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

QPP/CPP for FIRE?

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.

GIS/OAS


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.

CPP/QPP

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. 

mardi 12 juin 2018

Risk Shared Pension Plan

One of the latest creation in Pension Plan scheme is the Risk Shared Pension Plan(Shared Plans). In many ways, it's superior to the traditional DB and DC. In my mind it solves the great dilemma between offering an adequate pension for retiree and remove the risk of future expense and contribution volatility. In short it offer reasonable secure pension, stable and sustainable contribution requirement.

I believe that the objective of a pension plan should be to provide an adequate pension and funding it appropriately. For this end, Shared Plans provides an expected pension upfront to the member. Funding is made on current contributions. No one is behind to guarantee payment. If funding become insufficient, than benefits are cuts. To avoid the cuts, the current employee and sponsor can poney up more funds voluntary. The benefits are calculated in advance so that 97.5% of the time, there should not be any reduction of benefits.

A pension plan should aim to have stable contribution funding, be sustainable and be secure. These features makes the design to be more stable, contribution are known in advance. The sponsor is not required to pay more or less due to market return. Since DC sponsor(EE+ER) do not contributes more or less due to market return, why should the DB sponsor should? The design is substainable. If the fund disappear for whatever reason the outflows will be adjusted. The design is more secure.

For those who have DC account the principal problem is that employee have just about no clue on if it will be enough at retirement. Those who contribute often contribute not enough and do not adjust up their contribution. I believe that we cannot/should not expect that a person with no financial education be able to make financial decision without expert helps. Currently DC general philosophy is that the member knows best. DC guideline are for the plan to suggest to get help. Shared Plan instead provides a guideline for what their current contribution will be able to provide as a pension. If there's a short fall in contribution, warning bell activate to review the plan (either increase contribution or decrease pension). The employer of DC and Shared Plan are equally happy not to have to fund future funding issue.

For those lucky few who have DB, the employee often feel confident that his pension is known in advance and well funded. On the funding side, it is not the whole truth. The Employer must fund it. The guarantee is as strong as the company behind it and the current funding. Sears employee were angry to see their benefits cuts by 20% due to the company going down. Instead a Shared Plan would have seen that their pension to be cut far in advance and thus with lower pay cut.

mercredi 4 avril 2018

Accumulation-Dynamic Decumulation


Accumulation –Dynamic Decumulation Strategy

Executive Summary

Accumulation-Dynamic Decumulation (ADD) Strategy is an elegant solution for managing withdrawals through retirement. It withdraws a percentage of the available fund. These removes the risk of ruin at the expense of having volatile withdrawal. ADD also uses:
  • A smoothing of the fund:  This reduces the retirement date risk and applies a simple filter for a rational estimate of the fund over the long run.
  • An increase cap on the withdrawal and accrued withdrawal: This provides a provision for adverse deviation and reduces the retirement date risk.
  • A reserve: This manages the negative volatility of the portfolio. It provides protection over 95% of withdrawals.

You can see below the cash flow path in nominal terms at various retirement dates using this strategy.

Features:
  • No risk of ruin
  • No sequence of returns risk over the fund’s value
  • Reduces the date of retirement risk
  • Reduces the volatility of withdrawals
  • Perpetual withdrawals, high bequest* 
  • No direct protection against inflation 
For Spreadsheet testing please use either DropBox or GoogleDrive links.
Please consult the Full Study if you want to explore some more the method.


*May use ADD in combination with Variable Percentage Withdrawal to leave low bequest

Introduction 


The key challenge for preparing for retirement is how to ensure enough money for retirement. The two main methods are buying an annuity or managing our withdrawals. Annuities are safe, illiquid and do not leave money to heirs. Annuities are insured by a third party and as such should be honored. The mortality risk is handled by grouping a large number of participants together and averaging out the mortality. They offer low liquidity as they can’t be sold after they are bought. In their simplest form, they offer no lump sum at death. Managing our withdrawals keeps liquidity and often leaves more than the full principal at death. However, it offers no safety. This post is focusing on the latter method.

The Accumulation Phase

Often we look at decumulation in silo of the accumulation phase. However, there are advantages in looking at them in combination. During the accumulation phase, we can have an early discussion if and how much we want to manage decumulation versus buying an annuity. Buying an annuity requires a great lump sum at a fixed target date. For that objective, a low equity asset allocation is best. However, if you want to manage your withdrawals only a small portion of the fund will be used each year. Even if the market value at retirement is volatile, a small portion of the fund is still available. This enables us to be more aggressive in our asset allocation, even through retirement because the volatility of the rate of return will be spread along each year of retirement.

The volatility of the market still exists. I believe that we can reduce our negative behavior by looking at the linear smoothed market value (SMV – see annex for more detail) instead of the current market value. If we look at SMV, it has the same volatility as the 5 years returns of the market value. It also allows for an automatic sanity check on how things stand. In an economic crisis, SMV is higher than market value. It reminds us that the future is likely to be brighter than the past. In today’s market, SMV is lower than the market value. It tells us that the future is likely bleaker than the past. By extension making our percentage withdrawal on the SMV instead of the market value reduces the volatility of the withdrawals.  It is not a silver bullet as it often only delays the gains & loss. At best, short loss gains are compensated by short term gains, but there’s no guarantee.

Another step that can be taken through the accumulation phase is to create a provision for adverse deviation. A number of ways exist to do this. This strategy explores the idea of capping the “accrued” withdrawal by 115% from last year “accrued” withdrawal. The accrued withdrawal is what you would be able to withdraw if you retired today. This cap has two effects: Calculating it makes you aware of what you could withdraw today without working anymore; also it adds a buffer in case of economic crisis following high increases. These sequences of returns have often appeared in the past. In order to go even further in managing our expectations through retirement, this strategy cap the first retirement year withdrawal by 108% from previous year accrued withdrawal.

If we combine these strategies the retirement date risk is heavily reduced. The S&P500 had 25 times in the past 100 years of returns below 0%. If we go for a percentage withdrawal or a constant dollar strategy, we would experience 25 such reductions. Instead, if we combine capping and smoothing strategies, we only get 4 reductions in withdrawals between the accrued benefit the year prior retirement date versus at the retirement year. Here’s a comparison of these 4 events:


Year
Percentage Withdrawal
(25 events with reduced accrued)
Accumulation-Dynamic Decumulation
(4 events with reduced accrued)
1932
59%
76%
1933
90%
90%
1942
90%
91%
1975
75%
81%



While maintaining the accrued withdrawals is a fine accomplishment, a retiree who needed an extra year of interest would still not be able to retire. The ADD strategy do not adds money where none exist. Instead, it reduces this risk by making more conservative accrued withdrawal estimate prior retirement.

The sequence of return risk

The sequence of return risk for constant dollar withdrawal like the safe withdrawal rule leads to ruin risk. This risk can be avoided using a percentage withdrawal method. This method withdraws a percentage of the fund value each year. With this method or similar method, only the withdrawal fluctuates negatively from a bad sequence of return. Once the sequence returns to average, the fund and withdrawals go back to their original value.  We can also gain the insight that is if the fund loses 5% of its value, the withdrawal only drops by 2.5%.


The Decumulation Phase


In this strategy the main focus is not to manage the fund volatility, but the risk of the withdrawals. Ultimately, the withdrawals are not directly controlled by the market. The retiree decides how much and when he wants to withdraw his fund. A decumulation strategy elaborates a plan to manage them.

In a percentage withdrawal class, there’s no risk of ruin. Using an unsustainable rate of withdrawals will diminish the withdrawals significantly over time, but never to 0. Like demonstrated in the sequence of risk table a 0% return with a 5% withdrawal reduces the withdrawal by 80%. If the return eventually goes back to normal, the withdrawal will return to their original value.

To manage the withdrawal volatility risk, this strategy implements a reserve. 25% of the fund is put in a reserve fund. This fund will serve to pay for the difference between the withdrawal and 95% of any previous withdrawal. If the highest previous withdrawal was 100$ and the new withdrawal would be 80$, the reserve would pay 15$. This means that you need to be prepared that 5% of your withdrawal may not be available next year. For the following few years, you may have to remain at this level until market value returns to normal. To compensate, we increase the withdrawal of the regular fund accordingly. If you wanted to withdraw 6.5%, you need to withdraw at least 6.5%/75%=8.67% from the regular fund. 

A common question is how should the reserve be invested? 25% of the fund is a big portion of the fund. My tests indicate any advantage of being more in bond in the reserve fund. So instead using the same asset allocation than the rest of the fund seems appropriate.

Using a reserve fund has the advantage that we can easily apply a limit on its used. For example, this strategy applies a maximum reserve withdrawal of 10%. This allows for the floor to drop further if the reserve is unable to sustain their uses.  Having a reserve also provides the opportunity to have a significant emergency fund which can be used in time of need. If it is used, the protection erodes. In good time, the reserve is not used the reserve grows since no withdrawal is taken from it. My test showed that the protection is not eroded when we withdraw 50% of the excess above 35% level.

The smoothing and increase cap is also applied in the decumulation phase. The increase cap has to be modified to cap increase at 105% of previous withdrawal after retirement. This lower increase accounts for the withdrawal that is occurring after retirement. Having such a cap provides a great tool to have a constant increase in withdrawals. In case of consistent increase, the cap is increased by 1% each year above the previous mark. This allows recognizing more quickly the sustainable increase.

You may notice that it 105% is lower than the inflation in some of the past years. There’s a strong argument that going forward, the low inflation rate will be maintained. Going forward the US federal bank and bank of Canada has both a target inflation of 2%. The Canadian inflation targets have been stable for the past 25 years and the US for the past 5 years. These targets inflations have been met by both countries since their commitment to them. In the end, 105% increase cap provides another provision for adverse deviation.

Here’s two graphics of the Cash Flows versus Market Value in 1928 and 1965. After 1928, the S&P500 plunged in the great depression and recovered with difficulty in the following decades. By all accounts, it was one of the worst years to retire. 3 combinations are displayed: 100% equity using 6.5% ADD withdrawal; 100% equity using 5.5% ADD withdrawal; 50% equity using 5.5% ADD withdrawal.




A 1965 retiree would have faced better fate in nominal terms. However, the 70’s experience low returns and high inflations. The 80’s and 90’s in the other experience high returns.




Both cases were based on a scenario where 150,000$ were invested 20 years before retirement and 5,000$ with 3% increase each year up to retirement. This is why the initial cash flow is so different between each asset allocation.


For comparison with other decumulation strategy, we will compare them using two metrics. The first metric is the percentage of runs where the one withdrawal year is lower than 80% of any previous year. Under this metric the Safe Withdrawal Rate (SWR) is the safest method. In comparison the Constant Percentage Withdrawal (CPW) is the least safe. The Variable Percentage Withdrawal (VPW) with 50% equity to bonds asset allocation is less risky than the CPW. Otherwise, we can also get a feeling of the importance of each of the sub-strategy. The reserve is the most important strategy in order to reduce this risk. Removing it, allows for dramatic decrease in most of the asset allocation. The smoothing strategy is the least effective strategy. 

Risk II  <80%
100%/0%
90%/10%
80%/20%
70%/30%
60%/40%
50%/50%
ADD 5,5%
0%
0%
0%
0%
0%
0%
ADD 6,5%
1%
1%
3%
6%
10%
14%
ADD 7%
6%
14%
13%
14%
18%
19%
ADD 7% minus reserve.
100%
100%
100%
100%
67%
64%
ADD 7% minus cap
38%
32%
28%
26%
21%
21%
ADD 7% minus smooth
6%
6%
12%
12%
19%
23%
SWR
0%
0%
0%
0%
0%
0%
VPW
100%
100%
100%
100%
100%
29%
CPW 5,5%
100%
100%
100%
100%
100%
100%


The second metric is the Withdrawal Efficiency Rate (WER) as per Blanchett study. This metrics focus on how much the withdrawal was able to produce out of the fund. It shows if the methods were able to maximize withdrawal. We can see that the ADD strategy is rather efficient at the high withdrawal rate. None of the sub-strategy seems to affect WER negatively.
WER nominal
100%/0%
90%/10%
80%/20%
70%/30%
60%/40%
50%/50%
ADD 5,5%
64%
67%
69%
71%
73%
74%
ADD 6,5%
73%
76%
78%
79%
80%
80%
ADD 7%
77%
79%
81%
81%
82%
81%
ADD 7% minus reserve
77%
80%
82%
84%
85%
85%
ADD 7% minus cap
81%
81%
82%
82%
83%
83%
ADD 7% minus smooth
78%
81%
83%
84%
84%
84%
SWR
51%
54%
56%
58%
61%
63%
VPW
77%
77%
77%
76%
75%
74%
CPW 5,5%
74%
75%
77%
78%
79%
80%

Please consult the full study for further details and insight.

Annexe:

Full parameters list:


General :

a.       Portfolio asset allocation
b.      Accumulation-Dynamic Decumulation withdrawal rate. A higher than usual rate should be used. The sub-strategy reduces the effective withdrawal rate. 
Smoothing – smallest impact on the risk reduction :
a.       Number of years to smooth: 5 years is used. This is in line with economic cycle.
b.      Conservative rate of return: Using expected rate of return minus the variance seems to provide on average smoothed market value equal to the average market value.
c.       Corridor: If the market is very volatile the smoothed market value assessment is at maximum 20% off the real market value.
Increase Cap:

a.       Capping % prior retirement: 115%
b.      Capping % at retirement: 108%
c.       Capping % prior retirement: 105%
d.      Capping % increase: 1%. If the previous year withdrawal is cap, the next year cap is 1% greater than the previous year. This allows compensating more rapidly during high gains.
Reserve:

a.       Initial reserve fund % : 25%
b.      Maximum reserve withdrawal: 10%
c.       Reserve protection : 95% of previous withdrawal
d.       Maximum reserve %: When the reserve is greater than 35%, 50% of the excess is return to the main fund.

Simple example of the smoothing assuming a less than expected return

Data:


Year
2011
2012
2013
2014
2015
Average
Market value
500,000$
480,000$
490,000$
510,000$
530,000$
502,000$
Rate of Return
-4.0000%
2.0833%
4.0816%
3.9216%
N/A
1.7089%

·         Smoothed Value with corridor at 2015 = Min(CorridorMin; Max(CorridorMax; Smoothed Value)) = 558,359$
o   CorridorMin: 530,000*0.8 =  424,000 $
§  [Parameter] Corridor Minimum = 80%
o   CorridorMax: 530,000*1.2 =  636,000 $
§  [Parameter] Corridor Maximum = 120%
o   Smoothed Value = 1/5*500,000*(-(-4%)+5.67%)+2/5*480,000*(-(2.0833%)+5.67%)+3/5*490,000*(-(4.0816)%+5.67%)+4/5*510,000*(-(3.9216)%+5.67%)+530,000 = 558,359$
§  [Parameter] conservative rate of return = 5.67%

Simple example of the reserve

25% reserve covering 95% drop using an ADD withdrawal rate of 8%:
Year
2008
2009
2010
2011
2015
MV BoY
500,000$
286,700$
355,660$
350,162$
328,096$
MV NR BoY
375,000$
210,450$
251,698$
263,981$
247,720$
MV R BoY
125,000$
76,250$
83,962$
86,181$
80,376$






Withdrawal BoY
30,000$
28,500$
28,500$
28,500$
28,500$
Withdrawal NR BoY
30,000$
16,836$
20,136$
21,118$
19,818$
Withdrawal R BoY
0$
11,664$
8,364$
7,382$
8,682$






MV EoY
470,000$
258,200$
307,160$
321,662$
299,596$
MV NR EoY
345,000$
193,614$
231,562$
242,863$
227,902$
MV R EoY
125,000$
64,586$
75,598$
78,800$
71,693$
Rate of Return
-39 %
30%
14%
2%
N/A

Market Value: MV; Reserve: R; Non Reserve: NR; BoY: Begin of Year; EoY: End of Year

As expected in the financial crisis, the fund substantially shrinks during the 4 years. However, we are able to maintain a 95% of the initial withdrawal with relative ease. We can see that the fund value increase substantially after the fabulous year of 2009 & 2010. The 2011 return is 2%, less than the effective withdrawal rate (8%*75% = 6%). This lead to the Non-Reserve fund shrunk in 2012. The reserve would be able to withstand about 10 years at the end of 2012 regardless of future recovery.




Retirement risk

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