May 13, 2024

The One Percent a Week stock trading program's original mission was to buy at a 1% discount to each Monday's opening price. And sell at any time during the rest of the week with a 1% profit or liquidate the position at whatever price on Friday's close at the latest. Whether it be for a lower profit than 1% or a loss, which could occur often.

In the One Percent a Week Stock Trading Strategy - Part II, I will demonstrate a version of the program that can get close to it with no added effort. These modifications are also something you could do.

The 1% per week is ambitious; it's a yearly return of 67.7%,  (1 + 0.01)52 = 1.677. It makes the strategy's theoretical objectives very appealing. Even getting close would be appreciated.

This free trading strategy will serve as our starting point and include the modifications outlined in the previous article (see Part I).

                         CLICK HERE FOR THE PDF VERSION

However, before going any further, I would like to make something clear.

Let's recall that the only criteria for entering a trade were that it was a Monday and that you got your limit order in at 1% below the opening price. Under such trading rules, you are not investing. You are gambling, and the same math applicable to gaming and gambling will also dominate your game.

Will the market comply with your trading rules? Let's say it will oblige, meaning that the trade will be executed should it be executable under your trading rules and procedures.

We should also understand that we can set whatever trading rules we want; we are the only ones in charge of the game we intend to play.

The market will not ask questions or require any justification for our trading decisions. You issue a market order, and it is a done deal, no problem. If you issue a limit order, the order will sit on the order book until your price is met. Once the limit price is met, the trade will be executed. Your broker might add another condition, that is, if sufficient funds are available in your trading account.

The market does not provide you with any probability settings and will not give you any odds on your trade. All it can give you is a historical expectation: that the next tradable price will be about the same as the last, in probability, meaning most often.

The expected percentage difference from trade to trade is zero. That is also the definition of a martingale. Even though you are facing a martingale from trade to trade, it is not the case over the long term since there is an upside bias to market average proxies such as SPY, DIA, or QQQ (see chart #1 in the article: The Long-Term Stock Trading Problem). Only a low percentage of stocks (single digit) will have their closing price the same as the opening price after a day of trading.

The same will apply to price moves over a week, a month, a year, or longer. You are almost assured of a change in price the more time you give a trade.

Modifications Made To The Original Program

The modifications introduced in Part I were guided by simple common sense. It shifted the perception of what, why, and how the trading strategy should behave.

We ended with a simple trading strategy that generated a 52.89% CAGR over the last 14 years, far exceeding what could have been done using DIA, SPY, or QQQ. This remarkable result sets the stage for what comes next.

The final question from that article was can we do better? It didn't provide a direct answer but alluded to this forthcoming Part II.

In Part I, I removed the 1% discount request before entering a trade. The reason was simple.

If you buy some stock, it is because you anticipate it will rise in price. Yet, the original program wanted the stock to go down first before taking the trade, not by much, just 1%. Technically saying: show me some weakness; a 1% dip will be enough, and I'll buy. Weakness in a stock price is not limited to 1% drops and will usually continue to decline (majority of cases), by how much is not known, and that is a problem.

Even though requesting a discount is a legitimate request that will often be granted, it might not be in your best interest.

The 1% discount limit order was often met. But it also meant you were buying during a price decline. The stock price could continue to fall and put your trade in negative territory, having your position in the red from the start.

At most, you had 5 trading days for the price to recover and make that 1% gain. If not, the position would be liquidated on that Friday's close. We could call the whole thing a variation on buying the dip. And in many cases, a dip which might not have enough time to recover (48.72% of the time, according to Figure #6 in Part I).

It is sufficient for the stock price to recover for you to make that 1% profit. It is not a major task in the world of stocks. On a $100.00 dollar stock, you requested an entry price of $99.00 to be sold back at $99.99. You could get that within the few minutes following any Monday's opening bell. In the original version and using QQQ, that request was granted 805 times out of a possible 1,222 (68.57%) (see chart #2 in the previous article).

When the 1% discount request was granted, it did not mean that all those trades would make a profit; it did so in 460 cases and took a loss on the other 345 trades.

Long-Term Return Degradation

Switching from QQQ to TQQQ, its 3x-leveraged version, resulted in a significant upswing in return. However, this implied more risks since volatility would increase threefold. Based on the latest three-month averages, TQQQ had a volatility of 14.59%, while QQQ's volatility was lower at 4.84%.

Applying a three times leverage to ETFs or stocks is subject to long-term return decay. We can express that in simple terms, such as a 10% rise followed by a 10% decline is not getting back to breakeven: (1 + 0.10) ∙ (1 - 0.10) = 0.99, shows that you did not get back to even but only close to it.

If you take this example and place it in a gambling scenario where you win 10% of your stake or lose 10% and play 200 rounds on the flip of a fair coin, you would get for expectation: E[(1 + 0.10)100 ∙ (1 - 0.10)100] = 0.99100 = 0.366, leaving you with 36.6% of your original stake.

Yet, you played a fair game where you had a 50% chance of winning or losing. But here, because you played for percentages with 100% exposure, you were assured of losing even if your odds of winning a bet were 50/50.

It gets much worse if it happens over 1000 bets: E[(1 + 0.10)500 ∙ (1 - 0.10)500] = 0.99500 = 0.00657, almost destroying your capital, leaving you with 0.657% of your portfolio's original value. It is independent of how much you initially put on the table. What it says is that over the long term, you are screwed. You will technically lose it all or be left with less than 1% of what you put in. You had even odds in that game and were still assured of losing.

You will have to deal with this, no matter what. Short-term trading is not the same as investing. Gambling becomes part of the game if you make a lot of short-duration trades. You will be looking for your edge in the game you design and want to play.

A Time Limited Stop-Loss

As already mentioned, the original version of this program had a profit target of 1% but no defined stop-loss except for the forced exit on that Friday's close. Even in the modified version, where the profit target was raised to 7%, no added stop-loss was defined, either.

A 51.28% hit rate (380 positive trades) gives a lot of leeway for the impact of negative trades (361). On average, positive trades made 4.68%, while negative trades lost on average -2.93% (see chart #6 in the previous article).

Some consider that this phenomenon does not happen often. Yet trading on the boundaries of one standard deviation, a moving average channel, a Donchian channel, or any other type of channel could closely follow the above equation.

How many times within 40 to 70+ years will the price of a stock exceed one standard deviation or your profit target? Since a one standard deviation boundary will contain 68% of the data, some 32% of that data will remain outside that one sigma boundary. How many times will those barriers be hit? How many times will they be hit if you are the one setting similar boundaries?

The setting of fixed profit targets and stop-losses would do the same. How often do you see a trading program with a preset profit target and trailing stop-loss with the same percentage value? Yet, these are doomed from the start, and people still program those in. Go wonder why some strategies fail miserably.

A Solution To Long-Term Return Degradation

Because we will be dealing with this long-term return decaying function, we must address its impact and try to minimize it as much as possible. This phenomenon will be more severe as we are using a 3x-leverage ETF.

For example: [(1 + 0.15) ∙ (1 - 0.15)]100 = 0.975100 = 0.1027, and if you pushed higher: [(1 + 0.20) ∙ (1 - 0.20)]100 = 0.960100 = 0.01687. We should also consider: [(1 + 0.20) ∙ (1 - 0.20)]200 = 0.960200 = 0.0002846, or 0.02846%. You would have less than $300 dollars left on a starting million-dollar stake. That is not how you can build a retirement fund, or any investment fund, for that matter.

Notice that in an equation like [(1 + 0.15) ∙ (1 - 0.15)]100 = 0.975100 = 0.1027, it does not matter in which order all those trades occurred. You would still be left with 10.27% of your initial capital after executing those 200 trades. One trade a week would take at least 3.8 years years, resulting in a significant loss of money and time.

Let's apply this formula to the TQQQ scenario and give it the 7% profit target and stop-loss. The expected outcome of this strategy would be (1 + 0.07)380 ∙ (1 - 0.07)361 = 0.6140. Even with a positive edge (more winning trades than losing ones), your initial stake would go down.

If you added a small degree of protection, it could significantly change the game. For example, limiting the downside to average out at 6% instead of 7% while keeping your average profit target at 7% would give (1 + 0.07)380 ∙ (1 - 0.06)361 = 29.17, a positive outcome.

In the last simulation in Part I, we had (1 + 0.0467)380 ∙ (1 - 0.0293)361 = 741.55, which is already a different story.

Increasing the average profit per trade by 1% and reducing the average loss per trade by 1% would give the following: (1 + 0.0567)380 ∙ (1 - 0.0193)361 = 1,112,264.57.

You only need a little push to change the long-term outcome of your trading strategy. We are dealing with long-term averages on exponential functions, and the impact can be considerable, as illustrated above.

What is the average of our fund over the years F(t) = F0 ∙ (1 + gavg)t? It is related to gavg = [F(t) / F0]1/t - 1. We could also express it as (F(t-1) ∙ (1 + γ)) / F0]1/t - 1 = gavg, where we can see the dependence of gavg on the last year of return gamma, be it positive or negative. It also says that, for an exponential function, the heaviest weights will apply to the last few years of the series, especially if you have a shorter-than-average doubling time (1+gavg)t = 2n. An average CAGR of 5% has a doubling time of 14.25 years and at 10%, 7.29 years.

An average return of gavg = 0.20 has an average doubling time of 3.81 years. It means, on average, that your portfolio doubles every 3.81 years. It would multiply your original stake by the following sequence: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ... In less than 40 years, your portfolio could be multiplied 1,000-fold. A 25% CAGR has a doubling time of 3.11 years. Over the same 40 years, you would have 212.86 = 7,443 times your initial capital. We must look at the long-term game; it will be our future.

Fortunately, we have remedies for this return degradation phenomenon. One of my free publications, Fixed Fraction, provides a solution. It states that simply compensating for this return degradation is sufficient.

The provided formula for this was: F0 ∙ [(1+ f / (1 - f))W ∙ (1 - f)L] = F0 where f is the fixed fraction for both the profit target and stop-loss, W is the number of wins, and L the number of losing trades. The formula will compensate for the long-term degradation for any fraction f. It would give you back F0, but that also means you did not make any money, only that you did not lose any, which is a start.

To compensate for a ±10% profit target stop-loss channel we could use: F0 ∙ [(1+0.10) / (1 - 0.10))100 ∙ (1 - 0.10)100] = F0 ∙ 1 = F0, which compensates on the buy side of the equation.

By compensating from both sides, we get: F0 ∙ [(1+0.10) / (1 - 0.10))100 ∙ (1 - 0.10) / (1 + 0.10))100] = 34,097 ∙ F0you would turn the outcome completely around. A minor change: Simply compensating for both sides of the return degradation equation ensures a positive outcome for your portfolio.

Therefore, such a practice should be part of any portfolio you build. The above equation translates to requesting an 11.11% profit target instead of 10.00% and a stop-loss of -9.09% instead of -10.00%. It is not a difficult undertaking by any measure since you are the one setting those profit targets and stop-losses in your trading program.

The market already has an upward bias higher than that added 1.11% to your profit target. By taking advantage of this, you can halt the return degradation. It's a simple and effective way to improve your portfolio's performance.

The Switch To TQQQ

The switch to TQQQ from QQQ also had other implications. The one percent profit request was now insufficient. If the volatility had increased 3-fold, it meant that for a 1% move in QQQ, you should have a 3% move in TQQQ. Otherwise, the 3x-leveraged thing would not hold. But still, the original strategy stayed at requesting a 1% profit target. It was not adapted to trading TQQQ.

Increasing the profit target to 7% was sufficient to push the strategy to a 52.89% CAGR from the start of the TQQQ ETF in February 2010. Maintaining a 50% CAGR should also be a future objective. But there, we will have to wait and see the future as it unfolds. We have nothing to show that the same growth rate will be maintained over the next 20 years. However, if the simulation alludes to the strategy's potential, then the future is indeed promising.

You have a gambling system in place.

Every Monday, you stand ready to buy TQQQ IF it satisfies your entry conditions. One of those is: no price weakness. The price must be above the opening price, or you will pass. In the weeks you take a trade, you will wait to hit your 7% profit target. If you get it, you exit with your profit. If not, you are out with a smaller profit or a loss on that trade by that Friday's close.

What refinements could you bring to this task to improve this gaming strategy design?

Improving On The Strategy

Improving on this strategy might appear a monumental task since at this level (≈50% CAGR), it gets harder and harder to extract alpha points. It does not matter that you had a 52.89% CAGR over those past 14 years. It is going forward that will matter. Nonetheless, you might still want more, especially if you can easily get it.

The gambling preamble set the background for what would be mathematically required to improve this picture. Just like when, in the previous article, we upped the profit target to 7%, as in Figure #5. That hike in the profit target was a simple request that the market did not grant all the time. Also, many other potentially profitable trades were not taken due to the "no weakness clause".

The program stood ready to take a trade every Monday over those 14 years (742 weeks). Figure #6 gave a position count of 741, while Figure #4 had a 614 count. Limiting the entry to be positive and increasing the profit target increased the number of trades by 127 trades. We were more restrictive, yet we made more trades and generated more profits, ≈$30 million more.

To improve the strategy further, we have to address the outcome of the equation: (1 + 0.0467)380 ∙ (1 - 0.0293)361 = 741.55, the state it ended with.

We want to improve the average percent per winning trade and further increase the number of such trades while reducing the average percent loss per trade and the number of those losing trades. Whatever action we take that will impact those numbers and in the desired direction will benefit the trading strategy.

I expressed it before, this strategy is just gambling. The task at hand is: Can we make more bets? Can our profitable bets generate more profits? Can we make fewer negative bets with a lower average loss?

From the above equation, we see where we should put the emphasis. Whatever average we are dealing with, we still have to do it in a world of uncertainty. We are still gaming the system.

That is why we are labeling this a gambling strategy. In any situation where a gambler has a definite edge, he or she should exploit it. We want better results on our winning trades, fewer losing trades, and fewer losses of lesser magnitude. Most of all, we want this gambling strategy to pay out more; otherwise, the added effort might not be justified.

Step I

I started by concentrating on increasing the average profit per trade in the above equation and tackling the 4.67% reached in the last simulation in the previous article.

The program used the "LastOpenPosition.EntryPrice" as a reference point for its profit target. I did not notice that initially, but this meant that the price of reference was not on the current Monday's opening price but on the entry price of an earlier taken trade. It could have been a week before, even two or three weeks before, should some of those past potential trades not have been taken. It is why you see trades closed before Friday's close at less profit than the requested 7% profit target. That you have a profit of less than 7% on Friday's close is perfectly acceptable. However, closing a trade before Friday's close should happen only if the profit target is met.

So, when there was a price increase in the prior week (say 3%), I moved the price target higher by 1%. It was a reasonable request: the price showed some strength, having already improved in price, and the question became: Can it do a little more? My answer was yes, it should, and not it could. My predictive powers are not any better than anybody else. The strategy is playing a game of chance where the odds are in its favor, and I am taking advantage of that.

Figure 1: One Percent Per Week - TQQQ - Mod_1. Equity Curve

(Click here to enlarge)

Figure #1 shows the evolution of the equity curve. The CAGR came in at 56.66% over the same time interval as the tests in the last article, plus one week. The black line, hardly noticeable at the bottom of the chart, is the SPY benchmark, which was greatly exceeded. There is still a lot of light green on the chart, indicating a low exposure rate. It came in at 50.97%, as shown in Figure #2 below.

Figure 2: One Percent Per Week - TQQQ - Mod_1. Metrics
OPW Mod1 Metrics

(Click here to enlarge)

The number of trades increased by one since the test was a week later. The added trade was at a loss. We stayed with 380 wins and added a loss, making it 362 losses. Adding a loss is part of the game, and as long as we win the endgame, we can easily accept that. We will lose nearly half the trades anyway; we should be ready.

Here, a simple request for 1% more on our profit target was sufficient to generate over $18 million dollars more. All because you changed your rules of engagement and method of play. The change was not something out of the blue but a simple request that if part of the price move was already in motion, you had a better chance of achieving more, especially following a trend in which you favor strength over weakness.

The percentage of profitable trades remained low at 51.21% and close to the 51.28% as in the last simulation. That is reasonable; we added only one losing trade.

The request for higher profit did not change the entry price on any of those trades. They were still set to Monday's opening price. A trade occurs only if the entry buy limit condition is met. So, the only change to that strategy was the request for a slightly higher profit margin (+1%), a relatively small request in the stock world.

I haven't tried any other potential improvements to this gambling strategy yet.

Some will start to label this as curve fitting, especially since the CAGR is so high. What you have here is adapting to what is being traded and refining the method of play as any gambler would do as he or she gained more experience and understanding of the game they played. Moreover, any trading script is an iterative process, much like any other software. You add something to the code and then test it to see if it still runs and does the job. You do this until you get it right, meaning the program runs and does the requested task as intended.

Consider this: will a new Monday occur? Yes. Can I set a profit target of 7% for a 3x-leveraged ETF? Yes. Can I execute the trade only if it demonstrates strength? Yes. Can I step back if it doesn't? Yes. Can I increase the profit target for more potential profits if the price is already moving towards its target? Yes.

None of the above decisions were influenced by market fundamentals or Modern Portfolio Theory. They are all strategic gaming choices within a realm of uncertainty.

As the average percentage of winning trades suggests, you still operate with a near 50/50 probability. However, thanks to your designed edge, you're gaining a definite advantage in the game. A significant part of this is due to the disciplined gaming approach and exiting trades by the end of every Friday. No prolonged drawdowns.

The strategy is simple enough that it could even be executed by hand. A computer program is not needed to do the above. However, a program can bring you betting discipline.

You do the simulation to show that the rules you would like to implement make sense and that they at least generate profits from past market data. As to the future, it remains an unknown. Can 742 trades be an indication of the strategy's averaged potential? We have to observe that that number of trades itself makes it statistically significant.

You want to play the game. You want to win. Then, play to win.

You are building your game within the bigger game, the stock market, with all it represents, the good and the bad. And you want the assurance that you will win the game. It is much like playing roulette in a casino. In that case, you know beforehand that the more you play, the more you lose. The odds are not in your favor.

But here, you can structure your own game to take advantage of the game that is there. You become the better poker player, knowing when to hold them and when to fold them. You put your bet on the table when the odds are in your favor. You take your bet on rising prices on the assumption that you do not know if it will continue to rise, close to a 52/48 chance, but stand ready to take your profit. And if it is not coming by Friday's close, you liquidate the position.

The US stock market has an upward bias that has lasted over two hundred years.

We could give it odds of 52/48 to 54/46. It means you will win more bets than you will lose just by flipping a fair coin and always betting on the same side. So, your trading rules are based on the conviction that about the same odds will continue to prevail. You will win a little more than half your trades, and their average profit margin will be higher than your average percent loss on bad trades.

Going back to the equation and giving it more depth, we have:

OPW equation 1

with c(∙) as overcompensation factors, with Δzw and Δzl the added number of winning and losing trades.

In Figure #1, I added cto the compensation factor, requesting a higher profit margin. The strategy readily complied. The market was adjusting to the new trading rule, or the trading rule was adapting to the market. Whichever does not matter, but by doing so, we gained ≈$18 million, from technically what is a minor gaming decision, so it was not so bad.

We should see in equation #1 the multitude of solutions we can bring to our game by controlling those four factors: fw, cw, fl, and cl as well as the number of wins W and the number of losses L. We should also see that disproportionally increasing trades favoring the winning side will improve the overall return and go for Δzw > Δzl, adding more winning trades with higher profits and reducing the number of losing trades while also going for lower losses.

The added compensation factor (cw = cw + ~1\%) was to comply with equation (#1). I am the one fixing the betting rules, and you can too. In the end, it does become a personal choice.

Before Closing

I told my friend yesterday that adding a small (~1%) to the profit target to an already rising price could have quite an impact. I said that the (1%) discount request, if put back, would reduce overall returns despite the other improvements. I also told her it would be easy to demonstrate.

What is the value of that 1% discount?

Figure 3: One Percent Per Week - TQQQ - Mod_1. With 1% Discount - Equity Curve
OPW Mod1 With 1 percent discount
(Click here to enlarge)

I changed that one number in the program to revert to the 1% discount request before entering a trade and ran the test. I had the answer in a minute.

All other things in the program would not change, only the discount request. The results are not that surprising. The discount request was rather expensive, in the order of $40 million for this trading strategy. In Part I, the discount request was valued at $20 million. The discount request also negatively impacted the other improvements brought to the game.

The re-introduction of a simple 1% discount request drastically affected the portfolio's value, reducing it by two-thirds from $60 million to $20 million.

Figure #3 shows the reduced equity curve. It also highlights the underutilization of the available capital; exposure is only at 42.13%. The CAGR dropped from 56.66% to 45.33%, but it is still a pretty respectable number.

Figure 4: One Percent Per Week - TQQQ - Mod_1. With 1% Discount - Metrics
OPW Mod1 with 1% discount Metrics
(Click here to enlarge)

The hit rate (winning percent profitable) was 51.38% in Figure #2 compared to 51.21% in Figure #4, hardly any change. Yet, most trades had different entry and exit points. Nonetheless, the number of trades taken was reduced by 20.6%, 127 fewer trades.

The test demonstrates that small changes in the trading rules can have quite an impact. Like in any game of chance, you learn the ropes early, meaning the rules of the game, and then you let the game teach you how to play that game. The same as any gambler would do. You learn early that you do not go all-in with a pair of deuces in a poker game. Once in a while, you might win that bet, but most of the time, you will be out of the game.

If you have programs that request a percent drop in price before you buy, redo the programs without that discount request and see what happens.

In conclusion, buying strength, even if small, has its merits.


Related Papers and Articles

The One Percent a Week Stock Trading Program - Part I

The Long-Term Stock Trading Problem - Part II

The Long-Term Stock Trading Problem - Part I

 The MoonPhaser Stock Trading Program

Anticipating A Stock Portfolio's Long-Term Outcome

The Big Open Project

Sitting On Your Bunnies Might Be Your Best Investment Yet

Self-Managed Retirement Funds

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: May 13, 2024, © Guy R. Fleury. All rights reserved.