CFA Level II Exam · Backtesting and Simulation

Monte Carlo Simulation in Portfolio Planning

Updated 7 October 2026 · Fact-checked

Monte Carlo simulation draws thousands of random values from specified distributions for inputs such as returns and inflation. Each run produces one possible outcome. The results show the range of outcomes, the probability of meeting a goal and a sustainable spending level. Read the vignette's assumptions, then judge the output.

Understand Monte Carlo Simulation in Portfolio Planning

A portfolio plan depends on uncertain things: returns, inflation, spending and how long you live. A single average-return projection hides this. Monte Carlo simulation replaces one projection with thousands of random ones.

The idea is simple. You choose a distribution for each risky input, for example a normal distribution with a stated mean and standard deviation for annual returns. A computer draws a random value for each input in each period. It rolls the portfolio forward over the planning horizon, applying contributions or withdrawals. That gives one possible ending value. You repeat this many thousands of times.

The set of results is a distribution of outcomes. From it you read the probability of success (the share of trials where the goal is met or money lasts), the shortfall in bad trials, and percentiles such as the 5th percentile ending wealth. You can also test spending: raise or lower withdrawals until the success probability reaches the level the client accepts. That level is a sustainable spending rate.

Simulation can handle things that formulas struggle with: path dependence (the order of returns matters when you withdraw money), changing contributions, taxes, and correlated assets. You can add correlations between inputs by drawing them jointly.

The key limit is that the output is only as good as the inputs. It is built on assumed distributions and parameters. If they are wrong, the answer is precise but wrong. Simulation gives an estimate of risk, not a guarantee. Compare it with historical simulation, which resamples actual past data and makes no distribution assumption, but can only reproduce what already happened.

Key formulas to remember

Probability of success: Success probability = number of trials meeting the goal ÷ total number of trials; Failure probability = 1 − success probability. Goal can be a target wealth or money lasting through the horizon.
Portfolio value roll-forward (one period): Vₜ = (Vₜ₋₁ − withdrawal) × (1 + rₜ); Timing of the withdrawal matters. Use the order the vignette states. rₜ is the random draw for that period.
Lognormal return draw: Vₜ = Vₜ₋₁ × e^rₜ, where rₜ is a continuously compounded return; Use when the vignette says continuously compounded returns are normally distributed. Prices cannot go below zero.
Standard error of a simulated mean: SE = s ÷ √N; s is the standard deviation of the trial results and N the number of trials. Quadrupling trials halves the error.

How to solve Monte Carlo Simulation in Portfolio Planning questions

Use this order for any item-set question on Monte Carlo simulation in planning.

1Identify the decision: goal probability, risk of ruin, sustainable spending, or comparing methods.
2Find the inputs in the vignette: return and volatility assumptions, distribution, correlations, inflation, horizon, contributions or withdrawals.
3Check what is random and what is fixed. Fixed spending, assumed correlations and a chosen distribution are all assumptions.
4Read the output exhibit carefully: success rate, percentiles, or ending value ranges. Note whether they are real or nominal.
5Answer using the exhibit. For probability, count successes over total trials. For spending, pick the level where success meets the client's required probability.
6Test the conclusion against limitations: wrong distribution, unstable parameters, ignored fat tails or correlation changes.
7If the question compares methods, match the feature to the method: parametric assumptions versus historical data resampling.

Quickest way: Read the exhibit, then match to the client's threshold

When to use it: Use when the vignette gives a results table and asks which plan, spending level or conclusion is supported.

Underline the client's required success probability or acceptable shortfall.
Scan the exhibit for the highest spending or riskiest allocation that still meets it.
Check that real versus nominal and the horizon match the question.
If asked about weaknesses, look for the stated assumption (normal returns, constant correlation) and say it may not hold.

Common mistakes in Monte Carlo Simulation in Portfolio Planning

Treating the success probability as a guarantee.
A figure like 85% looks precise.
Fix: It is an estimate conditional on the assumed distributions. Say the result depends on inputs.
Thinking more trials fix bad assumptions.
Students link accuracy with simulation count.
Fix: More trials reduce sampling error only. They do not correct a wrong distribution or wrong parameters.
Claiming Monte Carlo uses historical data.
Confusing it with historical simulation.
Fix: Monte Carlo draws from a specified distribution. Historical simulation resamples actual past returns.
Ignoring order of returns when withdrawals are made.
Students use the average return as in a simple projection.
Fix: Poor early returns with withdrawals hurt more. Simulation captures this path dependence.
Mixing real and nominal values.
Exhibits may give nominal ending wealth while the goal is in today's money.
Fix: Check labels and convert using the inflation assumption before comparing to the goal.
Saying a simulation can add correlations that were not specified.
Assuming the software knows them.
Fix: Correlations must be input. If they are omitted or held constant, diversification may be overstated in a crisis.

Worked examples

Example 1

A planner runs 10,000 Monte Carlo trials for a client who needs a portfolio to last 30 years of retirement. The client requires at least a 90% success probability. Results by annual real spending: ₹6,00,000 succeeded in 9,350 trials; ₹7,00,000 in 8,820 trials; ₹8,00,000 in 7,400 trials. (1) What is the success probability at ₹7,00,000? (2) Which spending level is the highest that meets the requirement? (3) What does failing in a trial mean?

Show the solution

(1) Success probability = 8,820 ÷ 10,000 = 88.2%.
(2) At ₹6,00,000 success is 9,350 ÷ 10,000 = 93.5%, which is at least 90%. At ₹7,00,000 it is 88.2%, below 90%. At ₹8,00,000 it is 74%. Only the first meets the requirement.
(3) A failed trial is one where the portfolio was exhausted before year 30 under that random path of returns.

Answer: (1) 88.2%. (2) ₹6,00,000 per year. (3) The money ran out before the horizon ended in that trial.

Example 2

An analyst compares two approaches for a pension plan. Method A draws annual returns from a normal distribution with mean 7% and standard deviation 12%. Method B resamples the plan's actual annual returns from the past 25 years. (1) Which method requires a distributional assumption? (2) Name one advantage of Method A. (3) Name one weakness of Method B.

Show the solution

(1) Method A specifies a distribution and its parameters, so it is Monte Carlo. Method B uses observed data and needs no assumed distribution.
(2) Method A can generate scenarios not seen in the past and can be changed to test different means, volatilities or correlations.
(3) Method B can only reproduce outcomes in the 25-year sample, so it may miss extreme events outside that history. It also assumes the past is representative.

Answer: (1) Method A. (2) It can model unseen scenarios and change assumptions flexibly. (3) It is limited to the historical sample and may miss events not in it.

Exam tips

Always locate the stated assumptions in the vignette. Limitation questions usually hinge on one of them.
Read exhibits for percentiles and success rates. Do not recompute anything the exhibit already gives.
Know the contrast: Monte Carlo uses a specified distribution, historical simulation uses actual past data.
Remember that more trials reduce sampling error only.
With no penalty for wrong answers, never leave a question blank.

Monte Carlo Simulation in Portfolio Planning in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Monte Carlo Simulation in Portfolio Planning: frequently asked questions

What are the steps in a Monte Carlo simulation?

Specify the model and the distributions and parameters of the risky inputs, including correlations. Draw random values for each period, compute the outcome for each trial, and repeat many times. Then analyse the distribution of outcomes.

How is Monte Carlo used in retirement planning?

It simulates many paths of returns and inflation while the client withdraws money. The share of paths where money lasts is the success probability. The planner adjusts spending or allocation until the probability meets the client's target.

What are the limitations of Monte Carlo simulation?

Results depend on the assumed distributions and parameters, which may be wrong or unstable. It can understate fat tails and crisis correlations, and it can be complex and hard to explain. It estimates risk and does not guarantee outcomes.

Monte Carlo vs historical simulation: which is better?

Neither is always better. Monte Carlo is flexible and can create unseen scenarios but relies on assumptions. Historical simulation uses real data without a distribution assumption but is limited to what has already happened.