Monte Carlo Simulation for Portfolio Optimization

Monte Carlo simulation is a technique that solves complex problems by generating huge numbers of random scenarios and observing the aggregate outcome. Applied to portfolios, it's used to explore the space of possible weight combinations across several assets.

How it works for portfolios

1. You choose the assets (say, between 2 and 15 S&P 500 stocks).
2. Hundreds of thousands, or millions, of portfolios are generated with random weights.
3. Each one's historical return and risk is computed.
4. Plotting all of them, the shape of the efficient frontier emerges.

OjoAlTicker simulates up to 100,000 portfolios per horizon (quarterly and annual) in a vectorized way, then refines the result with an exact optimizer (SLSQP with multi-start) so it doesn't get stuck in a local optimum.

Advantages and limits

• Advantage: it needs no closed-form assumptions; it explores the problem "brute-force".
• Limit: it works with historical data. A portfolio that was optimal in the past isn't guaranteed to be optimal in the future — read the metrics as descriptive, not predictive.

Try the optimizer with your own assets to see the Monte Carlo cloud and the frontier in real time.