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 fun-and-games 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/(1000-40N) or, as a percentage, that's 4000/(1000-40N)%.
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/(1000-40N) = 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 10-year 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 10-year mark) can vary widely. For example a $50K withdrawal (at the 10-year mark) might give $50K/$500K =10% or $50K/$5M = 1%.
See this this online spreadsheet to see how 30- and 40-year 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 40-year Safe Rate" (say 4%).
If Sally jumps in at the 10-year 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 10-year mark (as a percentage of the 10-year 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 30-year "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 10-year mark)?
For a fuller discussion of this subject, see this excerpt from the NoFeeBoard.