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72c80ab | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 | """Portfolio Optimizer - Risk-aware allocation engine."""
import numpy as np
import pandas as pd
from scipy.optimize import minimize
from typing import Dict, List, Optional, Tuple
import warnings
warnings.filterwarnings('ignore')
class PortfolioOptimizer:
"""Portfolio optimizer with constraints and robust optimization"""
def __init__(self,
max_weight: float = 0.20,
min_weight: float = 0.0,
target_return: Optional[float] = None,
risk_free_rate: float = 0.04,
transaction_cost: float = 0.0003,
turnover_penalty: float = 0.001,
risk_aversion: float = 1.0):
self.max_weight = max_weight
self.min_weight = min_weight
self.target_return = target_return
self.risk_free_rate = risk_free_rate
self.transaction_cost = transaction_cost
self.turnover_penalty = turnover_penalty
self.risk_aversion = risk_aversion
def optimize_mean_variance(self,
mu: np.ndarray,
Sigma: np.ndarray,
current_weights: Optional[np.ndarray] = None,
long_only: bool = True) -> Dict:
"""
Mean-variance optimization with transaction costs
Args:
mu: Expected returns vector (n_assets,)
Sigma: Covariance matrix (n_assets, n_assets)
current_weights: Current portfolio weights (n_assets,)
long_only: If True, weights must be >= 0
Returns:
Dict with weights, expected_return, volatility, sharpe
"""
n_assets = len(mu)
# Objective: maximize utility = return - risk_aversion * variance - transaction_costs
def objective(w):
port_return = np.dot(w, mu)
port_variance = np.dot(w, np.dot(Sigma, w))
# Transaction cost penalty
if current_weights is not None:
turnover = np.sum(np.abs(w - current_weights))
tc_penalty = self.turnover_penalty * turnover
else:
tc_penalty = 0
# Negative utility (for minimization)
return -(port_return - self.risk_aversion * port_variance - tc_penalty)
# Constraints
constraints = [{'type': 'eq', 'fun': lambda w: np.sum(w) - 1.0}] # Fully invested
if self.target_return is not None:
constraints.append(
{'type': 'eq', 'fun': lambda w: np.dot(w, mu) - self.target_return}
)
# Bounds
if long_only:
bounds = [(self.min_weight, self.max_weight) for _ in range(n_assets)]
else:
bounds = [(-self.max_weight, self.max_weight) for _ in range(n_assets)]
# Initial guess: equal weight
w0 = np.ones(n_assets) / n_assets
# Optimize
result = minimize(
objective,
w0,
method='SLSQP',
bounds=bounds,
constraints=constraints,
options={'maxiter': 1000, 'ftol': 1e-9}
)
if not result.success:
print(f"Optimization warning: {result.message}")
weights = result.x
weights = np.maximum(weights, 0) # Clean small negatives
weights /= np.sum(weights) # Renormalize
# Compute portfolio metrics
port_return = np.dot(weights, mu)
port_vol = np.sqrt(np.dot(weights, np.dot(Sigma, weights)))
sharpe = (port_return - self.risk_free_rate) / port_vol if port_vol > 0 else 0
return {
'weights': weights,
'expected_return': port_return,
'volatility': port_vol,
'sharpe_ratio': sharpe,
'success': result.success
}
def optimize_max_sharpe(self,
mu: np.ndarray,
Sigma: np.ndarray,
current_weights: Optional[np.ndarray] = None) -> Dict:
"""Optimize for maximum Sharpe ratio"""
n_assets = len(mu)
def neg_sharpe(w):
port_return = np.dot(w, mu)
port_vol = np.sqrt(np.dot(w, np.dot(Sigma, w)))
if current_weights is not None:
turnover = np.sum(np.abs(w - current_weights))
port_return -= self.turnover_penalty * turnover
return -(port_return - self.risk_free_rate) / (port_vol + 1e-8)
constraints = [{'type': 'eq', 'fun': lambda w: np.sum(w) - 1.0}]
bounds = [(self.min_weight, self.max_weight) for _ in range(n_assets)]
w0 = np.ones(n_assets) / n_assets
result = minimize(
neg_sharpe,
w0,
method='SLSQP',
bounds=bounds,
constraints=constraints,
options={'maxiter': 1000}
)
weights = result.x
weights = np.maximum(weights, 0)
weights /= np.sum(weights)
port_return = np.dot(weights, mu)
port_vol = np.sqrt(np.dot(weights, np.dot(Sigma, weights)))
sharpe = (port_return - self.risk_free_rate) / port_vol
return {
'weights': weights,
'expected_return': port_return,
'volatility': port_vol,
'sharpe_ratio': sharpe,
'success': result.success
}
def optimize_min_volatility(self,
mu: np.ndarray,
Sigma: np.ndarray,
min_return: Optional[float] = None) -> Dict:
"""Optimize for minimum volatility with optional return constraint"""
n_assets = len(mu)
def variance(w):
return np.dot(w, np.dot(Sigma, w))
constraints = [{'type': 'eq', 'fun': lambda w: np.sum(w) - 1.0}]
if min_return is not None:
constraints.append(
{'type': 'ineq', 'fun': lambda w: np.dot(w, mu) - min_return}
)
bounds = [(self.min_weight, self.max_weight) for _ in range(n_assets)]
w0 = np.ones(n_assets) / n_assets
result = minimize(
variance,
w0,
method='SLSQP',
bounds=bounds,
constraints=constraints,
options={'maxiter': 1000}
)
weights = result.x
weights = np.maximum(weights, 0)
weights /= np.sum(weights)
port_return = np.dot(weights, mu)
port_vol = np.sqrt(np.dot(weights, np.dot(Sigma, weights)))
sharpe = (port_return - self.risk_free_rate) / port_vol if port_vol > 0 else 0
return {
'weights': weights,
'expected_return': port_return,
'volatility': port_vol,
'sharpe_ratio': sharpe,
'success': result.success
}
def robust_optimization(self,
mu: np.ndarray,
Sigma: np.ndarray,
mu_uncertainty: Optional[np.ndarray] = None,
Sigma_uncertainty: Optional[float] = None) -> Dict:
"""
Robust optimization with uncertainty sets
Uses worst-case approach: optimize for worst-case mu within uncertainty ellipsoid
"""
n_assets = len(mu)
if mu_uncertainty is None:
# Default: 20% uncertainty on expected returns
mu_uncertainty = np.abs(mu) * 0.2
# Worst-case return: mu - uncertainty
mu_worst = mu - mu_uncertainty
# Add covariance uncertainty
if Sigma_uncertainty is not None:
Sigma_robust = Sigma + np.eye(n_assets) * Sigma_uncertainty
else:
Sigma_robust = Sigma
return self.optimize_mean_variance(mu_worst, Sigma_robust)
def black_litterman(self,
market_caps: np.ndarray,
Sigma: np.ndarray,
risk_aversion: float = 2.5,
views: Optional[List[Dict]] = None,
view_confidence: float = 0.5) -> Dict:
"""
Black-Litterman model for incorporating investor views
Args:
market_caps: Market capitalization weights
Sigma: Covariance matrix
risk_aversion: Risk aversion parameter
views: List of view dicts with 'assets', 'direction', 'magnitude'
view_confidence: Confidence in views (0-1)
"""
n_assets = len(market_caps)
# Implied equilibrium returns
Pi = risk_aversion * np.dot(Sigma, market_caps)
if views is None or len(views) == 0:
# No views: use market equilibrium
return self.optimize_mean_variance(Pi, Sigma)
# Build view matrix P and view vector Q
P = []
Q = []
Omega_diag = []
for view in views:
assets = view['assets']
direction = view['direction'] # 'overweight' or 'underweight'
magnitude = view['magnitude']
p_row = np.zeros(n_assets)
for asset in assets:
p_row[asset] = 1.0 / len(assets)
P.append(p_row)
Q.append(magnitude if direction == 'overweight' else -magnitude)
Omega_diag.append(view_confidence)
P = np.array(P)
Q = np.array(Q)
Omega = np.diag(Omega_diag)
# Black-Litterman formula
tau = 0.05 # Uncertainty scaling
M_inverse = np.linalg.inv(tau * Sigma)
middle = np.linalg.inv(np.dot(np.dot(P, tau * Sigma), P.T) + Omega)
BL_mu = Pi + np.dot(
np.dot(tau * Sigma, P.T),
np.dot(middle, Q - np.dot(P, Pi))
)
BL_Sigma = Sigma + tau * Sigma - np.dot(
np.dot(tau * Sigma, P.T),
np.dot(middle, np.dot(P, tau * Sigma))
)
return self.optimize_mean_variance(BL_mu, BL_Sigma)
def compute_efficient_frontier(self,
mu: np.ndarray,
Sigma: np.ndarray,
n_points: int = 50) -> pd.DataFrame:
"""Compute efficient frontier points"""
min_vol_result = self.optimize_min_volatility(mu, Sigma)
max_ret_result = self.optimize_mean_variance(mu, Sigma, target_return=np.max(mu))
min_ret = min_vol_result['expected_return']
max_ret = max_ret_result['expected_return']
target_returns = np.linspace(min_ret, max_ret, n_points)
frontier = []
for target in target_returns:
result = self.optimize_mean_variance(mu, Sigma, target_return=target)
frontier.append({
'target_return': target,
'volatility': result['volatility'],
'sharpe': result['sharpe_ratio']
})
return pd.DataFrame(frontier)
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