Add initial investment reference line
ax.axhline(INITIAL_INVESTMENT, color='#34495e', linestyle=':', alpha=0.7, 
          linewidth=1.5, label='Initial Investment')

ax.set_title('Portfolio Growth Trajectories Over Time', 
             fontweight='600', fontsize=16, color='#2c3e50', pad=20)
ax.set_xlabel('Year', fontweight='500', fontsize=13, color='#2c3e50')
ax.set_ylabel('Portfolio Value ($)', fontweight='500', fontsize=13, color='#2c3e50')

# Modern legend styling
ax.legend(fontsize=11, frameon=True, fancybox=True, shadow=False,
         facecolor='white', edgecolor='#bdc3c7', framealpha=0.9,
         loc='upper left')

# Clean grid and spines
ax.grid(True, alpha=0.3, color='#ecf0f1')
ax.set_axisbelow(True)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['left'].set_color('#bdc3c7')
ax.spines['bottom'].set_color('#bdc3c7')

# Set reasonable y-axis limits to avoid extreme outliers
ax.set_ylim(0, 600)

plt.tight_layout()
plt.show()