probability


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Back in the days of printed newspapers, magazines, and newsletters the acquisition of news and information was easier, or so it seemed.  The reason it seemed easier is that there was much less of it.  Today, with the internet, 24-hour financial media, blogs, and every conceivable method of acquisition, information is overwhelming.  Once I realized that some information was actionable and most of the rest was categorized as observable, then things became greatly simplified.  Hopefully this article will shed some light on how to separate actionable information from the much larger observable information.  As you can see from the Webster definitions below they initially do not seem that different.

Actionable – able to be used as a basis or reason for doing something or capable of being acted on.

Observable – possible to see or notice or deserving of attention; noteworthy.

However, when real money gets involved the difference can be significant.  Let me give you my definition and then follow up with some scenarios.  The world is full of observable information being dispensed as if it is actionable.  All the experts, television pundits, talking heads, economists (especially them), most newsletter writers, most blog authors, in fact most of the stuff you hear in regard to the markets is rarely actionable.  Actionable means that you, upon seeing it, can make a decision to buy, sell, or do nothing – period.

I’ll start by mentioning Japanese candle patterns, a subject I beat to death in this blog over the past few months.  I have never stated anything other than the fact that Japanese candle patterns should never be used in isolation; you should always use them in concert with other technical tools.  Hence, Japanese candle patterns for me are observable information; not actionable.  Only when backed up by Western technical tools can they become actionable.  I demonstrated with in my article Candlestick Analysis – Putting It All Together.

Too often I hear the financial media discussing economic indicators and how they affect the stock market.  Initially it seems they forget the stock market is one of the components of the index of LEADING indicators; in other words, the stock market is better at predicting the economy.  First of all, economics can never be proved right or wrong since it is an art, just like technical analysis.  Economic data is primarily monthly, often quarterly, and occasionally weekly.  It gets rebased periodically and often gets adjusted for seasonal affects and everything else you can think of.  It just cannot reliably provide any valuable information to a trader or investor.  However, boy does it sound really good when someone creates a great story around it and how at one time in the past it occurred at a market top; it is truly difficult to ignore.  Ignore you should!  The beauty of the data generated by the stock market, mainly price, is that it is an instantaneous view of supply and demand.  I have said this a lot on these pages, but it needs to be fully understood.  The action of buyers and sellers making decisions and taking action is determined by price, and price alone.  The analysis of price at least is a first step to obtaining actionable information.  Using technical tools that help you reduce price into information that you can rely upon is where the actionable part surfaces.

I also seriously doubt anyone relies totally upon one technical tool or indicator.  If they do, then probably not for long.  I managed a lot of money using a weight of the evidence approach which means I used a bunch of indicators from price, breadth, and relative strength (called it PBR – see graphic).  Each individual indicator could be classified as observable, but when used in concert with others, THEY became actionable.

I think the point of this entire article is to alert or remind you that there is a giant amount of information out there and that most of it is not actionable; it is only observable.  Sometimes it is difficult to tell the difference so just think about putting real money into a trade based upon what you hear or read.  Real money separates a lot of people from making decisions based upon observable information, no matter how convincing it is.

I am really looking forward to speaking at ChartCon 2016.  The schedule shows me on at 10:30am PT where I’ll talk about the marketing of Wall Street disguised as research and show a couple of things about Technical Analysis that annoy me.

Dance with the Actionable Information,

Greg Morris

 

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Stats in law has been one of my bug-bears for quite some time. Lawyers, being very language based [as a rule] don’t seem to have any mathematical skills. My own law class, struggle to work out a basic % calculation.

Statistical significance, particularly when looking at ‘causation’ in law, has been a killing field for accurate legal argument.

As the American Statistical Association said,

Researchers often wish to turn a p-value into a statement about the truth of a null hypothesis, or about the probability that random chance produced the observed data. The p-value is neither. It is a statement about data in relation to a specified hypothetical explanation, and is not a statement about the explanation itself. …

Smaller p-values do not necessarily imply the presence of larger or more important effects, and larger p-values do not imply a lack of importance or even lack of effect. Any effect, no matter how tiny, can produce a small p-value if the sample size or measurement precision is high enough, and large effects may produce unimpressive p-values if the sample size is small or measurements are imprecise.

However;

The Court in the In re Chantix litigation got it exactly right:

While the defendant repeatedly harps on the importance of statistically significant data, the United States Supreme Court recently stated that “[a] lack of statistically significant data does not mean that medical experts have no reliable basis for inferring a causal link between a drug and adverse events …. medical experts rely on other evidence to establish an inference of causation.” Matrixx Initiatives, Inc. v. Siracusano,––– U.S. ––––, 131 S.Ct. 1309, 1319, 179 L.Ed.2d 398 (2011). The Court further recognised that courts “frequently permit expert testimony on causation based on evidence other than statistical significance.” Id.; citing Wells v. Ortho Pharmaceutical Corp., 788 F.2d 741, 744–745 (11th Cir.1986). Hence, the court does not find the defendant’s argument that Dr. Furberg “cannot establish a valid statistical association between Chantix and serious neuropsychiatric events” to be a persuasive reason to exclude his opinion, even if the court found the same to be true.

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IN THE SEARCH FOR THE NEW and different indexes that will power a new and different ETF, back-testing plays a critical role. Index providers, including S&P, Dow Jones, MSCI, Russell, Zacks and others can index just about anything. You want to rank the companies in the S&P 500 by earnings growth, then take the 50 top firms and weight them equally? Weight them by market capitalization? Go long the top 50 and short the bottom 50? They can build it. And then they back-test it. Indexes that look good in hindsight have a shot to become ETFs. Those that don’t, don’t.

Given our quantitative roots, we are sympathetic to the fact that backtests are often used as an input into making investment decisions. But past returns, as we all know, do not predict the future. And we think backtested results may be particularly problematic today. Very little fundamental data for US equities extends back more than 30 years, but the last 30 years were a period generally accompanied by two related phenomena: increasingly easy monetary policy and falling interest rates. In particular, the wave of liquidity and stimulus provided in the wake of the Tech Bubble coincided with unprecedented levels of credit expansion, rising asset correlations and record earnings volatility.

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I’ve been in Court for the last few days sitting on a jury. Yesterday, Counsel for the defense initiated their open, and called an expert witness: he was an image analyst. His CV, which he read out in Court was very impressive, and I was looking forward to an interesting and technical discussion: to this point the Crown and Police evidence had been a shambles of inepeptitude.

Essentially we were told the following: [i] there are 3 tests performed in an image analysis [ii] the methodology is specific in each test [iii] a conclusion is reached that rates from 1-6: 1 = no correlation, 6 = high correlation

The images were of an aggravated robbery of a petrol station by two armed robbers, and the analysis was designed to ascertain whether the defendent was in point of fact one of the robbers pictured.

Test 1 is the measurement of anatomical landmarks of the face: it is a quantitative test. Test 2 is an analyst’s visual subjective analysis of facial features. Test 3 is manipulation of the images: the images taken from the robbery, plus control images taken from the defendent. The two images are mixed and matched via technology and computers.

Due to hats and bandana’s worn by the robbers, only partial facial features were visible, thus, Test 1 and Test 3 could not be performed. This left only Test 2 the subjective assessment.

The Crown Prosecutor had a chance to cross examine after the presentation of the defense evidence. Did the Crown ever drop the ball. The problem was that the Crown had no idea of statistical investigation and probabilities.

The defense evidence resulted in a conclusion of 1 on the 1-6 scale, based on the following 4 significant differences. [i] the sideburns were different [ii] the robber had some undefined mark/depression on his right cheek [iii] the bridge of the nose appeared farther forward [iv] differences in the shape of various points of the ear.

This analysis could have been attacked immediately on the following basis: what is your confidence level in your conclusion? Now anyone who is vaguely versed in statistics knows that this is a basic, basic question.

The confidence level is calculated from your margin of error, or Z-score, your population or sample size, the distribution, which will provide you with your confidence level expressed as a +/-

The ideal outcome being a high confidence level at least 95%+ and a small margin of error, which you generate from your sample size and selected Z-score.

When you want to estimate a probability, a quick and dirty formula for the required sample size you need to get within the margin of error you need is n = 1/[MOE]*

The problem that the Crown sensed, but couldn’t quite get to, was the sample size of 1. Obviously a sample size this small is going to, particularly in light of the utter subjectiveness of the only Test applied, is going to provide a very low confidence level, and thus a very low probability of the conclusions drawn being statistically significant, and thus the testimony of the expert being taken with a large pinch-of-salt. Certainly his conclusion of 1 on his scale I feel was untenable.

Nonetheless, an interesting couple of days to observe the State in action. If I was concerned before, I have to say that now I am absolutely terrified. The level of ignorance, incompetence and total arrogance has to be witnessed first hand to appreciate just how bad things really are.

Wood has crunched the numbers on the distribution of closing prices. Guess what? They’re not a Gaussian distribution…what a shocker!

Read Mandelbrot for the research and mathematics into “Power laws” that can explain the distributions that occur on a fairly regular basis on Wall St.

Woodshedder has a statistics post, which I’m going to reproduce here as it concerns a lot of the work postulated by Dr Steenbarger and others relating to the current market action.

I want to introduce to all of you a statistical measure which has come to have a significant influence on the trading systems I am developing. Ralph Vince describes the measure very well in his book Portfolio Management Formulas. This measure is called the Z-Score, or the Runs Test.

I want to skip most of the statistical jargon and get right to the meat of the issue, but I will be happy to answer specifics in the comment section.

To understand why the Z Score or Runs Test is important, we need to digest Rob Hanna’s statement from his recent post How to Trade the Choppiest Environment in 50 Years. Rob writes, “As you can see, buying after strong days and selling after weak ones worked well for 40 years. In 2000 that changed, and the last year and a half is the worst it has ever been with regards to follow through. This would suggest that strategies that may have worked well for forty years or more could be suffering greatly now.”

Also, it is important to read Dr. Brett Steenbarger’s recent post Short-Term Reversal Patterns Among Global Equity Indexes.

Both authors conclude that short-term trend following is not working very well. We can test their conclusion by applying the Z-Score to the data from the indices. I should mention that both Bhh from IBDIndex and Damian from Skill Analytics have been instrumental in helping me flesh out the rest of the ideas presented below.

The Z-Score can determine whether wins or losses are dependent on previous wins or losses. Think of dependency in this way: Do wins begat more wins? Do losses begat losses? If so, this relationship would be described as a positive dependency. What if wins begat losers, and losers begat wins? This would be a negative dependency.

While Z-Score has traditionally been used to analyze the win and loss streaks of a trading systems, it seems that another application for the measure may be to analyze the win and loss streaks of the indices in order to determine whether there is any dependency. Are the sequences of wins and losses containing more or less streaks (of wins and losses) than would be expected in a truly random sequence? When digesting this, consider the fair coin, where one flip is equally as likely to be heads as it is tails. We want to determine if the indexes are trading as a fair coin, or one that is biased to heads or tails, or both.

Below are the Z-Scores for the S&P 500 (SPX), using all data available from yahoo, which goes back to 1950. In January of 1993, the S&P 500 SPDRs was introduced. I will quit using SPX data and use SPY data from 1993 forward.

All Data, 1950 to Present: Z-Score -9.359014

This negative Z-Score implies a positive dependency at a confidence level of much higher than 99.73%. In short, a positive close on the S&P 500 generally begat more positive closes, and losing days generally begat more losing days, over this broad time span.

1960 to Present: -7.196132

1970 to Present: -3.795268

Note that the positive dependency is decreasing, yet from 1970-Present, the confidence level is still above 99.73%.

1980 to Present: Z-Score .3465443

1990 to Present: Z-Score 1.692151

1993 to Present (With SPY Data): Z-Score 2.115444

Note that there has been a switch. The positive Z-Score implies a negative dependency, where buying begats selling, and selling begats buying. Be careful though with this data, as the score must be above 1.64 to have a confidence level of greater than 90%.

2000 to Present: Z-Score 1.3608623

2003 to Present: Z-Score 1.1696094

2006 to Present: Z-Score .4530397

2007 to Present: Z-Score 1.3030246

October 2007 to Present: Z-Score .3994188

Note that from 2000 on, the Z-Scores move lower. The highest score from this period, 1.303, gives a little better than an 80% confidence level. I interpret this data to mean that the S&P 500 is basically moving through a random walk, although the confidence level is not high enough to draw any firm conclusions.

January 2008 to Present: Z-Score -0.628093

February 2008 to Present: Z-Score -0.400456

March 2008 to Present: Z-Score -0.246511

April 2008 to Present: Z-Score -0.403907

May 2008 to Present: Z-Score -0.288564

June 2008 to Present: Z-Score 0.0022265

July 2008 to Present: Z-Score -0.09631

From January 2008 to the present, we begin to once again see negative Z-Scores. A negative score implies a positive dependency, where selling begats selling and buying begats buying. The scores are not significant enough to exhibit a high level of confidence.

Conclusions
The recent data show no definitive dependency, either positive or negative. This means that buying because the market has closed up or selling because it has gone down has not been working as well as in the past. Also, buying weakness or selling strength, in order to catch a reversal, has not been working as well either.

Right now, betting on the market, as represented through the SPY, is similar to betting on the flip of a fair coin. This data, while it may not prove the conclusion of Hanna and Steenbarger, certainly does not disprove it.

Implications for Further Research
It seems to me that keeping shorter and intermediate time frame of Z-Scores, update daily across the indices, could give the trader a head’s up that market conditions may be changing to be more favorable to trend-following or contrarian strategies.

The question boils down to positive and negative dependencies; or do stocks trend, or not trend. From 1950 to the present day the Z-score = [-9.359014] or a TRENDING market at a 99% confidence level.

If we present the same information in slightly more familiar terms;
1950-1968……..Bull market
1968-1982……..Bear market
1982-1999…….Bull market
2000-2003…….Bear market [cyclical]
2004-2007…….Bull market [cyclical]
2008……………Bear market [?]

Bull markets have lower volatility. Simply examine VIX data. Bear markets exhibit higher volatility. Volatility is range of movement. Why then the breakdowns in the Z-score?

Year…………………….Up days %………………..Down days %
1950-2007……………….53.6%………………………46.4%

Decades
1950……………………..56.9%………………………43.1%
1960……………………..54.2%………………………45.8%
1970…………………….51.3%……………………….48.7%
1980…………………….53.0%……………………….47.0%
1990…………………….53.7%……………………….46.3%
2000…………………….52.1%……………………….47.9%

Secular Bear Market 1966-1982
………………………….51.1%………………………..48.9%
Secular Bull Market 1983-1999
………………………….54.0%………………………..46.0%

Year
2002……………………44.2%…………………………55.8%
2003……………………54.8%…………………………45.2%
2004……………………55.6%…………………………44.4%
2005…………………..56%……………………………44.0%
2006……………………56.2%…………………………43.8%
2007…………………..54.6%………………………….45.4%

Some of the same information presented visually in the chart;

As can be ascertained on the longer “monthly” data, the market still trends, whether it be Bull or Bear, but the volatility in a bear can easily be seen to be higher. Higher volatility is uncomfortable for “TREND FOLLOWING STRATEGIES” there are more whipsaws due to the increase in the % of DOWN DAYS, as, you are trading into future price, and stop losses will take you out of trades.

In point of fact, the breakdown in trend following strategies can almost entirely be laid at the door of the stop-loss risk management tool.

Conclusions
The recent data show no definitive dependency, either positive or negative. This means that buying because the market has closed up or selling because it has gone down has not been working as well as in the past. Also, buying weakness or selling strength, in order to catch a reversal, has not been working as well either.

The short-timeframes are I feel distorted by the volatility and the increase in the number of “down” days that accompany a bear market. Thus the Z-scores in short timeframes, are not showing the trendiness of the market that a statistical analysis would discover in LONGER timeframes.

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