This retirement calculator runs a number of stock and bond return simulations on a portfolio being withdrawn from. It uses data from between 1995 – 2023 on Brazil’s annual IPCA inflation, annual Ibovespa returns, and annualized Selic returns.
The calculator has the ability to take groups of years and randomize the order of those groups. For instance, if you specify a group size of 5 the calculator will take the returns and inflation data of 1995 – 2000, then 1996 – 2001 and so on, and mix those groups in random order until it finishes running a simulation for the number of retirement years you specify. You can specify a group size of 1 if you do not want years grouped together, however grouping years may better simulate cycles of high inflation/interest and so forth.
Similar to Monte Carlo simulations, the calculator will run each simulation a number of times, then present a graph showing how many simulations were successful, the number that failed (ran out of money), and a chart of each of the simulations. You can optionally download a CSV file of the data from the simulations.
Notes on how calculations are performed:
Withdrawals: The amount withdrawn from the portfolio comes from your stocks and bonds in equal portion to their percentage makeup of your portfolio. The withdrawals are made at the beginning of the year, before the returns for the year are calculated. Inflation is added to the amount withdraw. Inflation is calculated using the prior year’s inflation level. For example, if your portfolio is 50% Ibov, 50% Selic, your initial withdrawal is R$40,000 and the year is 2003: At the start of the year R$20,000 is withdrawn from the amount used for stocks, R$20,000 is withdrawn from the amount used for bonds, then the returns are calculated for stocks and bonds using the lower amounts after withdrawals. For the next year the same process repeats, except the amount withdrawn is adjusted by 2003 inflation, which was 9.3%, so R$43,720 will be withdrawn at the start of the year, 50% from stock, 50% from bonds.
Pension income: The later income or pension amount is increased with inflation in the same way as withdrawals.
Rebalancing: Rebalancing occurs at the end of the rebalancing year. returns are calculated for the year first, independently for stocks and bonds, then the end of year amounts are rebalanced to the original portfolio levels. It would be equivalent to rebalancing Dec 31 of the rebalancing year.