Monte Carlo Simulation

Two retirees each start with $1,000,000 and withdraw $50,000 at the beginning of every year. Over twenty years they experience exactly the same set of twenty annual returns, but in reverse order from one another. Adviser Helena Vasquez observes that one ends with far more money than the other and must explain why.

1. A.The gap is explained entirely by the different geometric mean returns of the two sequences.Incorrect. Reversing the order of a fixed set of returns leaves the geometric mean unchanged, so it cannot explain the gap.
2. B.With withdrawals under way, the order of returns matters because early losses permanently shrink the base that later gains compound. This is sequence-of-returns risk.Correct. Withdrawals plus early losses lock in the damage, which no later run of good returns can fully repair.
3. C.Sequence of returns affects only accounts in the accumulation phase, so the difference must come from taking withdrawals at different points in the year.Incorrect. The effect is strongest in the withdrawal phase, and the stem states both withdraw at the start of each year.
4. D.The two outcomes must be identical because the average return is the same, so the difference is a calculation error.Incorrect. Identical averages produce identical results only when there are no cash flows in or out during the period.

Why: Once money is being withdrawn, the ORDER of returns matters enormously. A retiree who suffers losses in the first few years is selling assets into a falling market, which permanently shrinks the capital base that the later good years can compound. The retiree who gets the same bad years at the end has already banked years of growth on a larger base. This is sequence-of-returns risk, and it is the main reason advisers model retirement income with Monte Carlo simulation and cash buffers rather than with a single average return assumption.

A retirement planning tool runs 10,000 simulated market paths, drawing each year's return at random from an assumed distribution of returns and inflation, and reports that Sable Winthrop's withdrawal plan lasts 30 years in 84 percent of the trials. This technique is best described as:

1. A.A back test of Winthrop's actual historical account returnsA back test replays real historical data; this tool draws randomized returns from an assumed distribution.
2. B.A Monte Carlo simulation, which yields a probability distribution of outcomes and is only as sound as the return, volatility and inflation assumptions behind itCorrect. Randomized repeated trials producing a success probability is the hallmark of a Monte Carlo simulation.
3. C.An immunization strategy that matches asset duration to the liabilityImmunization is a bond portfolio technique for neutralizing interest rate risk, not a probabilistic projection.
4. D.A guarantee that the plan has an 84 percent chance of success regardless of the inputsThe probability is entirely conditional on the assumptions used; it is a model output, not a guarantee.

Why: A Monte Carlo simulation replaces a single straight-line projection with thousands of randomized paths, producing a probability distribution of outcomes rather than one deterministic answer. Its usefulness is that it captures sequence-of-returns effects that an average-return projection hides. Its limitation is that the output is entirely a function of the assumed return, volatility and inflation inputs, so the 84 percent figure is a modeled probability, not a promise.

A risk report tells the trustees of the Kelbrook Foundation that its $50,000,000 portfolio carries a one-year 95% VALUE AT RISK of $6,000,000. The trustees should understand this to mean that:

1. A.Under the model assumptions there is about a 5% probability of losing MORE than $6,000,000 over one year, and the measure says nothing about how large those tail losses could beCorrect. VaR gives a threshold and a confidence level, and is silent about the severity beyond the threshold.
2. B.The portfolio is expected to lose $6,000,000 over the coming yearVaR is not an expected value. The expected outcome for a diversified portfolio is normally a gain.
3. C.There is a 95% chance the portfolio will lose exactly $6,000,000The 95% attaches to staying within the threshold, not to any single loss amount occurring.
4. D.The portfolio cannot lose more than $6,000,000 in any one-year periodVaR sets no ceiling. Losses in the 5% tail can greatly exceed the VaR figure.

Why: Value at risk states a loss THRESHOLD at a stated confidence level over a stated horizon. A one-year 95% VaR of $6 million means that, under the model assumptions, there is roughly a 5% chance the portfolio loses more than $6 million over a year. Its central weakness is that it says nothing about the size of losses in that 5% tail, which can be far larger. It is a probability statement produced by a model, not a guarantee and not a forecast of the expected outcome.