Compare Historical vs Monte Carlo

Karsten picked up my article and published it over at ERN. I was fun collaborating with him, he’s a very smart cookie. In my recent analysis I thought about comparing FIREcalc, the kind of gold standard for historical based retirement calculators, and Monte Carlo. By comparing you can gain some insight into future variability in your retirement plan from 2 vastly different mathematical points of view. The Trinity study looks at historical return, in 30 year aliquots of time from 1925 to 1995. You can see already the Trinity stud is 25 years out of date. Between 1995 and today we have gone through 2 major recessions. The government is leveraged out the yin yang and they would love to loot your retirement funds to feed that beast.

The Trinity type approach uses a 50/50 portfolio as does Bengen’s earlier 1994 study and a 30 year time frame in the historical analysis. The authors give this caveat:

The word planning is emphasized because of the great uncertainties in the stock and bond markets. Mid-course corrections likely will be required, with the actual dollar amounts withdrawn adjusted downward or upward relative to the plan. The investor needs to keep in mind that selection of a withdrawal rate is not a matter of contract but rather a matter of planning.


FIREcalc is a calculator based on the Trinity methodology. It looks at aliquots of history, the length of the aliquot is set in the calculator as is yearly spending and starting portfolio value. It analyzes data from 1871 with latest data update earlier this year. The question it asks is what would have happened over history if I had the listed portfolio, and how many times historically would I have run out of money. It therefore only looks at the past in a deterministic way and presumes the past will somehow mimic the future

From FIREcalc home page:

How can FIRECalc predict future returns from past performance?

It can’t. And it doesn’t try….

Except for this kind of severe limitation FIREcalc is a very powerful planner. You can adjust all kinds of parameters like inflation and portfolio AA and even a granular portfolio mix like small caps and EM etc. It allows addition of SS income on a given date for both spouses, different spending models. A lot of time went into designing this piece of software. One problem I have is understanding how a portfolio of stocks and bonds starting in 1871 (6 years after the Civil War) provides some rational information about my portfolio ending in 2050. The program is widely used as proof of performance and many FIRE retirements are based on it’s presumptions and calculations. I don’t have a dog in that fight, people can do what ever they like and since I haven’t reached 2050 I don’t know if my presumptions will hold true. So I use FIREcalc for what it’s worth and use Monte Carlo for what it’s worth, and try to divine the tea leaves,

FIREcalc is deterministic not truly probabilistic. It looks at history and ask the question of failure in the past. Monte Carlo is entirely probabilistic but uses some historical parameters to determine the model, things like an averaged historical inflation, how assets performed both in risk and reward over some period, things like that so the model is not entirely divorced from history, but what the model predicts is a distribution of “probable futures” from most likely to least likely on both the down side and the upside. It tells you there is some chance of running out of money (10% line and below) and there is some chance of getting lotto like returns (90% line and above) and then there is the most likely result that lives on the 50% line, so Monte Carlo in some sense forward looking in terms of likelihood but NOT deterministic. Taken together the two calculators give some range of perspective.

I used a 50/50 AA, a 30 year retirement and a 50 year retirement. I used US Stocks and US Bonds in the MonteCarlo and used the asset mix native to FIREcalc except I adjusted the AA to 50/50 equity/fixed. I used 1M and 40K/year withdrawal and whatever the calculator calls historical inflation. Monte Carlo allows SOR stress testing but FIREcalc does not since it only looks at history.

30 years of 4% WR on FIREcalc with historic inflation

FIRECalc looked at the 119 possible 30 year periods in the available data, starting with a portfolio of $1,000,000 and spending your specified amounts each year thereafter.

“Here is how your portfolio would have fared in each of the 119 cycles. The lowest and highest portfolio balance at the end of your retirement was $-223,952 to $4,145,063, with an average at the end of $1,146,780. (Note: this is looking at all the possible periods; values are in terms of the dollars as of the beginning of the retirement period for each cycle.)

For our purposes, failure means the portfolio was depleted before the end of the 30 years. FIRECalc found that 6 cycles failed, for a success rate of 95.0%.”

The first failure seems around year 25.

The Monte Carlo predicts 97.98 success and

Year 16 start to fail. Interesting data..

A 50 year retirement:

“FIRECalc looked at the 99 possible 50 year periods in the available data, starting with a portfolio of $1,000,000 and spending your specified amounts each year thereafter.

Here is how your portfolio would have fared in each of the 99 cycles. The lowest and highest portfolio balance at the end of your retirement was $-1,641,644 to $7,055,125, with an average at the end of $1,022,915. (Note: this is looking at all the possible periods; values are in terms of the dollars as of the beginning of the retirement period for each cycle.)

For our purposes, failure means the portfolio was depleted before the end of the 50 years. FIRECalc found that 40 cycles failed, for a success rate of 59.6%.”

Monte Carlo 50/50 AA at 50 years:

59% success vs 91% predicted difference between the 2 calculations. Amazing!

80% AA at 50 years

“FIRECalc looked at the 99 possible 50 year periods in the available data, starting with a portfolio of $1,000,000 and spending your specified amounts each year thereafter.

Here is how your portfolio would have fared in each of the 99 cycles. The lowest and highest portfolio balance at the end of your retirement was $-2,339,116 to $20,646,899, with an average at the end of $4,071,620. (Note: this is looking at all the possible periods; values are in terms of the dollars as of the beginning of the retirement period for each cycle.)

For our purposes, failure means the portfolio was depleted before the end of the 50 years. FIRECalc found that 20 cycles failed, for a success rate of 79.8%.”

Monte Carlo at 80/20 and 50 years

80% vs 88% success rate. Note how increasing the AA to 80/20 made longevity worse for MC and better for FIREcalc on a 50 year retirement. This may be why FIREcalc-ers tend toward high AA, because the calculator predicts a better outcome and why Monte Caro-ists tend toward more stodgy allocations. The two calculators predict different futures that’s for sure! Personally I think much deviation is accounted for in the method of projection. All FIRE is based on projection and projection is deviant. It does not actually predict what it portends to predict. It’s like shooting a bullet at a distant target using Kentucky wind-age in a truly accurate gun, a tad to the left you miss the target by a mile but to the left. A tad to the right the opposite occurs. Both shots miss the target, but both misses give you information about where the target actually is. There is nothing says you can’t improve your aim. In fact that is what you do. Come a downturn you may well reduce your WR and change the calculus. You may use a mechanical re-balancing technique as risk management and come a downturn you may re-balance and super charge your post recession returns. The models tend to be static, life is dynamic . Another issue is these models project withdrawal and most people are unfamiliar with withdrawal but are used to accumulation. When you start withdrawal your risk profile is very different than when accumulating.

15 Replies to “Compare Historical vs Monte Carlo”

  1. Congratulations on being featured on ERN. That truly is the big time.

    Personally I use Monte Carlo analysis as the better guide for me and FIREcalc is more for entertainment value. Although if I do have analysis saying less than 5% failure I feel more confident because if it can survive over some major historical events it likely will do alright for the future

    1. I’m on that page as well but I found ERN’s variable Sharpe’s analysis compelling but not compelling enough to switch to the dark side 🙂

  2. It seems better to plan for variable withdrawals based on market performance than a fixed percentage, or keeping a large cash buffer for downturns. It also makes sense to keep fixed expenses as low as possible to accommodate variation.

    Off topic – I’m curious to understand more about your overall approach. It seems like a simplified version of efficient frontier investing would be to reduce or eliminate international exposure, and add a gold ETF (5-10%) and plan to land at around 50/50 US equity/US bond at retirement. Don’t over diversify, don’t chase dividends. You seem to favor individual stocks and BRK, but an equity index probably wouldn’t fare too much worse in terms of efficient frontier. What am I missing?

    What do you think about real estate exposure, personal property, rental property, and/or REITs? Also, if US stocks are overvalued now (CAPE ratios) and international less so in aggregate, might we not see higher than historical returns with international exposure?

    I find your blog refreshing and not the usual FIRE marketing nonsense, or writers hoping to make a buck on physician burnout. I can imaging a graph of the growth of the retire early niche against the lengthening of the bull market. Lots of Pollyanna thinking out there and I wonder what happens when we hit a major correction. I’m also interested in your thoughts on FIRE and how the doctoring trade has changed leading to so many wanting to cut back, work non-clinically, or get out altogether.

    1. Hi Robert, Insightful reply. I do use the efficient frontier and I do own GLD in the 5% range because of it’s behavior in a crash. I have written extensively on this. In a crash you need something to sell high and gold tends to explode in value when stocks crash, just the ticket. You can buy it back later when it’s cheap. I also believe in having 2 portfolios a large portfolio risked at a SD of 10% on the EF and a small separate portfolio risked at the Tangent on the EF. When the crash comes close the big portfolio and open the small. You can completely burn the small, because it’s point is to preserve the big, like a fuse, and you don’t really need to refund that if you use it because by preserving the big you keep your buying power later. You don’t run out of money till the end, so the fuse is an end game preservation play. My opinion is to fund it BEFORE you retire and let it sit there. If you never use it, buy yourself a Bentley in your old age. If you need it, it will save your butt. I also like mechanical re-balancing as a means of risk management especially with a small fuse portfolio. I did a small study and found portfolios are subject to negative returns only 20% of the time, so 80% they are making money so guarding against that 20% makes a difference.

    2. I own a little global and EM and REITS. I don’t find EM and global very useful. On the way up they provide a little diversity but have fairly poor returns compared to US, especially EM, but they have much bigger risk so when the crash comes all arrows point into the dirt and the arrows with the bigger risk get buried deeper and take longer to recover. If you’re down 50% takes 100% to get back, if you’re down 70%, 140% to get even. Unless you’re making very out-sized returns it will take forever to make 140%, so IMHO from a risk management perspective it’s a bad bet. EM is like 85% correlated and global like 90% the the added diversity is trivial. REITS are 73% correlated and BRK.B 52% correlated so thee actually do provide some non correlated diversity, bu suffer from the same excessive risk argument. I own Global EM REIT and BRK.B a little bit with %’s adjusted to keep me on the efficient frontier at 10% total risk on the portfolio. Risk is adjusted with BNDS CASH GLD which are strongly non correlated. I presently don’t hold a Tangent portfolio since I’m using cash to Roth convert. When I finish Roth converting the IRA will be in a tangent portfolio to control growth and keep me in the 12% bracket for a long time. I need a tax protected acct for bonds anyway so the tagent IRA will act like an annuity quasi inflation protected because of the increasing RMD schedule. The little dab of stocks in the tangent will round out the return and I will re-balance as needed. Look at my Parsing cash flow series for a more in depth analysis of my retirement portfolio optimized for taxes

    3. If you want to know my retirement approach more in depth look at my Parsing Cash Flow series, pus you need a means to accurately understand your budget and your budget limits

      My approach was to plan every year from retirement till age 92 or so then plan every year for my wife if I die. I was able to project my normative retirement cost (2.7M over 20 years) and stress test my budget to understand how tightening my belt felt and come up with a range of minimum and maximum budget constraints and set my actual average spending to be in the middle (108K/yr) I then set about Roth converting 1M from the TIRA to create a self insurance policy for disaster like extended medical care and severe inflation and possibly to meet a long stretch of SORR or increased taxes especially on my wife after my death. SS + Tangent TIRA + Brokerage and tax loss harvest provide my retirement income, the Roth my families protection. The brokerage plus THL effectively turns the brokerage into a Roth. I also optimized my taxes at every turn since what you get to spend is what they let you keep. After 10 years of growth or occasionally before I can open the Roth for fun money or if I want to buy a car or something. You have to plan for 2 end of life scenarios one for you and one for your wife

    4. I think much of the published doctoring retirement planning is fantasy. The things that kill you are bad SOR, excessive longevity, poor risk management, no clue about how to deflate a portfolio, taxes, excessive WR, no disaster protection and over leverage. If you haven’t addressed these specifically you’re pretty much flying blind. It’s really hard to squeeze 60 years of income out of a 30 yr pot of money. If you set up risk management correctly and don’t panic sell you can survive a down turn, but to understand downturn you either have to live downturns or study downturns. Downturns are dangerous like hitting the rapids on a river. It’s fast moving and takes skill to navigate. If you think you’re going to wing it you’re a dope. Human Capital is the greatest diversifier known to man but human capital has one path, down. It starts maximized when you are born and relentlessly decreases until about 65. Once it’s gone it’s gone. If you throw away 20 years of human capital to go sit on a beach or play with your winker in some side gig you’re truly are messing with FIRE. Medicine is a mess. The MBA’s are robbing the system blind and leaving physicians in the lurch. All the responsibility, none of the compensation while the jokers in the C suite rake it in and spend the day getting smashed. So I can well understand the desire to leave ASAP

  3. What are your preferred vehicles to buy gold in? Is it a sector fund like Vanguard has or is there some other avenue (unless you are actually buying and storing physical gold which I’m not sure I would want to do).

  4. Any thoughts on whether it’s best to hold GLD in taxable or pre-tax accounts? At first glance, taxable makes sense but on the other hand GLD will be sold if it appreciates significantly, to buy other assets.

    Xrayvsn – GLD is most popular. I have been using IAU because of a lower expense ratio. GDX is a gold miner ETF that might be used if tax loss harvesting is needed.

    1. I guess it depends on what fund/s is/are supplying your hamburgers. In my case until I RMD my brokerage is my source of income. I have it set up after I RMD a small TIRA plus SS will provide like 60% of my income as ordinary income and the brokerage will pay the rest up to the top of the 12%. Since the top of the 12% keeps me in zero cap gains land it makes sense to have my GLD in brokerage. If I had a big honkin IRA providing hamburgers I’d probably put the GLD in the IRA to help with the volatility in that account. The suggestion of IAU is a good one and GDX but since this is designed to protect in a downturn I would just tax loss harvest the portfolio for tax losses and use the GLD to pay for hamburgers.

  5. Hey Gasem,

    What always make me chuckle is the fact we have very similar plans. But we live in different countries and I have never used firecakc or Monte Carlo.

    Regardless of whatever tools we use, I bet we both take risk management very seriously.

    Plus we both appreciate vigilance, not being too optimistic, etc.

    1. I know right? It almost seems to be a common phenotypic expression 🙂 I just wrote a response on CD’s site and read your response as well. Your post very much echo’s my philosophy, I just happen to get turned on by the “math of it all” while you enjoy how streamlining improves portfolio and life’s efficiency. I love how you “can’t be bothered” but hone in with a scalpel severing sinew from bone. The hubby best understand that tiger-mom

  6. I think there’s something endearing in the kindred spirits of Dr. MB’s “simple and risk-averse is the only path I wish to tread” approach and your own engineer’s “devil is in the details so let’s dig into those details” approach. Two sides of a zen chemist, complementary and deeply grounded in empirical study. Keeps me coming back for more. You are making me reconsider a small gold allocation for the reasons you’ve mentioned repeatedly…belated congrats on the ERN guest post, happy to see your formal induction into the hall of huge brains (even if some of us recognized your membership all along).

    1. We all add what we can. I’m fortunate to have some time to spend researching and thinking, but I’m not a big brain, just an old geezer with a lot of scars who taught himself which paths not to tread. Big ERN is a big brain. MB is also amazing in the quality of her thought. Like a woman she just cuts to the heart of the matter while I twiddle the dials. Either IQ or XX chromosome it’s clearly genetic superiority

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