How It Works


Retirement Quant applies Monte Carlo techniques to simulate a retiree's portfolio during the defined retirement.   The base assumptions of the simulator are the length of the retirement period, the amount of initial retirement assets, the asset allocation, the asset return distributions, and the inflation rate distribution.

Each year’s entire withdrawal is made on the first day of the simulated year from the portfolio’s assets.  Withdrawals rise annually by the prior year’s inflation rate, modified by any decision rules in effect, and are deducted from the retirement assets.  At that time, the asset classes are re-balanced to the target asset allocation. 

Asset returns are calculated at the end of each simulated year.  The simulator allows the user to specify whether assets are distributed according to the standard normal distribution or lognormally distributed.  The default is that asset return relatives (defined to be 1+r, where r is the simple rate of return) are assumed to be lognormally distributed.  Asset returns are based upon historical performance.  To use this approach, the natural logarithm of the return relative for each year in the period is calculated.  The mean and standard deviation are then calculated from those values over the period sample.  For each year, the simulated return is obtained by generating a random number from the lognormal distribution with the appropriate mean and standard deviation and raising the mathematical constant e to that power to get the return relative.

A retiree's portfolio is simulated by performing the above calculations for each retirement year, e.g., 40 times for an assumed retirement of 40 years.  If the portfolio assets drip to zero during a simulated lifetime, the simulation is considered a failure.  An exception to this is if someone elects to use all of their assets to purchase an annuity.   Even though they have no assets, because they chose the resulting annuity income, the simulation is considered a success.

A retirement scenario is defined by a given set of initial values and base assumptions.  Each scenario is run 1000 times and the success rate of a scenario is the percent of successful simulations. The simulator is robust and allows decision rules to be turned on or off and base assumptions to be changed for each scenario.

The main simulator outputs of interest are:

1.   PVfinal - the present value of the withdrawal amount in the final year of retirement.  .  The discount rate used in the PVfinal calculations is the inflation rate observed in each year of retirement.

2.   PVtotal - the present value of the sum of all the withdrawals made during the retirement period.  PVtotal is the total purchasing power, in constant dollars, over a retirement period.  This number allows for comparisons between different scenarios and it is assumed that retirees prefer to maximize their withdrawals during retirement.  The discount rate used in the PVtotal calculations is, again, the inflation rate observed in each year.

3.  The success rate - In any profile, this number must not fall below the desired confidence standard.

4.  Legacy - this is the amount of assets in your estate at the end of your retirement.

In 1000 scenario simulations there will be 1000 PVtotal, PVfinal values, and legacy. To avoid having a few high values distort the results, the median values are used in the analyses.

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