Living in a Bayesian Land

Thomas Bayes was born in 1701 and dies in 1760.  He developed a statistical theory called Bayes Theorem.

I have read Bayes Theorem is the most tattooed theorem in the world.  Bayes was a Presbyterian minister and Presbyterianism is nothing if not about determination.  Yet Bayes approach is about probability.  Every other statistician of his day was about calculating the odds.  If you have a box of 20 black and while balls what’s the chance of pulling a black ball?   Bayes OTOH asked the question how to you come to know a better level of belief called the Posterior belief. 


If you have an old belief (prior) and no new evidence you have an old belief (same odds).  If you have new evidence that is reliable evidence then the belief changes and a new belief occurs (posterior odds).  The change in belief therefore is contingent on the reliability of new information.  Therefore you need a prior and you need evidence and the result is not deterministic but statistical.   

Let’s say you’re a FIRE type.  You bought MMM’s BS about “simple math”.  Let’s look a little deeper at “simple math” based on probability of success.  Boggleheads LOVE their 3 fund portfolio there are all kind of stanza written: low cost, you can’t beat passive index, FA’s suck, DIVERSIFY DIVERSIFY DIVERSIFY!    Then you pick a “number” out of thin air and apply simple math say 4% x25.  Lets say the “number” is 1M for easy calculation and conceptualization.   You choose a bogglehead 3 portfolio based on the “internet”.  You wouldn’t know a BH3 if it came up and bit you on the ass but that’s what Joe the Plumber uses and after all Joe is a plumber and knows how to braze copper pipe in a way that doesn’t leak, he MUST be a wizard!  Here are the survival chances of 1M, with 4% WR standard inflation and SORR for 30 years on a BH3:

Note as early as 15 years this portfolio starts to flunk.  You have a 86.87% chance of survival.  It means you’re broke 1/8 times.  It means 1M is not enough for a 4% WR and you need more or a side gig to reduce the WR, aka you need a job in retirement.  Let’s go from a BH3 to  a 50/50 VTSMX:VBMFX portfolio.  Note this portfolio has the same 50% VTSMX AA as the BH3 but reduces risk by substituting risky, highly correlated VGTSX allocation for a greater % of the non correlated VBMFX.  This 50/50 portfolio reduces the risk of the overall portfolio compared to BH3 and lives on the efficient frontier.

Same 1M, same 40K/yr withdrawal, same SORR and inflation, less risky allocation 98.46% success!   You’ll be dead well before this portfolio flunks.  There isn’t a hint of trouble till year 27.   This portfolio is based on the efficient frontier and Bayesian statistical analysis not Joe the Plumber’s dirty thumb nail analysis and MMM’s simple mindedness.   This portfolio is “enough”, survives nearly 99/100 times, and needs no side gig to pay for the added risk of stupid assumptions.  This is the power of quantitative analysis instead of the unproven narrative of internet fever dreams blasted at full volume into the FIRE echo chamber.     Hmmm… maybe Bayes was about probable determinism.   

As I think about this, this example is a systematic way to look at Suze O’s freakout and the recalcitrant FIRE response by reciting the “narrative” like it’s the Apostles’ Creed.  It turns out both formulations of the problem were wrong,  FIRE’s simple minded brain dead narrative and Suze O’s imprecise hand waving risk analysis.  You don’t need  10M and your money won’t survive by paying for your leverage with with too much risk. 

Bless you Thomas Bayes 

9 Replies to “Living in a Bayesian Land”

  1. Enjoy variations on this theme, Gasem, thanks for continuing to explore the simplicity of the 50:50, 2 fund portfolio.

    I sense even the Bogleheads are not completely in agreement on this issue:

    I still credit MMM with getting me interested in financial literacy, so I look up to him as an inspiring leader – one that by all means should be subject to critical thinking and independent judgement, but I suspect more good than harm has come from his musings.

    Appreciate your being there to assert the critique where it’s most needed.

    Thanks for having our collective backs,


    1. I guess it depends on what you mean by harm and by good. In my example his approach is good for 87% of the people but a nightmare for 13. Bayesian theory is a method that uses a multi step iteration multiplying the old probability by another probability that changes the old probability into a new more likely probability, and that “new probability” becomes the old and another crank of the wheel yields an even a more robust likelihood. This is how AI works it’s constantly honing and refining future “liklihoods” into a distribution of most likely and tailing down to unlikely or outside of the range of consideration. In other words there are mathematical tools just as easy to deploy as 4 x25 which are a far more accurate estimation of risk and knowing and characterizing your risk is tantamount to knowing your fate. The other problem is it gets repeated as dogma. When you jump out of an airplane it feels like you’re flying, the only bummer is the last millisecond when all the KE is converted into heat and tissue explosion aka the sudden stop. The chute and it’s deployment is nothing about the ride down it’s everything about avoiding the sudden stop. Same with portfolio design, the spending part is fine it’s the running out part that sucks. The “simple math” looks at return and ignores risk, or at most let’s risk fend for itself unsensed. The problem with Bogelheads is they misunderstand diversity. Diversity that saves you is non correlated diversity not just piling higher and deeper assets which are highly correlated. Here is a post I wrote on Wealthy Docs site regarding an excellent article he wrote on the features of bonds

      You missed the best feature of bonds, their correlation with stocks is virtually zero. Bonds provide a huge decrease in portfolio risk. Boggleheads are always talking about diversity. VTSMX has an expected return of 9.56% and a risk of 15.24%. VGTSX 6.11% and a risk of 17.14% and a correlation between the 2 assets of 85% If you made a 50/50 portfolio of these 2 assets the portfolio would have 7.82% return and 15,59% risk. If you substituted 50% VBMFX for VGTSX the resulting portfolio would have 7.13% return with 7.72% risk. The global fund provides the portfolio 9% extra return with 50% more risk. What this means is when VTSMX drops in half (50%) the VTSMX:VGSTX portfolio drops 52% This is not diversity but anti-diversity. The VTSMX:VBMFX bond stock portfolio with a 50% drop in VTSMX, only goes down only 25%. This means to get back to zero the foreign/us all stock portfolio has to go up 104% while the stock bond portfolio need only recover 50% In recovery 50% happens years before 104% so your portfolio is back to compounding much sooner.

      In addition the Bonds give you re-balance ammo. If you re-balance yearly and the market is going up you sell off some stock and plug that into bonds aka sell high to keep the AA constant. You do that for say 10 years and each year you’re selling a little bit high. NOW the market drops in half. The AA forces you to sell some of that bond money and plow it into stock, you are buying low with the little dab of sold high money you’ve been accumulating in non correlated bonds. Non correlated money does not loose its value in a stock crash by definition. This supercharges your recovery as the market turns around so not only don’t you fall as far, you spring back with a multiplier of extra stock. All of this is due to mechanical systematic investing (re-balancing), and non correlated diversity (risk management) provided by bonds.

      This is another way non correlated diversity saves your bacon. Certainly saving is better than not saving, and saving half is better than not saving half but there is method to the madness of how you do it that matters at least as much to the efficiency of the endeavor and it doesn’t involve riding a bike. I don’t really care what people do, but I do care all sides be known so intelligent “doing” can be done.

      1. Wow I read that BH thread those guys are so confused. Some have a kind of internal understanding of what “oughta be” but no real precision in how to think about it.

  2. Well I think MMM brought the message main stream since he seems to enjoy the notoriety. But honestly I see it all as common sense.

    Everyone knows that it is better to live within your means if you want to save some moola. Why would anyone need to read the internet for that?

    That’s why I stopped the blog. I seriously have ZERO to add to the topic. I just like to chat with a few other moneygeek docs.

    I think the best approach is your regular review of the plan Gasem. You keep vigilant and you stress test it. That’s the best any of us can do.

    1. MMM runs a media business and a brand. He sells his soap and reaps the profit. He’s no different than Dave Ramsey, Suze O or Tony Robbins. It’s designed to sell sells sell. Rap on brother Rap on. I’m a quant by nature so I sell quant soap. But I don’t profit and I don’t care about clicks or metrics so I don’t have as much of an agenda. I am super interested in the science and study of it all, what makes the economy work and the fact the other side of a trade is now occupied by an algorithm and not a person. What I write about should pretty much confirm you’re approach Dr MB. Can’t get much simpler than a non correlated 2 fund and an occasional re-balance.

  3. Hey Gasem, question on the 2 fund. I know you say that the 50:50 is the way to go through retirement. Do you suggest a sort of glide path to go on from younger to right before retire? Like in 20’s more weighted in equities and gliding down to the 50:50 split a few years before retirement.

    1. You can accumulate any way you like, since you are not living off the portfolio. The major thing that will change is the length of time it takes to accumulate, but also the efficiency. I accumulated at 75:25 plus I had a cash cushion which was not counted in my portfolio in case of job loss etc. I DO NOT count my portfolio as my net worth, but as one of a couple vehicles to replace my income after I left the workforce. The portfolio itself was 6 parts: SS equities, bonds, commodities, real estate, leverage. The portfolio was spread across 6 fund types: SS. post tax brokerage, TIRA which included a 401K, HSA, Roth and Tax Loss harvest which though not an “account” provides a store of wealth. Each of these provides a different but not unrelated function. Tax loss harvest for example allowed me to shift post tax assets from one equity to another without tax consequence so it acts like a tax free dividend of a fixed amount based on my tax bracket, or I could write off an additional 3K per year on my taxes and effectively plow that saving back into the market. I could maximize efficiency in that account or accomplish a specific investing goal and the taxes were “already paid” so it acts like a Roth. The HSA is to pay post retirement Medicare cost. The TIRA was associated with retirement funds accumulated through my business and is a roll over from those accounts as well as various post tax SEP’s and IRA’s my wife and I accumulated over the years. Because some TIRA is pretax and some is post tax the IRA disbursement becomes tax advantaged since the government taxes you only once so if I had 25% post tax and 75% pretax there is a formula that allows for an ongoing 25% writeoff on the ordinary income that comes out every time I extract money from the IRA. The Roth is insurance. I consider it a separate portfolio which will sit untapped forever to be transferred to my children UNLESS disaster hits and my wife or myself, or both need extraordinary income for say assisted living or big deal cancer treatment. I will Roth convert the TIRA but not empty the TIRA completely into the Roth. I will leave some in the TIRA to hold my bond allocation and let that go to RMD. A bond TIRA doesn’t grow much and so the annuity it produces acts more like an inflation protected source of yearly income that doesn’t generate a big tax bill. It starts at a certain amount say 25K/yr and grows to say 35K/yr in 10 years and $45k/yr in 20 years. A big honkin 70/30 AA TIRA would start putting out 100+k/yr and be putting out 250K/yr in 20 years all of that taxable. So by shunting TIRA to Roth I control my taxes well into retirement. Our SS will be about 50-55k/yr inflation adjusted so say 52K/yr. SS is 85% taxable so my tax bill on the first dollars (SS) of my retirement will be on only 44k. my RMD is 25K/yr but only 75% of that will be taxed or 18.75K so from RMD and SS I will make about 63K/yr. If you take standard married over 65 joint deduction you can make up to 104K/yr before breaking over into the 22% bracket, so I have 41K to fill up in the 12% bracket before my tax bracket advances. My income however is (52K SS + 25K RMD) for 77k meaning my income is taxed advantaged by 14K per year. In the 12% bracket you can take post tax money out of your brokerage acct cap gain tax free up to the top of the bracket so if my taxed income is 63K I will pull 41K from post tax bringing me to 104K plus the 14K extra from tax advantage SS and RMD or 118K. If I want more money to say buy a 30K car I will pull 30k more from brokerage and use some tax loss harvest to pay the tax on money over the 41K for zero extra tax. At 3.4% income growth in SS and RMD combined I figure it will take me 16 years into post age 70 retirement (age 86) to break over into 22%. In the meantime my WR on the brokerage account is well under 2% even if I buy a new car every 3 years (unlikely). So each of these accounts has a different function and a different AA. In my brokerage I hold GLD which is typically negatively correlated with stocks especially in a down market. That means as stocks go down GLD goes up. It’s the GLD I will sell in a crash (sell high) and let the stocks weather the storm. I will pull some dividend stream if needed from post tax stocks instead of reinvesting in a down market, not my first choice but dividends tend at least for a while to be relatively non correlated to the asset value of the underlying asset in a downturn so it’s a back up source of income, but I’d prefer to reinvest if possible, buy low. In addition I re-balance the AA and use that as a mechanical means to buy low sell high across non correlated diversity.

      So my portfolio is more complicated than 50/50 based on tax streamlining and diversification. My present Efficient Frontier AA is 56:45 down from 75:25 during my W2 days. I have quite a bit in cash as I Roth convert. The cash generates no income tax so I can Roth convert at the highest tax efficiency. It also means I am not taking money out of the portfolio since I already have 5 years of living and tax cost covered, which turns off SORR for a while If things look horrible based on economic indicators I have no problem heading to 45:55. It’s the risk that kills you in a crash so IMHO there is no shame in reducing risk in an impending crash. Reducing risk is NOT the same as getting out of the market, you are still fully invested just not as heavily risked. There isn’t a HUGE difference between 60/40 50/50 or 40/60. 8.32/9.02 is the 60/40 reward/risk pair and 7.17/6.32 is he pair for 40/60. 50/50 comes in at 7.75/7.64. VTSMX is 10.59/14.68 so if VTSMX drops in half (50%) you can expect 60/40 to drop 31%, 50/50 to drop 26%, and 40/60 to drop 21%. To get back to even VTSMX has to grow 100%, 60/40 62%, 50/50 52% and 40/60 42% It takes a hell of a lot longer to grow 100% than 42% and once growth has resumed there is no reason not to go back to 60/40 for a quicker recovery. As I Roth convert I’m using up cash so my Efficient Frontier AA will slowly start to creep back up automatically

      Despite all this dancing and contingencies, what I have read is 5 years before retirement you should glide down to 50/50 stay at 50/50 for 5-10 years and then glide up slowly after that till you die or reach some higher level of risk you’re comfortable with. The studies I read were academic PhD level data and not popular media, and were for about age 60 or 65 retirement and in my opinion reliable in the assumptions. The notion is once you’re old, you’re in a race to see if you run out of life before you run out of money and in a well risked portfolio it’s hard to run out of money. Look at the above case. The BH3 crapped out 13 times but started crapping out only 15 years into retirement. The 50/50 crapped out less than 2 times and it started it’s trouble 27 years into retirement, so you likely would be dead before you run out of money in the 50/50 case. The problem changes with RE however since stupid mistakes have much more time to develop and can overcome your wealth before you RIP. 40 or 50 years is a LONG time when it comes to leverage and accumulated error compared to 20 years. The 50/50 fund above didn’t show its error till 27 years effectively making it bullet proof for a 30 year retirement. I ran the 50/50 for 50 years and survival was 92% at 50 years dropping slowly after 27 years vs BH3 which had a 74% survival at 50 years and began to drop rapidly after 15 years. My impression is SORR is most significant early in retirement and 50/50 helps save you. My other articles on “life boat” and SORR re-sequencing on your site are additional means of protection in early retirement. My further impression is the earlier you retire the longer SORR has to work its disaster so the glide path for a 60 year old is different from a 45 year old, but then most 45 year olds don’t retire they semi-retire aka continue to work to mitigate that risk.

      The point of course is you can actually predict the “future” by studying a distribution of likely and unlikely statistically generated “futures” taking into account stresses like longevity, SORR, inflation, disbursement risk (4% v 3% v 2% WR for example) and understand then how much you need to accumulate in order to stand a good chance of success for a given lifestyle.

      Maybe I should turn this into “the shocking complex dance of a bullet proof portfolio” There is some stuff I didn’t cover like wills trusts and law suit protection but that’s a job for a lawyer and relevant to the specific state in which you reside. Also this is why I employ a FA as he is completely clued into this plan and can implement it for my wife in case of my demise. The wife’s situation as filing single complicates the tax picture so that needs to be considered as well but beyond the scope of this response.

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