What is a Monte Carlo simulation in financial planning?

A Monte Carlo simulation estimates how likely a financial plan is to succeed by running it through thousands of randomly generated market scenarios. Instead of assuming the same return every year, each scenario draws a different sequence of returns — good years, bad years, crashes and recoveries — and the plan is checked against every one of them. The result is not a single forecast but a range of outcomes and a probability of success.

The name comes from the casino in Monaco: like a roulette wheel, the method uses randomness to explore what could happen.

How it works

Define the plan: starting capital, contributions or withdrawals, horizon and goal.
Define the return model: usually an expected yearly return $\mu$ and a volatility $\sigma$ , sometimes with more realistic features such as fat tails.
Simulate: for each of thousands of paths, draw a return for every year at random and roll the portfolio forward, adding the contribution $C$ :

V_{t+1} = V_t \, (1 + r_t) + C \qquad r_t \sim \mathcal{N}(\mu, \sigma^2)

Count: the share of paths that reach the goal $G$ is the estimated probability of success.

P(\text{success}) = \frac{\text{Number of paths with } V_n \ge G}{\text{Number of paths}}

A simple illustration

A portfolio of €100,000 receives €6,000 a year for 20 years. The investments are expected to return 6% a year with a volatility of 15%. If every single year returned exactly 6%, the portfolio would end at about €541,000.

Across 10,000 simulated paths with those same assumptions, the outcomes spread widely:

Outcome	Portfolio after 20 years
Worst 10% of paths	below about €242,000
Median path	about €465,000
Best 10% of paths	above about €929,000
Chance of reaching €400,000	about 61%
Chance of reaching €500,000	about 44%

The same plan, across 10,000 paths. The spread - not the average - is what the simulation is for.

Two things stand out. The range is enormous: the same plan can end with a quarter of a million or close to a million. And the median path ends below the €541,000 of the steady-return calculation, because volatility lowers compounded growth. A plan built only on the average return would reach its target less than half the time.

How to use it

Judge a plan by its probability, not by a single projected number. Many planners aim for a success rate of 75–90%.
Test the levers: saving more, investing longer, lowering the goal or changing the allocation, and see how each moves the probability.
Look at the bad paths. The worst 10% of outcomes show what a plan must be able to survive.

Limits

The output is only as good as the assumptions. Expected returns, volatility and the shape of the distribution drive everything; optimistic inputs produce optimistic probabilities.
Simple models understate extremes. Normally distributed returns with no memory of the past produce fewer crashes and fewer long bad stretches than real markets.
It treats the plan as fixed. Real investors adjust their saving and spending along the way, which usually improves the outcome.

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