| import numpy as np |
| import pandas as pd |
| import cvxpy as cp |
| import logging |
|
|
| logger = logging.getLogger(__name__) |
|
|
| class PortfolioOptimizer: |
| """ |
| Given a DataFrame of pair‐level returns (columns = pair names, rows = dates), |
| solves a minimum‐variance allocation (or any convex objective). |
| """ |
|
|
| def __init__( |
| self, |
| pair_returns: pd.DataFrame, |
| min_weight: float = 0.0, |
| max_weight: float = 0.1 |
| ): |
| """ |
| :param pair_returns: DataFrame (T×N) of returns for N pairs. |
| :param min_weight: lower bound for each weight. |
| :param max_weight: upper bound for each weight. |
| """ |
| self.returns = pair_returns.dropna(how="all") |
| self.N = self.returns.shape[1] |
| self.min_w = min_weight |
| self.max_w = max_weight |
|
|
| def min_variance(self) -> pd.Series: |
| """ |
| Solve: minimize wᵀ Σ w subject to ∑w = 1, and min_w ≤ w_i ≤ max_w. |
| Returns a Series of weights indexed by pair names. |
| """ |
| cov = self.returns.cov().values |
| cov += np.eye(self.N) * 1e-6 |
|
|
| w = cp.Variable(self.N) |
| objective = cp.Minimize(cp.quad_form(w, cov)) |
| constraints = [ |
| cp.sum(w) == 1, |
| w >= self.min_w, |
| w <= self.max_w |
| ] |
| prob = cp.Problem(objective, constraints) |
| prob.solve(solver=cp.OSQP, verbose=False) |
|
|
| if w.value is None: |
| logger.error("Portfolio optimization failed.") |
| |
| w_opt = np.ones(self.N) / self.N |
| else: |
| w_opt = w.value |
|
|
| weights = pd.Series(w_opt, index=self.returns.columns) |
| logger.info(f"Min‐variance weights computed: {weights.to_dict()}") |
| return weights |
|
|
