my own simulation of Safe Withdrawal Rate fails

[falcon10]

Hey everyone, this is my first post. I'm confused about SWR (Safe Withdrawal Rate) because I've written a super-simple simulation of it, and it seems to fail a lot more than I'd expect. I'm hoping that I'm just doing something wrong here and that someone can set me straight.

The short version
Here's my spreadsheet that shows starting with $1M and spending an (inflation-adjusted) 3% each year fails (or loses nominal value) at the end of 30 years more often than I'd expect.

https://docs.google.com/spreadsheets/d/14T97cIQjZdRTby4YnFqZuHmZ4X_usa4pZLVKE4uTRPQ/edit?usp=sharing

The long version
I’m having trouble reconciling the standard “4% rule” advice and my own calculations based on S&P500 and inflation history since 1950.

To be on the safe side, for my analysis, I went with spending 3% of the original portfolio value rather than 4%.

When I simulate 3% spending for 30 years using actual S&P500 market data, I’m seeing far worse results than what I'd expect. I did the analysis for each 30-year period starting at 1950. The strategy fails (i.e. you wind up broke) 23% of the time, and you lose (real) value in your portfolio another 35% of the time. That means you only end up with more purchasing power than you started with 42% of the time.

I’m wondering if I’m doing something wrong here. The calculation is really simple. For each of the 30 simulated years, sell enough shares to fund an inflation-adjusted 3% spending. At the end (if your portfolio didn't go bust), see how well (or poorly) you did.

Here’s a spreadsheet with my results: https://docs.google.com/spreadsheets/d/14T97cIQjZdRTby4YnFqZuHmZ4X_usa4pZLVKE4uTRPQ/edit?usp=sharing. The first sheet shows it failing if you start in 1970 with $1M and spend an inflation-adjusted $30k/year. The second sheet shows that same experiment starting with years starting 1950-1989. The other sheets have the S&P500 and inflation data that I used.

Can anyone see what I might be doing wrong here? Suspects:

• Bad data?
• I’m assuming that the portfolio is 100% invested in a some cheap fund that mirrors the S&P500 results, with no transaction fees. Could that be a problem?
• I’m doing the calculations incorrectly?

Hopefully, the spreadsheet that I linked to is sufficient to understand what I'm doing. If not, I can share the (Python) code that carries out the calculation, though I can't vouch for its readability since I threw it together in an afternoon :)

[tampaite]

Column D doesn't make sense.

In 1996, $124k annual spending would put you in the top 1% of earners with your 4% withdrawal rate. That doesn't sound right.

[falcon10]

Where did you get your data from?

Oops, sorry, I meant to post that. Inflation data is from https://inflationdata.com/inflation/inflation_rate/historicalinflation.aspx. S&P500 data is from https://finance.yahoo.com/quote/%5EGSPC/history.

Column D doesn't make sense.

In 1996, $124k annual spending would put you in the top 1% of earners with your 4% withdrawal rate. That doesn't sound right.

Yeah, that would be a lot of spending for 1996, but this is just a hypothetical portfolio that starts with $1M in 1970. The spending is $30k each year, adjusted for inflation. Between 1970 and 1996, to spend $30k worth of 1970 purchasing power, you need $124k.

I think the ultimate success, failure, gains, and losses would be very similar with whatever amount the portfolio started with. For purposes of my simulation, you'd just need to start with enough money that you could buy enough shares that you can sell a handful of shares each year and you don't end up with too much unspent cash each year after selling shares.

[middo]

*Edit - just saw your updated post.


Also, is the S&P data inclusive of dividends, or just capital growth?  This would also affect the results.

[tampaite]

Yeah, that would be a lot of spending for 1996, but this is just a hypothetical portfolio that starts with $1M in 1970. The spending is $30k each year, adjusted for inflation. Between 1970 and 1996, to spend $30k worth of 1970 purchasing power, you need $124k.

I think that's the problem. the 4% rule everyone quotes isn't adjusted for inflation. It's straight 4%. As you noticed with inflation, 4% will run you out of money but it did last 26 years so if someone were to be in their 60s and started in 1970 with 30K number it would have lasted them into their 80s which is decent considering half of us will die by the time we hit 74.

[ctuser1]

Your spreadsheet show sequence of return risk.

A good discussion thread from bogleheads:
https://www.bogleheads.org/forum/viewtopic.php?f=1&t=236665

Basically, 70's were the double-whammy stagflation years. Markets did not return much, AND inflation roared. Result was that your withdrawal $$ to go up too fast for the market returns to keep up.

Notice how all failure years are clustered around dates such that the 70's are early enough in your retirement to put serious spanner in your wheel.

1962 - 1992   ran short in 1989         
1963 - 1993   $117,076   $543,437   -88.29%   464.18%
1964 - 1994   ran short in 1991         
1965 - 1995   ran short in 1988         
1966 - 1996   ran short in 1987         
1967 - 1997   ran short in 1994         
1968 - 1998   ran short in 1989         
1969 - 1999   ran short in 1989         
1970 - 2000   ran short in 1997         
1971 - 2001   $131,445   $583,435   -86.86%   443.86%
1972 - 2002   $8,044   $35,201   -99.20%   437.61%
1973 - 2003   ran short in 1996         

[MDM]

the 4% rule everyone quotes isn't adjusted for inflation.

Ah, but it is.

See
http://www.retailinvestor.org/pdf/Bengen1.pdf
http://www.aaii.com/files/pdf/6794_retirement-savings-choosing-a-withdrawal-rate-that-is-sustainable.pdf
https://www.bogleheads.org/wiki/Trinity_study_update
https://www.bogleheads.org/wiki/Safe_withdrawal_rates
for some reading.

[secondcor521]

OP, you're probably forgetting to account for dividends paid on the S&P every year.  I believe it averages about 2% per year.

Also, 1970 is one of the worst years to start.  The original 4% study shows success about 95% of the time, and the years that fail all start around the late 60's and early 70's.

AA also matters.  100% stocks doesn't do as well as 90% stocks.

Take a look at firecalc.com and cfiresim.com.

[BicycleB]

*Edit - just saw your updated post.


Also, is the S&P data inclusive of dividends, or just capital growth?  This would also affect the results.

I think @middo found the key error. @falcon10, you should add dividends to your sheet. Probably you should only sell shares to cover the income amount not covered by dividends.

[MDM]

*Edit - just saw your updated post.


Also, is the S&P data inclusive of dividends, or just capital growth?  This would also affect the results.

I think @middo found the key error. @falcon10, you should add dividends to your sheet. Probably you should only sell shares to cover the income amount not covered by dividends.

+1

E.g., see S&P 500 Return Calculator, with Dividend Reinvestment.

[ctuser1]

To be fair to OP, the yahoo link states:
*Close price adjusted for splits.
**Adjusted close price adjusted for both dividends and splits.

But the second statement seems incorrect because of two reasons:
1. In all cases close price = adjusted close, in the yahoo data.
2. The close prices of a couple of dates I checked matches the exact S&P close price. If it were dividend adjusted, it would be larger towards the later date, and also would have some "anchor" date.

So yes, Yahoo is probably incorrect here asserting it is "adjusted for both dividends.....".

[falcon10]

*Edit - just saw your updated post.


Also, is the S&P data inclusive of dividends, or just capital growth?  This would also affect the results.

Great point. That's probably it. I'll investigate and get back.

Also, @BicycleB, good point about only selling enough shares to cover income not covered by dividends. I'll make it do that. I suppose I'll need a variable for the tax rate on the dividends here too.

Thanks everyone for the quick and thoughtful responses!

[Kyle Schuant]

Count dividends. The point of owning shares is to get a share (hence the name) of the company's profit. Without dividends, stock purchase and sales are purely speculatory in nature, basically a Ponzi scheme.

[BicycleB]

The tax issue is tricky. With the high income of the example (starting amount similar to several million dollars in today's terms), you might have paid a lot of tax.

MMM's examples assume no tax simply because he posits that a person whose spend is low in dollars because of their badass thrift can avoid tax. In today's tax code, an individual can receive over $37,000 per year in qualified dividends without paying tax. But you have to consider your personal situation to determine whether you'd actually pay tax. Also, many investments go into tax advantaged accounts like 401k's. Those are tax free for now, but you pay tax at ordinary income rates when withdrawing income. Which tax rate depends on your income and status in the year of withdrawal. Calculating tax is important but tricky. It might be zero, it might be 20%, it might be something else.

I run my calculations tax free to evaluate initial returns on investment. Then at the end, when the income from all sources is combined, I calculate tax. If you don't meet your goal tax free, you know you won't meet it after tax, but a quick way to see if you're in the ballpark is start tax free. You could always subtract a high tax rate at the end to make sure you invest enough.

[vand]

As others have highlighted, its missing the dividend, so not reflecting total return.

Starting value 92.06, end value 740.74 is a 704% return, which is a 8.2% nominal return over the 27 years you've simulated, but we know the S&P has returned more than that nominal rate over time (I believe real return is about 7%, nominal better than 10%)

[ctuser1]

This exercise - despite missing dividends (or probably because of it) - is still quite valuable.

What this means is as follows.

Let's assume the scenario where we have:
1. 7% nominal return.
2. High 70's style inflation

In that case, even a 3% withdrawal rate is not safe from a sequence of return risk.

Both of the above is within the realm of possibility. Watch the Shiller vs. Siegel debate. If Shiller is right then we are looking at returns of 7% or lower. At the same time, the QE unleashed a lot of asset bubbles that did not trickle down to the real economy due to the massive inequality. If we were to return to 1960's economic polity (a good thing) with it's 90% marginal tax rates and such, then we'll probably start seeing real trickle down - and real inflation.

So it won't take catastrophe for the 3%-is-still-not-safe scenario to bear out. It can happen in "good" economic times.

I found that to be a bit unsettling!!

OP, do you mind posting the python script? I'd love to steal that and perhaps tweak the numbers a bit here and there and play around.

[MDM]

Let's assume the scenario where we have:
1. 7% nominal return.
2. High 70's style inflation

Negative real returns for a long period of time will cause problems for any retiree, regardless of withdrawal rate.  Whether that will happen is a different question.

[falcon10]

@ctuser1 interesting point. The thing that scares me the most about a buy-and-hold strategy is if the market bombs in the first few years of the strategy. If the market bombs 40% in your first couple years, then it's about the same as though you started with 40% less money in the first place. For that reason, it seems like your 3% or 4% real dollar amount should be noted as soon as the market stops bombing.

As an example, if I put $1M into VTSAX on year 1, but the market bombs and on year 3 my portfolio is worth $600k, then maybe I should be planning to spend 3% of $600k forever, not 3% of $1M forever.

One counterargument I can think of here is that maybe you can think of that $600k as advantageous because it's a market-bottom $600k (assuming you somehow magically know the market has hit bottom). In other words, if you were entering the market with a fresh $600k, it'd be a lot nicer to do it on year 3 (after the market just bombed and stocks are on sale) than on year 1. So you're really sitting on $600k of "year 3 stocks" rather than $600k of "year 1 stocks", and maybe that's enough fuel for the intestinal fortitude to keep spending 3% of $1M forever. Thoughts?

Wrt the code, sure, here it is: https://github.com/SudoMike/safe-withdrawal-rate. It's not the cleanest, and as of right now, it's not taking dividends into account, but I would welcome any feedback, questions, and pull requests. I'll try to get dividends in there if nobody gets there before me.

[ctuser1]

I found this dividend data:
https://www.multpl.com/s-p-500-dividend-yield/table/by-year

Looks like corporations used to give out much higher dividends back then. So excluding them would definitely mess up the results.

With this dividend data, the 1970s stagflation years do not look all that dismal at all.

I'll play with the script next weekend.

[BicycleB]

As an example, if I put $1M into VTSAX on year 1, but the market bombs and on year 3 my portfolio is worth $600k... you're really sitting on $600k of "year 3 stocks" rather than $600k of "year 1 stocks", and maybe that's enough fuel for the intestinal fortitude to keep spending 3% of $1M forever. Thoughts?

Exactly!

The 4% "rule" is an approximation that MMM, and the Trinity Study before him, use for simplicity. It worked in a large but not infallible set of past situations. 1965-1994 and 1966-1995 are two of the rare periods in which it is normally viewed as having failed. But in most cases, even a drop in the early years will be overcome by higher returns later. There's not a perfect correlation between high or low stock prices as measured by things like P/E or the S&P 500 index and the resulting returns, but there's some correlation - returns aren't all random.

The extent and reliability of the correlation, and how (if at all) to apply it when making investment decisions are common topics of finanical research and discussion. So is Sequence of Returns Risk (SORR), the fancy name for "What if my investments all drop 40% the day after I retire?" Two of the more accessible yet detailed analysts of these matters are Michael Kitces, a professional financial advisor, and "Big ERN", a financial blogger.

Michael Kitces mostly writes for professional financial advisors, so his commentary sometimes requires a bit of Googling - he may not explain all terms. But when he addresses a topic, he's usually giving good info. Here are some links to "Best Of" posts.
https://www.kitces.com/best-of-posts/
https://www.kitces.com/blog/what-returns-are-safe-withdrawal-rates-really-based-upon/

Big ERN does detailed studies of his own, and blogs about his conclusions at "Early Retirement Now." Can't guarantee they're perfect, but they look good. His ever-growing series on articles related to your question combines clear explanation, good background information, and in-depth discussion.
https://earlyretirementnow.com/safe-withdrawal-rate-series/
https://earlyretirementnow.com/category/safe-withdrawal-rates/

PS. I like the idea of doing some of the calculations yourself. In case you want to calibrate some of your calculations, or see what someone else did when focused on analyzing similar data while focusing on portfolio allocation, I find that fellow forum member Tyler's site portfoliocharts.com has excellant analysis tools using data from around 1970 on fwiw.
https://portfoliocharts.com/

[falcon10]

@BicycleB thanks for all the links! I'm looking forward to learning what some of the posts about SORR say.

One reason I was interested in writing my own tool to do the calculations was so I could test some variability in the person's behavior. For example, if the market dropped a lot, I'd probably tighten spending for a while until it came back up, so as not to deplete the lower value of the portfolio too quickly. So maybe that means I'd temporarily go from spending an inflation-adjusted 4%/year to 2.5% or 3%/year. I've been interested to see how that would affect the strength of the approach, and I plan to add more of that into my program.

The initial code that I posted at https://github.com/SudoMike/safe-withdrawal-rate/blob/master/investment.py has one variation of this (with the --spend_fixed_real_amount option), where the spending amount is directly taken as a percentage of the current portfolio value every year (rather than coming up with 4% of the initial amount and then inflation-adjusting it each year). I don't have any strong analysis of this strategy to report yet, but from looking at its results, it seems more stable/survivable in bad markets than the normal 4% rule. This is because if the market drops, you'll automatically be spending less (since 4% of the lower portfolio value = less spending). When the market goes up, you'll be spending more, but maybe that should be fine since the market's up.

[ender]

@ctuser1 interesting point. The thing that scares me the most about a buy-and-hold strategy is if the market bombs in the first few years of the strategy. If the market bombs 40% in your first couple years, then it's about the same as though you started with 40% less money in the first place. For that reason, it seems like your 3% or 4% real dollar amount should be noted as soon as the market stops bombing.

As an example, if I put $1M into VTSAX on year 1, but the market bombs and on year 3 my portfolio is worth $600k, then maybe I should be planning to spend 3% of $600k forever, not 3% of $1M forever.

One counterargument I can think of here is that maybe you can think of that $600k as advantageous because it's a market-bottom $600k (assuming you somehow magically know the market has hit bottom). In other words, if you were entering the market with a fresh $600k, it'd be a lot nicer to do it on year 3 (after the market just bombed and stocks are on sale) than on year 1. So you're really sitting on $600k of "year 3 stocks" rather than $600k of "year 1 stocks", and maybe that's enough fuel for the intestinal fortitude to keep spending 3% of $1M forever. Thoughts?

Wrt the code, sure, here it is: https://github.com/SudoMike/safe-withdrawal-rate. It's not the cleanest, and as of right now, it's not taking dividends into account, but I would welcome any feedback, questions, and pull requests. I'll try to get dividends in there if nobody gets there before me.

while there's an entire thread of thousands of posts dedicated to "stop worrying about the 4% rule"  (https://forum.mrmoneymustache.com/investor-alley/stop-worrying-about-the-4-rule/) this specific example is kind of lame.

If you retire early and the market immediately bombs, you can "solve" the problem in many ways. Whether that's going to work again, working a part-time job, or spending less (among many possibilities) you are going to be the most able and well equipped to start addressing any issue.

No one who FIREs on a planned 4% withdrawal should methodically withdraw exactly the same amount every year without adjusting or once considering market conditions.

It is also the case that at some point, some year (whether 2019, 2020, 2021... 2025, etc) will end up being another "top" to the market where FIREing will result in that condition. You can't know when that is. People have had that worry now for years though, so at some point you have to make a decision with only 70% or 80% of the information.

[Classical_Liberal]

Or someone can minimize sequence risk by choosing to invest in noncorrelating assets during the times the individual investor is most at risk for a sequence destroying capital at the exact wrong time.  The most commonly used noncorrelator is a total bond or Treasury bond fund.  Look up bond tent, or reverse glidepath.  I don't know why so many people are adverse to this strategy here, it's proven effective and common sense.