Monte Carlo Projections: how to estimate a stock's future

Nobody can predict the exact price of a stock in 6 months. But we can estimate the probability of the price being above or below certain levels. That's what Monte Carlo simulations are for.

The name comes from the famous Monaco casino, chosen as a metaphor for randomness. The method was developed by mathematicians Stanislaw Ulam and John von Neumann in the 1940s to solve nuclear physics problems. Today it is one of the most widely used risk management tools in finance.

What is a Monte Carlo simulation?

The Monte Carlo method applies thousands of random scenarios based on the asset's historical volatility. Each scenario is a possible price trajectory over time. By running, for example, 1,000 simulations, you get a complete probability distribution.

It's the same technique used by investment funds, investment banks and institutional risk managers to estimate the VaR (Value at Risk) of their portfolios.

The three scenarios and how to read them

Important: the pessimistic scenario is not "the worst that can happen", but rather "what happens in the 10% most unfavorable cases based on historical volatility". A black swan event (2008 crisis, 2020 pandemic) could exceed even that scenario.

How the simulation is built

The process has four steps:

• •Step 1: Calculate the historical volatility of the asset (standard deviation of daily returns over the last 252 trading days).
• •Step 2: Generate thousands of random numbers with normal distribution, calibrated with that volatility.
• •Step 3: Build a price trajectory for each random number, starting from the current price.
• •Step 4: Sort all final prices and extract percentiles P10, P50 and P90.

What volatility tells us about the scenarios

Volatility is the engine of the simulation. Companies with different risk profiles produce very different projections:

How to use projections in practice

Monte Carlo projections don't answer "should I buy this stock?" but rather "can I handle this risk?". The correct way to use them:

• •Define the maximum tolerable risk: If the pessimistic scenario (P10) implies a 40% loss and you can only absorb 20%, either reduce the position by half or don't invest.
• •Evaluate the asymmetry: Look for assets where the upside potential (P90 - current price) is at least 2x the downside potential (current price - P10). This is a 1:2 risk/reward ratio.
• •Compare assets: If two stocks have the same base expectation (P50) but one has much lower volatility, the first is more efficient in terms of risk.

Important limitations you should know

• •Past-based: The simulation uses historical volatility. If the market regime changes (interest rates, structural crisis), results partially lose their validity.
• •Don't predict discrete events: An unexpected earnings report, a takeover bid, a bankruptcy or a geopolitical crisis are not captured in historical volatility. They are "black swans" outside the model.
• •Assume normal distribution: Real markets have "fat tails" — extreme events occur more frequently than a normal distribution predicts.
• •Probabilities, not certainties: The base scenario is the most likely, not the one that will happen. In any specific case, anything within the range can occur.

Monte Carlo vs. fundamental analysis: are they complementary?

Yes, and it is precisely the most powerful combination. Fundamental analysis (Health Score, P/E, margins) tells you whether the company is solid. Monte Carlo projections tell you what the range of possible prices is given that risk profile. A company with a high Health Score and low volatility will have reassuring projections. One with a low Health Score and high volatility, very dispersed projections.

Frequently asked questions about Monte Carlo

How many simulations are enough?

With 1,000 simulations you already get a stable distribution. With 10,000 the percentiles are more precise but the practical difference is minimal. StocksAnalyzer uses a sufficient number to ensure statistically robust results.

Are 1-year projections reliable?

Less so than 3-6 month ones. The longer the time horizon, the greater the uncertainty and the wider the range of scenarios. For horizons of 2+ years, business fundamentals matter more than historical volatility.

What if the pessimistic scenario is very negative?

It means the asset has high volatility. It does not necessarily mean it will fall, just that uncertainty is high. You can still invest, but with a smaller position so the maximum tolerable loss does not exceed your personal limit.