April 22, 2024

My previous article, **The Long-Term Stock Trading Problem - Part I, **presented a table analyzing a 25-year-old planning for a long-term stock trading portfolio to last a lifetime. He or she, intending to retire at age 65 and continue holding their stock portfolio while withdrawing a yearly income stream for their living expenses and more.

The calculations were from the reference point of a 25-year-old living up to 95. The timeline was preset, as was the initial capital of $100k. The choices offered were the growth rates at which his or her portfolio might grow.

As the article referenced shows, some of those rates were easy to get. For instance, simply holding QQQ over the period could give an estimated 15% CAGR, which would already be more than reasonable once retired and leave an enviable legacy to their children.

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Here is a copy of the table from that article:

**Figure 1: Retirement and Legacy Fund**

The table in **Figure #1 **was limited to the presented case. There was a need for more flexibility, such as starting one's fund later than 25 but still having a trading strategy that could last until their 95^{th }birthday. Those numbers come with a margin for over and understating the outcome of 40 to 70+ years hence.

Referencing the previous paper again, its **Figure #1 **shows a linear regression over the last 200+ years for average market return, a straight line on its log scale, indicative of a steady exponential function. Getting into stocks at any point over the last 200+ years would have given you a wobbly line highly correlated to the one on that chart.

There is an equation for that linear regression: the future value equation. I use a slightly modified version of it: F(t) = F_{0} ∙ (1 + g_{avg})^{t} where g_{avg} = r_{_m_avg} + α_{avg}, thereby separating the average market return and the return premium coming from one's trading skills and know-how. However, it does not change the nature of that equation; it only enables the separation and identification of the source for that return.

The early years make little difference in this long-term stock portfolio-building process. For example, over the first five years, at a 10% rate (SPY as a proxy for the long-term market average), we have F(t) = F_{0} ∙ (1 + 0.10)^{5} = 1.61 ∙ F_{0}, a 61% increase. Whereas at age 70 compared to 65, we have F(t) = F_{0} ∙ (1 + 0.10)^{70} - F_{0} ∙ (1 + 0.10)^{65} = 299.37 ∙ F_{0}. On a $100k initial stake, the difference for those last five years would be $29,937,623 compared to $61,051 for the first five. We are not dealing with comparable amounts. Yet, only the timing of the time interval changed; both periods are just five years long.

Those differences will increase if you consider longer time intervals and different growth rates, as illustrated in **Figure #1**.

**Being More Flexible**

My friend asked me: What about people older than 25? How does it apply to them? That was an excellent question. So, I returned to the drawing board and made the above chart respond to changes in initial capital and starting age. While at it, I made monthly average income stream estimates for each scenario.

The initial design is the same in that you get the same numbers as in **Figure #1**, which showed 8 CAGR levels going from 5% to 40% in 5% increments. As the CAGR rises, the difficulty in reaching it will increase.

Like almost everywhere else in finance, there is no free lunch. With each increasing CAGR level, we expect to face increasing risks and the need to acquire more skills and expertise.

The question is: How much risk will we tolerate? How much will we forego in potential profits to reduce the drawdown pains? Even more basic, what is the risk I am taking, and do I have a proper definition for it? I know there is inherent risk in the stock market game. An example of market risk just from this morning: IZM was down 90% before being halted; it went from $50+ to $4 in a few minutes. I do not know why, but can see the current bid at $3.22.

**Part I** restated that r_{_m_avg} was given away almost for free. Buying SPY and holding for years is expected to give you that level of compounding, which is about 10% per year. However, as stated, you could improve on that by using QQQ instead, which would give you an average long-term 15% CAGR.

Since we require the investment/trading strategy to last for 70 to 80+ years, we are ready to sit on our bunnies to achieve our goals with a high probability of occurrence.

In the above-cited article, I touch on the choice of growth rates. That one could easily pick QQQ over SPY or DIA and get about five alpha points just from the selection process and average out over the years a 15% CAGR. Yes, the yearly returns will fluctuate. Yes, you could hardly predict which direction returns would take year after year. And, yes, you will not know the size of that return, up or down. But, if you wait long enough, things will, almost surely, average out to the decades-long average (refer again to Figure #1 in the last article). The regression line on stocks over the previous 200+ years (a straight line on a log scale) is a good enough approximation for the general market behavior.

**How About Starting At Age 35?**

**Figure #2 **below illustrates that point. We are still using the $100k initial capital, but starting at age 35. Since there was no change to the future value formula, all the numbers in **Figure #1 **were displaced ten years forward. As should be expected, the numbers you had at 65 in **Figure #1** are now at age 75 in **Figure #2**.

**Figure #2: ****Retirement and Legacy Fund (Start Age 35)**

The differences are easy to notice. In **Figure #1**, at 65, using the QQQ line, you had accumulated $26,786,355, but now, in **Figure #2**, it is reduced to $6,621,177. Over the first five years of retirement, you would get an average monthly income of $37,054. Your monthly income would increase by 10% per year. You would have beaten the system with the single decision to put your $100k in QQQ and sit on it. Pretty good.

Your legacy to your loved ones at 95 would be about $115,535,584, which is less than the $467,405,877 you would have left them if you had started at 25. It might be here that we can say that time is money. Starting at 25 or 35 is your decision, just as picking QQQ over SPY. These are simple decisions you can make before starting your journey to financial freedom.

There is no judgment implied in starting your retirement fund at age 35. Maybe you were unaware of those solutions or could not secure the initial capital due to all your other obligations.

Nonetheless, at 35, it should be easier to get the initial $100k. Your income should have increased over the previous ten years. You should have put more money aside and started building that retirement fund. If your current fund has an average return of less than 15%, it might be time to reconsider your approach. You deserve better than getting 5% or 10%, especially since the QQQ solution is so easy to implement.

At 35, it becomes imperative that you find ways to build that initial stake. Time is running out and getting more expensive. Buy a smaller house, a used car, or whatever. But find ways to put some money aside for your retirement. Well, you should get the point.

**How About Starting At Age 45?**

The same thing applies. The numbers in the top panel of **Figure #2** will slide to the right by ten years, and those in **Figure #1** by 20 years.

The impact is considerable. Again, using the QQQ line, at 65, your fund, in **Figure #3** below, is at $1,636,654 compared to $6,621,177 in **Figure #2**, and $26,786,355 in **Figure #1**. The delay in starting your fund gets more and more expensive. So much so that now your legacy fund (at age 95) would be $28,558,629 compared to **Figure #2**, which was at $115,535,584, and to **Figure #1**, which was at $467,405,877.

The top panel of those three figures shows the retirement fund's starting age and the initial capital invested. Therefore, you do have a decision to make. You should find ways to get that initial $100k and start as soon as possible. Get your parents to contribute to your cause. You will be able to pay them back with interest.

Choosing the 15% CAGR is easy: buy QQQ and hold on. You should buy more at any time you can afford it. You will be building a better life for yourself and your children and them for theirs. Your investment fund will become your retirement fund, which will become your generational fund, assuring the well-being of your offspring.

**Figure #3: Retirement and Legacy Fund (Start Age 45)**

**You Could Reshape The World**

In my brief paper, **The Age Of The Individual Investor**, I presented a compelling argument: individuals, simply managing and directing their retirement funds, have the potential to reshape our world. This idea still holds. Investing in QQQ can be seen as a vote of confidence in America. QQQ is a collection of the top 100 wealthiest corporations on NASDAQ. To cater to all investors, QQQ accumulates shares in proportion to the weights in the NDX index. These shares sustain these companies, distribute market risks, and support millions of workers. It's a win-win scenario: those 100 companies thrive, the workers benefit, your retirement fund grows, and society retains its freedom.

**The Starting Later Dilemma**

You are starting your retirement fund later than expected, say at 35; what can you do to recuperate the lost time? A simple solution to the future value equation is to start with more capital. The following table illustrates that starting with $170k would do the job at the 5% CAGR level. The numbers are even better than in **Figure #1**.**Figure #4: ****Retirement and Legacy Fund (Start Age 35 with $170k)**

However, the $170k is not enough for higher CAGR levels. Again, compare with **Figure #1**. You would have to raise the initial capital for each CAGR level to obtain close to the same results as in **Figure #1**.

**Figure #5: ****Retirement and Legacy Fund (Start Age 45 with $280k)**

**Figure #5** above approximates the needed capital for each CAGR level that will come close to the same outcome as in **Figure #1**. For the exact answer, one could use the following formula: A ∙ (1 + r)^{t} /^{ }(1 + r)^{t-10} = **B** where A is the initial capital over the longer interval, *t* the number of years, and *r* the growth rate considered. **B** will equal the needed capital to get the same answer as over the longer interval *t*. The above formula transforms added capital for time at the same CAGR level.

**Figure #5** makes the same case as **Figure #4** but for the person starting at age 45. It leaves only 20 years to build one's stock portfolio before reaching 65. So, initially, there is a need to increase starting capital to achieve about the same level for the 5% CAGR level. However, we should also notice in **Figure #5** that the higher CAGR levels would require more initial capital if we wanted to match the numbers in **Figure #1** or come close to it.

**Figure #6: ****Retirement and Legacy Fund (Start Age 35 with $170k)**

**Figure #6** makes the adjustments for the fund started at 35. The same formula is applied to the different growth rates. Look at the 35-column for the progression. You have to compensate for the time and the growth rate simultaneously, which is why the capital is increasing to obtain the results as in **Figure #1**.

**Figure #7** makes the same case for the fund started at 45. In this case, you have less time to compensate and need to put up more cash. That is easily understandable. Using the above equation, we can convert time for cash.

In **Figure #7**, the required initial capital gets relatively high as you increase the average CAGR over the period to achieve about the same values as in **Figure #1**. Some of those higher CAGR values might be considered unattainable even at 45.**Figure #7: ****Retirement and Legacy Fund (Start Age 45 with $280k)**

What could you do to improve the situation?

It is where your skills come in. You could inject some alpha in the conversion equation. The new equation would look about the same as the one above: A ∙ (1 + r)^{t} / (1 + r + α)^{t-10} = **B**. For example, we can use the $100k case of **Figure #1**with the QQQ growth rate of 15% and have 30 years to recuperate before retirement at 65. It would improve the case presented in **Figure #6**, and we would get the following: $100,000 ∙ (1 + 0.15)^{40} / (1 + 0.15 + 0.05)^{30} = $112,843. Five alpha points and $12,843 more would compensate for getting the same answer by age 65 as in **Figure #1**. The above formula enables you to recuperate the lost years by injecting more capital and adding trading skills and know-how.

You can use the lost years for money and skills conversion equation to reduce the required initial capital by adding more alpha. Five more alpha points would generate the following:

$100,000 ∙ (1 + 0.15)^40 / (1 + 0.15 + 0.05 + 0.05)^30 = $33,160.

It would recuperate that lost decade and do it using less capital.

The case where the 35-year-old has the initial $100k would require less alpha. How much more would be needed to achieve the same outcome as the 25-year-old at retirement time?

The answer is about half a percentage point.

$100,000 ∙ (1 + 0.15)^40 / (1 + 0.15 + 0.05 + 0.004842)^30 = $100,000.

Adding half a percent (to your five alpha points (0.05)) would be enough to catch up, which is not a significant effort. QQQ (0.15) was the benchmark, not SPY (0.10). QQQ is the more favorable choice, that you start at 25 or 35, for that matter.

Where would you get the added five alpha points? That is relatively easy, too. You could opt to trade the top 50 stocks in the QQQs and get a couple of alpha points there. Using your stock inventory, you could add a covered call program and generate 5 to 15% in added alpha points.

Your objective is to build a retirement that will provide you with a future income stream of substance. But you also want a legacy or generational fund for your children. You will do it for yourself, your children, and your country. Again, these are your choices, decisions, and money. It is also about your future, your family, your children, and your legacy.

**Related Papers and Articles**:

**The Long-Term Stock Trading Problem - Part I**

**The MoonPhaser Stock Trading Program**

**Anticipating A Stock Portfolio's Long-Term Outcome**

**Sitting On Your Bunnies Might Be Your Best Investment Yet**

**Make Yourself A Glorious Retirement Fund**

**The Age Of The Individual Investor**

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

**Take the Money and Keep it – II**

**Created: April 22, 2024, © Guy R. Fleury. All rights reserved.**