### Background

The Gen2 probability model we maintain for PRO subscribers for the SP500 provides for *short, medium, long-term and macro-term* probabilities of market troughs/peaks.

It does this by examining current up/down trends across the 4 time-horizons mentioned and compares them to a 30-year historical record of said trends with regards to both *duration of trend* and *gains/losses achieved for the trends*. By comparing the *duration* and *gain/loss* of the current up/down trend with the historical record, we can impute two probabilities, namely:

- The probability that the current trend will
*endure longer*and - The probability that the current trend will
*gain/lose more*.

To assess an appropriate probability of a *trend reversal for the current trend we find ourselves in,* we merely create and *average of the two above probabilities. *This provides us with a *likelihood assessment of a trend-reversal* taking place when considering the long-term historical record of past trends with regards to *both duration and gains/losses of said trends.*

To categorize historical trends into short, medium, long-term and macro *buckets *we need an *algorithm for trend classification *across these multiple time-horizons. The algorithm used by the Gen2 probability model considers intraday highs and lows on the daily SP500 candles to determine *true* tough-to-peak gains or peak-to-trough losses of trends and works simply as follows, which is an alternate spin on the popular “Zig-Zag” technical indicator:

- If we are in a
*down-trend*and there is a*higher low*within**x**-days ahead than*yesterday’s low*, then change to an*up-trend*. - If we are in an
*up-trend*and there is a lower high within**x**-days ahead than*yesterday’s high*, then change to a*down-trend.*

The values of ** x** used for our model for our various

*trend time-horizons*were determined through

*optimization research*based on what appeared to

*work best in general*in representing the targeted trends for the nearly three decade historical period, and are currently as follows:

- Short-term trends :
**7**days (market sessions) for 211 entries for the historical database - Medium-term trends :
**17**days for 89 entries for the database - Long-term trends :
**34**sessions for 45 database entries - Macro-term trends :
**72**sessions for 24 database entries.

The charts below depict the gains/losses (intensity) and durations for the short and medium-term trends respectively as of Wednesday, 24th January 2024. We note that if we view the current trend we are on as a *medium-term up-trend*, it has gained 19.49% versus a 11.2% historical average, which is one standard deviation above the mean. It is not shown on the chart, but this transcribes into a 22% probability the trend will continue, or conversely, a 78% probability the trend will reverse *based on the gains*. We also note that if we view the current trend we are on as a medium-term up-trend, it has lasted 59 sessions versus a 35-session historical average, which is 0.7 standard deviation above the mean. It is not shown on the chart, but this transcribes into a 26% probability the trend will continue, or conversely, a 74% probability the trend will reverse *based on the duration*.

The useful thing with these ACTUALS charts is if a trend has continued for some time, such as the deemed medium-term trend in the lower two charts above, we can draw a horizontal orange line showing the current gains/losses or duration so we can visually see how* often in the past*, and *when* these levels we are currently witnessing *have been exceeded*. These visual cues sometime are easier to digest and provide more dimensions (when and how many times) when assessing likelihood of reversal than a single dimension probability percentage derived from nonlinear math equations.

Below is the same chart depicting the deemed *long-term trends. *These translate into probabilities of a trend reversal of 53% according to the *current gains* and 47% according to the *current duration*.

Finally, here are the deemed macro-term trends:

### Introducing PCT

The selection of **x** in trend-determination along short, medium and long-term horizons, apart from our optimization research, is fairly arbitrary. It’s never perfect and is designed to capture intended trends for *most of the time. *But for a short-term up-trend using **x**=7 that suddenly comes to an end on a given day, what if using **x**=8 does *NOT* reverse the trend on the given day and the market pushes a new high after another 8 days? Is **x**=8 a better value to use than **x**=7? We can keep on with this argument until **x** gets sufficiently long enough to eliminate such choices but by then **x** will be too large to be useful as a “short term” trend latcher. In fact, it is perfectly reasonable that for the prior up-trend, **x**=7 was best in terms of timeliness but for this current up-trend, **x**=8 will be better for accuracy.

Let us examine a *very recent* example of this. On 29th December 2023 we were in an *up-trend*, and the *high* for the previous day, the 28th December, was 4,793.3. The high for the 7-day look-ahead was only 4,790.8, *below* the high of the 28th, so the algorithm marked 29th December as a *reversal day*, the first day of a *new short-term down-trend*. On 08 Jan 2024 the low for the 7-day look-ahead (4,714.8 on 17 Jan 2024) was *higher* than the low of the previous day (4,682.1 on 05 Jan), and thus we had *another reversal* day and a *new short-term up-trend ensued:*

On the surface, this looks *entirely reasonable *and appropriately captures a definition of short-term trends. We see that on the downtrend reversal day of 29 Dec, the probability of a short-term top on the previous day, the up-trend peak, was sitting at 91.4% an entirely appropriate warning of the impending short-term top.

**P**ersistent **C**urrent **T**rend (PCT) attempts to* avoid a reversal day* by *expanding the look-ahead* value **x** by the *minimum amount* to preserve the current trend. It is a tacit admission from the algorithm that “*Hey, this might not actually be a short-term reversal, and since x=7 is a generalized one-size-fits-all parameter, we can provide traders a more comprehensive review of the short-term risks by ignoring the reversal, but we’re going to have to find the smallest, larger value of x that will allow us to do this*.” In this particular instance, we were fortunate to only have to increase

**x**to 8 to maintain the current up-trend on 29th December, since the witnessed high 8 days into the future from the 29th was 4,798.5 on 11 Jan – higher than the 4,793.3 witnessed on 28th December:

So we are now giving the observer an *alternate potential short-term reality* – that the current short-term up-trend is *ongoing*. Note how for **x**=8, the probability of a market peak on 28th December was 89% as opposed to 91.4% witnessed with the **x**=7 trend algorithm. Also the PCT model is now flagging a probability of a market top on 24th January as 95% as opposed to the 41% from the **x**=7 trend algorithm which is now on the assessment that we are in a *new, young* short-term uptrend.

The chart sets we provide subscribers will include the PCT algorithm assumptions *in addition to the standard assumptions*, and they are available in the *PCT tab in *PRO>SP500 Charts . Both the probabilities of the duration and gains/losses are provided in the first two PCT charts, whilst the actual durations and gains/losses are provided in the bottom two PCT charts. Numbers in brackets represent readings for the prior day so we can assess how much the probabilities change from day-to-day:

Using the above example, we look at the top chart and take the PCT rally *duration* top-probability of 96% and average it with the PCT rally* gains* top-probability of 95% to derive a *two-dimensional average* market top probability of 95.5%

At this juncture the PCT algorithm is providing the investor/trader the opportunity to assess *multiple potential short-term realities*. Looking at the examples we provided above, in hindsight, it appears as if **x**=8 is indeed providing a more realistic and likely interpretation of the current short-term trend environment than **x**=7. We do *not* however use this as a reason to go and modify x to 8 permanently, since traders make heavy use of the short-term algorithm for market-timing and trend-following purposes, and we want the smallest value for x as possible that provides the most accurate *generalized* long-term results in order to *preserve timeliness*.

In this particular example shown, **x** only had to be increased from 7 to 8 to preserve the short-term uptrend, but you should note that on many occasions, **x** has to increase by quite large numbers to retain the persistent current trend assumption. In many cases x will jump into the mid to high teens to preserve a current short-term trend which means the PCT trend is *no longer a viable short-term alternate reality assumption*. In fact, large jumps triggered in PCT’s** x**-variable merely cement that the current **x**=7 short-term trend is most likely the *actual, true* short-term trend reality. At that stage, PCT is no longer suited to alternate reality assumptions on the short-term horizon but starts providing alternate realities for the medium-term trends. Thus, once PCT is in the teens it starts looking to *reversals in the medium-term trends* (**x**=17) to take its cues for finding alternate realities – this time on the medium-term timeframe.

### Pre-empting the look-ahead

We provide a specialized market timing chart in the *ST-ALGO tab in *PRO>SP500 Charts that allows short-term trend followers and market-timers to pre-empt **x**=7 short-term trends without having to wait for the full 7-days look-ahead to pass. Not only is it around 70% accurate in forecasting what the full look-ahead algorithm will provide as trends, but it does it with a 2-day lag as opposed to 7-day lag. Additionally, it also allows us to assess the risks of a future short-term **x**=7 trend reversal together with *target levels* for the SP500 that are most likely to trigger said reversals.

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