Overheard at the local coffee shop: Sam: I'll live for 40 years and need $40K per year and a 4% withdrawal from my $1M portfolio is safe so I'm happy. Sally: I'll also need $40K per year from my $1M portfolio. But I'll live for just 30 years, so I'll take out 10 years worth of $40K  that's $400K  leaving me with $600K. I'll spend the $400K on funandgames and withdraw $40K per year from what's left  that's the $600K. Sam: But you're withdrawing $40K from a $600K portfolio, not a $1M portfolio! Sally: Well, suppose I take out 5 years, that's 5 x $40K for fun & games. That leaves me with $800K. How's that? Sam: You'll be withdrawing $40K from an $800K portfolio, that's ... Sally: I can do the math! That's 40/8 or 5%. Is that safe, for just 30 years? Sam: I doubt it ... even for 30 years. Sally: How many years can I take out ... to play with? Sam: If you want $40K per year and you take out N year's worth, that's N x $40K, then, let's see ... Sally: I can do the math! What's left in my portfolio is $1M  $40K*N and I'm withdrawing $40K per year from this so ... Sam: That's a withdrawal rate of 40K/(1M  40K*N) or 40/(100040N) or, as a percentage, that's 4000/(100040N)%. Sally: I don't know if I agree with your formula. Let me check: Sam: Suppose you think x% is safe, then you'll want 4000/(100040N) = x so N = 25  1000/x meaning that ... Sally: I can do the math! I think maybe 4.5% is safe, for my 30 years.
submitted by KenM Overheard at the local pub: Sam: 10 years ago I decided I'll live for 40 years and my friend Mr Monte Carlo told me that withdrawing $40,000 per year adjusted for inflation from my $1M portfolio would be 99% safe. Sally: That sounds a great idea. Do you think I could do that starting now? Sam: Well, after 10 years of withdrawals, my next one should be $55,000 but the market isn't too good right now and my portfolio's only worth $800,000. However I trust Mr MC and as he told me at the beginning of the 40 years that I would be 99% safe, I intend to take the full $55K. Sally: That sounds even better, I really like your friend Mr MC . I only expect to live for another 30 years and my portfolio's coincidentally worth the same as your current $800,000. So I'll start withdrawing $55,000 now and still have the same 99% safety as you for the next 30 years. Sam: But that doesn't seem fair. My initial withdrawal rate was 4%. Yours will be 6.9%. I'd better get Mr MC to buy me a free lunch. Note: If Sam's portfolio is one of those 99% that survived, then Sally can assume Sam's portfolio and withdrawal amount (at the 10year point) and her portfolio is guaranteed to survive another 30 years ... and theres a 99% probability that this is the case. Getting a higher initial withdrawal rate shouldn't be surprising. Of a jillion $1M starting portfolios, after 10 years, some may be at $500K and some may be at $5M and they all have identical withdrawals ... yet 99% of them survive another 30 years. However, the withdrawal rate (at the 10year mark) can vary widely. For example a $50K withdrawal (at the 10year mark) might give $50K/$500K =10% or $50K/$5M = 1%. See this this online spreadsheet to see how 30 and 40year withdrawal rates compare.
Check out the online spreadsheet where inflation is incorporarted
Questions questions ...
Sam has a $1M portfolio and withdraws at the "Monte Carlo 40year Safe Rate" (say 4%).
If Sally jumps in at the 10year mark, then her portfolio is identical to his (for the last 30 years)
Of the 990 surviving portfolios, there will be plenty whose withdrawal rate, at the 10year mark (as a percentage of the 10year portfolio value), will NOT be the "MC safe" rate for 30 years. That poses interesting questions:
If one does MC simulations, then this Question might have an answer like 95%.
Now forget all about the jillion portfolios and calculate the 30year "MC safe" rate (say 4.5%). Question #2: How does the 4.5% "MC safe" rate for 30 years compare to the Distribution (at the 10year mark)? For a fuller discussion of this subject, see this excerpt from the NoFeeBoard. See also SWR and Monte Carlo and Monte Carlo consistency.
