HARS - Historical Actuarial Retirement Simulator

Author (bug reports welcome) Source code

This is free software. Use it at your own risk. No guarantees of correctness are made.

This retirement simulator simulates an initial set of assets with a savings accumulation phase followed by an income withdrawal retirement phase. The results associated with holding different ratios of stocks/bonds are reported.

The reported results show the probability of dying without running out of money (success). For a couple the death of one partner reduces the amount of income required to support the other partner, but simulation continues until both partners are dead.

To use this tool effectively, you should perform multiple runs of the simulator changing the input parameters in order to assess the sensitivity of your results to small changes in the inputs.

Equity returns are based on the historical returns reported by Shiller, but with the mean return adjusted to match a specified simulation parameter. This is because it seems unlikely that the return values of the past will be repeated, but they are still informative in setting the volatility of future returns.

Bond returns are assumed to be a fixed amount per year after adjusting for inflation, and as such most closely model TIPS.

An actuarial model of longevity is employed, in which the probability of death each year is taken from the U.S. Life Tables. Separate tables are used for men and women.

All input values and reported values are adjusted for inflation.

Current financial assets: $
Charitable ceiling: $

Assets above the ceiling will be given away at end of each year, and the total amount given away will be reported by the simulator. Use 0 if all assets retained.

Annual savings until retired: $ Enter 0 if already retired.
Annual living expenses once retired: $
Your age: Gender:
Your spouse's age: Gender: Set to -1 if plan to be permanently single.

Medical advances have historically increased life expectancy. If you wish to account for this occurring in the future you may wish to reduce stated ages slightly, by 1 year if you are under 70, by 2 years if you are under 55, or by 3 years if you are under 40. This will only have a small effect on the results.

Years until reach retirement: Set to 0 if already retired.
Proportion of income needed when one partner dead: % Irrelevant if permanently single.
Expected real return on equity after any taxes: %

This value is used for the geometric mean return value. Returns have a standard deviation based on the historical standard deviation. This separation is made because while the volatility of the market seems quite likely to recur, the level of returns is quite possibly less likely to recur on account of shrinking GDP growth or other factors, and also needs to be varied as part of any sensitivity analysis the user may wish to perform.
The value chosen for this parameter is crucial, so some time will be taken to explain the chosen value. According to Shiller the period 1926-2008 had annual returns of 6.3% = 4.0% dividends + 2.2% real capital gains. The P/E10 at the beginning of this period, end of this period, and average P/E10 during this period are roughly similar. This means it isn't necessary to correct the capital gains for the effect of a not expected to be repeated change in P/E10. According to the Social Security Actuaries the labor market x hours worked is expected to decline by 1.1% per year in the coming years, relative to 1965-2005. According to a macroeconomic rule of thumb this will produce a 0.7% drop in real GDP relative to 1965-2005. But the GDP for 1965-2005 is already 0.2% below that of 1929-2008 according to the BEA, so the total drop in GDP is 0.9%. It is debatable whether and to what extent this decline in GDP will flow through to reduced index returns, but we take the conservative approach and assume it all will.
It isn't possible to invest in an index, only a mutual fund that tracks the index but which also incurs expenses. Well run mutual funds have an expense ratio around 0.1%.
Taxes will vary, but a taxed investment paying dividends and capital gains in the presence of moderate inflation and a tax rate of 20-30% might incur a loss in value due to taxes of around 1.6%.
taxed return on equity = historical return - GDP correction - expenses - taxes = 6.3% - 0.9% - 0.1% - 1.6% = 3.6%
untaxed return on equity = historical return - GDP correction - expenses = 6.3% - 0.9% - 0.1% = 5.2%

Expected real return on bonds after any taxes: %

Will have zero standard deviation, hence holding TIPS or similar is assumed. Rates on TIPS vary somewhat, but they tend to average around 2.0%.
Taxes will vary, but a taxed investment paying dividends in the presence of moderate inflation and a tax rate of 20-30% might incur a loss in value due to taxes of around 1.1%.
taxed return on bonds = historical return - taxes = 2.0% - 1.1% = 0.9%
untaxed return on bonds = historical return = 2.0% = 2.0%

Equity in a secondary equity class: % e.g. international stocks
Simulation annual returns order: This has a major impact on portfolio success.

Advanced and infrequently used options

Asset depletion mode:
Go to bonds strategy percentile: %

If your portfolio is doing well you may wish to lock this in by switching to bonds. This input value specifies when to implement a go to bonds strategy as the percentile likehood such a strategy will prove successful. Typical values are 95-100%. Use -1 if you never wish to implement a go to bonds strategy. Go to bonds rarely makes a significant difference.

Correlation in returns between primary and secondary equity classes: %
Scaling factor applied to standard deviation of secondary equity class returns:
Simulation start year: Start of historical period for simulation returns data. Can set as far back as 1872.
Number of experiments to perform per simulation result: