March 26, 2024

After over ten years, I am switching back to **Wealth-Lab**. It is an excellent program with all its new features. I will be able to do whatever I want, whether it be on single stocks, groups of stocks, or portfolios of strategies.

The primary objective of any stock trading strategy is to meaningfully outperform market averages and make you money, no matter which software you use. Otherwise, why go that route? You could buy a low-cost market index proxy and expect those long-term market averages.

Not surprisingly, it puts the payoff matrix back in play: F(t) = F_{0} + Ʃ^{N} (**H** ∙ Δ**P**). A single equation that states that whatever the outcome of your trading strategy playing the stock market investment game, the net generated profit or loss over the entire investment period will be F(t) - F_{0} = Ʃ^{N} (**H** ∙ Δ**P**).

**So, what do we need to do?**

We need to gain a long-term vision of what we want to accomplish. It is not like a night at the casino. We need purpose, planning, and assurances since investing in the market is usually for the long term. We want to win. After 20, 30, or 40+ years, we want to say that we achieved a growth rate on our holdings commensurate with our efforts and know-how.

The strategy designs must evolve to include what will be needed at the multi-portfolio level. Operating multiple trading strategies will require more than trading a single stock or portfolio. A stock portfolio grows exponentially, making it a more significant concern than just scaling up.

The first problem will be how much capital you will have. Initially, that is F(0) = F_{0}, a major equation component. Should ever: F(t) < - [F_{0} + Ʃ^{N} (**H** ∙ Δ**P**)], game over; you lost it all. Making a single bet on a single stock using all your capital and hoping for the best might not be the most assured way to get there. However, buying a single ETF market proxy (SPY, DIA, QQQ) will get you there. But then, you will get the same average return of either SPY, DIA, or QQQ. If you want more than that, it might require taking more market risks, depending on your trading methods.

**What are the long-term expectations?**

For a single stock, we have F(t) = f_{0} + Ʃ (h_{i} ∙ Δ_{i} p), where the gains come from trading the stock multiple times (for *i* = 1 to n). For a portfolio of stocks, we would have: F(t) = Ʃ f_{0,j} + Ʃ h_{d,j} ∙ Δ_{i} p_{d,j}) where *i *identifies the trade number from *i* = 1 to N, and (d,j) is the date timestamp *d *of trade *i* on stock *j*. We can reorganize this data vector into a payoff matrix: F(t) = Ʃ F_{0,j} + Ʃ (**H**_{d,j} ∙ Δ_{i} **P**_{d,j}), which carries the same information. It will include all the trading activity in all the stocks in the portfolio. The structure lets the portfolio expand by increasing *d *and *j*. Any new trade will increase *i*.

**Multi-Portfolio Level**

The problem gets more complicated at the multi-portfolio level. An easy portfolio to construct would be using the 100 stocks in the NDX index and rebalancing every week. As a start, see the following article: **QQQ To The Rescue**, which runs such a strategy.

We could resume the strategy's trading activity on those 100 stocks to F(t) = Ʃ F_{0,j}+ Ʃ (**H**_{d,j}∙ Δ_{i} **P**_{d,j}) where again *i *goes from *i* = 1 to N. In this case, N is close to predefined, N = 100 ∙ 52 ∙ y, where *y *is the number of years to hold the portfolio. For example, over 20 years, the number of trades would be 100 ∙ 52 ∙ 20 = 104,000. It should be slightly higher due to replacements, as some stocks drop out of the NDX for whatever reason. An estimate could be roughly 200 to 400 more trades over those 20 years. That is less than 0.2% to 0.4% of the total.

Playing the 100 stocks in the NDX index is the same as playing the 100 stocks in QQQ, which constantly tracks the NDX index. The QQQ rebalancing strategy (see above link) should give close to the NDX return over those 20 years. F(t) = Ʃ F_{0,j}+ Ʃ (**H**_{d,j}∙ Δ_{i} **P**_{d,j}) ~ → F_{QQQ} + Ʃ (**H**_{QQQ}∙ Δ **P**_{QQQ}).

A single trade (buying QQQ and waiting it out) has, in all probability, a slightly higher return than making over 104,000 trades over those 20 years. Should you want an argument against trading, this could be it. On the other hand, weekly rebalancing QQQ will outperform SPY or DIA over the long term.

Which trading methods using the 100 stocks part of QQQ could produce more than just buying QQQ outright? That is the question.

How about changing the trading day or time of this rebalancing? The same equation would hold. The numbers would be different for almost all trades. Even so, it would not change the outcome by much. The 104,000+ trades would likely have a slightly lower outcome than holding QQQ for the duration. Why would slicing the 100-price series slightly differently not produce about the same thing as holding QQQ?

**Trade Slicing**

What kind of trade slicing would generate a better outcome than just holding QQQ?

For a single trade, we have q ∙ Δp = ± x, where *x *is the profit or loss. The problem could be considerable since there might be over 104,000 trades to take care of, if not more. What would be the size of each of these trades q ∙ p since you have limited capital? How much could they generate in profits? What should be a guiding light?

Improving trade timing could be a route to take. However, this would require predictive abilities to outguess general price direction. For instance, even if out of context, taking a position in the 100 QQQ stocks every other week for a week should generate about half the outcome of holding QQQ for the duration, something like ½ Ʃ (**H**_{d,j}∙ Δ_{i} **P**_{d,j})≈ ½ Ʃ (**H**_{QQQ}∙ Δ **P**_{QQQ}). Just common sense. So, it might not be with less market exposure that you will outperform QQQ. Rebalancing every week will only assure you of approaching QQQ's overall return. Furthermore, should you try equal weights in your QQQ trading program, you will underperform QQQ, which is value-weighted.

Does this mean you have to go with probable outcomes, and if so, how would you evaluate those probable outcomes beforehand? Making predictions in the stock market has often proven to be ephemeral. A wrong trade can be very costly and detrimental to your portfolio.

However, some of it does not need that much forecasting. The US long-term market averages, on average, have risen for over two centuries. It should be sufficient to declare a historical upside market bias. The upward market trend has been averaging about 10%. We could make a bold forward prediction: F(t) = F_{0} ∙ (1 + 0.10)^{t }with *t* greater than 20 years. We might not know if we will get that 10% average on a year-over-year basis. However, we should expect it over the long term.

**Anticipating the portfolio's long-term outcome**

Then, we need to predict upswings and downswings in price gyrations. But that is even more difficult. Many have tried, and many have failed. Could we not simply follow the long-term trend? Would this not lead to getting the long-term market average?

What would make your trading methods better than most? As Yogi Berra once stated, as others: "It is difficult to make predictions, especially about the future."

First, in trading, you need, most of the time, to be right and in the right direction. It is the hit rate, and the overall profit-to-loss achieved that matters. Once you realize this, you will also have to consider another important factor: the number of trades taken to achieve your goal. There might need to be more since time will enter the equation. How long will it take to achieve those goals? In a probability setting without guarantees, you will have to play averages. What will your endeavor's outcome be, on average, over the years? How can you make estimates on that? More importantly, how will you make sure to achieve your objectives?

A year decline of 50% will reverberate over the years: F_{0} ∙ (1+g_{avg})^{n} ∙ 0.50 ∙ (1 + g_{avg})^{t-n} = F_{0} / 2 ∙ (1 + g_{avg})^{t}. It would be the same as if this 50% drawdown occurred in your last trading year. It also shows how significant such a drawdown is. For instance, do the math: $1,000,000 / 2 ∙ (1 + 0.20)^{30}= $118,688,157. The $500,000 you might lose in your first year is similar to an opportunity cost of $118,688,157. Should some effort be deployed to reduce those drawdowns since they have long-term consequences? It is simple: the market is not kind. It will gobble up all you want to throw at it and will not even say thank you.

So, we have q ∙ Δp = ± x for one trade. For many trades, we should get Ʃ^{N} (q_{i} ∙ Δ_{i}p_{i}) = Ʃ^{N} x_{i}, where (Δ_{i} p_{i}) is the price difference (exit - entry) for trade *i*. The total profit from all executed trades is X = Ʃ^{N} x_{i}, and the average profit per trade is Ʃ^{N} x_{i} / N = x_{avg}. Therefore: Ʃ^{N} x_{i} = N ∙ x_{avg}. And that is the game you should play: x_{avg}, the average profit per trade. It is not complicated math.

You can slice and dice any stock price series in as many pieces as you want. The first objective remains to outperform just holding the stock over the investment period: F(t) = F_{0} ∙ (1 + g_{avg})^{t}. Your trading results should exceed - to make it worthwhile - having put your money in an indexed fund, such as F(t) = F_{0} + Ʃ^{N} x_{i} ≥ F_{0} ∙ (1 + g_{spy})^{t}, where g_{spy }is the average long-term growth rate of the S&P 500 index.

Whatever your portfolio's growth rate g_{avg}, if it does not exceed the S&P 500 index, what you did over the trading interval was insufficient since g_{avg} < g_{spy}. You had a better scenario just holding on to SPY and with little effort on your part.

**Outguessing price movements**

The path of any stock price is erratic, as if on a quasi-random walk. Nonetheless, you must outthink, if not outsmart, its randomness, not just once in a while, but most of the time. You need to determine if the stock is going up or not by how much and how long it might take. What if your estimates were wrong? How would you handle the consequences, and at what cost?

The more you trade, the shorter the trading interval, on average. Shortening the trading interval should result in a lower expected return per average trade. However, short-term price fluctuations can have significant price gaps. Daily, you will find stocks that moved by ±10%, even a few with 50% gains and more. Should you annualize some of these trades, they would represent high yearly returns. The same goes for significant down gaps; some can obliterate a position.

If you intend to do 100,000+ trades over the next 20 years, you should be more concerned about averages than any single trade. A $1,000 profit or loss on a trade will impact the average by $0.01. Yes, by only one penny. And each time your average profit per trade increases by one dollar, you will add $100,000 to your trading account. Consequently, you want to push the average profit per trade x_{avg }as high as possible.

The easiest estimate is you can get the long-term market average with little effort. How much are you expected to make over the next 20+ years would be something like F(t) = F_{0} ∙ (1 + 0.10)^{20} = 6.7 ∙ F_{0}, where the 10% growth rate is the expected long-term market average for something like SPY, the S&P 500 index tracker. After 20 years, your initial stake grew by 6.7 times without any other effort but waiting for it. If you started with $1,000,000, you would get $5.7 million just for sitting on your hands.

Therefore, your trading strategy has to outperform this basic investment strategy. Otherwise, you are wasting your time and money on a doomed endeavor destined to produce less than what was readily available. The bar is not that high, yet many have difficulty exceeding the market average by actively trading. It is estimated that about 75% of traders do not outperform the market average (read SPY as a market proxy). However, I do not know how anyone could have confirmed such a statement. They never provide corroborating and worthwhile studies on it.

Your task is easily delimited. You outperform SPY, or you do not. And you cannot go on the premise that maybe you could. You have to be sure you will win. Otherwise, again, you might be losing your time. And time only goes in one direction. It is not like a simulation that you can do over and over again, optimizing on some variable. The rerun button on life, as in - let's do it all over again - is simply not there. You cannot restart your life a hundred times.

Outperforming SPY is also straightforward. Instead of picking SPY as your investment vehicle, switch to QQQ, the NDX index tracker. QQQ deals with the top 100 stocks on NASDAQ, compared to SPY, which tracks the top 500 in the S&P 500 index.

The move will add growth to your portfolio due to the stock selection process. The reason is simple. The top 100 stocks of NASDAQ will generate a higher average return than the 500 stocks of SPY by construction, as the chart below can attest. The 400 stocks not in the NDX index, part of SPY, can only drag the overall average down.

**SPY vs DIA vs QQQ**

However, it is not the first 20 years that should interest you. It is the next 20 to 40 years after that. Your stock portfolio should exceed your lifespan. It should survive you and be your legacy to your children. Let them, in turn, expand it. Your legacy could do just that. One thing is sure: you will not be taking it with you.

If the first 20 years could give you F(t) = F_{0} ∙ (1 + 0.10)^{20} = 6.7 ∙ F_{0} at the 10% rate. At the 15% rate, it would be F(t) = F_{0}∙ (1 + 0.15)^{20}= 16.36 ∙ F_{0}. And with a growth rate of 20%, you should get: F(t) = F_{0}∙ (1 + 0.20)^{20}= 38.34 ∙ F_{0}.

If you add 20 years to those numbers, you would get respectively F(t) = F_{0} ∙ (1 + 0.10)^{40} = 45.26 ∙ F_{0} and F(t) = F_{0}∙ (1 + 0.15)^{40} = 267.86 ∙ F_{0}, and F(t) = F_{0}∙ (1 + 0.20)^{40} = 1,469.77 ∙ F_{0}. By then, you would have been at it for 40 years. If you started at 25, you would already be 65, ready to retire, and start withdrawing funds for your living expenses from your still-growing stock portfolio. I suggest you review some of my recent articles on the subject.

No matter what, it is always your choice. Do you do it or not? The ball is at your feet.

Created: March 26, 2024, © Guy R. Fleury. All rights reserved.