Decumulation strategy for Vampire

Decumulation strategy for Vampires

Ever wonder why vampires are mostly viewed as having wealth beyond measures? For them, even saving a small fraction of their income would make them filthy rich. Remember the adage of saving early. The reason behind is that any balance left untouched for a long period grows to huge sum. 

Lets be real, a lazy vampire wouldn't want to work forever. Why be immortal if it is for a life of force labor? How early could a vampire stop working and just live off what he has accumulated? To answer this, we need to be real. How much would our vampire need in retirement? A million? How much should he spent each year 120k per year? 

How should vampires game the system? Let's say that they worked their mortal lifespan and accumulate, let's say, a million dollar. Would a vampire need to work? Or would he be able to live a lavish life? How would it evolve through time? Would he need to work again?

An immortal strategy would rely on keeping the principal intact. The first instinct is to remove the increase of the balance, like Dave Ramsey often quote, lets say you have 1 million and lets consider that the past historical average return of the stock market is 12%. Then out of it, you can comfortably lives on 1200k a year. Not bad. If you spent in excess, you will go broke. If you spent under the million would grow each year. 

However, our vampire would rapidly hit a wall. Such a thing as fluctuating market returns exist. Unless vampire overrun our world, they would only be a small part of the world and wouldn't be able to influence the entire market. In fact at 12% withdrawal would have only lasted at the worst historical time, the balance would have gone to 0 in less than 5 years. In other words, this would force our vampire to endure another lifetime of work and misery. If we slash in half the withdrawal to 6%, the worst historical period would force him back to slave work after 10 years. This is unacceptable.  

Before going further, lets not forget about an obscure concept of finance. Lets consider the impact of inflation. If say all your need costed 100k currently, but 104k next year, then we would have faced 4% inflation. Ideally we would reflect our vampire specific inflation, but lets take a proxy using the US inflation. If we did, it surprisingly increase the worst historical period before going back to work to 13 years, using the 6% withdrawal rate. This is because the worst period of returns were in the 1930s where the US faced deflation (ie your need of next year costed less than 100k).  Thus the vampire needs grows each year due inflation. 

Okay, with this established, what would be the safest withdrawal rate our vampire could use and never have to work again. To establish this, I gathered historical data from 1928 to 2023 for the returns on stocks/bonds and inflation. If you are curious see at bottom for all my reference. 

Our vampire would be safe to withdraw 3.5% per year of its initial balance if he elected an asset allocation of 40% bonds/60% stocks. In other word, even if he was unlucky and retire at the worst possible time in the last 100 years, he would have been fine to withdraw 35k from a 1 million initial balance. If we rather used a 100% stocks asset allocations, then he could have withdraw 23k out of that million. 

The last 100 years faced many troubling time. One of the worst was the period of 1929/1930 where the black Fridays occured. If we exclude the years 1929/1930, we can bump the withdrawal to 3.7% in an all stocks asset allocations. This is more or less in line with the 4% rule out there that was calculated by the trinity's study and Bengen's study for us mere mortal over a 40 years lifespan. 

A curious data point we see in the historical return is that the return just prior to those worst period is often golden. for example the return in 1928 were of 40%. Between 1923 to 1928, their initial balance of 1923 would have made be multiplied by 350%! This makes me a little less sympathetic towards the 'rich banker' who lost it all. What the hell did they do with so much increase in the wealth? Lets hope our vampire is more wise and less cupid. 

One way to mitigate this effect would be to use moving average estimate of the balance. Moving average are simply the averages of the last 5 years of balance adjusted by an estimated return. I will refer you to my spreadsheet for more info on this method. 

Another troubled period was around the 1970s; during this time, the issue was not around bad returns. Rather it was inflation. The cost of living increase at around 8% for the whole decade and 3 years above 10%! An underlying reason of the 1970s inflation was due to gas price. Perhaps our vampire could go back its horse riding days not follow the general inflation? Otherwise, I am not convinced that such elongated inflation should occurred in the future. We saw a single year at 8% in 2022 and every government bank in the world raise try to break the pattern like it was the plague.   

Vampire are known to be schemer. Let's further assume that our vampire is a planner. It would be expected for the vampire to prepare his retirement. Let's say he has $567k. At 12%, that should grow to a million easily in 5 years. A good vampire planer would thus take a withdrawal of x% * of the minimum between that million, the smoothed average or the balance at retirement. Using this conservative approach, the 100% stocks allocation safest rate of withdrawal increase from the 3.2% to 3.8%. As a side note, lowering the 100% stocks would have lead to worst results. 

I will explore further tricks that our vampire could use to further increase his laziness and wealth in future post. He could well be somewhat flexible about what he can withdraw. If the writing on the bloody walls appears and failure is on the horizon, wouldn't a vampire cut his spending? What about that pesky inflation? Could he skimp on it, instead of following exactly like a mindless ghoul? 

If you are curious you can grab my data and calculations from this file. It uses the excellent data from Aswath Damodaran, adamodar@stern.nyu.edu. It essentially provides you with the data from 1928, just prior to the black friday, up to today. For the inflation data, please go to the free resource of the us inflation calculator. 

Let me know what you think! 

Qu'est ce que le risque financier%

 

Un des termes centraux en finance est le risque. C’est un terme qui cache beaucoup de sous-entendu. Il est souvent mal compris. Hors des finances, on parle de risque d’échec. « C’est risqué de sauter à côté d’une falaise ». En finance, le risque est plutôt la grandeur des variations futures. « Chez nous, on garde la température entre 20 et 30 degrés. Chez-vous entre 10 et 40. C'est plus risqué ». Finalement, le terme est parfois vu comme étant exclusivement négatif (variations négatives). Je vais tenter de clarifier.

Pour tes investissements, le plus grand risque est celui de la volatilité. Autrement dit, en investissant 1$ va-t-on avoir après 1 an entre 0,90$ et 1,50$ ou entre 0,99$ et 1,03$. Le premier cas sera plus risqué car il varie plus. Toutefois, ce risque additionnel est compensé. La moyenne du premier est 1,20$ et du second de 1,01$. Si on répète l’expérience sur 2 ans, alors on pourrait être chanceux durant la première année et malchanceux la seconde. Alors sur 10 ans, on se rapprochera de la moyenne. Plus bas, il y a deux graphiques qui montrent les rendements par percentile après un certains nombres d’années. 50% des rendements passés se retrouvent dans le vert foncé et 50% dans le pale. Les bonds sont peu risqués et les actions le sont plus. Toutefois, les actions vont rapporter plus d’argent. Après quelques années, on voit :

• Le meilleur rendement des bonds est inférieur au 50^ième percentile des actions (7.5%).

  • Sur 20 ans, les actions (50^ième percentile) produit = 1.075²⁰ = 4.25x notre investissement.

• Le pire rendement des actions est égale au 50^ième percentile des bonds(3%).

  • Sur 20 ans, les bonds (50^ième percentile) produit = 1.030²⁰ = 1.81x notre investissement.

Le second risque majeur est celui de ruine complète. Autrement dit, quel est le risque que mon investissement de 1$ deviendra 0$. On devrait investir dans plusieurs compagnies. Tu possèdes une petite partie dans près de 10,000 compagnies. Le risque de tout perdre revient à dire que ces 10,000 compagnies feraient faillites en même temps. C’est quasi impossible. Toutefois si on investit dans 1 seule compagnie ou encore dans 1 seul secteur (ex : les trains), c’est tout à fait possible de tout perdre ou presque. Une autre définition serait le risque de perdre une partie: 1$ deviendra moins que 1$. Pour les bonds, le risque est moins de 15%. Pour les actions, il diminue de 30% après 1 an à moins de 15% après 7 ans.

Finalement, plusieurs autres types de risque existent. Le risque de l’inflation, autrement dit est-ce que le litre de lait de 1 $ aujourd’hui sera de 2$ dans 10 ans. L’inflation ces dernières années est d’environ 2%, mais elle a été parfois au-dessus de 10% et la moyenne est de 4%. Tous les graphiques plus haut sont des rendements sans inflation. Si on rajoute l’inflation, le risque de ruine disparait quasiment pour les bonds et disparait après 10 ans pour les actions. D’autres risques mineurs sont :

• Le risque de la devise, autrement dit est-ce que le dollar canadien va chuter dans le futur.

• Le risque du taux directeur, est-ce que le coût pour investir sans aucun risque va changer.

Pour conclure, il y a plusieurs « risques » reliés à nos investissements. Il est risqué de prédire combien l’on aura dans le futur. Toutefois, il ne faut pas avoir peur du mot risque. En général, ça revient à dire que l’on est moins certains de cet investissement que de l’alternative. Dans tous les cas, ces incertitudes sont souvent accompagnées de gloire et fortune.

Millionaire Study review of stats

I have recently read the millionaire study(1) by Dave Ramsey. It is a treasure trove of invaluable statistics from real life millionaires. It is a good complement of the Millionaire next door in revealing the habit of the wealthy. The main purpose of the study was to confirm that everyone can become a millionaire. But, from reading in the stats,I do not arrive at the same conclusion. Secondly, the study make me doubt at the efficiency of the self-improvement toward money goal. Finally, there is a wide gap between the general belief in what is needed to reach millionaire status. What is needed to be a millionaire is simply savings and investing your money. 

 Being uneducated drastically reduces your chance to be a millionaire. The study shows that only 2% of the millionaires have only a high school diploma and 0% without it. Thus it seems that for reaching millionaire status it is a prerequisite that you have at least a 4 year college degree (84% of millionaires). Intelligence, or at least having the skill set to pass exams seems to be highly sought as most of the millionaires (55%) were « A » students. 

 One of the harsh reality of the study is that many of the self-improvement movement seems meaningless in order to achieve wealth. Setting personal goals like many self improvement books is irrelevant on the path to millionaire status as exactly the same proportion of millionaires and in the general population does it. Similarly, both millionaires and the general population strive to always try to improve their habits at similar proportions. The millionaire reading habit is a tad bit higher than the general population, but as earlier mentioned , most are highly educated, so I would not be surprised if it was simply a reflection of this. Another belief in the self improvement movement is to seek wisdom from mentors. It seems that millionaire disagree as slightly less than the general population reach for mentors wisdom. 

 The main difference the general population has versus millionaires is the knowledge of how to attain millionaire status. The general population believes in the need to come from a rich family(77%), take big risks with your money(67%), inherit it (62%)or have a 6 figure salary (62%). Millionaires disagree with these beliefs. This is probably illustrative of their own path to wealth. Only 31% believe in the need to come from a rich family, 16% to take big risks, 35% to inherit it and 35% to need to earn a 6-figure salary. 

 In conclusion, it seems that being good at school & savings/investing is the path to wealth. You can skip the self improvement book as it sadly does not seem to help. 

(1)The National Study of Millionaires – Finding From the Research Study Behind Chris Hogan’s Everyday Millionaires (2019). Research by Tony Lemonis, Jameson Murray, Tim Smith and Natalie Wilson

The Magic Dollar

A goblin came to my home yesterday. Like many goblin, he was a banker. He owed a favor to my great grand-fathered. To repay his debt, he offered me betwen receiving a million dollar or a magic dollar. That magic dollar and his children would double every day for a month. What would be the best choice?

We could select according to our intuition, but there must be a trick. One million is too good to be true. We must always be aware of what is too big to be true. If the goblin proposed it, the magic dollar is most likely worth as much. Lets take of our pencil & paper!

The dollar become 2$ after 1 day. He grows to 64$ after 7 days. That's a bad start for this choice, lets continue. After the second week, the dollar accrue to 8,192$.

It does not seems possible that the magic dollar is the right choice after almost half the month completed. The almost entirety of the road is still ahead (991,808$). What do you think, should we continue the experience?

For the third week, we pass to 131,072$ mid week. Finally 2 days later, we arrive at the mid-point at 524,288$. It took us 20 days to arrive to this point. How much days would be needed to arrive at a million?

Of course if the magic dollar double, it will take one day. At the end of the third week we are well over the million. The fourth week is staggering. We do not know what to do with our dollars. We pass by the 16 millions mark mid-week and above the 100 millions at week end.

The last few days are nothing to sneeze at. At day 30, we are at 500 millions and at the 31^th, we arrive at over 1,000$ million. If the goblin strike at your door, my best advice would be to ask him to come back in December or January to reach that 1 billion!

Now, lets come back to reality. 1 dollar invested in accessible asset do not double each week, but after roughly a decade. If you are able to put away 100,000$, then you can expect to have another 100,000$ at the end of 10 years. To be more precise the type of investment and his return determine the exact time to double.

Types of investissement	Gold or cash	100% Bonds	60% Equity 40% Bonds	100% Equity
Interest rate	2%	3,4%	5,5%	6,9%
Double after	35.0 years	20.7 years	12.9 years	10.4 years
30 years later on 100$	181$	273$	498$	740$

We can conclude two truths on these numbers.

• It will not suffice to invest 100,000 for your retirement, even with 30 years of time horizon. We must also contribute each year to retirement

• The type of investment as a rather big impact, You would have 5 times more money if you invest in equity versus in cash at the bank.

Value of the Magic Dollar = 2^{(number of days - 1)}

The cost of a 70 years annuity versus an eternal annuity

  

A while back, I read a sensational paper who was trying to scare us 🙀(classic, I know). He wrote that he was amazed of the cost of paying a 70 years annuity to an exec who left early with reprimand! Wow, given the cost of an annuity, how titanic would a 70 years annuity be worth? Well the journalist did not explore the exact cost 🙉, but continued to ramble on the excessiveness of this golden parachute. For an actuary, I think that the journalist left a golden nugget there. Sadly, a 70 years annuity is well not that of a high price tag versus a classic 30 years annuity.

One reason to look at this subject is that one of the fear 🙀of the FIRE, Financially Independant Retire Early, community is the fear of longevity. How much more a 30 years annuity is compared to that of an 70 years annuity... 

First, why would you want a 70 years annuity if you are not an executive? That would be like having an annuity for yourself and your children. The game “The Talos Principle” illuminated my though on the subject. The little robot🤖you play is the millionth generation of a serie of “IA”. Each previous generation died trying to escape various trap and puzzle. Each generation slowly learning to get better. At the game end, you prove that you are finally a robot🤖worth waking up. I reflected that we are also a generational species. We build on the shoulder of giants. From a financial perspective, both my grand father and father were not rich. Quite middle income. Although that is true, it is also true that if the earlier would have put 10$ in the S&P500 in 1900 (roughly 250$ in current day), I would be a millionaire 💰. (source: OfficialData.org). Why didn’t my father given me 10,000$ when I was born? I would have been already a millionaire 💰. 

Why would we want the next generation to start from nothing? The trill of the hardship? I never lived near the rich. Never seen the silver spoon effect. However, I have seen my fair share of adult with no aspiration. None of them were rich or started rich. Why really wonder how many wealthy do nothing of their lives vs poor one. It is great to have dreams and grits but I fail to see how it is related to the lack of money. Having infinite money means that you can procure what ever you want. Having a dream to do something do not require any money. Having money do not preclude someone to dream. Between having debt up to my eye ball or having a 6 figure net worth, I would select to be rich💸. Thus it make sense to try to attained a generational annuity.

From my actuarial background, I have learn the formula for calculating the worth an annuity. At 5% interest rate, a 50k yearly payment for 5 years is worth about 215k. It make sense. If you kept 250k aside, it would provide for exactly 5 year worth of 50k. At 5% return, you get a small discount of 35k. Interestingly, if you wanted a 20 year 50k fixed annuity at 5%, it would not cost 4x. It cost 620k. The trick here is that 5% interest on 1 million dollar is 50k. 1 million💰offer an eternal yearly payment of 50k. Compared to a 30 years annuity (like would you probably elect at 65 to provide a lifetime ending at age 95) cost 770k so for 30% more, instead of having a finite pension, you get an infinite one.

IQPF, which relies on historical data, expert opinion, RPC and RRQ, provide that roughly the expected rate of return in the future should be about 7% if you invest 100% in equity. Thus 1 million💰would provide either 70k annuity per year or 50k + 2% increase per year (to offset inflation).

For me, that 30% increase in cost is well worth to provide an enduring legacy for eternity. And finally a 70 years annuity cost roughly 3% less than an infinite. So it appears that the executive should have offered to pay for that extra 3% to ensure that all of his legacy will never be missing money ever again. I am not sure why the journalist or anyone would find the cost of a 70 years annuity so much greater than a 30 years one. They are in the same bulk part cost. Finally, the FIRE crowd might not be completely be appeased, but I hope this will help them have a fresh look at the real extra cost of having a longer time frame than the Retire late crowd 😆.  

Better metrics - Moving Average & Smoothed Average

Today’s main metric to inform us on how are funds are doing is the Market Value. The Market Value(MV) is highly volatile from day to day. Relying on this metric increase the likelihood of bad investment behavior like selling low, buying high. Also it magnifies, the risk of ruin of the safe withdrawal rule. Most financial planners agrees that one of the key advantage they bring to the table is to make investor stick to the plan. Instead of showing the highly volatile current value of the fund upfront, I suggest to show and use the Moving Average(MA) or the Smoothed Average(SA) as the primary metric.

At a high level, Moving Average and the Smoothed Average are the average of the last years market value adjusted for the time lag. I will explain later in details both metrics exact calculation.

These metrics, MA & SA, have 1 key advantage over the market value, they have lower volatility. Without taking into consideration cash flow both MA&SA produce near identical returns. Therefore, we can safely look at the Moving Average only for clarity at first. Here is a table summarizing the expected 1 year rate of return over the various strategy without cash flows.

Based on historical return (1918-2015) of the S&P 500 and the Moody Seasoned AAA Corporate Bond Yield

We quickly see that the volatility is substantially less in the moving average metric than the market value. The worst years would only affect the Moving average by -7% vs more than triple in Market Value change, -25%, in a 100% equity. That worst variation in Moving Average, -7%, 100% equity is less than the impact on the market value, -11%, at 50% equity/50% bonds portfolio.

If the purpose of buying bonds is to reduce the pain of losing money, why not also take a metric that automatically protect yourself from exuberance of the market.

Here’s a graphic to compare the three metrics through time. The graphics shows the Market Value in blue, Moving Average value in red and Smoothing Average in green (real$) using 100% equity allocation. In order to remove the impact of the ever increasing S&P, I divided each metrics by the average geometric return (7.1%) from 1922. In other word, 1 at 2015 means 631x a fund invested at 1922 (real$). A value of 2 means that the current value is 2x(1+7.1%)^(Yr-1922). At 1930, we can see the MV and the MA are equal at around 1.8. This means that both metric are the same value.

Overall, we can see that the Moving Average return is roughly the same as the Smoothed Average. Secondly, we see that these are reasonable metrics that are about average return like if we were doing the average of the future and the past value. Finally, we do not see the peak that is so characteristic of Market Value Highs and Lows. Instead we notice a smoother ride all along the way.

If we look at the exuberance of the market in 1928, the Market Value was 2.36x above the average return. The Moving Average was 1.64x in 1928. Thus if we were going to show the Moving Average, the investor would have a feeling that he is less rich than he truly is because the market was overwhelmingly hot. Thus, it would have led to a better predictor. Indeed, the irrational investor would have been happier to see a lower decline during the 1930s years than the sharp decline that the Market Value produce. By comparison instead of a drop of 30% over the following years in Market Value, the Moving Average would have a drop of 13%.

Obviously, the Moving Average do not protect against a drop in the market. It only spread its effect. So in the 1970s we see that the market would have drop and drop some more. The MA just trailed behind in the high end during these year, finally to settle to nearly the same value.

These lower drops using Moving Average will help the investor rationalize gain and loss over times. If the purpose of buying bonds is to reduce the pain of losing money, why not also take a metric that automatically protect yourself from exuberance of the market.

The second advantage is that it actually reduce somewhat the risk of ruin using a 4% rule of thumb. For example think of an extraordinary year, using Market value, the 4% rule of thumb would start you withdrawing from the highest peak and thus increasing risk of ruin. Instead using moving average will take a conservative view of the situation and automatically suggest to wait before pulling the trigger. It gives the investor a sense of perspective relative to time as to how well or how poor his strategy returned. However, it is not a silver bullet as much as being flexible in your spending after retirement.

The main disadvantage most widely known against Moving Average is that it hides the current value. Therefore right before the 2008 crash, the moving average would be lower than the market value and right after the 2008 crash, the moving average would be higher than the market value. I would argue that this is exactly the sort of attitude you need to take in order to refrain from doing irrational behavior.

Secondly, you cannot go sale at the Moving Average price. Ex: Market Value = 100$ and the Moving Average = 90$. You will not be able buy at 90$ market share. If you sale at 90$, than you would lose 10$ vs the market value. My counter argument to this disadvantage is that you cannot sale at the displayed market value on your statement that was produce 2 weeks ago at a price tag 1 week earlier. Market is very volatile day to day! Unless you are doing the transaction yourself (go DIY!), you will always suffer a lag. Also, if you are not going to sale the whole funds tomorrow, say 0.33% per months for foreseeable future aka 4% per year, than the price today will only impact a small portion of your wealth. It is not indicative what will be 4% next year or even 0.33% next month.

Currently at January 2020, we are experiencing a somewhat over valued market by perhaps 10%. Using this metric, I would suggest the person waiting to pull the plug to consider some level of conservatism in its estimated net worth and consider it perhaps 10% less than what it is currently. Obviously you would need to redo the math over your own fund to have a more inform consideration.

I hope that I was able to convince you of the usefulness of the metrics. In any case, here is the intricacy of the methodology. 

The Maths

Let’s start by the Moving Average. The Moving Average is a simple technique that simply takes the average of the fund value. In its more common application over a few days or month, we usually do not adjust for expected interest. Our purpose should be to have years to years less volatile portfolio funds value. This is why I would suggest to use the 5 years average. Over such a long period, I would suggest to multiply the result by twice the conservative rate of return. See below example. Using these Market Values, the 5 years average is 263,757$ without adjustment. Then assuming a 6.8% return, we get a Moving Average of 300,848$.

To see the advantage of going with a more complex metric as Smoothed Average, we need to enter some cash flow. After adding some random deposits throughout the years, here’s what the graphic looks like:

Now we can see the advantage of the Smoothed Average (in green). The Moving Average (in red) often drags its feet after we entered cash flow. Conversely, the opposite would occurs if we entered withdrawal instead.

The Smoothed Average is more complex and fits the need where there are any cash flow. Secondly it insert a bias by giving more credibility to the older balance. It will put a credibility of 80% (4/5) over the return 4 years ago, 3/5 over the return 3 years ago, 2/5 over the return 2 years ago and finally 1/5 over last year return. The Smooted Average formula is complex:

SA = MV2017 +4/5*(MV2016+CF2016/2)*(ExpectedRoR-RoR2016) +3/5*(MV2015+CF2015/2)*(ExpectedRoR-RoR2015) +2/5*(MV2014+CF2014/2)*(ExpectedRoR-RoR2014) +1/5*(MV2013+CF2013/2)*(ExpectedRoR-RoR2013).

Here’s a data example with above average return. The Smoothed average would be 298,384$ = 284,067 + 4/5*235,207*(6.8%-21%) + 3/5*264,722*(6.8%-(-11%)) + 2/5*276,271*(6.8%-(-4%)) + 1/5*258,520*(6.8%-7%)

Common adjustment include putting a corridor on these metrics. The corridor will limit the SA & MA between 120% or 80% of the MV. Ideally this corridor is unbiased and reflects the current fund. Other even more complex SA method exist which leads to slightly different average, but in essence this simple SA captures most of what we want.

On the Pros;

• It fluctuates a lot less than the fund value
• It delays the immediate impact of a sustain change which leads to lower rash decision
• It remove unsubstantial change which leads to lower folly decision
• It reduces the fund in period of high value and increase it in period of low value.

On the Cons:

• It doesn’t reflect the value of the fund directly. If you would sale the fund, no one is going to give you the Smoothed Value.
• It lags behind the real curve, if the interest rate is below real average rate of return or is in front of it if using too optimistic rate.
• It delays sustained change.
• Huge stress would be recognize over a long period. Thus the impact of the 2008 is felt even in when market were up a few years later.

Ode to Risk

Ode to Risk

Why should we invest in the company vs lending the company? In other word why should we invest in equity vs bonds?

First let’s concede that not everyone is built to withstand high level of volatility. It is far better to stay invested in a low return fund than to change strategy when things goes bad and reinvest after the market recovery. You must not be half convince of the below, but totally convince and go back to this article or to your saved thinking on the matter at the next crash to prevent you doing a yoyo.

Personally, I am convinced after research that the best way is to be 100% in equity. Here are my arguments.  

High level argument

Companies are concerned to maintain good credit level in order to have lower interest rate to pay for the future loan in order to be able to take on more profitable project. In case of bankruptcy, bonds gets repaid first and equity holders are often left with nothing. Thus bonds are safer than equity. Also, bonds have known interest rate when issued thus repayment fluctuates less than the value of the company.

However, no company would start borrowing at a rate of return higher than the project rate of return. If they did, they would get bankrupt. Thus rate of return of equity must be greater or equal over the long term than the borrowing (bonds rate). As an owner we can thus expect to receive more than the lender.

By spreading the risk throughout the entire market, you are no longer concern of any one company but to the overall risk. In a diverse index funds, bonds & Equity are protected against a catastrophic event. At this level though, there are still lot of fluctuation for equity.

In-detail argument (no withdrawal)

Why should you accept the risks that equity offers vs bonds? I have compare the return over various period (data : S&P500 and Moody AAA corporate bonds over 1968 to 2015) over various allocation.

Since the market is indifferent of investing a thousand dollar or a million, I simplified the return as a multiplier of a 1 unit of fund. The Tab 1, looks at the return (constant $) without withdrawal. The more the cell is blackened, the more the results are likely to occur. Thus we can see at time 0, all funds are at 1x (ie 1,000). After 30 years, Tab 1.a reports 2x-10.5x (ie 2,000-10,500) vs Tab 1.c which reports 3.5x-20x (ie 3,500-20,000)

First, let’s concede that we do see some drop below 0.5x in the 0 to 5 years range in the 100/0 allocation that we do not see in the 50/50 allocation. If we continue our analysis, we get the summary table

Let’s first compare what happens in the 50/50 allocation vs the 100/0 allocation:

• Let’s admit that the worst after 10 years is substantially rosier in the 50/50 than the 100/0 (0.91x vs 0.67x). However, note that this reflect a single series of event in the past 100 years. Also note that the difference is 73%.
• The worst 25% percentile of the 50/50 allocation are always similar or worse than the worst 25% percentile of a 100/0 allocation (After 1 year, 0.99x vs 0.96x). This is in-line with the fact that only about ¼ of the years returned negative return over the last 100 years.
• This means that you can expect only better result or about in 75% of the case with a 100/0 allocation than a 50/50 allocation.
• The worst 50/50 is the same as the worst 100/0 after 23 years of investing at 1.5x. This is highly interesting for the most conservative folks out there. After 20+ years, you are just losing money by having a lower allocation.
• In other words, you are certain (based on historical results) to have a lower results with a 50/50 allocation after 20 years. Thus you are trading an uncertain gain for a certain loss going for a 50/50 allocation.
• At 30 years, the average 50/50 is worse than the worst 25% of 100/0 (5.47x vs 5.78x). If you fear the worst 25%, than be happy to know that you would beat on average of 100/0 beat it after 30 years.
• I have an easy time to concede that we want to minimize our lost. However, it makes no sense to aim for it.
• At 30 years, we see that the best 75% of 50/50 is a little underneath the worst 25% of 100/0 (6.58x vs 5.78x). We could be tempted to think that the upside (75%) of a 50/50 is enough rosy. However, it is almost the same as the worst (25%) of a 100/0.
• In other word, if I’m unlucky, I will do more than a lucky conservative (50/50) would make.

Perhaps a in between method would produce better results, however they are similar

• It’s easy to see that the worst of 100/0 is lower most of the time than the 75/25. However, please note the size. Having 74% vs 64% is a difference of 10%. In other words, 100,000$ over a million. If the size difference was bigger I might concede this, but at this level, it is not enough significant. Can’t you take a 10% cut in your spending for a year?
• At the worst 25%, they are always similar or worse in the 75/25 than the 100/0 scenario.
• At 22 years, the worst 75/25 match the worst 100/0 at 1.5x.
• At 30 years, the best 75% of 75/25 is the same as average of 100/0.

In-detail argument (withdrawal)

You may raise objection that sequence of return risk or withdrawal will more than offset any gains without withdrawal. Let’s look at what happens if we adjust for a simple withdrawal strategy. Let’s withdraw 4% of the current fund and guarantee at least 75% of all previous withdrawal. This would be similar/or better than a SWR of 4% with a 3% floor. See the Tab 2 for the results.

First, let’s concede that we do see some drop below 0.5x in the 0-15 years range in the 100% Equity allocation that we do not see in the 50%/50% allocation. However, if we continue our analysis of it we get the summary table

When we compare these, we quickly see that results are well below the no withdrawal strategy. Indeed, we see the ugly head of sequence of risk. The 10-20 years worse years are more disappointing than before or after.

• We can see the difference of the worse between 50/50 to 100/0 is only 15%. However, after 10 years, the difference of the average is 22%.
• Thus you would lose more on average for a lower pain in the short term.
• At 7 years, all allocations are having similar worst 25% (0.9x). This means that on most case (75%) if would be advantageous to be in 100/0 after 7 years.
• At 22 years, all allocation are having similar worst (0.63x). It would be thus just advantageous to be in 100/0 than the other allocation.
• At 30 years, you are sacrificing more than 1x (ie your entire initial withdrawal) with going with a 50/50 rather than a 100/0.

Finally, we can go back at the question: if there’s a drop, how long does it take for us to earn back our money? The answer can be found in an expansion of Table 1. At the 14 years mark the worse real $ 50/50 would finally be over the 1x mark. The inflation is a major culprit for this. However, let’s remind us that 50/50 means that we are 50% in equity. Thus a 50% drop would still means a 25% in a 50/50 scenario. For a 75/25 allocation we need to wait 17 years so that worse hit the 1x. However, the 100/0 allocation hit the mark after 18 years, 4 years after the 50/50.

If you withdraw with the simple strategy of 4% of current fund (guaranteed 75%), the stats are worse. Only the 100/0 crosses the in the money point for the worst case scenario at the 30 years mark. The others do not have the luxury of getting even.

As my ode to risk, I hope I was able to convey the reason I think that a heavy equity allocation is superior to a 50/50 or even a 75/25 equity allocation. In the end, I would summarize my analysis as,

• Low derisking gain going at a 50/50 for a major loss often.
• Gain of a low equity is only felt in the worst scenario. Even then as time passed, the worst of 100/0 is better than all the other allocation.
• The worst 25%  results are better in a 100/0 almost all the time. All better odd returns better results in a 100/0. 
• After 30 years you would always lose out using a lower allocation.