(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.
Sample simulation output:
Code: Select all
#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
I can run the program with different assumptions for the mean and standard deviation of after-inflation returns of the stock market if there is interest. The Fortran code is here.