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.