Financial Calculations & Valuation Advanced

Markowitz Mean-Variance Portfolio Optimization in Python (SciPy)

Find the optimal asset allocation weights that maximize the Sharpe Ratio using SciPySLSQP optimization and historical covariance matrices in Python.

#pandas#numpy#scipy

Problem Statement

Equal-weight portfolios ignore asset correlations. This script uses Sequential Least Squares Programming (SLSQP) to compute exact portfolio weights that maximize risk-adjusted return.

Formula / Core Logic

Portfolio Variance = W^T * Cov_Matrix * W Objective: Minimize (-Sharpe Ratio) subject to Sum(W) = 1 and 0 <= W_i <= 1.

Installation

pip install pandas numpy scipy

markowitz-portfolio-optimization-efficient-frontier-python.py

import numpy as np
import pandas as pd
from scipy.optimize import minimize

def optimize_max_sharpe(returns_df, rf=0.05):
    mean_ret = returns_df.mean() * 252
    cov_matrix = returns_df.cov() * 252
    num_assets = len(mean_ret)
    
    def neg_sharpe(weights):
        port_ret = np.dot(weights, mean_ret)
        port_vol = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
        return -(port_ret - rf) / port_vol
        
    constraints = ({'type': 'eq', 'fun': lambda w: np.sum(w) - 1})
    bounds = tuple((0, 1) for _ in range(num_assets))
    init_w = num_assets * [1. / num_assets]
    
    opt = minimize(neg_sharpe, init_w, method='SLSQP', bounds=bounds, constraints=constraints)
    return dict(zip(returns_df.columns, np.round(opt.x, 4)))

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Frequently Asked Questions

Q: How do I prevent 80% allocation into a single stock?

Change `bounds = tuple((0, 0.25) for _ in range(num_assets))` to cap any single position at 25%.