May 6, 2020

In my previous article, the point was made that you could win the game relatively easily simply by prescheduling your future trading activity based on your portfolio's initial set up. The portfolio value equation was put on the table with a reachable long-term objective giving a purpose to the whole process. You did it for your own retirement account or as some legacy fund you might want to leave behind or build a generational fund with philanthropic views. Those are things for you to decide. All I can do is help you design your long-term portfolio for whatever reason you may have.

I will build scenarios based on the portfolio payoff matrix equation presented in the prior two articles of this series (see related articles below). The purpose is to show the range of what you can do based on your own portfolio settings and long-term objectives and also show where's the money. I hope that with the examples provided you will be able to build your own and know what to expect based on your numbers.

First, let's restate the portfolio's payoff matrix equation from a previous article:

F(t) = F0 + Σ (H ∙ ΔP) = F0 + y ∙ rb ∙ j ∙ E[tr] ∙ u(t) ∙ E[PT] = F0 ∙ (1 + g)t

where y is the number of years the rebalancing is applied, rb is the number of rebalance per year, j the number of stocks in the portfolio, and tr the expected turnover rate. u(t) is the betting function and E[PT] the expected average profit margin. The portfolio has its equivalent growth rate in g.

Scenario 1

Scenario 1 starts with 1 million, trades for 10 years with a monthly rebalance on 200 stocks with a turnover rate of 40%, a starting trade unit or allocation of \$5,000, and a 2% average profit target.

The outcome is the long-term generated profits and its equivalent CAGR. All we have is the application of the formula with its 9,600 trades over the 10-year time interval.

Changing the preset conditions will change the outcome.

Doing the same as above but for 20 years will result in:

Scenario 2

In scenario 2, doubling the number of years doubled the number of trades, increased profits by a factor of 3.25 while close to maintaining the CAGR. By adding more time, we start to see the impact of the law of diminishing returns. But this can be compensated for, however, it is not done in these examples.

Scenario 3

Evidently, if you increase the initial capital, it will directly impact the long-term profits, but still maintain its compounding rate of return. It increased the bet size u by a factor of 10, the same factor as with the initial capital.

Scenario 4

Under the same conditions, scenario 4 shows a weekly rebalance while maintaining the profit margin objective. The picture changes considerably. You are still only requesting an average 2% profit on a trade, but you are doing it more often, and it adds up. You are now at a 16.99% CAGR.

Scenario 5

Scenario 5 does the same as scenario 4, but for 30 years, and again you can see the impact of return degradation, but as I have said, this can be compensated for.

Scenario 6

In the above chart, the request for the average profit on a trade was raised to 3%. This, evidently, has a direct impact on the 124,800 trades that will be executed over those 30 years. The "request" might be small, but over the years it will simply add up.

Each of the scenarios presented is a matter of choice, on how you want to handle your own portfolio going forward. It is depending on a program to do what it was programmed to do, and since you do know what is coming your way, you can gain the confidence needed to put it in motion knowing exactly what you are doing.

The above portfolio equation can be controlled even further. For instance, increasing the growth rate of the bet sizing function will impact final results.

Scenario 7

The increase in the bet sizing function in scenario 7, even if relatively minor, had a tremendous impact. It raised the strategy's CAGR to 21.3% over those 30 years for what should be considered an administrative move.

Scenario 8

In scenario 8, the bet sizing function was further increased, pushing the strategy's CAGR to 26.80%.

The What Is It You Want

Each of the above scenarios are choices one has to make. Some of those choices have more impact than others. But, it remains our abilities and risk averseness that prevails here. You cannot find a way to raise your bet size function to 1.15, then go back to scenario 6. You do not have 10 million as initial capital, then go back to scenario 2. You have more skills and capital than in scenario 8, then push for more. Your choice does not change the portfolio equation, it is more you trying to make the best of it with what you have. You have more, you can do more just as you can do less. (see related books).

The portfolio payoff matrix formula says you can grow big if you start big. But, it can also do well starting with a lower initial capital.

Scenario 9

Scenario 9 above is on the same basis as scenario 8. Here, the initial capital was reduced to 1 million, the same as in scenario 1. The impact was to simply reduce the bet size. And yet, it managed to maintain its 26.80% CAGR over those 30 years. The long-term profits are still more than enough to retire on. For comparison, one million invested at a 10% CAGR for 30 years would give \$17,449,402. That is 1.06% of what of scenario 8. And based on \$100,000 over the same period, it would generate \$1,744,940 or 0.106% of scenario 8. This is putting emphasis on the value of the initial capital.

You could tweak scenario 9 along the way. For example, requesting a slightly higher average profit margin, like going from 0.03 to 0.04. It would give:

Scenario 10

That was a minor change done over those 124,800 trades but it was sufficient to increase the overall CAGR to 28.02%.

A simulation based on something close to scenario 7 and 8 has been presented in my recent articles. So, I know these things can be programmed up or down. You are dealing with a program. It does not know any better than what you put in it. I make my programs follow the portfolio's payoff matrix equations and give them directives and goals to achieve.

The main thing here is time and compounding. You do a 17.16-year simulation, it will take a few minutes for your computer to execute. Going forward, in real life, it will be 4,324 trading days or 6,054 calendar days. That is a lot of time monitoring and waiting after your computer to do its job. In reality, not so much of your day's time per se since the trades are all prescheduled and executed by your machine. Nonetheless, the end reward will be there.

It is really up to you to make your trading strategy do what you want with the resources you have and under your own conditions and constraints. With the above formula, you could rebuild any portfolio you want. You simply just have to put in the time and persevere.

May I wish you all the best.

Related Recent Articles:

The Portfolio Rebalancing Gambit. Part II of III

The Portfolio Rebalancing Gambit I

Reverse-Engineer For More Profits

Portfolio Doubling Times II

Durability And Scalability