The Strategist System™ Tutorial
In this part of our Tutorial we will briefly describe the origin and evolutionary development of our Strategist™ approach to stock market modeling, and then go into more detail about various aspects of this unique System. The development of this System has been stimulated by its heavy use of three of our favorite subjects: physics, mathematics, and computer programming.
Some History
Our earliest use of EDES/Model was in attempting to predict the near-term trend of commodities prices based on up to 11 different market parameters. This effort was not very successful, but it began our interest in the stock market as a ‘mathematical’ system that might be amenable to numerical solutions. We marketed EDES/Model for several years to engineering companies, and in particular a well-known vacuum cleaner manufacturer has used EDES/Model to model (and hopefully abate) vacuum cleaner motor noise.
Today we use EDES/Model to generate all of the neural networks that we use within our Strategist System (over 50 in all).
Mutual Fund Timing Research (1999-2001)
In 1999 we began to tackle the problem of predicting the near-term performance of mutual funds. Actually, our focus wasn’t on mutual funds themselves, but rather on their ‘subaccount’ equivalents that are used within variable annuities.
During this time our search for an accurate ‘timing’ signal for mutual funds was only partially successful. It did, however, lead us to an interesting method that we continue to use (the ETF Decomposition of Mutual Funds), and which has recently found an even newer use in determining the ‘equivalent composition’ of a portfolio of stocks (see PORTCORR report).
Mechanical Trading System (MTS)(2000-2001)
In early 2000 we began to develop what is usually called a MTS or Mechanical Trading System. The basic idea was to automatically generate buy and sell signals for a series of stock portfolios (drawn from a ‘universe’ of suitable stocks), and using all available indicators and oscillators (including those of our own design) in order to produce signals with the highest possible accuracy.
By the middle of 2001 we were using the output portfolios from this complex program for actual (profitable) trading. It was about then that we came up with the idea of generating a market timing signal (MTI) by examining the current holdings of the various portfolios in a very special way. This led us to a formulation of our ‘core’ idea: the Maxwell-Boltzmann Distribution analogy. When we began to develop this preliminary idea our MTS gradually evolved into a Preprocessor, whose primary purpose was to provide the data necessary to calculate the MTI value, and all that remained of the original MTS were the 10 primary portfolios (L/1-L/10) that are currently shown in our NEWPICKS report.
*** From this point onwards our material has been extracted from our weekly TimerTrac™ Broadcasts, and although it has been reformatted and regrouped in order to make it more logical, and more readable, a total rewrite is planned for the near future. In the meantime, additional material from the weekly Broadcasts will continue to be integrated into this Tutorial. Future material will deal with Intermediate-Term Signals and Portfolios, Mutual Fund Scores and Recommendations, and Special Tactics for Different Trading Approaches, as well as further expansion on the existing topics.
Special Topics
Table of Contents:
I. The “Core” Idea: the Maxwell-Boltzmann Distribution
II. The MTI and its Derivatives
III. A Spectrum of Timing Signals
IV. The Grail System (1000 Stock/ETF Models)
V. The PORTSTAT Portfolios (Grail System)
VI. Mutual Funds
VII. The Prediction Table (Day Trading)
VIII. Differential Signals
I. The “Core” Idea: the Maxwell-Boltzmann Distribution
1.1 The “Core” Idea: Maxwell-Boltzmann Distribution, Market ‘Temperature’, and the MTI
We know little about how other companies generate their market timing signals because this kind of information is extremely proprietary, but we don’t mind divulging our own general approach … and we would be happy to share insights with other market timers. As a guess, however, considering the enormous popularity of Neural Networks, they appear to be commonly used to generate market-timing signals all by themselves. We also like neural networks, and in fact we currently employ over 50 different neural network models (most with 11 independent variables) in our timing system. These neural networks, however, are only one single component of our ‘central method’, which is based on an analogy with the Maxwell-Boltzmann Distribution of Statistical Mechanics. This results in a unique approach to the market-timing problem. A gas that is at a certain temperature will have molecules traveling at varying speeds, ranging from very slow to very fast. According to the Maxwell-Boltzmann Law, the ‘distribution’ of molecules in a collection of ‘speed brackets’ will correspond to the absolute temperature of the gas. We have utilized this same approach to produce a Market ‘Temperature’ Indicator (MTI), which is effectively also a Market ‘Timing’ Indicator. Instead of a container full of gas molecules we use a Mechanical Trading System (MTS) that develops buy and sell signals for thousands of stocks utilizing standard technical indicators (plus several new indicators of our own design). Our Preprocessor then maintains a ‘spectrum’ of Portfolios of different sizes, and with quite unusual ‘buy’ and ‘sell’ Rules. By looking at the number of holdings in each portfolio of this portfolio spectrum (and the ‘shape’ of the resulting curve) we can construct a Market ‘Temperature’ Indicator (MTI).
Having used a spectrum of stock portfolios to generate the MTI, we can now in turn use the MTI to develop customized stock models for a large number of suitable stocks. These resulting models gain in accuracy because they have access to the MTI in addition to the use of standard technical indicators. These 1000 signals, of which our QQQQ signal is the most important, are called Grail System™ signals. The average ‘Long’ period of these signals is about 12 trading days.
2.1 MTI and its Derivatives (Part 1): The Market Timing Indicator (MTI)
Our ‘thermal’ approach to the stock market yields a Market Timing Indicator (MTI) that can vary from about –1.0 (during a hard sell-off) to about 2.5 (during a powerful rally). The equivalence of this indicator to a market ‘temperature’ can be seen if we multiply our MTI by 100 and interpret the result as a Fahrenheit temperature. The MTI then ranges from about –100 deg. F (Antarctic winter) to about 250 deg. F (an undersea thermal vent). A temperature of 98.6 deg. F (an MTI value of 0.9860) is pretty close to our ‘stable point’ for QQQQ. This is the MTI value at which QQQQ will most likely stay in a tight trading range: neither gaining nor losing appreciably. At slightly lower ‘temperatures’ individual stocks may still be profitable Longs, but by the time our ‘temperature’ turns negative the likelihood of making profits drops to near zero – and our mutual fund timing indicator will finally switch to the ‘sell’ state.
2.2 MTI and its Derivatives (Part 2): Hedging (Allocation) Vectors
The concept of equity allocation is extremely important; obviously, any investment strategy will perform better if it can prevent the investor from being overly ‘long’ at the wrong times – or with excessive cash holdings when the market is strong. Our approach to this problem is based on having the accurate MTI (Market Timing/Temperature Indicator) value generated by our Preprocessor. We use the term ‘vector’ loosely, but we are talking about allocating funds between 3 different asset classes: Longs (Stocks and ETFs), Shorts, and Cash. We also use the term Hedging Vector because of the ‘short’ component. We have found that 4 different Hedging Vectors are useful:
(#2) Aggressive Hedging Vector: Longs and Shorts only (no Cash component)
(#1) Standard (Official) Hedging Vector: Longs, Shorts, and Cash
(#0) Non-Shorting Hedging Vector: Longs and Cash only
(#3) “Prudent” Hedging Vector: Longs and Cash only
All of these vectors (asset allocations) are dependent strictly on the current MTI value, and they may fluctuate (a bit more than we would like) from day to day. The general idea is to select an allocation vector appropriate for one’s individual strategy, and then try to adjust daily holdings so as to keep relatively close to the prescribed percentages. The Aggressive Hedging Vector, of course, never maintains a cash position; it is designed for portfolios that maintain Long holdings hedged by an appropriate level of ‘shorts’ (e.g., of QQQQ). The Standard (Official) Hedging Vector is a bit more conservative in that it will maintain a cash holding, and this vector is used in deriving our Market Color Code (see the previous TimerTrac Broadcast). The Non-Shorting Hedging Vector is more conservative; it assumes that a ‘safe’ amount of equity is devoted to stocks or ETFs, with the balance held in cash. Finally, the “Prudent” Hedging Vector is the most conservative of all; it is easily generated by taking the ‘smallest’ Long allocation implied by any of the other 3 vectors.
These asset allocation vectors are intended for use by investors who construct their own stock/ETF portfolios by selecting ‘a la carte’ from available equities with current ‘buy’ or ‘hold’ signals. Our ‘official’ portfolios, on the other hand, incorporate their own forms of ‘hedging’ or asset protection, and thus require no further actions from the investor – although it never hurts to be a bit overcautious when dealing with the stock market.
2.3 MTI and Derivatives (Part 3): Market Color Codes
Our Market Color Codes are modeled on the Homeland Security Advisory System, with the colors GREEN, BLUE, YELLOW, ORANGE, and RED. Our color codes are derived from our Hedging/Allocation Vectors (Long, Short, Cash), which in turn are calculated on the basis of our MTI (Market Timing/Temperature Indicator). These colors have the following meanings: GREEN (a strong buyers market), BLUE (a medium-strong market), YELLOW (a market calling for reducing equity at risk), ORANGE (a dangerous transitional state: can flip either way), and RED (a shorting market). Everyone has color codes, of course, but they are meaningless unless they tend to exhibit ‘logical’ patterns – not randomly flipping from color to color.
A meaningful market Color Code should satisfy two criteria: (1) over time the ‘majority’ colors should reflect what the market actually did (e.g., a long-term uptrend or downtrend, and (2) colors should transition from one state to the adjacent state (e.g., BLUE to GREEN) a lot more frequently than they transition from one state to a ‘distant’ state (e.g., GREEN to ORANGE, BLUE to RED, etc.). We might call this kind of analysis ‘market chromodynamics’.
Over the past 4+ years (8/16/02-present) we have had the following total color ‘counts’:
GREEN 304
BLUE 331
YELLOW 123
ORANGE 153
RED 167
Our ‘majority’ color was BLUE (a medium-strong market), closely followed by GREEN (a strong market). These “long” colors definitely outnumber our distinctly ‘short’ colors of ORANGE and RED, and all in all seem to be ‘reasonable’ based on the fact that the market has been rising for most of this period.
It is even more important, however, to look at the ‘stability’ of the Market Color Code. If we look at the number of ‘transitions’ from one color to the ‘adjacent’ color, and from one color to another by skipping a single color, and from one color to another by skipping two colors, etc., then we have:
Adjacent Color 312
Skipping 1 Color 55
Skipping 2 Colors 9
Skipping 3 Colors 2
This seems very reasonable; it is 5.6 times more likely that no color will be skipped than that one color will be skipped. It is 6.1 times more likely that one color will be skipped than that two colors will be skipped, and finally, it is 4.5 times more likely that 2 colors will be skipped than that 3 colors will be skipped. These figures confirm the ‘stability’ of the color code indicator – it doesn’t randomly flip from one color to another; rather it displays a smooth nature that hopefully offers some real insight into the current state of the market.
III. A Spectrum of Timing Signals
3.1 A Spectrum of Timing Signals
Over the years we have evolved four kinds of market signal, each with a different time horizon. Listing them from the longest to the shortest time frame we have:
Mutual Fund Timing Signal (MFTI). The mutual fund signal is based strictly on the MTI value, and it changes state rather infrequently. When the MTI goes to sufficiently negative (sub-zero) values it will switch to a ‘sell’; when the temperature ‘thaws’ sufficiently it will switch to a ‘hold’; finally, when QQQQ goes to a ‘buy’ state then the mutual fund signal will switch to a ‘buy’. Note that all mutual funds are covered by the same signal; selection of the ‘best’ funds is accomplished by periodically comparing short-term performance.
Intermediate-Term Signals. The intermediate-term stock/ETF signals are generated by performing both a fundamental and a technical analysis. These ‘traditional’ signals may stay constant for weeks or months at a time.
Short-Term Signals (Grail System). The most accurate signals are based on the MTI value, technical indicators, and on the recent prices and trading volumes of each stock. The average Long signal lasts about 11 days.
Day-Trading Signal. This signal (for QQQQ) requires a special approach. In order to predict stock market motion on a daily basis one has to turn to a generalization of Japanese Candlestick Patterns.
IV. The Grail System: 1000 Stock/ETF Models
4.1 Grail System: Part 1: The Modeling Process
In generating our timing models we start off with a universe of about 9,000 stocks and ETFs. The first step in the modeling process is to winnow down this large number into a more manageable set of equities that meet some essential criteria:
(1) stock price >= $10.00 per share (although we allow some exceptions, especially for ETFs)
(2) suitable volume to ensure reasonable liquidity (again, some exceptions are made for ETFs)
(3) a stock history that goes back at least to 8/16/02 (the beginning of our current optimization period)
(4) sufficient volatility to ensure reasonable trading profits.
(5) reasonably high correlation with QQQQ (we prefer stocks that are ‘tech-ish’ in nature, although we allow many exceptions).
After applying these criteria we end up with about 1,600 ‘selected’ equities that are then used as input to our Preprocessor, and ultimately used to generate either intermediate-term (I/T) or short-term (S/T)(Grail System) timing models. Virtually all of these ‘selected’ equities are used to build intermediate-term models, while only the ‘best’ 1,000 equities are used to generate our short-term (Grail System) models. Our Preprocessor simulates trades on these 1,600 ‘selected’ equities, and constructs the spectrum of ‘synthetic’ portfolios that are used to gauge the current ‘temperature’ of the market in a manner analogous to the way in which the temperature of a gas can be measured by examining the distribution of gas molecules in a spectrum of energy (speed) bands. A follow-on step uses this information to calculate the MTI (Market Timing/Temperature Indicator), and also a raw ‘proto-QQQQ’ signal (<QQQQ>). Since the MTI is ‘tuned’ using QQQQ as a reference, we obtain not only the MTI value but also a set of raw ‘buy’ and ‘sell’ signals for QQQQ during this step. The raw QQQQ signal (<QQQQ>) is then used to generate our 1,000 Grail System (short-term) stock/ETF timing models. To do this, the raw signal is modified by empirically determined rules, which take into account the specific price and volume history of the stock. For example, if the raw QQQQ signal tries to switch from a ‘S’ (short) to a ‘L’ (Long) state, the empirical rule may countermand this transition for a particular stock due to its recent price or volume behavior. Each of our 1,000 Grail System models incorporate several dozen such empirical rules that take into account the specific price and volume history of the equity. All such models are called ‘First Generation’ models since they are derived from the raw QQQQ signal (<QQQQ>). One of these models is the one for QQQQ itself; although it is derived from the raw QQQQ signal its accuracy increases greatly when the optimization process generates transitional rules for it as well. In part 2 we will discuss the idea of ‘Second Generation’ models.
4.2 Grail System: Part 2: More on the Modeling Process
As discussed in Part 1, our Preprocessor program has the following tasks:
(1) From an initial ‘universe’ of about 9,000 stocks determine a ‘selected’ set of equities (about 1,600) that are suitable both for the simulated trades in the Preprocessor’s spectrum of synthetic portfolios, and for the eventual generation of tradable stock/ETF timing models (1000 short-term and 1600 intermediate-term models)
(2) Determine the MTI (Market Timing/Temperature Indicator) value by simulating trades on these 1,600 equities – buying and selling for each of the 100 portfolios used by the Preprocessor, and in accordance with the specific rules for each portfolio. In addition to the standard set of technical indicators we employ some unique ones of our own design, e.g., the “Nibble” Indicator and Generalized Candlesticks. The MTI value is then deduced by looking at the current portfolio populations (and the overall ‘distribution’ of holdings) in a manner analogous to determining the absolute temperature of a gas by looking at the distribution of molecules in a spectrum of energy (speed) bands (the Maxwell-Boltzmann Distribution). Determine the raw ‘proto-QQQQ’ timing signal, hereafter denoted as <QQQQ>. This is a time sequence of ‘L’ and ‘S’ signals that represent the first ‘cut’ at a QQQQ model. It is then used to develop the official Grail System (short-term, S/T) QQQQ model, and all of the other 999 stock/ETF timing models in our Grail System.
The next step in the modeling process is the generation of our 1,000 short-term (Grail System) models. This is done by taking the proto-QQQQ (<QQQQ>) signal as a base, and modifying its L>S and S>L transitions based upon the specific price and volume history for a stock or ETF. These initial models are called ‘First Generation’ models since they are generated directly from the <QQQQ> signal emitted by the Preprocessor. Note that our official QQQQ timing model is itself a First Generation model that is produced from the raw <QQQQ> signal.
At this point the back-tested accuracies, annualized gains, and average maximum drawdowns (AMD) are calculated for all models over the past 5 years. As expected, the QQQQ model is generally one of the most accurate models – with a back-tested Long accuracy of about 97% for 35 Long trades. This high accuracy is to be anticipated because the proto-QQQQ (<QQQQ>) signal is used to generate the QQQQ model, and the MTI value itself is ‘tuned’ in such a way as to maximize the correlation with QQQQ. Nonetheless, there are always a few stocks or ETFs that have perfect (100%) back-tested trading accuracies, e.g., IWW (iShares Russell 3000 Value Index). This is the ETF that we currently use to create our ‘Second Generation’ models. At the present time two other ETFs, and one stock, also exhibit back-tested accuracies of 100% (EWQ – iShares MSCI France Index Fund, IXG – iShares S&P Global Financial Sector, and NEWP – Newport Corp). Since these are much more narrowly focused than IWW, it is clear that IWW is the optimal choice.
Unlike QQQQ (the NASDAQ 100), IWW is an ETF that is very broadly based – reflecting a much larger segment of the market. By using this highly accurate signal for IWW we can ‘improve’ the accuracies of those short-term (Grail System) models that are a little less “tech-oriented”, or that otherwise are so volatile that they benefit greatly from being ‘stabilized’ by the IWW signal. This ‘extension’ from a ‘tech’ (QQQQ) timing signal to a broader-based timing signal (IWW) compensates for the narrowness of our initial focus on calculating the MTI based on QQQQ, rather than the market as a whole. The next step in the modeling process is to try incorporating the IWW signal into each of the First Generation models (those emitted strictly on the basis of the <QQQQ> signal), to see if the back-tested accuracy, annualized gain, or average maximum drawdown can be improved. This process is successful in about 30% of cases, and these new Second Generation models (those based on <QQQQ>/IWW) then replace their less accurate First Generation counterparts. In addition to raising the performance of the bottom tier of models, this bootstrapping process also produces some new ETFs that now back-test at the 100% accuracy level:
EWG - iShares MSCI Germany Index Fund
IJH - iShares S&P MidCap 400 Index Fund
IVE - iShares S&P 500/Barra Value Index
IWV - iShares Russell 3000 Index Fund
ELG - streetTRACKS DJ Wilshire Large Cap.
At this point we have not extended this idea to
‘Third Generation’ models, but this is still under study.
4.3 Grail System: Part 3: Model Accuracy
When timing the overall market, or individual stocks, predictive accuracy can be gauged by using actual historical (published) signal data, or by using back-testing methods. With neither approach, of course, can we be certain that past performance levels will be attained in the future. Actual performance figures based on published data are always preferred, but such data is not available when a model has been changed (hopefully, improved); once a model has been modified, previously published signal data is no longer relevant. With a complex and evolving system such as ours, we necessarily rely quite heavily upon back-testing methods.
Our predictive accuracy depends on the time horizon involved. With our QQQQ day-trading signal, actual published signal data over the past 7 months establishes the fact that we can predict the daily movement of the market with an accuracy of about 67% (two out of three). What we are really talking about here is predicting whether QQQQ will close higher or lower than its Open price – once we know the Open price. We utilize our Generalized Candlestick (RaDiSH Transform) approach to generate our day-trading signal, and back testing over the past 5 years suggests an upper limit on daily accuracy of about 70% -- so our actual accuracy level of about 67% seems quite reasonable.
There are three other time horizons that we can examine by using our different modeling approaches: (1) our short-term (S/T) Grail System models (average Long period = 12 trading days), (2) our intermediate-term (I/T) Star System models (average Long period = weeks to months), and (3) our Mutual Fund Timing Indicator (MFTI) (average ‘buy’ period = several months to a year or more).
Although on a daily basis (QQQQ day-trading, for example) we can only predict the market direction with an accuracy of about 67%, our short-term Grail System models are capable of a much higher degree of accuracy. This is due to the fact that these models, which are based on our ‘thermal’ market timing approach, focus on the stronger short-term trends and ignore the more random daily fluctuations.
Although our QQQQ model is our most important model, and QQQQ is in fact the equity that we use to ‘fine tune’ our MTI value, QQQQ is not always our most accurate model. Current back-testing results over the past 52 months show that our QQQQ model is about 94% accurate for a total of 35 Long trades, that is, a score of 33 wins and 2 losses. This is, of course, extremely good, but our IWW (iShares Russell 3000 Value Index) model back-tests at a 100% accuracy for 32 Long intervals during the same 52 month period. Over the same time period the back-tested accuracies of our other 998 Grail System models range from about 75% to 100%.
As we move into 2007 (and as things look as of 12/29/06) we can say that both our QQQQ model and our IWW model remain in the ‘buy’ state. Coupled with the fact that our MTI value remains greater than 1.0, and our neural networks are still growing more optimistic, it is likely that 2007 will start off with some further market gains. Beyond this, however, there is no way that our models can tell us how long the current rally will continue. Since our QQQQ and IWW signals have been almost continuously in the ‘buy’ state since 9/11/06, and have already racked up appreciable gains, the models may very well call for a ‘sell’ in the very near future … without imperiling their amazingly high accuracies. In other words, if a model has just ‘switched’ to a ‘buy’ then we might expect that the ensuing Long period will be on the order of the ‘average’ retention period for that equity (e.g., 12.14 days for QQQQ and 14.53 days for IWW), but when our models have been in the ‘buy’ state as long as they have … then their predictive power is much diminished.
4.4 Grail System: Part 4: Model Accuracy (continued)
The subject of model accuracy is complicated by the fact that we have total control over at least 4 major model parameters; depending on how we construct our ‘penalty function’, we can try to maximize annualized gain, minimize drawdown, minimize trading frequency, and/or maximize trading accuracy. By over-weighting any one of these parameters we can achieve almost any desired target, but this of course would be accomplished at the expense of the remaining parameters. Our approach has always been to optimize our models for ‘realistic’ trading conditions, and a key part of this is our use of our Perfect Trader™ program that determines the ‘natural’ drawdown and trading frequency for a specific equity. In other words, we do not try to optimize just one of these four major model parameters; rather, we guide the drawdown and trading frequency towards their ‘theoretical’ values, and then try to strike a balance between annualized gain and trading accuracy. As a result, our back-tested trading accuracies actually have some inherent validity.
It is interesting to see how predictive accuracy gradually increases as we move through our system, starting with the Preprocessor, then moving on to the MTI calculation algorithm, and finally looking at the 1,000 Grail System models.
(58% Accuracy) Preprocessor Phase 1: Our Preprocessor (which was originally a complete Mechanical Trading System) actually consists of two phases. In the first phase we utilize all of the standard technical tricks (and a few of our own design) to generate buy and sell signals for a carefully selected set of about 1,600 equities. It turns out that the average Long trading accuracy produced during this first phase is about 58%.
(65% Accuracy) Preprocessor Phase 2: In the second phase the idea is to pick and choose among the equities in the ‘buy’ state in order to fill a spectrum of Long and Short portfolios. The populations (and distribution patterns) of these highly synthetic portfolios is eventually used to calculate our MTI (Market Timing/Temperature Indicator) value, but the first 10 of these Portfolios are actually ‘tradable’ … and are summarized in our NEWPICKS report. By following specific rules for buying and selling, the average accuracy of these 10 portfolios reaches as high as 65%.
(73% Accuracy) MTI Calculation: When the Preprocessor’s data is used to determine the MTI value we gain a further boost in accuracy. Our MTI algorithm constructs, and then tunes the MTI value in order to maximize the annualized gain for QQQQ Longs. This produces a raw QQQQ signal which we denote as <QQQQ>, and which has an accuracy of about 73%.
(86-94+% Accuracy) First Generation Grail System Models: Once the proto-QQQQ (<QQQQ>) signal is available we then begin the construction of short-term models for 1,000 stocks and ETFs. These models utilize the MTI value (and the <QQQQ> raw signal), plus the recent price and volume history for the equity, in order to produce an equity-specific timing model. When this is done the average accuracy (back-tested) of all 1,000 models turns out to be about 86%, while the accuracy of the final QQQQ model is currently 94% … and will occasionally fluctuate as high as 97% as a result of minute changes in the Preprocessor (the Butterfly Effect). A few models, however, will produce back-tested accuracies of 100% at this point, e.g., IWW. As previously discussed, all models produced directly from the raw QQQQ signal (<QQQQ>) are called First Generation models.
(100% Accuracy) Second Generation Grail System Models: Although a very few models (e.g., IWW) will actually produce a back-tested accuracy of 100% as First Generation Models, we can proceed to Second Generation models by doing a kind of ‘bootstrapping’ … taking advantage of the 100% accuracy produced by a ‘key’ model like IWW. By incorporating the <IWW> signal into the model (in addition to the <QQQQ> signal), the overall accuracy of hundreds of models can be boosted – and the accuracy of several dozen models will jump to 100%. At the present time we have 24 models (out of 1,000) that show a back-tested Long trading accuracy of 100% over the past 4.5 years.
4.5 Grail System: Part 5: The Butterfly Effect
Our Preprocessor has 1,340 empirical constants that define the technical criteria for buys and sells, and also define the explicit rules used by its spectrum of Long portfolios to acquire Long positions … and then dump them. Our Grail System of 1,000 short-term custom stock/ETF timing models requires 48 empirical constants per model … yielding a total of 48,000 empirical constants. Finally, our PORTSTAT system (50 official stock/ETF portfolios) requires 25 empirical constants per portfolio … yielding a total of 1,250 empirical constants. This gives us 50,590 constants that ‘ought to have’ optimal values assigned to them. In other Broadcasts we will discuss why we need so many constants, but in this one we will limit ourselves to discussing the ‘Butterfly Effect’ and the resulting need to continuously optimize the Grail System models (with their 48,000 constants).
The ‘Butterfly Effect’, of course, is an attempt to describe in a simple manner what it means to have a ‘chaotic system’; a butterfly flapping its wings in one part of the world can cause winds and storms in another distant part of the world. Now, many theorists contend that the market is itself a ‘chaotic system’, and hence inherently unpredictable. The very existence of our ‘thermally-based’ market timing model, of course, is a direct contradiction of this theory. Nonetheless, there is undeniably a lot of chaotic behavior in the market, and this acts like the noise or static detected by a shortwave receiver. A shortwave receiver requires sophisticated electronics in order to filter out the static and produce a clearly audible signal … and this also requires periodic fine tuning as the received signal is gradually affected by the layers of atmosphere through which it is passing.
Our Preprocessor (and its follow-on MTI calculation algorithm) has a lot in common with a short-wave receiver. It, too, is a delicate precision instrument that requires tuning – and periodic maintenance – for proper operation. All of our 1,000 Grail System stock/ETF models are heavily dependent on the MTI (Market Timing/Temperature Indicator) value produced as part of the Preprocessor Phase. Although these models are additionally dependent on technical indicators that are functions of the price and volume history for the equity, the MTI remains the most important element. The MTI, however, is a very delicate signal – and it will exhibit minor variations whenever anything changes in the Preprocessor phase. Why should things change? The answer is that the Preprocessor builds a large spectrum of synthetic Long portfolios from a selected set of about 1,700 stocks and ETFs. These portfolios (of which the first 10 are shown in the NEWPICKS report) are then historically traded (stocks are bought and sold for each portfolio in accordance with its own customized set of rules), and then the MTI value is calculated by examining both the current populations, and population distributions, of these portfolios. The ‘Butterfly Effect’ for us has its root cause in the fact that equities eventually die (companies go out of business and their associated stock symbol vanishes), or because one of our selected equities has to be replaced by another equity for various reasons (e.g., the Grail System model for the equity never attain acceptable accuracy or drawdown values, or it proves difficult to obtain the necessary ‘fundamental’ data for the equity, or the equity becomes too thinly traded to be useful, etc.).
Whenever an equity must be ‘replaced’ in the Preprocessor’s selected set, then this causes an unavoidable shift in the generated MTI value because the entire history of buys and sells (and portfolio generation) has been slightly altered. This shift is small, but it causes significant perturbations in the Grail System models that depend on the MTI value. Note that we never just ‘delete’ an equity from our selected set == we ‘replace’ it. Since our MTI value is also sensitive to the ‘total number’ of Long holdings in the Preprocessor, we don’t want to cause further variations by increasing or decreasing the size of our ‘selected set’ of equities.
4.6 Grail System: Part 6: Modeling and Penalty Functions
The generation of timing models for specific stocks and ETFs is a very difficult and cpu-intensive process. We start with the MTI (Market Timing/Temperature Indicator) value produced in our Preprocessor stage, and then go on from there with technical methods (using High/Low/Open/Close prices plus Volume) in order to produce the ‘best’ model for a given equity. This currently involves 48 numeric parameters for each equity, and since we maintain 1000 specific models (our ‘Grail System’ models), this gives us 48,000 numbers to optimize.
Optimization of a model requires definition of a “Penalty Function”. The one we use requires maximizing the annualized percentage gain for Longs (and secondarily the annualized percentage gain for Shorts), while minimizing the Average Maximum Drawdowns (for Longs AND Shorts), while at the same time achieving a ‘reasonable’ trading frequency (Long retention period). This, of course, presents a problem if one tries to lower drawdowns ‘too much’, or to force the trading frequency too high, or too low. The best course of action is to determine the ‘intrinsic’ drawdown and average trading frequency for a given equity, and then try to steer towards these ‘natural’ values.
We believe that the stock market as a whole, and stocks in particular, have an ‘intrinsic’ drawdown and trading frequency that are largely invariant with respect to time. If this is the case, then optimal timing models for a stock MUST reflect these natural values. In order to determine such values, we developed a program that we call the Perfect Trader™ (aka the “God” Program). This program looks at 5+ years of price history for a given stock, and then determines the optimal trading points (buys and sells) that would have produced the greatest annualized gain over this time span – and using a complete knowledge of the entire past and future price history of the stock in order to do this. Of course, the “perfect” program would have a zero drawdown since it could trade every day with perfect knowledge of the stock’s daily direction. So, we introduce the rule that any trade must be held for at least 3-4 market days. When this rule is imposed, the program rapidly converges to a ‘solution’ for these intrinsic values: annualized percentage gain, average maximum drawdown, and average Long retention period (i.e., trading frequency). We then use this information to generate our 1,000 models; the Penalty Function is optimized in such a way that the annualized gain is maximized, while the average maximum drawdown and Long retention period values are forced to converge to their ‘intrinsic’ values. We believe that this process produces a ‘natural’ model, which reflects the unique characteristics (rhythm) of the equity.
V. The PORTSTAT Portfolios (Grail System)
5.1 Grail System: PORTSTAT Portfolios Part 1: 5 Classes of Portfolios
The MTI (Market Timing Indicator) produced by our ‘thermal’ approach, and the resulting QQQQ timing signal form the basis for our Grail System of 1000 stock and ETF models. These customized models function at a swing-trading frequency, with Long periods averaging about 12 market days, and are ideal for the construction of portfolios. Over the years we have evolved our short-term portfolio system so as to offer 5 different ‘classes’ of portfolios, with each class representing a family of portfolios that vary in the maximum number of positions that they will allow. All of these portfolios can be seen in our daily PORTSTAT report.
The 5 classes form a ‘spectrum’ of portfolios that, starting from the ‘U’ ultra-conservative ETF-only portfolios gradually increase in (back-tested) annualized gains, while at the same time increasing in maximum drawdown and trading frequency. It is always recommended that new investors start with the more conservative portfolios, especially during weaker market periods, and only move up to the more aggressive portfolio classes as they gain experience with our signals and our methods.
The “U” (ultra-conservative ETF-only) portfolios consist exclusively of the larger (more liquid) ETFs, and they range in size from 6 ETFs up to 15 ETFs. The corresponding portfolio ‘names’ are P6U, P8U, P10U, P12U, and P15U. These portfolios are designed so that they progressively drop (and do not replace) positions as ‘sell’ signals are generated during a weakening market. These portfolios offer respectable annualized gains, while at the same time offering the lowest possible drawdowns and trading frequencies.
The “E” (ETF-only) portfolios are similar to the “U” class portfolios but include more of the smaller ETFs. Also, these 13 portfolios, ranging in size from 1 (P1E) to 15 (P15E) ETFs, are slightly more aggressive – staying more active in the market at lower MTI levels. Still, these should be very ‘safe’ portfolios.
The “C” (Conservative) stock portfolios do not include ETFs, and they hold from 4 (P4C) to 25 (P25C) stocks. These 8 portfolios produce higher annualized gains than are possible with ETFs, but have a higher potential drawdown and trading frequency as a result. These 8 portfolios, however, are the safest stock portfolios that we know how to construct. Like the ETF-only portfolios, these stock portfolios protect their assets by reducing their holdings when the market is weak (low MTI level).
The “N” (Normal) stock portfolios hold a maximum of 1 (P1N) to 20 (P20N) stocks, and these 12 portfolios offer probably the best balance between annualized gain, maximum drawdown, and trading frequency. Like the “C” portfolios they deal exclusively with stocks, and they protect themselves by gradually trimming their Long positions as the market weakens. Their maximum drawdowns and trading frequencies are higher, but then so too are their potential annualized gains. Nonetheless, the volatility of these portfolios may be greater than some investors can deal with.
Finally, the “H” (Hedging) stock portfolios form the most aggressive class in the PORTSTAT report. These 12 portfolios vary in size from 1 stock (P1H) to 20 stocks (P20H), and they actually carry out a ‘hedging’ strategy that uses an increasing degree of QQQQ ‘shorting’ to stabilize the portfolios during market downturns. These portfolios potentially offer very high annualized gains, but their drawdowns and trading frequencies are generally too high for most traders to contend with.
5.2 Grail System: PORTSTAT Portfolios Part 2: Optimization
The Strategist™ System is very much an assemblage of empirical rules and empirical constants, although based upon a simple but powerful analogy with the thermodynamic relationship between the temperature of a gas and the associated distributions of gas molecules within a spectrum of speed bands (the Maxwell-Boltzmann Distribution). No one ever said that predicting the market would be easy, and of course, prevailing ‘wisdom’ is that it is quite impossible (i.e., the market is likened to a random walk), and thus we are not surprised at the unavoidable fact that continuous ‘tuning’ is essential. We have used the ‘short wave receiver’ analogy before: like tuning a receiver to pick up a weak signal obscured by static, detecting signals heralding market direction also requires careful tuning to eliminate the ‘static’ (chaotic variations) that is in fact characteristic of the stock market. So, every day we tune, tune, tune…
As mentioned previously, our Preprocessor requires 1,340 empirical constants, our Grail System (short-term timing models) requires 48,000 constants, and our portfolio system (PORTSTAT) requires 1,250. In this article we will discuss the portfolio system: why there are so many constants, and why they require tuning.
We have 50 official portfolios that are divided into 5 major classes, each one of which is denoted by a letter: H, N, C, E, U. The portfolios within a class come in different sizes (the maximum number of allowable positions), and so examples of the portfolio naming system are: P4H, P6N, P6C, P4E, P8U (the numeric value represents the maximum number of holdings). Each portfolio is defined by 25 empirical constants, the most obvious of which are those defining the maximum number of permitted holdings, and the parent ‘class’ to which the portfolio will belong (e.g., ETFs only). These constants require incessant tuning because our Grail System models are continuously tuned, and our Grail System signals are continuously tuned because our Preprocessor (our ‘shortwave receiver’) is highly sensitive to changes in the ensemble of stocks and ETFs that it analyzes. The most common cause for variation in the Preprocessor is a company that has gone out of business, or whose stock is no longer traded. This requires substituting an alternate stock to replace it, and this ripples through the entire period of time that the Preprocessor is analyzing, causing changes in its spectrum of portfolios, and resulting in small changes to the MTI (Market Timing Indicator) calculation. And small changes in the MTI cause larger changes downstream (the ‘Butterfly Effect’).
From our Grail System™ we ‘know’ a lot of important attributes about 1,000 different stocks and ETFs: (1) the ‘expected’ average Long retention period and trading frequency, (2) the ‘expected’ annualized gain, (3) the ‘expected’ average drawdown per Long period, and (4) the ‘expected’ accuracy of each Long or Short trade. Remember that these ‘expected’ values tend to reflect the natural (inherent) characteristics of the equity because of our use of our Perfect Trader™ program. The portfolio system (PORTSTAT) utilizes the latest available parameters for each stock or ETF in order to determine what to buy or sell, and when to buy or sell it, based upon its private set of empirical constants.
The “H” (Hedging) portfolios are a bit of a different case because they are the only portfolio Class that will hold short positions (of QQQQ); all other portfolio classes protect their assets by simply dropping holdings, and leaving those empty ‘slots’ in cash. Nonetheless, the portfolio constants are tuned in two different directions: (1) tuned so that portfolio drawdowns and trading frequencies tend to decrease as one progresses from the H Class portfolios, through the N, C, and E Class portfolios, and ending up with the U Class portfolios, and (2) tuned so that portfolio drawdowns decrease as one moves to larger portfolios (holding more positions). So, part of the tuning process involves ‘shaping’ the portfolios so that they behave as one would expect: less drawdown for larger portfolios (but also lowered annualized gain), and less drawdown and lowered trading frequencies as one moves from the aggressive end of the spectrum (the H portfolios) to the ultra-conservative end (the U portfolios).
Each individual portfolio thus has a Class (H,N,C,E,U), a sizing constant (the maximum number of positions), a large number of constants that determine which Grail System stocks (or ETFs) are appropriate for that portfolio, and specific rules for when to buy or sell them – and all of these constants must result in the proper portfolio ‘shape’ discussed above.
The larger (or more conservative) portfolios tend to focus more on stocks or ETFs that are very liquid (high daily volume), based on the premise that such portfolios will be used for large investments. The more conservative portfolios tend to use stocks with longer retention periods so that the trading frequency is minimized; the larger portfolios do much the same thing in order to reduce what would otherwise be an unacceptable churning rate. The smaller portfolios tend to focus on stocks with higher annualized gains (within acceptable drawdown ranges), while the larger or more conservative portfolios put more stress on trading accuracy.
It should always be remembered that the annualized gains, drawdowns, and other portfolio statistics are based on ‘back-testing’ … and thus may not be representative of ‘future’ performance. It is always recommended that investors start with the “U” or “E” (ETF-only) portfolios, and only slowly move up the chain to the higher performance (but more volatile) stock portfolios as they gather experience with this system … and exercise extra care when they contemplate using the H portfolios at the aggressive end of the spectrum.
VI. Mutual Funds
6.1 Mutual Funds (Part 1): ETF Decompositions
We have always been active in tackling the standard problem of mutual funds: how to know which fund to buy for the best ‘future’ performance. The issue, of course, is that we never know the exact ‘current’ holdings of a given fund. We may know the top 10, or top 25, holdings once or twice per year, and we generally know something about the overall emphasis of the fund (utilities, international, technology, real estate, financial, mid-cap value, hybrid, growth and income, etc.), but without knowing the exact current holdings it is impossible to predict the near-term future performance of a fund. All that one can normally do is to look at the very recent price history, and at the current state of an overall Mutual Fund Timing Indicator (MFTI). We have a good MFTI, and we have utilized price histories to help rank funds for rebalancing purposes, but the question is: is it possible to do better? We believe that one further step can be taken, and this is based on the mathematical idea of decomposing a given entity into a linear weighted sum of ‘basis’ entities. In this case, we find a weighted sum of 5 ETFs that will duplicate the recent price history of a mutual fund, and we then attempt to ‘score’ the overall mutual fund by using the current buy/sell/hold signals for these equivalent ETFs.
By using a set of 150 different ETFs it is possible to use Linear Regressions on weighted sums of 5 different ETFs that will result in very close approximations to the recent price history of a mutual fund. In this process, Monte-Carlo methods are used to try to find an optimal decomposition out of the hundreds of billions of possibilities. It turns out that this method works rather well. The resulting decompositions generally have a high R**2 (correlation coefficient) value, a very low RMS percentage error in the predicted price, and (most importantly) seem to find the components (sectors) that the mutual fund is supposed to have. For example, in decomposing a mutual fund for energy stocks, we find component ETFs that are energy-oriented:
FUND: ENPIX ProFunds Ultra Energy Inv. 0.9996 0.0964 10.00
ETF: IYE 48.50% iShares DJ US Energy Sector
ETF: XLE 40.53% Energy Select Sector SPDR
ETF: EWO 4.48% iShares MSCI Austria
ETF: IXC 4.35% iShares S&P Global Energy Sector
ETF: GG 2.14% GoldCorp
This mutual fund (ENPIX) has a correlation coefficient of 0.9996, an RMS percentage price error of 0.0964%, and a ‘score’ of 10. The score of 10.0 means that all 5 component ETFs are in the ‘buy’ state (scored at 2.0 each, according to their weighting factors). Now, we don’t have the foggiest idea why Austrian stocks, or Gold stocks, should be components (although they are rather small components), and this is probably mathematical ‘noise’, but this decomposition does ‘confirm’ that at least 93% of the mutual fund is indeed invested in energy stocks. A complete set of recent mutual fund decompositions can be seen at http://www.schulenberg.com/download/MUTCOMPS.TXT
VII. The Prediction Table (Day Trading)
7.1 Prediction Table (Part 1): Generalized Candlesticks: The RaDiSH Transform
Candlestick patterns are fascinating, but rather useless in their normal form. They can be removed, however, from the realm of art and mysticism by transforming them numerically to a set of dimensionless, time-invariant numbers. This can be done with the trading volume as well, and this so-called RaDiSH Transform produces a set of 5 pure numbers that fully describe the latest candlestick pattern and volume. This set of numerical data can then be modeled by a neural network to produce an estimate of the ‘average’ price for a given stock on the following day (the average price, H, is the High plus the Low divided by 2). By having an estimate of the ‘average’ price that the stock will hit on the next day, and by looking at the Open price that morning, one can with some assurance predict whether the stock will gain or dip during the day. A fascinating discovery is that a neural network model generated for the R,D,S,H,V parameters of one stock will work very well to predict the near-term behavior of hundreds of unrelated stocks. Note that this method effectively ‘finds’ all productive candlestick patterns – without knowing what they are
***The problem of predicting the direction of the stock market on a day-to-day basis is an extraordinarily difficult one. Obviously, there are absolute limits on the theoretical accuracy of such predictions because there is no way to anticipate news events that occur after the Open. It is clear that an approach to this problem must depend exclusively on technical indicators, since fundamental data can have little bearing on such short-term events. Ultimately, all such technical indicators must rely on the four daily prices for a given stock (Open, High, Low, Close), plus the trading volume, and this suggests the use of “generalized” candlestick methods.
Generalized candlesticks utilize dimensionless, time-invariant transforms of these 5 daily numbers, and incorporate them into a neural network model which attempts to predict the “average” price (H) of the stock/ETF for the next day. The average price is the sum of the High and the Low values, divided by 2. In predicting the day’s outcome for QQQQ, for example, it is necessary to use the actual “open” price for QQQQ on a given morning. Then, by comparison with the H value (the estimated ‘average’ price) it is possible to predict with some accuracy whether QQQQ will rise or fall during the day. Based on an ongoing analysis (currently using the last 71 trading days), it appears that it is possible to predict QQQQ’s daily direction with an accuracy of about 67%. This says quite a lot about the ultra short-term predictability of the market; knowing the Open price of QQQQ (and its recent price/volume history) we might be right two times out of three in predicting how QQQQ will end up 7.5 hours later. Of course, the QQQQ prediction accuracy can be driven up much higher if one refrains from making ‘calls’ on those days when the probabilities for gains are very small. In back testing, predictive accuracies of 80-100% are possible by restricting predictions to just the strongest days. However, this is a losing proposition because the number of trades is then too small to make maximal profits. No, it is better to trade more often, even if the predictive accuracy is lower.
***In trying to achieve the impossible – predicting the market on a day-to-day basis – we have shown that the “generalized candlestick” approach (the RaDiSH Transform) provides the best possible results. Even then, based on many prior days of price (Open,Close,High,Low) and volume data, and knowing the Open price of QQQQ in addition, the odds are only about 2 out of 3 (67%) that we can predict the final outcome for QQQQ on any given day. Still, these are pretty good odds, and the accuracy can be driven far higher if the direction is predicted ONLY for those days on which there is a stronger signal. Given that the accuracy of QQQQ day-trading signals is only about 67%, despite the fact that QQQQ is our most accurate signal, there is little point in trying to predict the daily direction of any other stock or ETF.
Whereas the RaDiSH Transform (generalized candlesticks) approach is suited for ultra-short-term predictions, more accurate timing models for stocks and ETFs can be constructed by utilizing the MTI (Market Timing Indicator). These ‘thermally-based’ models generally have a Long period of about 12 trading days (averaged over 1000 different models), and provide excellent accuracies with minimal drawdowns. In back-testing over the past 4 years, the average trading accuracy for such models is about 81% for a total of 30-40 Long periods. QQQQ, of course, is just about the most accurate model with its Long accuracy of 94-97%, while the IWM model (surprisingly) is currently maintaining a 100% trading accuracy.
The construction of models based on an MTI value depends on optimizing a Penalty Function that involves many variables: annualized gain, average maximum drawdown, Long trading frequency, etc. It turns out that the best way to accomplish this is to utilize parameters generated by the Perfect Trader™ program. This program determines the intrinsic drawdown, annualized gain, and trading frequency that are based on ‘perfect’ trades (trades with complete knowledge of the price history of a stock over the entire range), but with the restriction that trades must be held for at least 4 days. The optimization process can then attempt to approximate these intrinsic characteristics while it is optimizing the Penalty Function utilizing the MTI values, plus the price and volume history for the stock. This procedure results in a ‘natural’ model, which best reflects the actual dynamics of the equity.
7.2 Prediction Table (Part 2): Market Open Signature (MOS)
We define a Market Open Signature (MOS) as a triplet of plus or minus signs, depending upon whether QQQQ, SMH, and SPY have opened ‘higher’ (+) or ‘lower’ (-) than the previous day’s Close. Thus, for example, a MOS of (++-) would mean that QQQQ and SMH had opened higher, but that SPY had opened lower than the previous day’s Close. The MOS thus defines 8 different market ‘starting’ conditions. Similarly, we can define a Market Close Signature (MCS) by using a triplet of signs to show whether or not these 3 ETFs Closed higher or lower than the previous day’s Close. The MCS then describes 8 different market ‘ending’ conditions. There are thus 64 possible ‘paths’ that the market may follow during the day: from 8 different starting conditions (MOS), to end in one of 8 different ending conditions (MCS).
Our daily Prediction Table (the PREDTABL Report) contains an analysis of these MOS to MCS transitions over the past 5 years, and these are broken down by the MTI (Market Timing/Temperature Indicator) Range that the market was in when the MOS pattern appeared. In other words, with 5 years of data available for analysis, the data is grouped into MTI ranges, e.g., 1.0-1.2, 1.2-1.4, etc. Table I of the Prediction Table then allows us to look at the ‘profit probabilities’ for the day based on the current value of the MTI, and on the MOS (Market Open Signature) that existed at the market Open. For each ETF (QQQQ/SMH/SPY) we have two historical probabilities: (1) the probability that the ETF will Close higher than its Open, and (2) the probability that the ETF will Close higher than the previous day’s Close. The first probability, of course, defines the likelihood for successful ‘day trades’, while the second probability gives us an idea of whether the market is likely to gain, hold, or fall during the day.
This kind of analysis is useful in developing an optimal strategy for each trading day. It is extremely accurate in that it is derived exclusively from historical price data (Open and Close prices for each of the 3 ETFs), and otherwise its accuracy is dependent ONLY on whether or not our MTI (Market Timing/Temperature Indicator) value is accurate or not.
VIII, Differential Signals
8.1 Differential Signals (the diffhist Report): Stock Index Futures
We currently calculate 3 Differential Signals, that is, signals that try to show the relative strength of one market index compared to another (although we do this with ETFs rather than with the indices themselves). Our $NQ-RU signal compares the Nasdaq 100 (QQQQ) against the Russell 2000 (IWM), $NQ-SP compares QQQQ against the S&P 500 (SPY), and the $NQ-DW signal compares QQQQ against the Dow (DIA). The objective is to try to identify as often as possible those opportunities in which one ETF can profitably be held Long while a second ETF is shorted. Clearly, such ‘hedged’ trades hold out the promise of negligible losses in the event that both ETFs rise or fall simultaneously – or significant gains if one guesses the direction correctly.
The DIFFHIST report (http://www.schulenberg.com/download/diffhist.htm) shows the back-tested Differential Signals ($NQ-RU, $NQ-SP, $NQ-DW) as signed pairs, e.g., +/-, -/+, +/+, and -/-. About two-thirds of the time we are able to generate ‘hedged’ pairs (+/- and -/), while the remaining signals are unhedged. Obviously, there will be many times when the entire market is going to move strongly up or down … and in those cases we do not want to be ‘hedged’, but rather fully Long or fully Short. The trick, however, is to find as many ‘hedged’ opportunities as possible in order to minimize risk (drawdown).
Whenever a ‘hedgeable’ situation cannot be found, we revert to using our standard Grail System signals for the ETF pair (QQQQ vs. IWM, SPY, DIA). For comparison purposes the rightmost 3 columns in the DIFFHIST report show the ‘straight’ Grail System signals for each ETF pair. Use of these signals results in higher gains -- but also higher drawdowns – than use of the Differential Signals.
To calculate a Differential Signal we proceed as follows (in the case of QQQQ vs. IWM, for example):
(1) Develop a price timeline for a ‘synthetic’ equity to be known as $NQ-RU by dividing the Close price of QQQQ by the Close price of IWM,
(2) Normalize the price by applying a multiplier so that it scales to a reasonable stock price,
(3) Calculate a suitable Volume by taking the Geometric Mean of the QQQQ and IWM volumes (square root of the product of the volumes),
(4) Calculate an effective ‘timing’ value by dividing the relative timing value of QQQQ by the relative timing value of IWM,
(5) Use the Grail System™ to generate an optimized model for this new ‘synthetic’ equity, and
(6) Apply a filter with high and low cutoffs to identify the strong +/- cases (QQQQ Long and IWM Short) and -/+ cases (QQQQ Short and IWM Long), with the remaining cases resolved by resorting to the Grail System signals (resulting in a lot of unhedged situations).
We then set up a ‘simulator’, which calculates the resulting annualized gains, drawdowns, and trading frequencies so that the filter cutoff values can be set optimally for best performance (maximizing annualized gains and minimizing drawdowns).
A comparison of simulation results (for 4.5 years) for $NQ-SP (QQQQ vs. SPY) with the Grail System signals for the QQQQ/SPY pair shows:
Differ. Signal: $NQ-SP: Annualized Gain = 50.08%; Maximum Drawdown = -4.03%; Trading Accuracy = 78.23%
Grail Signal: QQQQ/SPY: Annualized Gain = 67.65%; Maximum Drawdown = -6.52%; Trading Accuracy = 84.40%
The mostly ‘hedged’ Differential Signal $NQ-SP thus offers the advantage of a considerably lower drawdown than that resulting from use of the Grail System signals alone. Although the annualized gain is quite a bit lower, the ability to greatly reduce drawdown becomes extremely important if stock index futures are being traded rather than ETFs.
(2/16/07)
Go to Part 1 of the Tutorial