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}
        )

    # Bounds: no short selling (0 to 1 per asset)
    bounds = [(0, 1) for _ in range(n_assets)]

    # Initial guess: equal weight
    w0 = np.ones(n_assets) / n_assets

    if target_return is not None:
        # Minimize volatility for given return
        result = minimize(portfolio_volatility, w0,
                         bounds=bounds, constraints=constraints)
    else:
        # Maximize Sharpe ratio
        result = minimize(neg_sharpe, w0,
                         bounds=bounds, constraints=constraints)

    weights = result.x
    ret = weights @ expected_returns
    vol = portfolio_volatility(weights)

    return {
        "weights": {f"asset_{i}": round(w, 4) for i, w in enumerate(weights)},
        "expected_return": round(ret, 4),
        "volatility": round(vol, 4),
        "sharpe_ratio": round((ret - risk_free_rate) / vol, 4),
    }