A deterministic projection assumes a single return each year — say, 7% — and compounds the portfolio forward. The result is a single number that gives no indication of how likely that outcome actually is, or how bad things could get if returns deviate from the assumption.

This approach has three critical limitations for endowment planning:

Each "path" in a Monte Carlo simulation represents one possible sequence of annual asset class returns over the projection horizon, generated by randomly sampling from the assumed return distribution for each asset class while preserving the correlation structure between them. With 1,000,000 paths, the simulation explores a comprehensive range of market environments — from extreme bear markets to extended bull runs — and every combination in between.

The large path count serves an important statistical purpose: it stabilizes the tails of the distribution. With 10,000 paths, the 1st percentile outcome might shift by 5-10% between runs. With 1,000,000 paths, the extreme tail statistics are stable enough that an investment committee can rely on the 5th percentile (P5) and 95th percentile (P95) as robust downside and upside reference points. This is critical when the committee's primary concern is not the median outcome but the severity of bad outcomes.

One of the most important technical challenges in portfolio simulation is generating random returns that respect the correlation structure among asset classes. You cannot simply draw independent random numbers for each asset class — public equity and private equity tend to move together, while fixed income often moves differently. Generating returns that preserve these relationships is essential for realistic portfolio simulation.

Cholesky decomposition is the mathematical technique used to address this problem. It takes the correlation matrix specified by the user (or by capital market assumptions) and decomposes it into a lower-triangular matrix that, when multiplied by independent random draws, produces returns with exactly the desired correlations. The result: when public equities decline 20%, private equity and real assets tend to decline as well — with the strength of the co-movement matching the correlation assumptions the investment committee has reviewed and approved.

A percentile fan chart is the most common visualization of Monte Carlo results for endowment portfolios. It shows the portfolio value distribution at each future year as a set of percentile bands:

For board presentations, the most commonly referenced percentiles are the median (P50) for the central expectation and P10/P25 for downside risk assessment. A committee might say: "Our median projection shows the endowment reaching $247M in 10 years, but in a P10 downside scenario — which we should plan for — it would be $141M, and our spending policy would need to adjust."

The probability of depletion — the percentage of simulation paths in which the portfolio value reaches zero or a critically low threshold within the projection horizon — is one of the most intuitive risk metrics Monte Carlo simulation provides. For a perpetual endowment, this probability should approach zero; for a foundation with a defined spend-down horizon, it becomes a planning parameter.

A depletion probability of 8.4%, for example, means that in roughly 1 out of 12 market environments, the portfolio would be exhausted before the end of the projection horizon — a level that most investment committees would consider unacceptably high and that would prompt a review of spending rate, asset allocation, or both.