How Monte Carlo simulation models uncertainty
A single projected line tells you only what happens if returns arrive in a perfectly smooth average. Real markets never behave that way. A Monte Carlo simulation replaces that one guess with thousands of randomised future paths, each drawn from the same expected return and volatility you set in the calculator. By running 10,000 independent trials, we build a full distribution of outcomes rather than a single number — and the shaded band on the chart is the 10th-to-90th percentile envelope of that distribution. The width of the band is a direct, visual measure of uncertainty: the more it spreads as the horizon extends, the less confidence any single prediction deserves.
The most useful figure the simulation produces is not the average — it is the P10, the outcome that 90% of paths beat and only 10% fall below. Planning toward a fixed date using the headline number quietly assumes you will be lucky. Planning toward the P10 assumes you will not be, which is the safer foundation for any goal whose deadline you cannot move.
Reading CAGR correctly
CAGR — the compound annual growth rate — is the single smoothed rate that would carry your starting balance to its ending balance over the period, as if the portfolio grew by exactly that percentage every year. It is valuable because it makes portfolios of different sizes and time spans directly comparable. But CAGR deliberately hides the journey: two portfolios can share an identical CAGR while one climbed steadily and the other lurched through a 40% drawdown along the way. CAGR also differs from the simple average of annual returns — because losses compound against a smaller base, the compound figure is always lower than the arithmetic average, and that gap widens as volatility rises. Always read CAGR next to a volatility figure; on its own it flatters a turbulent portfolio.
Assessing portfolio risk
Risk is never one number. Volatility — the standard deviation of returns, shown as σ in the calculator — measures how widely returns scatter around their average, but it treats upside surprises and downside shocks identically. Maximum drawdown, the largest peak-to-trough fall, captures the loss that actually tests an investor's nerve and cash-flow needs. The Sharpe ratio ties the ideas together: it expresses the return earned per unit of volatility above the risk-free rate, so a higher Sharpe means you were better compensated for the risk you carried.
Leverage interacts with every one of these measures at once. It scales expected return, but it scales volatility and drawdown just as hard, and it adds a financing cost that compounds against you in flat markets:
- Volatility rises roughly with the square root of leverage, so a 2× position is considerably more than twice as nerve-testing in practice.
- Drawdowns deepen faster than gains improve, because a leveraged loss must be recovered from a smaller base of capital.
- The model assumes you hold through the worst of it. In reality, forced selling at a low locks in the damage permanently.
Switching the display currency converts figures at today's mid-market rate; it does not hedge the underlying portfolio. Treat every projection here as an educational illustration of probability, not a forecast — the value of using a tool like this is building intuition for how return, time and risk trade against one another.