beliavsky / retirementspending

Fortran simulation of spending rules in retirement

Retirement Spending Simulation

Simulation in Fortran 2003 of spending and asset allocation rules in retirement, motivated by a Morningstar study, discussed in a Wall Street Journal article The 4% Retirement Rule Is in Doubt. Suppose that

(1) A retiree will withdraw annually the same amount from savings, adjusted for inflation, as long as she lives.

(2) Annual after-inflation stock market returns are normally distributed with known mean and standard deviation.

(3) The investor rebalances annually to have a constant fraction of savings in stocks.

Then the two decisions for the investor to make are how much to spend annually and what fraction of savings to keep in stocks. The program simulates the probability of savings lasting N years given the spending rule and stock market allocation. Parameters describing spending and asset allocation and stock market returns can easily be changed.

Compile with gfortran -std=f2003 kind.f90 stats.f90 ziggurat.f90 xruin.f90

Output:

      #sim   avg_ret    sd_ret
     10000      0.06      0.15

 spend            spent  spent   years_surv   years_surv
  rate  leverage median   mean       median         mean   wealth_avg  wealth_surv    p10    p20    p30    p40
 0.020    0.0000  0.800  0.800      41.0000      41.0000       0.2000       0.2000 1.0000 1.0000 1.0000 1.0000
 0.020    0.5000  0.800  0.800      41.0000      40.9867       1.7227       1.7285 1.0000 1.0000 0.9999 0.9966
 0.020    1.0000  0.800  0.796      41.0000      40.7936       7.1893       7.3493 1.0000 0.9987 0.9917 0.9782

 0.030    0.0000  0.990  0.990      33.0000      33.0000       0.0100       0.0000 1.0000 1.0000 1.0000 0.0000
 0.030    0.5000  1.200  1.179      41.0000      40.1650       0.9740       1.1111 1.0000 1.0000 0.9763 0.8749
 0.030    1.0000  1.200  1.168      41.0000      39.8441       5.4993       6.1338 1.0000 0.9905 0.9469 0.8963

 0.040    0.0000  0.960  0.960      24.0000      24.0000       0.0400       0.0000 1.0000 1.0000 0.0000 0.0000
 0.040    0.5000  1.600  1.419      40.0000      35.9466       0.3888       0.7836 1.0000 0.9873 0.7713 0.4828
 0.040    1.0000  1.600  1.473      41.0000      37.5720       3.9787       5.3301 0.9997 0.9539 0.8361 0.7455

Row 6 of the table above means that if the investor spends 3% of the initial portfolio value, adjusted for inflation, and invests the 100% of savings in the stock market, which has average after-inflation returns of 6% with standard deviation of 15%, that the probability of the savings lasting 30 years (column p30) is 94.7%. If the annual spending rate is 4%, the 30-year survival probability falls to 83.6%. The investor should decide whether spending 33% more per year is worth a higher risk of running out of money. Using different return assumptions, Morningstar recommends 3.3% as a safe withdrawal rate.