Why Single-Scenario Projections Fall Short
Many people use single-scenario calculations like "at 5% annual return over 30 years, you'll have 30 million yen," but real markets don't deliver a steady return every year. One year might be +20%, the next -15%, with wild swings in between. Even with the same average return of 5%, the sequence of returns can dramatically alter the final asset value. Sequence risk - the danger of a market crash coinciding with the withdrawal phase - is a fatal risk that single-scenario projections simply cannot capture.
Monte Carlo simulation uses the mean and standard deviation of returns derived from historical market data to generate thousands or tens of thousands of future scenarios using random numbers. Each scenario is evaluated to determine whether assets are depleted, producing results like "there is an 87% probability that funds will last 30 years." This approach provides a broad outlook encompassing worst-case, median, and best-case scenarios.
Setting the Right Assumptions for Your Simulation
The accuracy of a Monte Carlo simulation depends heavily on its assumptions. The mean return and standard deviation vary depending on the time period and data source used. For example, the annualized return of U.S. equities over the past 30 years is roughly 10%, but over the past 100 years it is about 7%. Inflation rate, tax rate, and the rate of increase in withdrawals (inflation-linked) are also critical parameters. Whether you fix the annual withdrawal amount or set it as a percentage of the remaining balance also significantly changes the results.
Asset allocation also affects outcomes. A 100% equity portfolio has a higher average return but also a larger standard deviation, increasing the risk of asset depletion in worst-case scenarios. Books on retirement planning and asset allocation provide detailed guidance on adjusting asset allocation by age.
Success Probability Distribution from 10,000 Simulations
Let's analyze the results of running 10,000 Monte Carlo simulations for a case where 30 million yen in initial assets is withdrawn at 1.2 million yen per year. Assuming a portfolio of 60% equities and 40% bonds (expected return 5.0%, standard deviation 10.5%), the probability of funds lasting 30 years is approximately 82%. In the median scenario, about 12 million yen remains after 30 years, but in the bottom 10th percentile scenario, funds are depleted by year 18.
Reducing the annual withdrawal to 1 million yen raises the success probability to 93%, while increasing it to 1.5 million yen drops it to 68%. This sensitivity analysis reveals that the withdrawal amount has a greater impact on success probability than the return assumption itself. Simply reducing post-retirement spending by 200,000 yen per year can extend the fund's lifespan by 5-7 years.
Turning Simulation Results into Action
If the simulation's success probability falls below 80%, countermeasures such as reducing withdrawals, extending the retirement age, or revising asset allocation are necessary. The 4% rule (setting annual withdrawals at 4% of initial assets) is said to have a roughly 95% success rate over 30 years based on U.S. research, but considering Japan's low-interest-rate environment and the characteristics of yen-denominated assets, lowering it to 3-3.5% is safer.
The key is not to run the simulation just once. By recalculating each year with actual returns and adjusting the plan, you can respond flexibly to unexpected events. Books on retirement withdrawal strategies are also helpful for thinking through concrete exit strategies. Start by entering your own conditions into our simulator and comparing multiple scenarios.