Portfolio Optimization Guide

Portfolio Optimization Guide

A skill for implementing and researching portfolio optimization methods, from classical mean-variance optimization to modern robust and factor-based approaches. Covers Markowitz theory, Black-Litterman, risk parity, and machine learning-enhanced portfolio construction.

Mean-Variance Optimization

Classical Markowitz Portfolio

import numpy as np
from scipy.optimize import minimize

def mean_variance_optimize(expected_returns: np.ndarray,
                             cov_matrix: np.ndarray,
                             target_return: float = None,
                             risk_free_rate: float = 0.02) -> dict:
    """
    Markowitz mean-variance optimization.
    expected_returns: array of expected returns for each asset
    cov_matrix: covariance matrix of asset returns
    target_return: target portfolio return (None for max Sharpe)
    """
    n_assets = len(expected_returns)

    def portfolio_volatility(weights):
        return np.sqrt(weights @ cov_matrix @ weights)

    def neg_sharpe(weights):
        ret = weights @ expected_returns
        vol = portfolio_volatility(weights)
        return -(ret - risk_free_rate) / vol

    # Constraints
    constraints = [
        {"type": "eq", "fun": lambda w: np.sum(w) - 1},  # weights sum to 1
    ]
    if target_return is not None:
        constraints.append(
            {"type": "eq", "fun": lambda w: w @ expected_returns - target_return}
        )