October 18, 2017
You invest and trade in stocks not only to get richer but also to build up a retirement fund either, for yourself, your children or others, from which at some point in time you would want to extract cash for living expenses or whatever other purposes.
My last article (A Price Tag on Alpha - Part III), of a 3-part series, concluded with the realization that should one have a stock trading strategy that is generating some alpha, then he/she/they might be better off implementing it for themselves. Other benefits could be had. One I would like to address is the building of a retirement fund.
Design Objectives
The objective is to design a long-term retirement fund using a few lines on a chart to delineate what it is we want to do over time. This might be viewed as starting from the end. But, I see it more as planning where we want to go. After having set this plan will be left finding ways to implement it.
The modification to bring to the equation presented in Part I: F(t) = F_{0}∙(1+ r_{m} + α)^{t} is to add a retirement deduction term to be applicable after reaching the retirement date: F(t) = F_{0}∙(1+ r_{m} + α – d_{t})^{t} with d_{t} representing the percent deduction to be made. Therefore, we should see a change in the slope of the equity curve at time t_{d} since the combined returns (r_{m} + α) will be reduced by this d_{t} percentage.
We can easily design the building blocks of a retirement fund using line segments on a log chart where compounding curves are seen as straight lines. We can take advantage of that and plan the outcome of a long-term portfolio having deposits and withdrawals over its intended 30+ year time horizon.
We can use the first 20 years to build the portfolio, and use the next 10 to give a preview of what could come next. The timeline could be extended on either side of some retirement date. We will focus on how long the portfolio could last after the retirement date and on its benefits.
#1 Retirement Plan – 10% CAGR – 30 Years | |
(click to enlarge)
Chart #1 displays, on a log scale, what this 10% CAGR fund would look like over the years: a straight line. If we assume that buying a low-cost index fund could generate this 10% CAGR, then what you get is in the no alpha column. And, on the face of it, our job is done.
Chart #7 in Part III shows on a log scale the same information as in chart #2 of Part I. The randomly generated portfolio variations appear more subdued when looked at from this long-term perspective. Making the CAGR line an acceptable estimate and representation of the randomly generated path.
I wanted the example to be more useful. So, I added deposits and withdrawals as either amounts or percentages. The lines of interest are on the chart where we can see their impact. Rebuilding this in Excel, or variations thereof should be relatively easy.
What can we say about this design?
We can add or withdraw money from the fund. From any point, the equity line will grow at its applied CAGR. Our interventions would be independent of what the market does having been arbitrarily set in time. Even though, it will have an impact. However, they would still follow close to the equity line as depicted in chart #7 of Part III.
In this design (chart #1), cash deposits are made in years 3, 5 and 7, and withdrawals occur in years 10 and 12. Starting at year 15, 5% of the equity is withdrawn for whatever purposes. Years 15 to 20 are considered as pre-retirement withdrawals. From year 20 onward, withdrawals are made while in retirement.
Of note, referring to chart #1, even after reaching retirement (year 20), the equity line is still growing. Therefore, one could extract his/her 5% indefinitely as the fund continues to grow. One serious advantage is that those withdrawals are also increasing at a 5% rate per year. This has the same impact as if having indexed our retirement income at a 5% rate all by ourselves, a byproduct of what we are doing.
This is a major departure from converting to an annuity at retirement for a fixed income stream and seeing your retirement portfolio slowly depleted over a specified time interval.
So, with just a few lines on a chart, we were able to design a retirement plan that could suit many scenarios. What would be left is to find two things: the initial capital and that 10% CAGR.
As for time, the most important of ingredients, you will have to live it out day by day, that you build your retirement portfolio or not.
The 10% CAGR is almost too easy to obtain. You can buy shares in SPY, DIA, or others, and the job is done. You want to make a deposit to your fund, buy more shares. You want to make withdrawals, sell some shares. That's it, a complete 30-year plan in a nutshell. You certainly can do this by yourself.
Notwithstanding, we might want more in our retirement. Easy, we could opt to extract 10% as retirement income. This would look like the following chart where upon retirement the portfolio is being reduced at a 10% rate.
#2 Retirement Plan – 10% CAGR – 30 Years – 10% Withdrawals | |
(click to enlarge)
We can observe that the equity line went flat after year 20. It is understandable, on one hand, we were making 10% and on the other extracting 10%. As long as the equity line has a slope greater than zero, you can improve our portfolio. Note that whatever amount you extract from your retirement portfolio, it will not be there to help it grow.
All very simple facts expressed with just a few lines on a chart.
Should you increase the withdrawals to 15% after retirement, you would get more upfront cash, but the amount extracted would decrease at a 5% rate year after year as well as reduce the equity line. It could run for another 25 years before crossing the $1M mark again. By then, your take would be about $150k for that year. So, yes, one has to plan the withdrawal rate in order to sustain one's lifestyle. As shown, in this case, it can be done by having the withdrawal rate not exceed its CAGR: (r_{m} + α > | – d_{t} | ).
The Added Alpha Scenario
The picture changes drastically when adding a 15% alpha as shown in the last article series.
#3 Retirement Plan – 15% Alpha – 5% Withdrawals | |
(click to enlarge)
Chart #3 illustrates this huge return difference compared to chart #2. The early deposits appear almost trivial in this new context. Even though funds are extracted at a 5% clip, the fund continues to grow at a 20% rate (see Equity line). The 5% retirement withdrawals are increasing at 20% per year.
This is more than having an inflation-indexed pension! It is an expanding lifestyle, a portfolio that continues to grow. And, at the same time, providing a worthwhile expanding retirement income. No known annuity program could ever achieve such a thing. It seems as if all that might be required is to make the same bet on America as Mr. Buffett has.
Should you increase withdrawals to 10% per year, you would still be left with a fund that is growing at a 15% rate. Your withdrawals, your retirement income, would also be increased by 15% per year as illustrated in chart #4.
#4 Retirement Plan – 15% Alpha – 30 Years – 10% Withdrawals | |
(click to enlarge)
Any retiree could survive on that level of income knowing that he/she could get more the year after.
This is on the basis that you are doing it yourself, that you have this 15% alpha trading strategy, that it can persist for decades, and that you had the initial stake to make it go.
If you did not have it, then you might consider delegating the task to someone else who will charge for the service. But here it is, a hedge fund with a 2/20 fee structure presenting a historical 25% CAGR due to its fees will reduce the outcome to the equivalent of an 18% CAGR as was shown in Part III.
Therefore, if you could on your own generate 8% alpha, you would get the same outcome as if a hedge fund could have generated a 15% alpha on your behalf. It might also be part of the reason why some people might not be prone to pay that high a fee for the hedge fund's extra performance given that they could close to match it with less effort by doing it themselves. And, I would add, generating an 18% CAGR is not that hard to do.
Starting with either, your savings, or an initial stake you put together some other way, you can go about building this long-term stock portfolio. I do not see this as a difficult thing to do. On my website alone, you will find more than a dozen different ways to do just that and more.
An alternate question would be: why change your 18% CAGR for a hedge fund's 25% CAGR when what you will end up with is an 18% CAGR? Someone else's CAGR could become valuable to you if and only if their net CAGR is better than what you could have achieved on your own. Only then could you put a price on this added net CAGR above your own.
That EXTRA BEFORE
Naturally, doing it yourself has the premise that you can design a stock trading strategy where the 15% alpha is not only available but also executable. Otherwise, this 15% alpha could be just a pipe dream.
However, any positive alpha generation has the advantage of providing you with a potential plan. It tells what you can and cannot do with a consequence to each action. It will be your trading strategy that will make all the difference.
For sure, if you do not plan for this future, how do you think you will ever get there?
It is not in year 19 that you will suddenly wake up and say: I will catch up this year! Just look at the numbers. No trading system will give you that, you had to be there all along and let your portfolio grow day by day, year after year.
Should you be more daring and find the added capital to start with a $10 million dollar fund, then the numbers will become impressive as illustrated in the following:
#5 Retirement Plan – $10M – 25% CAGR – 10% Withdrawals | |
(click to enlarge)
Figure #5 should not need commenting. But, it does put some emphasis on the initial stake and on the value of the efforts required to get it. The opportunity cost is the difference between chart #5 and chart #4, and it depends on your ability to raise capital, not your trading strategy.
Do It Yourself
You design on paper where you want to go. Starting with a single line on a chart! All the charts presented are an illustration of this. From there, you ask the question: how can I do this, using whichever chart you want? What can I do to reach my objectives?
Preferably, you should design your own, adapt it to your circumstances, make it yours. See what you can do with the means you have.
The Excel file is easy to build, so are the charts. At least, it will provide you with a long-term plan and help you better determine your objectives. It could be your guiding light for the next 30+ years. Chart #5 tells you what could be. Your skills and resources will provide you with what you can do.
You are left with finding ways to execute those plans. At a minimum, the 10% CAGR scenario is easily achievable. Any added positive alpha will simply improve the outcome. The more alpha you can get, the better. You can generate more than a 15% alpha, then go for it.
To obtain those alpha points will definitely require your skills since all this depends on the trading strategy you will use. You need confidence in it to carry it out for decades which in turn implies that the trading strategy must be sustainable for decades.
Building a portfolio is a long-term endeavor. It is not making a few bucks on a trade and then hoping to make another one soon. The process is a lot more engaging than that. It requires all your attention, especially if you want to extract those extra alpha points out of what is available out there.
Related articles:
A Price Tag on Alpha - Part I
A Price Tag on Alpha - Part II
A Price Tag on Alpha - Part III
Stock Portfolio Alpha Definition
Created... October 18, 2017, © Guy R. Fleury. All rights reserved