""" SFM_ch12_crypto =============== Cryptocurrency Markets: Bitcoin Analysis Description: - Download BTC-USD and S&P 500 data - Compare return distributions and volatility - Stablecoin peg stability analysis (USDT, USDC) - Rolling volatility comparison - Correlation dynamics between BTC and traditional assets Statistics of Financial Markets course """ import numpy as np import pandas as pd import matplotlib.pyplot as plt import yfinance as yf from scipy import stats import warnings warnings.filterwarnings('ignore') # --- Standard chart style --- plt.rcParams['figure.facecolor'] = 'none' plt.rcParams['axes.facecolor'] = 'none' plt.rcParams['savefig.facecolor'] = 'none' plt.rcParams['savefig.transparent'] = True plt.rcParams['axes.grid'] = False plt.rcParams['font.family'] = 'sans-serif' plt.rcParams['font.sans-serif'] = ['Helvetica', 'Arial', 'DejaVu Sans'] plt.rcParams['font.size'] = 8 plt.rcParams['axes.labelsize'] = 9 plt.rcParams['axes.titlesize'] = 10 plt.rcParams['axes.spines.top'] = False plt.rcParams['axes.spines.right'] = False plt.rcParams['axes.linewidth'] = 0.5 plt.rcParams['lines.linewidth'] = 0.75 plt.rcParams['legend.facecolor'] = 'none' plt.rcParams['legend.framealpha'] = 0 def save_fig(name): plt.savefig(f'../../charts/{name}.pdf', bbox_inches='tight', transparent=True) plt.savefig(f'../../charts/{name}.png', bbox_inches='tight', transparent=True, dpi=300) plt.close() print(f" Saved: {name}.pdf") print("=" * 70) print("SFM CHAPTER 12: CRYPTOCURRENCY MARKETS") print("=" * 70) # ============================================================================= # 1. Download Data # ============================================================================= print("\n1. DOWNLOADING DATA") print("-" * 40) tickers = {'BTC-USD': 'Bitcoin', 'ETH-USD': 'Ethereum', '^GSPC': 'S&P 500', 'GLD': 'Gold'} prices = {} returns = {} for tick, name in tickers.items(): d = yf.download(tick, start='2018-01-01', end='2024-12-31', progress=False) p = d['Close'].squeeze() prices[tick] = p r = np.log(p / p.shift(1)).dropna() returns[tick] = r print(f" {name:12s} ({tick}): {len(r)} observations") # Download stablecoin stable_tickers = ['USDT-USD', 'USDC-USD'] stable_prices = {} for st in stable_tickers: d = yf.download(st, start='2018-01-01', end='2024-12-31', progress=False) stable_prices[st] = d['Close'].squeeze() print(f" {st:12s}: {len(stable_prices[st])} observations") # ============================================================================= # 2. Descriptive Statistics # ============================================================================= print("\n2. DESCRIPTIVE STATISTICS (annualized)") print("-" * 40) print(f" {'Asset':<12} {'Return':>10} {'Vol':>10} {'Skew':>8} " f"{'Kurt':>8} {'Sharpe':>8}") print(" " + "-" * 58) for tick, name in tickers.items(): r = returns[tick] trading_days = 365 if 'USD' in tick else 252 ann_ret = r.mean() * trading_days ann_vol = r.std() * np.sqrt(trading_days) skew = stats.skew(r) kurt = stats.kurtosis(r) sharpe = (ann_ret - 0.02) / ann_vol print(f" {name:<12} {ann_ret:>10.4f} {ann_vol:>10.4f} " f"{skew:>8.2f} {kurt:>8.2f} {sharpe:>8.4f}") # ============================================================================= # 3. Stablecoin Analysis # ============================================================================= print("\n3. STABLECOIN PEG STABILITY") print("-" * 40) for st in stable_tickers: if st in stable_prices: p = stable_prices[st] dev = p - 1.0 print(f" {st}:") print(f" Mean deviation from $1: {dev.mean():.6f}") print(f" Std deviation: {dev.std():.6f}") print(f" Max deviation: {dev.max():.6f}") print(f" Min deviation: {dev.min():.6f}") print(f" % within +/-0.01: " f"{(np.abs(dev) < 0.01).mean() * 100:.1f}%") # ============================================================================= # 4. FIGURE: Crypto Analysis (6-panel) # ============================================================================= print("\n4. CREATING FIGURE") print("-" * 40) fig, axes = plt.subplots(3, 2, figsize=(14, 14)) # Common date range for BTC vs S&P comparison common_idx = returns['BTC-USD'].index.intersection( returns['^GSPC'].index) btc_r = returns['BTC-USD'].reindex(common_idx).dropna() sp_r = returns['^GSPC'].reindex(common_idx).dropna() common = btc_r.index.intersection(sp_r.index) btc_r = btc_r.loc[common] sp_r = sp_r.loc[common] # Panel A: Cumulative returns colors_p = ['#E67E22', '#8E44AD', '#1A3A6E', '#2E7D32'] for (tick, name), color in zip(tickers.items(), colors_p): p = prices[tick] cum = p / p.iloc[0] axes[0, 0].plot(cum.index, cum, color=color, linewidth=0.8, label=name) axes[0, 0].set_title('Cumulative Returns (Normalized)', fontweight='bold') axes[0, 0].set_xlabel('Date') axes[0, 0].set_ylabel('Growth of $1') axes[0, 0].set_yscale('log') axes[0, 0].legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=4, frameon=False) # Panel B: Rolling 30-day volatility window = 30 for (tick, name), color in zip(tickers.items(), colors_p): r = returns[tick] trading_days = 365 if 'USD' in tick else 252 vol = r.rolling(window).std() * np.sqrt(trading_days) * 100 axes[0, 1].plot(vol.index, vol, color=color, linewidth=0.6, alpha=0.8, label=name) axes[0, 1].set_title(f'Rolling {window}-Day Volatility (%)', fontweight='bold') axes[0, 1].set_xlabel('Date') axes[0, 1].set_ylabel('Annualized Volatility (%)') axes[0, 1].legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=4, frameon=False) # Panel C: Return distribution comparison (BTC vs S&P 500) axes[1, 0].hist(btc_r * 100, bins=100, density=True, alpha=0.5, color='#E67E22', edgecolor='white', label='Bitcoin') axes[1, 0].hist(sp_r * 100, bins=100, density=True, alpha=0.5, color='#1A3A6E', edgecolor='white', label='S&P 500') axes[1, 0].set_title('Return Distribution: BTC vs S&P 500', fontweight='bold') axes[1, 0].set_xlabel('Daily Return (%)') axes[1, 0].set_ylabel('Density') axes[1, 0].set_xlim(-15, 15) axes[1, 0].text(0.95, 0.95, f'BTC Kurt: {stats.kurtosis(btc_r):.1f}\n' f'SPX Kurt: {stats.kurtosis(sp_r):.1f}', transform=axes[1, 0].transAxes, ha='right', va='top', fontsize=8, bbox=dict(boxstyle='round', facecolor='white', alpha=0.8)) axes[1, 0].legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=2, frameon=False) # Panel D: Rolling correlation BTC vs S&P 500 roll_corr = btc_r.rolling(60).corr(sp_r) axes[1, 1].plot(roll_corr.index, roll_corr, color='#1A3A6E', linewidth=0.8) axes[1, 1].axhline(y=0, color='gray', linestyle='--', linewidth=0.5) axes[1, 1].fill_between(roll_corr.index, 0, roll_corr, alpha=0.15, color='#1A3A6E') axes[1, 1].set_title('Rolling 60-Day Correlation: BTC vs S&P 500', fontweight='bold') axes[1, 1].set_xlabel('Date') axes[1, 1].set_ylabel('Correlation') avg_corr = roll_corr.mean() axes[1, 1].text(0.05, 0.95, f'Mean: {avg_corr:.3f}', transform=axes[1, 1].transAxes, ha='left', va='top', fontsize=9, bbox=dict(boxstyle='round', facecolor='white', alpha=0.8)) # Panel E: Stablecoin peg stable_colors = ['#26A17B', '#2775CA'] for st, c in zip(stable_tickers, stable_colors): if st in stable_prices: axes[2, 0].plot(stable_prices[st].index, stable_prices[st], color=c, linewidth=0.5, label=st.replace('-USD', '')) axes[2, 0].axhline(y=1.0, color='#DC3545', linestyle='--', linewidth=0.8, label='$1.00 peg') axes[2, 0].fill_between(stable_prices[stable_tickers[0]].index, 0.99, 1.01, alpha=0.1, color='gray', label='+/- 1% band') axes[2, 0].set_title('Stablecoin Peg Stability', fontweight='bold') axes[2, 0].set_xlabel('Date') axes[2, 0].set_ylabel('Price (USD)') axes[2, 0].set_ylim(0.95, 1.05) axes[2, 0].legend(loc='upper center', bbox_to_anchor=(0.5, -0.15), ncol=3, frameon=False) # Panel F: QQ-plot of Bitcoin returns stats.probplot(btc_r, dist="norm", plot=axes[2, 1]) axes[2, 1].set_title('Bitcoin Returns: QQ-Plot vs Normal', fontweight='bold') axes[2, 1].get_lines()[0].set_markerfacecolor('#E67E22') axes[2, 1].get_lines()[0].set_markersize(2) axes[2, 1].get_lines()[0].set_alpha(0.4) axes[2, 1].get_lines()[1].set_color('#DC3545') plt.tight_layout() save_fig('ch12_crypto') print("\n" + "=" * 70) print("CRYPTOCURRENCY ANALYSIS COMPLETE") print("=" * 70) print("\nKey findings:") print(" - Crypto returns exhibit much higher volatility than equities") print(" - Heavy tails are more pronounced in crypto markets") print(" - BTC-SPX correlation varies significantly over time") print(" - Stablecoins generally maintain their peg") print("\nOutput files:") print(" - ch12_crypto.pdf: 6-panel crypto analysis")