SWRs and 70 years of withdrawals

akratic · Post by **akratic** » Sat Jan 28, 2012 1:50 am

As my net worth grows, I've been thinking about SWRs. Ideally my investments do well enough that my assets last forever, but actually what I really care about is them lasting 70 years.
Let "real cagr" be your yearly return after subtracting inflation and investment taxes. In other words, 25 years of assets with a real cagr of 4% would last forever. 25 years of assets with a real cagr of 0% would last 25 years.
I wrote a script that finds what real cagr is needed in order for your assets to last 70 years for various levels of wealth. The results are below. The number on the left is your starting net worth in years. The number on the right is the real cagr you need to make it 70 years.
10 => 9.99%
11 => 9.08%
12 => 8.31%
13 => 7.65%
14 => 7.09%
15 => 6.60%
16 => 6.16%
17 => 5.77%
18 => 5.42%
19 => 5.11%
20 => 4.82%
21 => 4.56%
22 => 4.31%
23 => 4.09%
24 => 3.88%
25 => 3.69%
26 => 3.51%
27 => 3.33%
28 => 3.17%
29 => 3.02%
30 => 2.88%
31 => 2.74%
32 => 2.62%
33 => 2.49%
34 => 2.38%
35 => 2.26%
36 => 2.16%
37 => 2.05%
38 => 1.96%
39 => 1.86%
40 => 1.77%
41 => 1.68%
42 => 1.60%
43 => 1.52%
44 => 1.44%
45 => 1.36%
46 => 1.29%
47 => 1.22%
48 => 1.15%
49 => 1.08%
50 => 1.02%
For example, if you retire with 25 years of net worth, your assets last 70 years if you get a 3.69% real cagr, and they last forever if you get a 4% real cagr or higher.

Mirwen · Post by **Mirwen** » Sat Jan 28, 2012 1:56 am

ooh, this is super neat. Thank you. Can you tell me more about how to calculate real cagr. Maybe give an example?

George the original one · Sat Jan 28, 2012 1:57 am

Ah-hah! This info can be used as an early-warning system, to judge whether one should temporarily go back to work.

akratic · Post by **akratic** » Sat Jan 28, 2012 2:03 am

Suppose the following:

- 8% return on your investments for the year

- 50% of your investments tax sheltered, 50% taxable

- 25% taxes on your taxable investment income

- 3% inflation
First you pay taxes on your taxable half. You lose 8% * 50% * 25% => 1% off the top. So you have 8% - 1% => 7%.
Now you lose 3% to inflation. So you have 7% - 3% => 4%.
Your real cagr for the year is 4%. This is the amount of money you actually earned.
Next year your investments return 16%, with the same inflation and tax situation. This next year your real cagr is 11%. (16% minus 2% to taxes and 3% to inflation)
Your two year real cagr is slightly tricky. It's 7.44%, and the math is here. You might think it's 7.5%... (4% + 11%)/2 but it's a little more complicated.
I hope the examples helped!

Mr. Overlord · Post by **Mr. Overlord** » Sat Jan 28, 2012 2:30 am

This is awesome, thanks for posting this.

Mirwen · Post by **Mirwen** » Sat Jan 28, 2012 2:36 am

Wow, this suggests that I need a lot less than I was figuring to retire. The examples did help.

akratic · Post by **akratic** » Sat Jan 28, 2012 2:46 am

Yeah, remember getting high "real cagrs" is hard though. For example, last year, including dividends, the S&P 500 returned 1.9%. If inflation was 2% or higher, and you were fully invested in the S&P 500, your real cagr for the year would be negative.

Mirwen · Post by **Mirwen** » Sat Jan 28, 2012 2:56 am

Well I'm figuring base returns of 7-8%, 3.5% inflation and little if any tax. It ends up being roughly 25 years, which is what a lot of people recommend, but I always figured I needed more for some reason.

LiquidSapphire · Post by **LiquidSapphire** » Sat Jan 28, 2012 3:10 am

Thanks for this calculation; very insightful! And I agree with George that it could be helpful as a withdrawing metric or an early warning system. Thanks for the food for thought. I wonder if I can find some past CAGR info for various AAs.

secretwealth · Post by **secretwealth** » Sat Jan 28, 2012 6:45 am

This is really, really cool. I'd love to see a full chart of CAGRs to last 60 years, 50, etc.

akratic · Post by **akratic** » Sat Jan 28, 2012 3:10 pm

@secretwealth, your wish is my command
The rows are for a starting amount of net worth in years.
The columns are to last that many years. My original post was just the 70 column.
NW 20 30 40 50 60 70 80
10 7.76% 9.31% 9.76% 9.92% 9.97% 9.99% 10.00%
11 6.53% 8.25% 8.78% 8.97% 9.05% 9.08% 9.09%
12 5.46% 7.34% 7.95% 8.17% 8.27% 8.31% 8.32%
13 4.51% 6.55% 7.22% 7.49% 7.60% 7.65% 7.68%
14 3.67% 5.85% 6.59% 6.89% 7.03% 7.09% 7.12%
15 2.92% 5.22% 6.03% 6.37% 6.52% 6.60% 6.63%
16 2.23% 4.66% 5.53% 5.90% 6.07% 6.16% 6.20%
17 1.61% 4.15% 5.07% 5.48% 5.67% 5.77% 5.82%
18 1.03% 3.68% 4.66% 5.10% 5.31% 5.42% 5.48%
19 0.50% 3.25% 4.28% 4.75% 4.98% 5.11% 5.17%
20 0.00% 2.85% 3.94% 4.43% 4.68% 4.82% 4.90%
21 -0.46% 2.48% 3.61% 4.14% 4.41% 4.56% 4.64%
22 -0.89% 2.14% 3.31% 3.87% 4.15% 4.31% 4.41%
23 -1.29% 1.81% 3.04% 3.61% 3.92% 4.09% 4.19%
24 -1.67% 1.51% 2.77% 3.38% 3.70% 3.88% 3.99%
25 -2.03% 1.22% 2.53% 3.16% 3.49% 3.69% 3.80%
26 -2.37% 0.95% 2.30% 2.95% 3.30% 3.51% 3.63%
27 -2.70% 0.70% 2.08% 2.75% 3.12% 3.33% 3.47%
28 -3.01% 0.46% 1.87% 2.57% 2.95% 3.17% 3.31%
29 -3.30% 0.23% 1.68% 2.39% 2.79% 3.02% 3.17%
30 -3.58% 0.00% 1.49% 2.23% 2.64% 2.88% 3.03%
31 -3.85% -0.21% 1.31% 2.07% 2.49% 2.74% 2.90%
32 -4.11% -0.41% 1.14% 1.92% 2.35% 2.62% 2.78%
33 -4.35% -0.60% 0.98% 1.77% 2.22% 2.49% 2.66%
34 -4.59% -0.78% 0.82% 1.64% 2.10% 2.38% 2.55%
35 -4.82% -0.96% 0.67% 1.50% 1.98% 2.26% 2.45%
36 -5.04% -1.13% 0.53% 1.38% 1.86% 2.16% 2.35%
37 -5.25% -1.30% 0.39% 1.26% 1.75% 2.05% 2.25%
38 -5.46% -1.46% 0.26% 1.14% 1.64% 1.96% 2.16%
39 -5.66% -1.61% 0.13% 1.03% 1.54% 1.86% 2.07%
40 -5.85% -1.76% 0.00% 0.92% 1.44% 1.77% 1.98%
41 -6.03% -1.90% -0.11% 0.81% 1.35% 1.68% 1.90%
42 -6.22% -2.04% -0.23% 0.71% 1.26% 1.60% 1.82%
43 -6.39% -2.18% -0.34% 0.61% 1.17% 1.52% 1.75%
44 -6.56% -2.31% -0.45% 0.52% 1.08% 1.44% 1.67%
45 -6.72% -2.43% -0.56% 0.43% 1.00% 1.36% 1.60%
46 -6.89% -2.56% -0.66% 0.34% 0.92% 1.29% 1.53%
47 -7.04% -2.68% -0.76% 0.25% 0.84% 1.22% 1.47%
48 -7.19% -2.79% -0.86% 0.17% 0.77% 1.15% 1.40%
49 -7.34% -2.91% -0.95% 0.08% 0.69% 1.08% 1.34%
50 -7.49% -3.02% -1.04% 0.00% 0.62% 1.02% 1.28%

karim · Post by **karim** » Sat Jan 28, 2012 5:23 pm

Just a quick question one your real CAGR. Does that include your withdrawal rate? So that the real CAGR = Yield on investments - taxes - Inflation - Withdrawal rate?

akratic · Post by **akratic** » Sat Jan 28, 2012 7:06 pm

No, withdrawals aren't included in the real cagr calculation. It's just roi - taxes - inflation.
I'm assuming your expenses remain constant throughout, and just move up by inflation. For example, suppose you retire with $500k of assets and $20k/year of expenses. This is the 25 years of net worth row. I assume you continue to have $20k/yr of expenses, adjusted for inflation, forever. The question is how long your assets last depending on how your investments do (their real cagr).
As an aside, if you happen to manually set your expenses every year to be equal to your real cagr, your money will last forever by definition. Some years you'll have to live on negative money when your real cagr is negative though.

secretwealth · Post by **secretwealth** » Sat Jan 28, 2012 7:17 pm

Akratic, this is truly awesome! This has given me a lot to think about.

akratic · Post by **akratic** » Sat Jan 28, 2012 7:17 pm

@LiquidSapphire, you motivated me to finally package up some CAGR numbers I found from a PP poster (probably Clive...)
Check it out: CAGR.png
I like how this shows different countries, but it's too bad that it only goes back 36 years. It's also too bad that it doesn't have inflation numbers.
The PP column is the 4x25 version of the Permanent Portfolio
The 70/30 column is the typical Boglehead Portfolio of 70% stocks (or complicated things that are 99% correlated with stocks...) and 30% intermediate term bonds.
I don't know where exactly this data came from, so I'm not sure if the Stock returns include dividends, etc.
Another place you can find data like this is the Simba Spreadsheet on Bogleheads.
If you find any other good sources of CAGR numbers let me know. I wonder if FIREcalc could be reduced to a CAGR number for each of the different date ranges and asset allocations.
One thought I've had recently is that investors seem to either bias the last 150 years of world prosperity and go 70/30, or bias the last 35 years that were great for gold and go PP (like me). I wonder what will be right for the future. Fortunately, needing only a 3.69% real cagr, and falling, I'll probably be fine whatever happens.

jennypenny · Post by **jennypenny** » Sun Jan 29, 2012 7:00 pm

@akratic--thank you! I've been trying for a year to get my DH on board with the ERE thing. He's gone along with me, but he never fully accepted that he could retire fairly quickly. He looked at your chart this morning and everything clicked into place for him. We printed out the chart, hung it up, and agreed to more cuts. I think he'll be joining me YEARS sooner then he'd originally planned. Thanks again.

LiquidSapphire · Post by **LiquidSapphire** » Wed Feb 01, 2012 5:24 pm

Thanks for that info akratic... the more I think about it the more the PP intrigues me in spite of the huge cash and gold components. If one runs Firecalc, expecting to be able to keep at least half of pricipal at all times over 30 years, you pretty much need to have a 2% SWR. However, it seems that with the PP, ever getting to half of principal would be pretty unlikely, even a 50% drop in stocks only drops your whole portfolio by 12.5%, and hopefully your other assets will make up most if not all of that loss. Unlikely that you would have a 10% drop in total 5 years in a row, or anything like it, with the PP.
Interesting, interesting stuff! Thanks very much for the food for thought. I wish I had extra CAGR info, I don't, but if I ever find any I will be sure to throw it your way to see if you can work any magic with it