A Monte Carlo simulation draws thousands of scenarios at random. The draw follows a statistical law (the “distribution”) that you choose yourself. And that choice decides everything: the same portfolio can show 95% success under a normal distribution and 78% under Student-t. Before you look at your success rate, check the distribution that produced it.
The best-known: the famous bell curve. Returns spread out symmetrically around the average. Most years deliver a “normal” return, and extremes (crashes or booms) are assumed to be very rare.
With an 8% average and 15% volatility, this model predicts that 68% of years land between -7% and +23%, and 95% between -22% and +38%. A -50% crash? Statistically near-impossible. Yet it happened in 2008 and again in March 2020. The model is wrong, the markets are not.
The log-normal fixes the main flaw of the normal: a return cannot drop below -100%. You cannot lose more than what you own. It is also asymmetric: losses are bounded, gains are not.
An asset at $100 that loses 50% is worth $50. To get back to $100, it needs +100%, not +50%. This multiplicative asymmetry governs markets: the log-normal accounts for it, the normal does not. That is why professional financial models (Black-Scholes, VaR, Markowitz) are built on it.
Even the log-normal misses the truly extreme shocks. The 2008 crash (-38%), Black Monday 1987 (-22% in a single session), and the Covid drop of March 2020 (-34% in one month) are events the normal calls “impossible” and the log-normal calls “extremely rare.” The Student-t distribution adds fatter tails to reproduce these black swans.
For a first projection, log-normal. It is the default in serious tools and the right pick 90% of the time. For the final decision (“I quit my job in six months”), rerun the simulation under Student-t with 4 to 6 degrees of freedom. The success rate will drop by 5 to 15 points. That is exactly what a stress test is for: showing you the real margin, not the comfortable one.