Performance Summary
Created by the author with data from Norgate
CC stands for (Previous) close to (Current) close natural log return, that is the buy and hold return. $CC shows CC converted to the current value of $1. CO stands for close to open natural log return and $CO shows CO converted to the current value of $1. HLd stands for the difference between the natural log return of previous close to daily high and the absolute value of the natural log return of previous close to the daily low.
Created by the author with data from Norgate
These results are absolutely astonishing. TQQQ is very close to making 1000 times the initial investment, while SOXL still has 3 months to break the 10 year 2500x barrier.
In this article, we will examine how such results can be accomplished.
Weighted Price Implications
Whether and how to weight daily price, is usually a theoretical discussion that reminds me of the medieval issue of how many angels can dance on the head of a pin. This application is the first time that I’ve noticed material, objective implications of weighting.
The daily close price of an equity is artificial, as it attempts to measure the exact position in time of a wave. All in all, the daily close is a reasonable approximation, but it’s strategic usefulness is analytically dubious.
Adjusting Strategies criticized the statistical concept of Dimensionality Reduction for stock price analysis.
” Dimensionality reduction, … is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.”
This idea certainly has merit, but for it to have important practical value, it should be possible to demonstrate that daily high and low prices have no effect on closing prices. Daily high and low numbers are known exactly while the daily close is not.
Academia seems to tiptoe around this issue, seeking refuge in the apparent incoherence of Principle Component Analysis. Why not just look at the data?
Specter/FF5 produces better returns using a weighted price. The daily weighted price is currently calculated as:
(High + Low + Close) * .3334
This is commonly known as the Typical Price. Previously, I had been using this weighting:
(Open + High + Low + Close + Close) * .2
Frankly, I avoided using typical price in the past because it involves dividing instead of multiplying. Computers like multiplying better than dividing. Finally (after 20 years) I convinced myself it is OK to multiply the sum by .3334 instead of dividing by 3.
The typical price has better returns over the test period than the previous weighting. That suggests it is producing more relevant numbers. Typical price values the close as 33% of the weighted price instead of the previous 40%.
Neo-Classical Specter/FF5
This was initially elucidated in Timing The 3x Bulls, Theory Into Practice. Neo-Classical Specter/FF5 considers xCF to be a buy signal in addition to the five Classical signals (x00, x33, xMM, xCC, and xFF). Soon afterwards. during detailed examination, I suspected that the idea was dubious because one would buy and hold through xFF to xCF to xCC transitions… silly rabbit.
As understanding of the signals has improved over the last few months, Neo-Classical has regained respectability. Moreover, including xCF in uptrend determinations also improves returns; perhaps because in Neo-Classical there are more long signals than flat signals.
Moving Average Lengths
The four moving average lengths analyzed are:
- 3 Day
- 7 Day
- 13 Day
- 21 Day
All four of the analyzed lengths beat buy and hold convincingly.
Created by the author with data from Norgate
Note that the four strategies all have less time in market risk than buy and hold. All four strategy results beat buy and hold convincingly for every member of the magnificent seven except, ironically, for SOXL 3 and 7 day strategies.
It is difficult to understand how returns like this, with many different strategies, can achieved if market movements are random.
Trend Following
Adjusting Strategies didn’t go into the different trend following signal streams derived from the four average lengths. It is possible to combine any of the trend following streams with any of the strategy lengths. Neo-Classical Specter/FF5 buy signals are always followed. If a flat signal appears and trend following is active, a buy signal replaces the flat signal.
The returns presented in this article are based on 3 day trend following signals. 7 and 13 day trend following also have their good points.
Trend following works better with Neo-Classical Specter/FF5 than Classical. The addition of the sixth default buy signal improves returns substantially over Classical.
This changes the ratio of buy signals to flat signals. For the four default lengths:
- 3 day. Uptrend = Less than 21 buy signals in 50 days.
- 7 day. Uptrend = Less than 26 buy signals in 50 days.
- 13 day. Uptrend = Less than 29 buy signals in 50 days.
- 21 day. Uptrend = Less than 31 buy signals in 50 days.
The 5,3,2 sequence of the differences is pretty cool.
Neo-Classical Trend Following Returns
Trend following increases profitability substantially with the notable exception of the 21 day.
Close to Open and High Low Difference
These two measures are critically important and apparently totally ignored by analysts. CO – Close to Open is the sum of natural log returns of previous Close to Open. CH – Close to High is the sum of natural log returns of previous Close to High. CL – Close to Low is the sum of natural log returns of the absolute value of previous Close to Low. HLd – High Low Difference is CH minus CL.
CH and CL measure “flapping.” That is critical for understanding volatility even if academics consider it noise. That is another fascinating subject.
The importance of CO and HLd is illustrated in the FF5 finite state matrix.
The long totals for SOXL cross foot to the numbers on the performance summary at the beginning of the article. Note that x30 is the most dangerous state during non-trend following – flat conditions; but is quite good when trend following is active.
The differences of CO and HLd between long and flat states are amazing. These numbers are not easy to isolate without this specific application framework. I suspect that they don’t appear clearly in analysis based on sequential dates.
Call me sentimental, but I thought TQQQ was worth showing even though it will be lucky to return 1000 times an initial investment before November.
Current Conditions
Trend following has not been active for any of the four lengths since the end of July. Signals are basically alternating between xCC, xFC, xFF, and xCF. xFC becomes a decision when it appears, but otherwise the other signals are long. xCC tends to pick up extra volatility when it appears in these conditions, probably mostly because it is about the wort that things get.
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