mercredi 9 janvier 2019

Statistic of Ivy League millionnaire

Statistic can be deceiving. It’s even easier to deceive or genuinely fail to understand their implication. I’ve just heard such of leap of reason.

Chris Hogan have just release his new book, Everyday Millionaires(2019). I did not read it yet. I’ve heard a startling statistic that 10% of the millionaire come up from Ivy League. 90% did not gone to Ivy League in order to get millionaire.

Photo by Vasily Koloda on Unsplash

It seems on the surface that it tells us that you don’t have to go to Ivy League to be millionaire. This is true. The reverse is not so evident. According to a simple google search, we see that the % of American who have gone to Ivy League is roughly 0.2% (Quora). The statistic is probably off. The percentage of millionaire in America is roughly about 11% (DQYDJ).

If we merge the three statistics, than we can tell that going to Ivy League has a huge correlation to becoming millionaire. They are massively over-represented! The argument goes along the line:
  • If I go to any university : I got 11% chance to become millionaire.
  • % of American who have gone to Ivy league and are millionaire (10% * 11% = 1.1%).
  • If I go to an ivy league university : I got more than 500% chance to become millionaire (0.2% * 500% < 1.1%).

Probably some of these statistics are incorrect. 500% chance of becoming millionnaire is illogical. At least they are incoherent. Regardless, it gives a rough idea that most Ivy league graduates are going to be millionaire. They are mostly all going to be. 

samedi 5 janvier 2019

Saving Rates - Including Interest

There are many ways to calculate saving rate. Saving Rate = $SAVED/$IN. Various debates exist around each terms. Items up for decision:
  • Should we use Pre-tax or post-tax as the $IN?
  • Should we look at the family as a whole or per person?
  • Should we use House payment/debt (the portion other than the interest on loan) as $SAVED?
  • Should we use Interest received as $SAVED & $IN?
  • Should we recognize DB accrued as $SAVED & $IN?
  • Should we include Social Security (CPP/QPP contribution)?
  • Should we set a Saving Rate or set a retirement goal.

Let’s go deeper in the rabbit hole of Interest on Saving. Including Interest will have the immediate effect of increasing your saving rate.  At the basic level, including/excluding anything do not change your retirement date or how much actual earning you save. However, if by including or excluding some items some features may be highlighted or new strategy can be discovered.

Interest is define for this article as the total return of your retirement fund regardless of its origin (growth of stock, dividends or coupon). Compounding interest informs us that interest will exponentially grow as time passed. Near retirement, interest will largely outgrow our saving. Why save at all, if you save 2,000$ while the fund grows 200,000$ due to interest?

After including the interest both in the $SAVED & $IN, I’ve created ways to reduce the amount saved from earnings while the Interest grew. Given a fixed saving rate, this has the effect of delaying retirement by a few years. Thus the below strategy are more in-line for those who would like to be Financially Independant(FI), but not Retire Early. Get a higher raise than your boss wants to!

"Get a higher raise than your boss wants to!"

Tweaks & issues

The overall objective of the methods proposed below are to decrease saved earnings while reaching retirement. Thus this has the positive impact of giving you a bigger raise than your employer gives you. 

This strategy makes more sense if you increase your your replacement ratio. A 60%-70%, or (1-Saving Rate)% would not work as you expect to spend your entire earnings at retirement. Thus to keep your standard of living you would need a 100% replacement ratio.

Lowering your saved earnings would delay retirement all thing equal. As often the case things do not need to be equal. You could modify your Saving Rate after applying the below strategy to give more or less the same initial saved earnings or retirement date. In the simple strategy below, I did not adjust and thus get a higher retirement date. In the second strategy below, I did adjust. 

From an administrative issue/market volatility issue, you may want instead to use your expected withdrawal rate (3%, 4% or 5%) instead of experienced interest. This way, a bad return year or a great year will not mess up your saving strategy. Personally, I like to go with 5% withdrawal as it provide no risk of ruin and decent inflation increase using the Accumulation-Dynamic Decumulation method.

Simplest way

The first formula that come to mind is to remove the interest from what you need to save as earning.  If you have a lower than 50% saving rate, this strategy fails as you would not need any saving quickly. At 15% saving rate, this force you to stop saving at half your career.

Instead, a small tweak to this strategy is to recognize a percentage of the interest. 
Ex: if you made 20,000$ of interest this year, only recognize 10,000$ of it. The weight to use is hard to determine. At 15% Saving Rate, using a 30% weight of Interest seems appropriate as it delays retirement by 4 years and small save earnings near retirement. At 30%, you get a 4 years delays at 50% weight of interest. At 50%, you get a 4 years delays at 90% weight of interest.

Below is a table summary  of the extra available spending with/without the strategy1 at 25% the way to retirement, 50% and 75%. It use the 4 years delays with vs without the strategy and weight discuss above and using a family salary of 100,000$.

Next, here a graphic showing how the saved earnings compared in the 15% Saving Rate simple strategy for a family with 100,000$ salary :

See google drive file, sheet Inc. Int with Weight.

More complex way

The first strategy have issues. Most of the decline in saved earnings is near the end.  It leave a difficult parameter to set up (weight of interest). Also it still have relatively large saving near retirement or no saving for a number of years prior retirement depending on the weight. To fix this, let’s look at the following formula:

Think of it this way, in the scenario where Saving Rate = 50% = (Save Earnings + Interest)/ (Earnings + Interest). When you start saving, you would need to have Save Earnings = 50% of Earnings. When you are at retirement, than you would need Interest = 50% of Earnings. Using this nice equilibrium, we can adjust any other saving rate by applying a similar accrual pattern.

This strategy ends up at retirement with almost no contribution and enjoy Spending increase 5% more than your boss give you (which decrease as you age to a spending increase of +1%).

To get similar retirement age however, we need to be more aggressive in saving in our early years than the previous strategy. Below is a summary result of comparable saving rate incl./excl. Interest and the Extra Spending along the way where Retirement age is the same for both Scenarios. 

See google drive file, sheet Inc. Int Max SR inc.


Where ever you are in this journey you could think of implementing the above strategy or part of it. Otherwise, you could also adjust the strategy to say that you are going to have 10 years of higher saving and then drop back to follow these strategies. Many different path exist for the DIY.

While there is a great focus in increasing saving, we need to be conscious of why we are saving. Saving for saving sake makes no sense. Dying with millions in our bank with no plan is not a wise approach to life.

If we were immortal, than this sort of approach makes even more sense. It would be foolish to have to save for the rest of eternity for saving sake.

1: Both scenario using a goal of 100% replacement ratio and the same Saving Rate. If you have a lower goal, you could adjust the formula. If you wanted the same retirement date, increase your saving rate after applying the strategy to get it. Based on Fund = 0$ starting saving at age 20. For example say retirement age =65, 25% of the way is (65-20)*25%=11 years after saving start (age 31). 

jeudi 25 octobre 2018

Retirement risk

There are two main ways to handle decumulation: annuities, self-managed(DIY) decumulation. The main advantage of annuities products is the guarantee by the sponsor. DIY decumulation have no guarantee and thus is more risky. On the up side, DIY are very flexible.

The Single life Annuity promise a stream of payment which stops at death. By design, it leave nothing to the heirs. Obviously, you could combine it with a life insurance, or guarantee in order to leave money to heirs, spouse or dependant.

By having tens of thousands of member, the sponsor will face on average the expected mortality. Member who dies later will be offset by the one who dies young. Sponsors are still at risk expected mortality to rise in the future. Future increase can be mitigated by having higher mortality based on the latest trend.

The DIY decumulation does not benefit of such risk reduction. The expected mortality is roughly age 85. However, the oldest man on earth is age 115. If you retire at age 55, that's a 20-60 years life spends. About 50% of the population will die however between -5/+5 years of the life expectancy. An 80 years old life expectancy is 86 for a Canadian female. If you survive up to 85, it grows to 89. We cannot be sure in advance if we will die early or not. In addition with you have a spouse, the chances that one of you goes on to live to 90 are great. To counter this, we need to protect for an extended life spends.

However, mortality is not the only risk. The biggest risk of DIY and annuity product is investment returns. Assuming constant rate of return is overly optimistic and naïve. The standard deviation over equity is about 18% and 7% for bonds. The classic strategy to deal with this risk is to have a conservative asset allocation with lots of bonds which have lower volatility. Going one step further, you can immunize against the bonds interest volatility using duration matching and cash flow matching. These options however, all suggest dropping the rate of return from what the equity offer to what short term bonds offers. This can means to reduce return by 2x and more over time.

Next, there is the sequence of return risk. This is the risk that a negative sequence of return prior to receiving a positive sequence of return. The annuity products are less affected by this risk as they have annuity starting each years. The law of average applies. Half will face negative sequence and half will face positive sequence. For DIY, the problem can be quite significant. The classic way to mitigate is to have a higher bonds allocation. That will reduce the volatility that you will face, but it will reduce your rate of return. Some have now recommended to have higher equity allocation after a few years though.

Finally there is the inflation risk. This is a lesser risk than the other. However, if inflation start to pick up, this may become a serious issue. Both DIY and annuity products face this risk. The solution in the annuity products is to get some bonds with inflation protection.

mardi 14 août 2018

The shocking math of accumulation

The shocking math as to why vampires must be rich? 

There's a two main mathematical formula that determines on average the expected gains of any vampires. The composed interest accumulation formula focus on the accumulation of a Lump Sum amount for a number of years. The other is the future value of a serie of contributions.

A vampire have thus a lot of possibility to becoming rich. Either he can invest a lump sum of money or a smaller contribution over a period of years. A third possibility is anything in between. Let's explore the vampire timeframe first of a 100 years of investing.

Knowing that the past last century rate of return for a all equity was in excess of 10%, a 73$ investment would be enough to be a millionnaire. Else, the vampire with less than 10$ to spare each year would be a millionnaire also. All in all, it's super easy for a vampire to become rich.

From the above table, we can compare the lump sum strategy to a contribution strategy. The Lump Sum requires 11%/15%/21% less contribution at 10%/7%/5% interest rate. However, the lump sum is 10x/15x/21x more than the yearly contribution strategy. If you are able, it makes sense to fund early and have lower contribution in the future. I haven't read anyone doing it except when in retirement. For a person to be able to act on having lower contribution in the future, we need to have a well though out plan, to be able to live frugally at the beginning and be able to live expensively at the end. It is a rare combination. 

Over 100 years, it is staggering the impact of interest. It requires 50x more contribution to fund a million at a conservative asset allocation than an aggresive one. If we look at Lump sum, it takes 100x more lump sum to get there.

Now let's see over a human life of 35 years investment:

In order to retire a millionaire, we would require about 36k/94k/181k to compound to 1 million. The impact of interest rate is still very much felt.

The way I think about it, if you were able to split at your death 1,2 million and that you would have 3 childs and 9 grand-childs, then each grand-childs would be able to become millionnaire at age 65 easily.

mardi 7 août 2018


Photo by Overture Creations on Unsplash

FIRE is an acronym for Financially Independent/Retire Early. That community looks to retire in their 30's or 40's. While challenging, it seems to be an attainable goal if you are willing to cut expense and save the remain. There's a few types of FIRE categories:

  • Lean FIRE who tries to cut their expense to the minimum, lower than 20,000$ per person.
  • Barista FIRE who tries to get a small job to cover a low income.
  • Fat FIRE who tries to retire with a few millions, thus generating 80,000$+ pensions. 

One of the challenge for the US is that their social security is poorly funded. Actuaries have asked for decades for changes in order to make the program sustainable. Major changes are still missing.The two mains venues is to cut benefit or increase contributions.

However, Canada programs are much different.  The likelyhood of serious reduction in benefits is close to zero. This article will explore the impact of the Canadian system on FIRE. Canadians have 4 majors social securities: GIS/OAS, CPP/QPP. For ease of reading, I only reported the 2018 numbers.


The Old Age Security(OAS) is not pre-funded. Instead it is an expense from the general revenues. There have been some back&forth in changing the retirement date, but the OAS pension remained the same 7,160$ per year increase by inflation (100% of CPI). It is safe to say that it will be there at your retirement. There's no impact on retiring early on OAS amount.

The Guarantee Income Security(GIS) is to insure canadians over age 65 a minimum pension. It is severly claw backs. At 18,096$ of income, the GIS is 0$. Reducing it, equals to taking away from the poor and old.This is a major reason why it should not go away.

Lean FIRE implication

For them, GIS is a huge blessing. Let's say that you were aiming for 20,000$ pension. GIS&OAS, you would only need a 6,561$ from your RRSP or other sources and you will get 13,438$ from GIS&OAS.  If we apply the 4% rule, that's 164,000$ fund require at age 65. You only need to fund the other 13,438$ until then. Also if you plan to live on less , the GIS&OAS gives a floor income of 17,854$ to all above age 65. So an extreme frugal person would require 0$ to be coastal FIRE in Canada.

Fat FIRE implication

For Fat FIRE, the OAS is going to be claw back based on income. It will start to be claw back at 75,910$ and will be completely claw back with an income in excess of 123,302$. These claw backs amounts are also indexed by inflation (100% CPI).

TFSA strategy 

The RRSP/DB/DC/CPP/QPP are all vehicles which their withdrawal counts as income. However, the TFSA does not count as income for both GIS and OAS. While the maximum of 5,500 may be small, the sum of contribution untill age 64 is 253,000. If we account for an interest of 7%, that's 1,8 million each. If you are near the margin, an idea would be to first withdraw from RRSP. If you are able to live off RRSP until age 65. Then at 65 when the GIS/OAS starts, you can withdraw from the TFSA which is not counted against your income. You could thus aim to maximize the GIS or OAS payout.

Deferral strategy 

The other strategy is to defer the OAS. This moves makes you ineligible for GIS. For each year of deferral, the OAS is increase by 7.2%. If you maximize this strategy to defer the OAS at age 70, that's 36% more. Also the OAS is increase each year by inflation (about 2%). Said otherwise, the OAS jump from 7,160$ to 10,751$. Using the current low interest rate, this is actuarially advantageous to do in general. If you are afraid of market downturn, this may be an advantageous flexibility.


The Canadian Pension Plan and the Quebec Pension Plan are for the most part identical. Both plans have experience major change in 2010's and the past few years. Both plans are fully funded and with 0% failure probability for the next 70 years. Both plans are invested in the public market. As their size is gargantuan, they were able to command higher return.

CPP/QPP provides roughly 25% * Lesser of(Average Canadian Salary OR Your Average Salary). The exact calculation is complex. The latest change was to expend both the 25% and the salary coverage. It will cover 33% * (114%*Average Canadian Salary OR Your Average Salary) for service after 2019. The average Canadian salary is increase by the Canadian increase in wage (roughly CPI+1%).  The payment after retirement are index by inflation (CPI). Currently we would expect a maximum 13,610$.

FIRE consequence 

Like your southern neighbor, the "Average Salary" is a reduction in disguise for FIRE community. In the US, the average is done over 35 years. In Canada, the years taken depends on years worked after 18. The average is done over #years working after age 18 * 83% for CPP or *85% for QPP. A CPP/QPP starting at age 65, that would be 39 and 40 years average. If you retire early at age 30, you would have only a maximum of 12 decent salary. Any 0$ income is thus an effective reduction to the full amount. On top of the standard reduction, that's an additional 30% reduction! 4,083$ instead of 13,610.

Thus if you are able to report a side hustle after age 30, that would improve drastically the CPP/QPP you would get.

Lean FIRE implication

 If you were considering to retire on 20,000$ or less, it is interesting to see that CPP/QPP + OAS/GIS can easily returns at least that amount. The only difficulty would be to be able to successfully manage the withdrawal until age 65.

Fat FIRE implication

Fat FIRE usually implicates later retirement. If you retire at age 45 instead, the reduction is about 70%. Similar to the OAS, it is generally recommended to delay start at age 70 if you are expecting a high pension. That way the CPP/OAS is increase by 42%. If we takes into account the 70% and the increase of 42%, both roughly cancel each other. The wage adjusted CPP further improves the increase(about 3% per year). You would expect a 15,683$ CPP/QPP pension. Out of a 80,000 pension, that's  roughly 20% that you would not need to worry to fund.Thus you could pursue a more conservative approach to bridge until age 70 and then be assured to get the safety of a secured, improved and indexed pension.  

Should we go with a "Roth conversion" Canadian equivalent?

The Roth IRA is similar to the TFSA and the traditional IRA is similar to the RRSP. If you were to invest in RRSP while in high tax bracket and transfer the RRSP to the TFSA when in a low tax bracket, you would got the tax deduction going in and no tax or little tax going out.

However, Canadian enjoys the possibility to contributes to both at the same time. If you are able, you should maximize both accounts. Additionally, while it is possible to transfer RRSP to TFSA, the transfer do not create TFSA room. This limit the use of the conversion.

As presented in the TFSA strategies, you could try a strategy to minimize tax by withdrawing from the RRSP before CPP&OAS starts in order to minimize the claw backs. Also if you have room near retirement, you could switch the TFSA to the RRSP to get some tax deferred dollar just prior your retirement.

vendredi 27 juillet 2018

The long game - Crazy news, stock XYZ lost 20% today

Photo by Pierre-Yves Burgi on Unsplash

Like every so often we just heard of the demise of Facebook and Twitter both lossing about 20%. Facebook drop from 220$ to 175$(79%) in a day. Twitter gone from 42$ to 34$(80%).  My initial knee jerk reaction was: Wow, the whole market must have crash. At face value, this is yet another reminder that individual stock are very risky aka volatile price.

Did the market crash? 

The market just did not care about these corrections. S&P500 was up by 1% during the last 5 days. NASDAQ who focus more on the internet industry slightly drop by 0.5%. Given an anual 7% return, we would expect a 5 days average increase of about 0.09%=1.07^(5/365). The S&P500 1% is 10x more this! The illusion of average and volatility makes the analysis more complex. At the end of the day, S&P will experience many 5 day 1% increase and decrease. Only on multiple years average is the expected rate of return start to emerge.

Why did Facebook and Twitter demise didn't move the needle? The impact of 1 or 2 companies over S&P (about 500 companies) is less than 1%. This is why stock diversification is so important. Even if Twitter and Facebook drop by 50%, the whole market would have only slightly adjusted to the event. If you have gone the active investing path, it is typical to invest in about 16 companies. A facebook loss of 50% would reprensent a loss of 3% a much bigger impact. A bigger impact would be felt, but both active and passive investing usually tries to mitigate a single company disappointing results.

Did these companies crash?

We may think that this is just a good reminder of the "danger" of individual stocks. As most article goes, individual stock picking is a dangerous exercice. Sure, if you have had bought one of these two stocks last week, you would have lost 20%. Individual stock varies quite a lot more than aggregated stocks. However, what the news often fails to report is the loss compare to 1 year or 3 years prior if any. In this case, Twitter would report a 150% gains in the last year and a 11% annualized return. Twitter were a big looser in the 2016-2017 and been an incredible winner since last year.

Twitter last 3 years (excluding dividends if any):  

Facebook on the other hand face a growth of 3% this year, but a steady growth of 31% annualized over the last 3 years. The 20% loss barely made a dent in their growth of the past few years.

Facebook (excluding dividends if any): 

As a simple investor who rarely look at stocks and there returns track the media news feed or latest investment advice would lead to irrational takes on the market. In this instance based on the news, buying Facebook or Twitter may be seen reasonable since they may be at a discount. However, truth of the matter, a 20% discount would be less than having invested in either 1 year ago where no news occured. Doing market timing based on the news or investment advice seems to be a recipe for disaster.

I would recommand to buy global index if you are unwilling to do some major reasearch on the whole market. On the long run there have been no global index crash that have never recovered.

In the end, its funny to report that both Twitter and Facebook reported a solid last year increase in value. Even a 20% loss is meaningless in this time frame. Go for the long game, unless you are a bot!

vendredi 22 juin 2018

Financial illiteracy

Photo by Roman Mager on Unsplash

In the recent study from CIA, there was some disturbing news on how weak the financial literacy was in Canada. In order to fight the good fight here's a few points that everyone should be aware of :

  • The cost of an annuity is near its expected terms * amount. 
  • Inflation have a dramatic effect even in these low inflation times.

Annuity Puzzle
If ever you want to guess the value of a pension annuity, multiply the annuity by 11-15. In the study, they've asked a 1,000 person to how much would they willing to pay for a 100$ monthly annuity. Based on the above, that would be 13,200$ to 18,000 (100$*12*11 to 100$*12*15). 660 persons in the study responded that it should be below 3,000$ ! I understand that they do not have great publicity, but that's a high discrepancy. The risk of the insurer not able to honor the annuity is slim. Many laws, oversight agency, reserve and insurance exist in order for the insurer to honor their policy contract. 

The magic number out there if you are to personnaly manage our withdrawal is 25(4% rule)! Based on Accumulation-Dynamic Decumulation you can get away with 20-16.7 (5%-6%) if you are able to bear some fluctuation and not perfect inflation protection. That would mean a value of 20,040$, 24,000$, 30,000$. Over 84% reported that they would not accept to pay more than 9,000$! 

Please be aware, having constant payment until your death have a substantial cost. Probably more than you believe to be, but mostly not because of "insurance profits and margin". 

Inflation exist!
As the saying goes : A dollar today is worth more than a dollar later. However, the reverse is also true, A dollar later is worth less than a year later. Would you believe that 310 persons would rather have a pension of 2,358$ steady (not indexed for inflation) than 2,358$ indexed for inflation. This is like free money at no cost that would not get picked! 

While more understandable, 540 persons would rather get 1,966$ steady income than 2,358$, even though that at 1-3% inflation the indexed pension would surpass the steady one before 10 years in. In the grand scheme that leaving some money on the table, but at least you get to use it when you are younger. 

On the other hand after the research showed the participant of the amazing power of inlation, 40% would rather get 1,551$ indexed for inflation than 2,358$ steady pension. This would break even around 20 years in retirement. 

If we look at this through the lense of the 4% rule, it's amazing that it get so much traction as inflation is so missundertood among the population. Without fear of inflation, you can get away with a safe withdrawal rate (at 60% equity allocation) of 4.6%. Said differently, you would need 14% less funds to retire. With Accumulation Dynamic Decumulation with a 6,5% withdrawal rate, you need a 49% less funds to retire. That means a year or a decade of earlier retirement. Not too shaby if you do not believe in inflation. 

Statistic of Ivy League millionnaire

Statistic can be deceiving. It’s even easier to deceive or genuinely fail to understand their implication. I’ve just heard such of leap of...