Dec. 21, 2021

The purpose of the previous 5 articles was to show the relative ease of setting up your own indexed retirement fund, manage it and prosper even with little intervention of your own. Was given a recipe on how to do just that. A single common-sense decision could get it started, one you could make at any time of your choosing.

You simply copied an imitator of a market index and followed its weighted index. The QQQ ETF was used for that very purpose, an index tracker tracking the NASDAQ 100 index. It was demonstrated that you could trade QQQ's 100 highest valued NASDAQ stocks, or simply buy QQQ outright and hold it for the duration with a slightly better CAGR, as should be expected.

I design long-term stock trading strategies. If any of them cannot survive or produce enough over a 10-year simulation period, they are thrown away. If I find them biased, I also throw them away. Rather, they are put on a not-to-do list as a reminder to never again use such unproductive trading procedures.

Ten years of data should be enough to show a strategy's strengths and weaknesses. And from there, you could add performance enhancers, reduce and/or remove weaknesses, or add new features. You could even design contingency procedures for things that might happen in some future that has not happened in your simulations knowing that they might in fact happen going forward. The extra code might not be used, but that is not the point. The just-in-case point remains nonetheless valid. And a few lines of protective code do not cost that much.

It will be your retirement, therefore, I suggest you take care of it yourself. At least, you can trust a person you have known for quite some time: that is you. Don't mind me or anybody else, we have no part of your solution. Period. And nowadays, you cannot count on your government for when it will be your turn to retire.

Your retirement is all about you, your investment decisions, and how you will manage to get there with what you have learned, saved, and earned. Your objective should be to make your retirement fund large enough to have a worry-free and well-financed retirement to last you for more than a lifetime. In other words, you want to enjoy your retirement for a long time and not run out of money before you die.

The first roadblock you will meet is the money thing to start the ball rolling. How much capital (F_{0}) do you have at your disposal to embark on this relatively long-term financial journey? The second problem is related to time *t*, how much of it do you have? And the third will be what kind of average rate of return *g* can you achieve on your money?

You are not being sold a can of beans here. You can verify everything that was said in the previous 5 articles. You can run the same tests using the same program and obtain the same results. You have easy access to the program itself. I have nothing to do with it and it is free. Clone it, and do your own tests. Modify the program if you want to. Should you opt to modify it, I suggest adding some downside protection.

That should be relatively easy too. A first step might be to go to the sidelines should your portfolio decline by some percentage amount. Note, however, that interrupting a compounding process might not be that wise, but at times might be warranted. There are a lot of methods you could implement to reduce the portfolio's volatility and drawdowns. However, it is not what I would like to cover at this time. It is more about the things you can actually do, what is important in building up your own indexed retirement fund.

**It is Your Retirement Fund**

First and foremost, your fund will need to survive and prosper enough to have made its undertaking worthwhile.

If your portfolio does not or cannot survive over the long term, or does not appreciate sufficiently, you will probably have wasted not only your precious time but your money as well. You do not have that many 20-year trials available, you have a limit on those.

You need to understand the tools at your disposal and make them work for you. Appraise the trading or investment methods available, and then plan for where you want to go. Determine how you can finance and achieve your goals. Note that your objectives could be achieved using other types of assets as well. You are not confined to stocks only, but presently, it will be about stocks and the management of it all. What is proposed will not be that time-consuming either.

I will again use the QQQ strategy presented in those previous 5 articles to make my points. I expect you will verify all of them, especially the math. There will be an equal sign on the table. As such, it is not some kind of opinion, it is much more. It is a statement of fact. Something that only answers to yes or no, equal or not equal. It does not come with a maybe this or that. An equal sign is true or it is not. It has no emotions, no herd mentality, and does not respond to astrology, or your psychology whatever it may be.

Building a long-term retirement fund is the same as for building anything else, you need to plan for what you are going to do and what should be the ultimate outcome of it all. You do not just go out and say: someday, I will retire. Yes, you will. But, you could do it in style by being well prepared, at least, moneywise. For the rest, well, that is your problem.

The formula to determine your future portfolio value is simple: F(T) = F_{0} ∙ (1 + g)^{t}. It has been the same for ages. It is the same formula used for compounding interests. The future value depends on your initial capital F_{0}, the average growth rate *g* you can achieve, and how much time that growth rate will be applied.

That is it, and technically, problem solved.

To isolate the growth rate, you can rearrange the equation: [F(T) / F_{0}]^{1/t} -1 = g. Time *t* is a major component, it will take a lot of it to get to where you want to go. So, start as early as possible, otherwise, you might have to speed up the process by finding ways to increase F_{0}, *g*, or both. You could also opt to give it more time since your fund will be under your control.

A retirement fund does not need to stop at retirement time either. Since you will be managing it yourself, it could continue for another 30^{+} years and more with a lesser growth rate since you would be withdrawing some of it for your living expenses or for other purposes. You should design your portfolio to survive your retirement giving you the ability to withdraw as much as you need without ever running out. The ball is in your court, you are in charge, it is your retirement fund after all.

So, the first step is: take charge. It is all about you. And the end result is all for you and your loved ones to enjoy. It is also your choice to not do any of it resulting evidently with F(T) = F_{0}, the do nothing, or, could do none of it scenario.

**TIME**

First, you will not get there overnight. Time is the critical factor. I have to stress that building a retirement fund is a long-term endeavor. It will take years.

Draw your own timeline, determine what you want and then figure out what it is you can do. Unfulfilled dreams are not what you want to end up with. Therefore, start by being as realistic as possible without sacrificing optimism as to what you can actually do. If you want to start your fund with 1 million and you do not have it, it will be the first problem that needs to be solved. And if you think you can get the same results starting with $ 10,000 know right away you will be mistaken.

Say you are 45 and have 20 years before retirement at 65 and then have some 30^{+} more years thereafter. You can adjust your timeline, in this case, the younger the better since time is really on your side.

I will base all calculations on an initial fund of one million. Find ways to gain access to this million or more. If you already have it, good, if not, move the decimal point to the left. Ten times less for initial capital should produce 10 times less for final result.

A million could grow to: F(T) = 1,000,000 ∙ (1 + 0.20)^{50} = $ 9,100,438,150 should you get Mr. Buffett's 50-year long-term average CAGR (g ≈ 20%), or use the QQQ strategy presented in previous articles. That is what is at stake. Mr. Buffett started with 10,000,000 over 50 years ago, so you could add a zero to the above figure.

You do not need that much, I understand. But since you will be doing the job yourself anyway, why not do the best you can. This is not a pipe dream, it is actually something you can do on your own with little effort if you want. This was also demonstrated in my prior articles using the QQQ weekly rebalancing strategy.

After the first 20 years, your fund should be in the vicinity of: F(T) = 1,000,000 ∙ (1 + 0.20)^{20} = $ 38,337,599. From which you could start withdrawing some income and still have your portfolio continue to grow. Even a 4% rule of thumb withdrawal would give you $ 1,533,503 on your first year of retirement. It should be enough to pay for the beer with family and friends until the next withdrawal which will be even higher. Anyone could definitely survive starting with a self-indexed million and a half income per year. You could do better, evidently, but, your baseline objective is pretty much set.

**Withdrawals**

The main reason to build a retirement fund is for the freedom it will bring when you retire. You should be able to do whatever you want. A lot of that stuff will require money, some source of income. This also implies that your fund should not be depleted too quickly. You want your fund to last for as long as you live and still have a lot left over for your loved ones, or whatever other reasons you might have had to pursue this wealth appreciation journey.

You need to find ways to make your fund last, and most probably, for a long time.

Say you just retired at 65. This means you need this retirement fund to supply you with income for another 30 years and maybe more. 30 years where you should not even worry about running out. This is where you needed to be a little creative, but actually not by much.

You have your fund that has grown at an average rate of g = 20% for the past 20 years. You think it can be sustainable. At least, it is your goal to maintain this CAGR level or better. You know that *g* will oscillate over time and that after some 20 years, you should be in the vicinity of *g* and that should be enough. If you can do better, go for it. As you go along, you will find better ways anyway, meaning ways to further increase *g*, I know I could.

From the previous formula, after 20 years, we had: F(T) = 1,000,000 ∙ (1 + 0.20)^{20} = $ 38,337,599. We need to add what will happen next. Starting with the first year of retirement, your fund will grow at a lesser rate due to its yearly withdrawal rate (say about 4%).

We could have something like: F(T)_{(t ≥ 20)} = F(t)_{(t = 20)} ∙ (1 + 0.20 - 0.04)^{t}. Starting with year 20, a 4% withdrawal is made every year. But, base on the equation, the portfolio would continue to grow at a 16% CAGR implying that the 4% you are taking out is also growing at a 16% rate per year. This should beat any fixed annuity you might purchase.

That is how you should use your own self-made index fund. You are the one making it happen. Each year you get some 16% more than the year before, and you can do this for as long as you want, your fund will continue to grow at its long-term average g ≈ 20%. Evidently, the outcome will not be that smooth. It will be more erratic, but the final outcome F(T) might still have been generated by something nearing g = 20%.

In fact, any portfolio that can sustain a growth rate superior to its withdrawal rate will increase with time. All what is required is simply to have: (1 + g - w) > 1.0. Withdrawals will increase or decrease by this rate difference.

So, it is not just you, it is anybody that can achieve a higher return than the withdrawal rate that can benefit from such procedures, even if *g* was just 5%, the portfolio would still grow. And getting only 5% is well below historical averages. The implication for you is tremendous: F(T) = 1,000,000 ∙ (1 + 0.20)^{20} = $ 38,337,599, while F(T) = 1,000,000 ∙ (1 + 0.05)^{20} = $ 2,653,297.

There is a cost to the withdrawals: it is measured by the slower portfolio growth rate. But then again, it is your money and you can do with it whatever you want. In retirement you should indulge, it is why you worked so hard all your life, to be well off with your loved ones and take care of them. The cost of withdrawals is more like an opportunity cost than anything else.

The money you withdraw stops appreciating, it stops compounding. And since you have a lot of time to consider (some 30^{+} years), it just adds up. Nonetheless, access to the yearly withdrawals was the main reason for building this retirement fund in the first place. So, do indulge.

You are stuck with the future value formula: F(T) = F_{0} ∙ (1 + g)^{t}.

And when applying an annual percent withdrawal, we get: F(T) = F_{0} ∙ (1 + g - w)^{t}, a lesser rate of portfolio appreciation. Note that with a withdrawal rate *w* higher than *g* (w > g), the portfolio value would decline over time.

**The Notion of Doubling Time**

The future value equation is all you have to work with.

The amount you put to work is a major factor since it will be compounding over time. And there, time becomes even more impactful since the last few periods of these time series become the most valuable. It can make quite a huge difference when a higher growth rate *g* can be applied over an extended period of time. We need to master this equation and what it says.

For instance, we could look at *g* in terms of doubling times. That is the rate of change needed to double one's portfolio over a given time period, the equation is: (1 + g)^{t} = 2^{n}. The following chart shows the doubling time for g = 2.5% up to g = 40% and gives how much time is required to double at each growth rate.

The above chart is easy to read. If you have a 5% CAGR, then the doubling time is 14.25 years. Doubling again will require 28.50 years. Your $ 100,000 initial capital would require 28.5 years to reach $ 400,000, and 42.75 years to reach $ 800,000. If you think you will be able to retire on that amount, good luck. But be prepared, it might be really rough. Even inflation at 2.5% will reduce your buying power to g = 2.5% which will now require some 28.16 years to double in size.

With a 2.5% rate, some 56.32 years are now needed to reach $ 400,000. Add 56 years to your current age, and then realize that this future outcome represent peanuts on which you will not be able to survive financially independent for very long. It could even make the whole endeavor not even worth pursuing.

You should want at age 65 and beyond to have more than just peanuts to survive on. You have in the QQQ rebalancing strategy something that will be much better. Make it the minimum you could do. If you can do better, great.

The sequence of doubling times (2^{n}) is easy: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192,... Anybody can multiply by 2. Each doubling time generates as much as whatever was produced from all previous periods. Whatever time was required to reach 512 times your original portfolio, one more period would add 512 times to push the portfolio to 1024 times. And then doubling again would push you to the next level in the series, and so on. Each doubling is as much as all that preceded.

Does it matter knowing the doubling time? Not really, but, it does stress the point that you do have a limited time to reach your goals. Should you want to reach 10 doubling times to get: 2^{10} ∙ F_{0} = 1024 ∙ F_{0}, you would need to go through all the previous levels in the series. At an average 5% CAGR, it would take 142.5 years to get there.

Do you seriously think you will survive that long to retire, or that you will be there? You have to find ways to increase that CAGR to something that can reach your goals. For instance, Mr. Buffett has had an average 20% CAGR, giving him an average doubling time of about 3.81 years, thereby having at least 2^{13} = 8192 times his original portfolio. His last doubling time represented 4096 times his initial stake, that is as much as he had done over the previous 46 years. There lies the power of compounding.

**The Initial Capital**

Starting at the same time as somebody else using 10 times more capital with the same growth rate *g*, we cannot say you would reap the same rewards. In the first case, a 20% CAGR gives: F(T) = 1,000,000 ∙ (1 + 0.20)^{20} = 38,337,599 while with $ 100,000, we have: F(T) = 100,000 ∙ (1 + 0.20)^{20} = 3,833,760.

You put 10 times less upfront, you get 10 times less as outcome. It is what the future value formula says. Period. The point is that the initial capital is a crucial factor in this equation. F_{0} is independent of what you are going to do, of the game you want to play. It is what you have even before you start playing this compounding game.

You put 10 times less upfront, you will get 10 times less as outcome too. F(T) = 10,000 ∙ (1 + 0.20)^{20} = 383,376. Do notice the difference in end results which were only based on the initial amount. Just to balance the scale, consider: F(T) = 10,000,000 ∙ (1 + 0.20)^{20} = 383,375,990. The only difference is the original amount put to work F_{0}.

You simply cannot outperform someone starting with a much higher stake than yours and having the same CAGR. The only recourse would be to generate a catch-up growth rate, meaning to grow your portfolio at a faster pace.

F(T) = 1,000,000 ∙ (1 + 0.20)^{20} = 100,000 ∙ (1 + 0.346422)^{20} = 38,337,599.

A 20-year average growth rate of 34.64% is evidently harder to realize, but it still can be done. The easier route is effectively to find more capital.

The above is to stress the importance of the initial trading capital and that more effort should be put into getting it even higher, even if you have to borrow some of it and make arrangements to pay it back with interest.

Your objective is a simple gain factor: gf = F_{T} / F_{0}. Put that back in the equation: [F(T) / F_{0}]^{1/t} -1 = g would give: gf^{1/t} -1 = g. The following chart illustrates this point.

Starting with the initial capital and the gain factor, we get the required CAGR to reach that goal over the specified time interval. To reach 100 times your original capital, will require a 25.89% CAGR to do it in 20 years, but only a 12.20% to do it in 40 years. I would go for at least the 1,000 times original capital knowing that I could do even better.

Whatever CAGR you get, the same as anybody else, their initial capital and how long they have been at it will make a difference. Why should somebody that started 10 years earlier with 10 times more money have to pay you something while you are just starting off? The rich will continue to get richer, but, the not-so-well-off will also continue to raise their standard of living. The gap between the rich and the poor will inevitably continue to widen. It is built in the future value formula. All participants have their own initial capital, growth rate, and time spent on the job.

As long as your own growth rate is higher than your withdrawals, you will be making a profit. And as long as your growth rate will exceed your cost of capital and withdrawals, your portfolio will also continue to grow and indirectly index your annual withdrawals.

Consider the following hypothetical scenario. Say, you borrow 100,000 and promise 1,000,000 as payback in 20 years' time. That is the equivalent of 12.20% compounded for 20 years. And you make this deal 10 times to get 1,000,000 knowing that in 20 years you will have to pay back 10,000,000 to honor your promises. You use this million to generate: F(T) = 1,000,000 ∙ (1 + 0.20)^{20} = 38,337,599, and you are left with $ 28,337,599 for your services. Your 10 friends or clients get their million dollars as promised while you get the rest. It might be less than projected, but you would still be ahead of the game as long as you can increase your portfolio at a higher rate than 12.20%. That is not very hard to do. You could take the QQQ example in my recent articles as a basis to build this retirement fund. As simple as that.

In order to achieve your own goals, you would have to generate something higher than just a 12.20% CAGR over the next 20 years. And you should find ways to secure and exceed this outcome.

Should you raise your own CAGR to 25%, it would have for result: F(T) = 1,000,000 ∙ (1 + 0.25)^{20} = 84,128,065 from which you would again take out the 10 million to pay back your clients leaving you with $ 74,128,065. More than enough to pay for the beer.

Note that there are no management fees, they are not even considered. For not being bothered with withdrawals or fees for 20 years, you agree to the 10 to 1 payback, and on that promise, make sure you will deliver.

In 20 years, you could offer the same deal again. This time, take your clients 1 million and raise it to 10 million in 20 more years. To you, the cost is the same. They are happy, they get their 10 million and you do make every effort to make it happen. Your program continues to do the same and provides you with this 20% CAGR over those added 20 years. But this time you are operating with $ 84,128,065 for initial stake which would generate: F(T) = 84,128,065 ∙ (1 + 0.20)^{20} = 3,225,268,100.

So, for sure, you would have all that is needed to pay them back. Your own withdrawals would have kicked in at year 20 and would be indexed at (g - w - c) where *c* is the equivalent cost of funds. First-year withdrawal would be: 4% ∙ 74,128,065 = 2,965,122, and again, more than enough to pay for all the beer you want.

**Related Articles**:

**Build Your Own Indexed Retirement Fund**

**Take the Money and Keep it – II**

**Use QQQ - Make the Money and Keep IT**

**A Trading Strategy Of Interest - PART II**

**A Trading Strategy Of Interest**

**The Makings of a Stock Trading Strategy – PART II**

**The Makings of a Stock Trading Strategy – PART I**

Created: Dec. 21, 2021, © Guy R. Fleury. All rights reserved.