Below took a few minutes so please forgive any errors and please forward with any suggestions. I can't post Excel for some reason, but even when returns are positive, the inter year returns can swamp any yearly positive returns. If returns are negative for the first few months and then positive the rest of the year, even ending in a positive return, due to the fixed withdrawal, the balance will shrink and slowly bleed out any 4% SWR.
The first case is that of a uniform monthly return with fixed withdrawal at 4%, the second is a negative 6 months, then positive 6 months, ending the year positive, but due to fixed withdrawal rate of 4%, balance is negative despite the overall return of the market being positive. The third is down-up return with no withdrawals. If returns are more volatile inter year, the balance will bleed out more with a fixed SWR.
There are many other issues with the stats of the 4% rule (normal distribution vs skewed and relevant range violations) but below is a pure math and returns based critique.
Beg value $100,000
Return 6.00%
Monthly 0.50%
SWR 4%
Mon SWR 0.003333333
Uniform
Value Cash End
Jan $100,500 $333.33 $100,166.67
Feb $100,667.50 $333.33 $100,334.17
Mar $100,835.84 $333.33 $100,502.50
Apr $101,005.02 $333.33 $100,671.68
May $101,175.04 $333.33 $100,841.71
Jun $101,345.92 $333.33 $101,012.58
Jul $101,517.65 $333.33 $101,184.31
Aug $101,690.23 $333.33 $101,356.90
Sep $101,863.69 $333.33 $101,530.35
Oct $102,038.00 $333.33 $101,704.67
Nov $102,213.19 $333.33 $101,879.86
Dec $102,389.26 $333.33 $102,055.93
Total Return 1.88%
Beg value $100,000
Return Jan-Jun -6.00%
Monthly -0.50%
Return Jul-Dec 8.77%
Monthly 0.73%
SWR 4%
Mon SWR 0.003333333
Down-Up
Value Cash End
Jan $99,500.00 $333.33 $99,166.67
Feb $98,670.83 $333.33 $98,337.50
Mar $97,845.81 $333.33 $97,512.48
Apr $97,024.92 $333.33 $96,691.58
May $96,208.13 $333.33 $95,874.79
Jun $95,395.42 $333.33 $95,062.08
Jul $95,756.83 $333.33 $95,423.50
Aug $96,120.88 $333.33 $95,787.55
Sep $96,487.60 $333.33 $96,154.26
Oct $96,856.99 $333.33 $96,523.66
Nov $97,229.09 $333.33 $96,895.75
Dec $97,603.90 $333.33 $97,270.57
Total Return -1.91%
Same as Down-Up data
No withdrawals
Value Cash End
Jan $99,500.00 $- $99,500.00
Feb $99,002.50 $- $99,002.50
Mar $98,507.49 $- $98,507.49
Apr $98,014.95 $- $98,014.95
May $97,524.88 $- $97,524.88
Jun $97,037.25 $- $97,037.25
Jul $97,746.43 $- $97,746.43
Aug $98,460.80 $- $98,460.80
Sep $99,180.38 $- $99,180.38
Oct $99,905.22 $- $99,905.22
Nov $100,635.36 $- $100,635.36
Dec $101,370.84 $- $101,370.84
Total Return 1.88%