Negative Compounding Exercise

[marko]

Slow Sunday morning at the marko household.

Just for fun, I was wondering if I could figure how much my portfolio would last if I literally cashed it all out, put it in a bank vault and withdrew 8% of each year's balance.

My compounding model subtracted 8% from each previous year's balance. I figured 8% to accommodate 3% inflation and 5% spending. To my surprise, in 20 years (age 90) I'd still have a respectable balance; enough for another 5 years. Even at 10% I'm still good.

Now, most here know how mathematically challenged I am so I'm wondering if the model is correct.

Yes, I do realize that spending/expenses/inflation are non-linear but without having to account for portfolio growth (which is very non-linear) I'm curious if I'm on the right way of thinking.

 

[marko]

Never mind. I found the flaw: After 12 years I'd end up with less than my current spending and by year 20 I'd have virtually nothing to spend despite a decent balance.

 

[skyking1]

you'd need some sort of oddball exponential modeling, or, just a flat rate and bye bye balance in a predictable manner.

 

[pb4uski]

Never mind. I found the flaw: After 12 years I'd end up with less than my current spending and by year 20 I'd have virtually nothing to spend despite a decent balance.

Yes, that is the problem.

If you have $100 and withdraw 8% annually after 19 years you have $20.51 [$100*(1-8%)^19] so you only get to spend $1.64 in year 20 vs $8 in year 1.

 

[marko]

Yes, that is the problem.

If you have $100 and withdraw 8% annually after 19 years you have $20.51 [$100*(1-8%)^19] so you only get to spend $1.64 in year 20 vs $8 in year 1.

I would've deleted the thread but couldn't figure out how.
Thanks anyway, pb4

 

[ERD50]

A simple arithmetic way to do what you are looking for is to just divide your stash by the annual withdraw amount, and that tells you how many years you can withdraw that. Or go the other way round, and divide by the number of years.

For simplicity, assume your portfolio just manages to keep up with inflation, by doing that, you can think of your spending as being adjusted for inflation (well, more or less - I guess the dwindling portfolio means that has less effect, I might need to think more on that, or do a spreadsheet, but conceptually it's pretty close I think).


EX 1: You have a $1,000,000 stash. You want to spend $50,000 a year. $1,000,000/$50,000 = 20 years. Then you have zero left.


EX 2: You have a $1,000,000 stash. You want to know how much you can spend a year to last 30 years. $1,000,000/30 years = $33,333.33. Then you have zero left.


And I think this is worthwhile exercise for a frame of reference. We should always question the models, they will have errors. This is a sort of basic test. Of course, it ignores the realities of the portfolio moving up/down (sequence of returns risk), but it's a good check on whether the models are making sense or not (or maybe you made an input error).

IIRC, even the worst runs in FIRECalc showed compound returns slightly above inflation, so the above should be quite conservative ( a 3.33% WR for 30 years, a 2.5% WR for 40 years, etc). IIRC, FIRECalc seems to resolve to ~ 3.3% inflation adjusted WR for a 'forever' portfolio - at some point it is self sustaining, years no longer matter (until the asteroid strike).

edit/add: No, don't delete the thread, it was a simple mistake that others might make. I think it helps to see these and the clarifications.

-ERD50

 

[Jerry1]

And I think this is worthwhile exercise for a frame of reference. We should always question the models, they will have errors. This is a sort of basic test. Of course, it ignores the realities of the portfolio moving up/down (sequence of returns risk), but it's a good check on whether the models are making sense or not (or maybe you made an input error).

Agree, this is a worthwhile exercise, a basic test, a check on the output of other models. As for ignoring the realities of the portfolio, I’m not sure there is any model that captures that. Historically, yes, but forward looking models have their issues. One can never accurately predict return, inflation or spending. In the end, they’re only planning tools, not prediction tools. The exercise is probably more valuable that the outcome presented by any given model.

 

[marko]

For simplicity, assume your portfolio just manages to keep up with inflation, by doing that, you can think of your spending as being adjusted for inflation (well, more or less - I guess the dwindling portfolio means that has less effect, I might need to think more on that, or do a spreadsheet, but conceptually it's pretty close I think).

-ERD50

Thanks. I need to think a bit more about what I just bolded. Of course, I'm not looking for great granularity; windage is good.

 

[RobbieB]

The big take away I got from this exercise is that stashing a lot of cash is not a good investment strategy.

 

[marko]

The big take away I got from this exercise is that stashing a lot of cash is not a good investment strategy.

Obviously. My attempt was to see how I'd do if my portfolio made zero gains over the course of many years; i.e. pretty much a worst case scenario (asteroids aside)

 

[marko]

However: the complication is that for the first several years, 8% would presumably exceed normal spending requirements. As such, you'd likely push X% back into the 'bank' for a number of years, further extending the life of the portfolio. I think.

But now we're not into a simple calculation are we?