Bearish sentiment builds

Investors are always looking for the door. Even when returns are abundant and investor sentiment is wildly bullish, shareholders know that plump investment accounts are but paper profits - only real when the trigger is pulled and equity is once again cash. The degree to which investors look more nervously to the exit is proportional to the degree to which their equity positions are compromised. How we measure that compromise helps us identify critical shifts in investor sentiment and recognize high-risk market periods.

Stock Trends is by design a categorical reporting framework that gives us a measure of aggregate investor sentiment and a metric for determining when market participants are feeling the squeeze and most ready to dash for the cash. The Stock Trends Bull/Bear Ratio is now serving notice that the exit doors are wide open.

Most market analysts look at benchmark indexes of price level, pointing to areas of support and resistance to anticipate market rallies and corrections. Certainly, the 6% drop in the S&P 500 index from the market high in September sounded alarm bells. But we have had corrections of 5% and more multiple times during the bull market run since 2009. Can we expect this is just another typical and expected correction that will soon be subdued? Price level analysis can conjecture about that, but a measure of market breadth is the best barometer of how sentiment has truly shifted.

The Stock Trends Bull/Bear Ratio measures the distribution of Stock Trends trend categories and tells us something quite simple: are the majority of stocks trending positively or negatively? Are the diversified holdings of investors buoyed by a rising tide or sinking in aggregate?

The Stock Trends trend indicators categorize individual trends by the conditions of a simple moving average study. The base categories -Bullish or Bearish - are determined by the relationship of the 13-week and 40-week moving averages of price. If the 13-week average price is above the 40-week average price the stock is categorized as Bullish. If it is below the stock is categorized as Bearish. This is a factual reporting of past price performance.

The price smoothing aspect of average prices gives us a clearer idea of trends, and although these longer-term time parameters are lagging in nature, they do make it possible to characterize long-term price movement. It is this long-term price movement that most shifts the balance of investor sentiment and creates heightened periods of anxiety about equities.

Stock Trends tabulates the Bull/Bear Ratio for individual North American exchanges. The New York Stock Exchange Bull/Bear Ratio has been plummeting since August, and is now at 1.07. The Nasdaq Bull/Bear Ratio dropped below 1.0 in June and is now at 0.66. When we look at the composite of both major exchanges - some 5,660 common stocks that currently have Stock Trends trend indicators - we get a good look at the trend breadth of the U.S. stock market.

The graph below highlights periods where the Stock Trends Bull/Bear Ratio for the combined Big Board and Nasdaq exchanges has been rated as 'Bullish'. These shaded areas tell us when investor sentiment provides more fertile ground for market rallies and rebounds. There will be times when the S&P 500 index rallies without broader market support , like in late 2006, but these can represent divergences between large cap and small cap performances. Generally, a strong bullish investor sentiment is characterized across the stock market. The Stock Trends Bull/Bear Ratio gives us that representation of market breadth.

Where are we at now? The U.S. market Bull/Bear Ratio has been flirting with a Bearish investor sentiment reading since the market top in the summer, and has now dropped to 0.7. Canadian investors sentiment has also dipped into Bearish territory - the Stock Trends TSX Bull/Bear Ratio fell below 1.0 this week (now at 0.85).

Investors should take note that this aggregate North American trend condition makes the market vulnerable to a crash as investors increasingly weigh in about making an exit. The S&P 500 index's 4.1% recovery last week may be heartening, but fading investor sentiment should keep investors on high alert.

Stock Trends RSI +/- pattern analysis

Stock Trends Reports new Profile tab now also includes a pattern analysis of the RSI +/- indicator. This analysis looks to answer questions about a stock's volatility in particular price trends and how weekly price movement provides an indication of probable outcomes for the coming week. The Stock Trends RSI +/- indicator is a simple binary marker of weekly price performance relative to the benchmark market index. If a stock (all North American trading issues and indexes covered by the Stock Trends analysis) outperforms the benchmark (the S&P 500 for U.S. stocks, the S&P/TSX Composite index for Canadian stocks) the stock is assigned a (+). If it underperforms, it is assigned a (-). This binary notation of price performance can be a useful framework for an event sample space and inference model. From this we can derive probabilities of certain outcomes and estimate one week returns (%). Binary events are always interesting. They provide a simple modeled sample space of possible outcomes. The most common example is the flipping of a coin. We know when we flip a fair coin that there is a 50% chance that the outcome will be heads, and an equal 50% chance the outcome will be tails. How does this kind of random event compare to the binary RSI +/- event? Indeed, there is no surprise when the Stock Trends data reveals that almost all stocks have a near-50% chance of turning up an RSI +/- on any given week. But that is for a sample space that includes all the data. For instance, for IBM the Stock Trends weekly data shows that of the 1,800 weeks covered, 49.5% of observations show an RSI (+) as the weekly indicator. Although some stocks like INTC show a 51.6% probability of a (+) over their history, the mean value across all stocks tends to 50%. A question that comes from this random-like event becomes quite apparent: how does this probability change under different market characteristics? For example, if a stock is in a Stock Trends Bullish trend, what is the probability of an RSI (+) indicator? We can also ask what is the probability we will see an RSI (+) in the upcoming week if the previous week was also a (+) while the stock is in a Bullish trend? Using the samples of the stock's data history that match certain patterns of market performance and underperformance we can also derive similar probability statements. Although this analysis operates under the assumption of randomness in market returns, we are looking at the pattern of past performance and estimate the probability of an outcome derived from the event sample space. In short, like a gambler looking for evidence of an 'unfair' coin that can be capitalized on, we are looking for evidence of a pattern that provides us with better probabilities of a desired outcome than the base probability - which is 50%. Introduced in last week's editorial, the Stock Trends Reports Profile section is the first element of the Stock Trends Inference Model - the implied population parameters and distribution of like Stock Trends indicator combinations. Also presented was a heatmap that ranks the estimated returns of stocks in an industry group. These elements of the inference model focus on homogeneous patterns across markets and estimates 4-week, 13-week, and 40-week returns for individual stocks. The RSI +/- pattern analysis differs by focusing on patterns with the stock itself, estimating returns based on these internal samples. Last week AAPL was presented as an example, so we'll use it again for illustrating the RSI +/- pattern analysis. Below we can see the most recent history of the weekly Stock Trends indicators for AAPL. The current RSI +/- indicator is (-). In this analysis two categorical variables - the Stock Trends trend indicator and the RSI +/- indicator - are inputs. The output is the returns, or percentage change in price, in the week following the observation. What kind of returns (%) do the data show after the observation of a particular pattern of RSI +/- indicators when a stock is labeled in a specific trend? Here is the current RSI +/- pattern analysis of AAPL: To repeat, only weeks of the AAPL data showing the same trend indicator as the current trend indicator (strong Bullish) of AAPL are evaluated. Here we are looking to find how the binary RSI +/- probabilities differs from the probabilities we already understand about the aggregate for this and most stocks - a near 50% chance of either a (+) or a (-). Is the coin somehow biased in a particular trend? If so, to what degree? In this case, given the current RSI +/- patterns for AAPL, what does the data history tell us about how the stock performed subsequently to these patterns when the stock was in the same Bullish trend? The length of the longest pattern of RSI +/- indicators for each stock analyzed depends on the data available. Here the longest pattern measured is 6-weeks long. However, practical usage of the analysis probably lends itself best to periods of three or four weeks. In any event, the probabilities for binary outcomes as the pattern extends is of interest in evaluating the quality of the probabilities of the shorter term patterns. In the current AAPL example, the patterns all suggest that the current market underperformance indicated by the (-) will most probably be followed by a market outperformance (+). Of course, with a given probability of market outperformance we would like to know the returns expectations. If AAPL does outperform the market next week, what is the expected change in price in the coming week? The analysis above defines intervals for the returns expectations for AAPL for each length of the pattern - here from one to six weeks. This type of short-term price movement analysis can be used in tandem with the longer-term analysis provided by the Stock Trends Inference Model and detailed above the RSI +/- Pattern Analysis on the Profile tab of each Stock Trends Report. It can also be profitably used in short-term options trade setups, something Stock Trends will be able to advise about in the future.

The new Stock Trends Report Profile section

A much longer time in coming than originally planned, the new Stock Trends Report 'Profile' section is installed on the Stock Trends website. Available for most common stocks and exchange traded funds, the Profile report now features the Stock Trends Inference Model introduced in the past year. This analysis attempts to answer the very important question: what return expectations do the Stock Trends Reports imply? 

If you were lucky (?) enough to take statistics in your previous studies, you are probably reasonably versed in statistical inference methodology. You will know about measurements of central tendency and variability. You will know about the 'mean' and 'standard deviation' - both as descriptive statistics of a sample and estimated parameters of a population. And you will also know about sample spaces and probabilities. The Stock Trends Inference Model is an application of these basic statistical methods. 

 

If you were lucky enough to have avoided a statistics course in school, be assured this model can be explained in very simple and clear language. I've tried to do that in the editorials I have already written about this analysis, but let's summarize here. First, though, a description of methodology  should always be preceded by a statement of the research question and the biases of that question. 

 

Because the departure point for any model is the assumptions that underlie it, it's important to fully understand the fundamental premises of the Stock Trends Inference Model. The primary assumption is a core tenet of technical analysis - that price patterns repeat themselves. In order to illustrate this and display empirical observations of patterns market technicians must assert that these market price and volume patterns are homogeneous across markets.

  

What does that mean? It means that a price pattern observed in one market can be meaningfully applied to another market. A moving average crossover, for example, carries significance as much in AAPL as it does in ZNGA. A head-and-shoulders pattern found in the chart of IBM in 1980 a template for one in BAC in 2010 (please note: not factual dates for this example). 

 

If the application of technical patterns depends upon the premise that these patterns repeat themselves, what use is the observation of an historical pattern if it does not offer some predicative accuracy? It is not enough to be doctrinaire in our answer and provide anecdotal evidence of positive outcomes. We must provide a larger number of outcomes as evidence. 

 

Of course, no matter how large the sample size of the outcomes we present, the evidence will always be just a portion of the total number of possible outcomes across markets and across time. When we look at possible outcomes we must understand that these outcomes are not based on the market conditions of a particular moment. That would be unsatisfactory and biased. Because we cannot possibly know what will happen in any particular market, we must instead look at the estimating the character of all markets in a given condition. 

 

In the Stock Trends Inference Model the given condition is represented by the Stock Trends indicator combination. That combination is the aggregate of the Stock Trends trend indicator, the length of time the current trend category (BULLISH or BEARISH), the length of time of the current trend indicator, the 13-week Relative Strength (RSI) indicator value, the 1-week RSI +/- indicator, and the volume indicator. These indicators quantify and categorize a market condition in terms of trend and price momentum. Distinct combinations of these indicators qualify particular trends by price momentum and volume characteristics. 

 

If we look at the current Stock Trends indicator combination of AAPL, for example, we can see that this stock is in the 31st week of being labeled with a (strong) Bullish indicator and that it has been in a BULLISH trend category for 52-weeks. Its 13-week Relative Strength indicator (RSI) value is 109, indicating AAPL has outperformed the S&P 500 index by approximately 9% over the past 13-week period. The current RSI +/- indicator is (+) , indicating the stock outperformed the benchmark market index in the past week. Finally, there is no Unusual Volume indicator, indicating that last week's trading volume was not high or low enough to be assigned either a high or low volume indicator. 

 

 

 

 

Taken as a composite, these indicators tell us that AAPL is in a relatively solid long-term trend. Given these characteristics of a stock's trend and its length of trend, as well as its price momentum, what does this particular categorization imply about future price movement? 

 

Of course, we cannot precisely know what is to happen in the future. All we can do is look upon what has happened in the past and make some kind of estimation of what will happen in the future. Using statistical methods we can translate past observations of what has happened into a probability statement about what will happen in the future. The Stock Trends Inference Model attempts to do this. 

 

Below is the current Stock Trends Inference Model report found under the Profile tab of AAPL-Q. 

 

The first section shows the Sample distribution plot and estimated returns distribution for three different periods - 4-week, 13-week, and 40-week. In this case the sample - derived from the 30-year history of Stock Trends data - is 616 records of stocks which sported similar Stock Trends Report indicator combinations to the current indicator combination of AAPL. From this sample we are measuring the subsequent price performance over the three different periods. 

 

 

 

 

 

 

Here we ask of this sample: what kind of returns (%) did other stocks have which previously exhibited similar trend and momentum characteristics as defined by the Stock Trends indicator combination? 

 

The green density plot for each of the three periods is displayed. Each shows how the returns were distributed. This plot shows where most of the returns tended toward (central tendency) as well as the variability of the returns (variance). We are interested in measuring central tendency and variance of the sample because with those statistics we can estimate the average return and variance of the population of all returns associated with this Stock Trends indicator combination. Remember, the population of all returns is much large than this sample size - it includes returns not in this database. It includes future returns - the returns investors are most interested in! 

 

Using statistical inference methods we can estimate the mean of a population within a certain range, or interval, and we can be certain of that interval to a defined degree. Here our model is 95% certain of the mean intervals. Since we are most concerned about the lowest estimate of the interval, we know that there is only a 2.5% chance that the mean of the population is less than the low end of the interval. 

 

For the investor it is more meaningful to interpret the mean interval of the population as the estimated return of a portfolio of stocks that have the same Stock Trends indicator combination.  From this theoretical portfolio we can make another important assumption: that returns of randomly chosen samples, when estimated as the portfolio population, will have a normal, bell-shaped distribution. This assumption is an extension of a well-understood probability theory rule: the central limit theorem. 

 

This assumption - and evidence - of randomness in market returns provides us with a very useful framework for making probability statements about the expected return of a stock. With an estimated population mean, an estimated standard deviation of the distributions we can derive probability statements about observing a return above specific values from a normally distributed sample space. 

 

In short, the Stock Trends Inference Model translates our samples into an estimated return and gives us the probability that a return will better a given, benchmark return. 

 

What should that benchmark return be? It's not difficult to see that the base return we should measure against is the return of a randomly selected stock. If we are measuring returns based on the randomness of outcomes of a categorized sample (our Stock Trends indicator combinations), the base return should be the return we would expect if we randomly picked a stock across the broad market. Indeed, any trading system results should be measured against the results of a randomly selected portfolio.  If you can't beat the monkey, why bother? 

 

The base period random return benchmarks are as follows: 4-week (0%), 13-week (2.19%), and 40-week (6.45%). Each of these returns are the return means of over 500,000 samples taken at random over a 30-year period. Not surprisingly, the annualized return of randomly selected stocks is basically equivalent to long-term market returns - 8%. This sobering fact should remind market timing traders that no matter what analytical framework used, the returns generated by a buy-and-hold approach must be discounted, regardless of what the market actually provided during a particular period. 

 

 

I'll be looking at Stock Trends Inference Model analysis in the future, and pointing out ways to turn this analysis into profitable managed trades. Also, I'll be introducing an additional new analysis under the Profile section. It is a pattern recognition analysis that also employs statistical inference. Expect this content addition very soon.  

 

Another recent content addition to the Stock Trends Reports on the website is the charting application. This is a third-party application provided by Tradingview. For subscribers interested in marking up a chart of a given stock, Try it out! It also provides additional content including current intra-day pricing (15-minute delay), recent news headlines, social media comments from StockTwits, as well as technical and fundamental data. 

 

 

Emerging markets invitation

Emerging market stocks are earning back investor confidence. When the 'risk-on' button has been pushed market-timing traders are prepared to rotate into foreign equities at the earliest sign of sustained price momentum. Considering the muted volatility of the broad North American stock market, evidence of a blooming sector rotation to overseas equity risk is a welcome technical signal for investors.

In U.S. dollar terms, Brazilian equities are outperforming U.S. equities by 13 per cent since the end of January. Southeast Asian markets - Indonesia, Thailand, and Philippines in particular - are also setting a much better pace than U.S. stocks. These markets are currently labeled as Stock Trends Weak Bearish () - indicating that the primary long-term bearish trend category is shifting - or have recently had a Bullish Crossover () and changed to a Stock Trends Bullish () trend. Many have rallied nicely in the past month. It's not surprising to see a surge in the number of stock picks that fit the emerging market theme.

The most recent Stock Trends Picks of the Week report features over twenty emerging market stocks and ETFs. Bank, communications, utilities, and energy stocks lead this group.

Emerging market stocks and ETFs on the move

Trend	RSI	Issue	Price($)	wk%chg	Vol(00s)
	138	Banco Bradesco SA (BBD)	15.30	2.8	423586
	121	Banco Santiago - Chile (BSAC)	24.91	8.1	25892
	122	Bancolombia S A (CIB)	56.79	2.6	20410
	120	Comp. Brasil. de Distribuicao (CBD)	48.41	3.4	22919
	120	Companhia Energetica (CIG)	7.31	2.2	249327
	108	Empresa Nacional Electricidad (EOC)	43.82	3.1	5512
	115	Enersis SA (ENI)	16.11	2.9	31405
	103	iShares Core MSCI Emerging Mkt (IEMG)	49.78	1.5	67434
	101	iShares Intl Preferred E.T.F. (IPFF)	24.82	2.8	1893
	111	iShares Latin Amer 40 E.T.F. (ILF)	38.67	2.9	34038
	117	Ishares Msci Brazil Capped ETF (EWZ)	48.48	3.8	828316
	103	iShares MSCI Emerg Mkt E.T.F. (EEM)	41.61	1.9	2784643
	102	iShares MSCI Malaysia E.T.F. (EWM)	15.84	1.5	71161
	105	iShares MSCI Singapore E.T.F. (EWS)	13.59	1.7	67869
	111	iShares MSCI Thailand E.T.F. (THD)	76.34	1.7	12381
	106	LATAM Airlines Group S.A. (LFL)	15.50	3.3	26946
	103	Morg Stan Em Mk Debt (MSD)	10.15	0.5	2920
	115	Mrk Vectr Indonesia E.T.F. (IDX)	25.54	0.8	7854
	125	Paranaense De Energia Copel (ELP)	15.08	7.3	19917
	104	SCHWAB EMG MKT ETF (SCHE)	24.70	1.5	11655
	102	SPDR DJ Int Real Estate E.T.F. (RWX)	42.70	1.1	13119
	129	Telecom Argentina (TEO)	20.82	7.3	7144
	107	Telefonica Brasil (VIV)	21.41	4.6	88363
	104	Templeton Emg Mkt Incm Fd (TEI)	14.50	0.9	6251
	110	Ultrapar Participacoes Sa (UGP)	25.71	3.1	12621
	104	Vanguard FTSE Emerging Markets (VWO)	41.24	1.9	622375

The Relative Strength Indicator (RSI) provides a measure of the strength of a stock’s 13-week price movement relative to the S&P 500 index. Stocks outperforming the index have an RSI value above 100.

But should investors be jumping on these stocks now? Timing is everything for active traders, but is now the time for investors with a longer trade horizon? For the technician evaluating a multi-year chartof the iShares MSCI Emerging Markets ETF (EEM-N), for instance, the answer to the question would come from further price development above a long-term price formation that indicates consolidation. Even the impressive spring rally that has propelled Brazilian stocks is not convincing enough when measured against the backdrop of a bearish long-term trend. How can we know if the rewards will match the risk inherent in these markets?

Stock Trends indicators report on price trends, but they also give guidance on what kind of future returns those trend categories imply. Sampling indicator combinations like the ones currently sported by these emerging market issues and statistically measuring post-observation returns gives us a more quantitative interpretation of this group of performing stocks and ETFs.

For example, the sample of 145 stocks that have had similar Stock Trends indicator combination and trend longevity as the iShares MSCI Brazil Capped ETF (EWZ-N) gives us an expected return below the expected market return for the coming 4-week, 13-week and 40-week time periods. The graph below shows the distribution of 13-week returns of the sample and the assumed normal distribution of the population of stocks with similar Stock Trends indicators.

The sample density distribution is filled in green. The assumed population distribution - a normal distribution - is outlined in blue. The vertical yellow line indicates the estimated population mean return. The vertical red line indicates the base return of a randomly selected stock.

The following heatmap graph ranks some of the issues highlighted here by estimated returns implied in the market conditions categorized by the Stock Trends indicators. The estimated returns (%) of 4-week, 13-week, and 40-week periods are discounted by the base period expected market returns. The green elements of the map represent progressively higher performance expectations. Yellow elements represent market performance, while red elements represent progressively lower performance expectations.

Ranking of returns expectations: 4-week, 13-week, 40-week

 

What does this tell us? The statistical inference analysis doesn't give the investor much confidence about returns over the next three quarters for many of these issues. This is not to say that these emerging market issues are not now in nascent stages of bullish trends, but the markers of more promising return expectations in the immediate future are not yet in place. For more conservative investors there is no need to jump on these risky markets yet. 

Data-driven technical analysis

The stock market is a great laboratory. Considering the immense scope of data fueling asset valuations and ultimately influencing market price behaviour, it's not surprising that quantitative models are increasingly used to harness this data. Where analysis frameworks formerly tended to be doctrinaire - whether fundamental or technical - data science is now interjecting a new standard. Data-driven analysis is a booming business.

For technical analysts the rigours of data science present a challenge. The foundation of technical analysis is clearly stated in its primary tenets: the market is transparent, prices trend, and move in identifiable patterns that repeat themselves. The chartist is a practitioner of pattern recognition. But how well do these patterns hold up to data science methods? Does the data support the chart patterns and indicators that are the bread and butter of market technicians?

Although many very successful traders have made their fortunes and fame out of technical analysis, skeptics of the profession have always weighed in. And rightly so. Even market technicians self-proclaim their craft as equal parts science and art. However, those two endeavours don't often mingle well. Science is far too precise to indulge anecdote or flourishes of doctrine unsupported by the cold currency of hard evidence. Art is often too subjective or personal to codify. But quantitative analysis demands codification and measurement of variables.

There is no shortage of technical analysts peddling doctrinaire assertions. Typically, almost every chart pattern presented lacks supporting quantitative evidence of predicative value. The language of the market technician largely fixates on what amounts to textbook, anecdotal guidelines. When assertions about probable outcomes are ventured, seldom do statistical measures accompany them. A recent article published by a technical analyst, for instance, said the following:

"The highest probability setups are the ones that have all the key moving averages on the right side of them. That doesn't mean that other setups will not work, it just means that the odds are slightly higher when this does occur."    See 'I like pullbacks on Vipshop'

Here the use of the word 'probability' implies some kind of definition of a sample space and its measurement. Unfortunately, most technicians offer neither. Statements like the above are bandied about as doctrine, but have no data to back them up. For the data scientist this is verboten.

We now live in a world where data can give us the answers we need, and whether we like the answers or not we must let the data confirm or refute our hypothesis about relationships between variables - or even prove causation if necessary. If you are serious about technical analysis it is important to learn the language and process of data science.

In an effort to address these higher standards I have started to model Stock Trends in the garb of quantitative data analysis. The Stock Trends indicators translate weekly market data into categories, giving the investor a quick and effective way to put current North American stock prices into a trend context. This categorical data fits into a number of data science approaches that transform the Stock Trends indicators into simple statistical models.

This is now an important departure point for any technical methodology - how does the data support an analysis framework? In this case, do the Stock Trends indicators tell us something meaningful about future share price movement? For instance, how meaningful is a Stock Trends Bullish Crossover, alternatively referred to as a Golden Crossover in the lexicon of technical analysts?

The Stock Trends indicator combinations provide an effective data foundation for a statistical inference model. Every week traded issues on the major North American exchanges are codified by these indicator combinations. As an example, last week the Stock Trends indicator combination for Fedex (FDX-N) was represented in the Stock Trends Report:

Fedex's stock is labeled as Stock Trends (strong) Bullish ( ). It has been a (strong) Bullish stock for 8-weeks, and has been categorized in a Bullish trend for 71-weeks (see trend counters). The stock has under-performed the S&P 500 index by 4% in the past 13-weeks, as indicated by the Stock TrendsRelative Strength indicator (96). Last week it also underperformed the benchmark index, as indicated by the RSI (-) sign. Finally, there is no unusual volume indicator, as defined by Stock Trends. This combination of Stock Trends indicators codifies market characteristics of Fedex's stock at this moment.

What does this Stock Trends indicator combination tell us about future price movement? Can we assert some probability statement that is based on data evidence? If we want to generalize about a market condition like the one categorized by this Stock Trends indicator combination we must first make anassumption: market conditions are non-specific to a security. This is an integral premise of technical analysis - that patterns evident in one security have relevance in patterns evident in another security.

In order to assign probability statements a sample space of possible outcomes must be defined. We can estimate this sample space through statistical inference methods. In the case of the Stock Trends indicator combinations we can ask the question: how did other stocks with similar indicator combinations perform in the past?

The answer to that question is found in the data. By extracting all like combinations in the 30-year data history we obtain a sample of stocks from which we can measure the post-observation returns. This statistic will measure the change in share price after 4-weeks, 13-weeks, and 40-weeks.

The sample extracted from the data finds 91 other like observations - stocks that sported similar Stock Trends indicator combinations in the past. The distribution of returns for each of these periods is of interest, but here is the sample distribution of post-observation 13-week returns for stocks with similar Stock Trends indicator combinations as the current Stock Trends Report of Fedex.

The sample density distribution is filled in green. The assumed population distribution - a normal distribution - is outlined in blue. The vertical yellow line indicates the estimated population mean return. The vertical red line indicates the base return of a randomly selected stock. 

Expected 13-week returns (%) implied by the Stock Trends Inference Model can be summarized briefly:

For 13-week CLOSE returns estimation, with 95 % confidence, the 13-week CLOSE mean return of the population of stocks with a similar Stock Trends indicator combination to FDX will be inside [ 5.688 %, 10.137 %], with probability of 2.5 % we will have a mean return below 5.688%.

The mean return 7.91% and standard deviation of 12.26% tell us that a normal distribution of 13-week CLOSE returns implies a probability of 67.97% that the expected return will be above the base 13-week random return of 2.19%.

FDX is listed in the current Stock Trends Inference Model (ST-IM) Select stocks ST Filter report. 

Stock Trends Inference Model Select stocks

The new Stock Trends Inference Model (ST-IM) Select stocks report has been published for a few weeks now, and reports for previous weeks are also being populated gradually. Subscribers can monitor the current selections to see how they perform. The inference model is an application that translates the Stock Trends data into a unique actionable tool for investors. Let’s review the methodology again.

The ST-IM Select stocks report includes all stocks with a Stock Trends indicator combination that show statistical evidence of predicting future performance better than base period random returns (see The random outcome benchmark). For instance, last week’s ST-IM report for the New York Stock Exchange includes the SPDR Retail exchange traded fund (XRT). The current Stock Trends Report for XRT shows that the ETF has been in a Bullish category for 120 weeks and has sported a strong Bullish indicator for the past 7 weeks. It is under-performing the S&P 500 by 5% over the past 13-weeks (RSI 95), but out-performed the benchmark market index last week (RSI +/- shows a +). There is no unusual volume indicator.

This Stock Trends indicator combination is matched by 63 similar combinations in the 30+ year Stock Trends data history. When these groupings are applied stocks with a share price lower than $2 are not included with stocks with a share price $2 and higher. Also, indicator combinations with weekly volume of trading below 100,000 are grouped separately. The resultant sample that fits the current Stock Trends indicator combination of XRT is shown below:

weekdate exchange symbol X4wk X13wk X40wk 1 1983-05-20 N CEG -6.41 -2.43 -1.55 2 1986-07-11 N DF -4.26 -13.03 -8.78 3 1986-11-07 N CNL 0.69 1.38 -1.50 4 1987-09-11 N TIN 0.00 -29.41 -18.49 5 1992-12-25 N PPL -1.36 7.60 7.17 6 1993-04-16 N CCK -6.72 -11.54 -2.23 7 1993-05-21 N DSM 1.16 3.56 -6.07 8 1994-01-21 N SO -5.50 -8.09 -7.54 9 1995-05-26 N SWY 6.26 5.93 58.72 10 1995-07-14 N HMA 12.67 9.93 73.97 11 1995-07-21 Q ABCW 6.18 28.96 27.30 12 1996-05-03 N IVC -0.95 16.19 -1.90 13 1996-06-28 N BDX -6.68 9.67 13.41 14 1997-04-04 N RDN 12.51 43.51 67.53 15 1997-05-30 N WBS 9.94 31.35 58.02 16 1997-05-30 T NDN 9.54 3.49 22.02 17 1997-05-30 N NWL 3.42 3.27 28.76 18 1997-06-06 N BAC 7.49 -10.09 9.36 19 1997-06-06 N MTB 2.69 10.45 43.28 20 1997-06-13 N BBT 6.26 20.98 49.68 21 1997-06-27 N PDE 9.53 51.13 12.37 22 1997-07-04 N BA 6.00 -5.78 0.00 23 1997-07-18 N CLI 11.30 17.01 9.82 24 1997-07-25 N ESS -3.44 4.17 2.07 25 1997-08-15 N UVV -1.39 4.52 -1.59 26 1997-10-17 N BCE -2.41 9.22 36.60 27 1998-02-13 N TJX 16.49 25.91 31.26 28 1999-07-30 N GD -7.34 -17.65 -15.33 29 2002-12-06 N BKT 0.13 3.17 -8.24 30 2003-05-23 Q PVTB 4.91 40.30 94.47 31 2004-12-24 Q PMTI 9.68 17.77 12.33 32 2005-03-25 Q CHRW -8.19 8.19 42.42 33 2005-06-17 N ATR 0.84 -2.41 9.36 34 2005-07-08 T BXE 20.99 28.48 15.99 35 2005-07-08 N MEE 12.93 17.83 -11.68 36 2005-07-22 Q ESLR -9.35 25.80 109.35 37 2005-08-26 T CNR -1.63 13.66 21.82 38 2005-12-02 Q LUFK 7.04 15.45 26.05 39 2006-01-06 N CVD 10.73 13.87 30.61 40 2006-01-06 N FTO 11.58 43.94 42.36 41 2006-01-27 N GD 2.87 10.75 19.04 42 2006-02-24 T FDG.UN -4.29 -17.25 -48.02 43 2006-09-29 N KSU 8.68 6.11 42.11 44 2006-11-24 Q GOLD -1.01 6.61 5.46 45 2007-02-23 N EME -0.75 3.15 -13.42 46 2007-05-04 N AFG 0.56 -21.43 -23.83 47 2011-03-11 N TSI -0.18 -1.85 -4.07 48 2011-06-03 Q AAPL -0.05 8.91 58.74 49 2011-11-18 N KED 3.96 20.22 26.69 50 2012-01-13 N PRGO -3.82 7.34 21.39 51 2012-02-03 N WCN -4.10 -4.40 -4.49 52 2012-02-03 T CU 9.45 14.68 5.26 53 2012-02-17 N MJN 5.63 7.27 -10.74 54 2012-02-24 T THI 1.65 4.11 -12.52 55 2014-01-03 N STC -1.07 1.83 NA 56 2014-01-24 Q CHTR -4.82 NA NA 57 2014-02-07 T RCH 8.38 NA NA 58 2014-03-21 N AIG NA NA NA 59 2014-03-21 N MMM NA NA NA 60 2014-03-28 N DDM NA NA NA 61 2014-03-28 N UDOW NA NA NA 62 2014-03-28 T MSI NA NA NA 63 2014-04-04 N XRT NA NA NA 64 2014-04-04 Q FELE NA NA NA

The table shows the week of the matching combination with subsequent (post-observation) returns for 4-week, 13-week, and 40-week periods. Some of the records at the bottom of the table are too recent to have generated returns for the subsequent periods and are denoted with a “NA”.

The sample reveals that although there are similar records throughout the data history, they cluster around certain market environments or moments in time. These clusters are important aspects of the samples that we can evaluate in another model, but for the purposes of this inference model they are not significant. We are looking to define a population – all stocks that have a similar quality of trend and price momentum as defined by the Stock Trends indicator combination. From the sample above we can estimate the relevant parameters of this population.

The sample subsequent returns (4-week, 13-week, 40-week) are the statistics we measure. Here is the summary for the three periods:

For 4-week CLOSE*  returns distribution estimation, with 95 % confidence, the 4wk CLOSE mean return of the population of stocks with a similar Stock Trends indicator combination to XRT will be inside [ 1.206 %, 4.282 %]

[1] "With probability of 2.5 % we will have a mean return below 1.206"

Mean return 2.74% and standard deviation of 6.94

Normal Distribution
For 4wk CLOSE P(R> 0)=65.37% probability that the 4-week return will be above the base 4-week return (0%).

57.89% of 57 sample returns are >0%

For 13-week CLOSE returns distribution estimation, with 95 % confidence, the 13wk CLOSE mean return of the population of stocks with a similar Stock Trends indicator combination to XRT will be inside [ 5.044 %, 12.495 %]

[1] "With probability of 2.5 % we will have a mean return below 5.044"

Mean return 8.77% and standard deviation of 16.51

Normal Distribution
For 13wk CLOSE P(R> 2.19)=65.49%  probability that the 13-week return will be above the base 13-week return (2.19%).

72.73% of 55 sample returns are >2.19%

For 40-week CLOSE returns distribution estimation, with 95 % confidence, the 40wk CLOSE mean return of the population of stocks with a similar Stock Trends indicator combination to XRT will be inside [ 10.272 %, 24.276 %]

[1] "With probability of 2.5 % we will have a mean return below 10.272"

Mean return 17.27% and standard deviation of 30.73

Normal Distribution
For 40wk CLOSE P(R> 6.45)=63.76% prbability that the 40-week return will be above the base 40-week return (6.45%).

57.41% of 54 sample returns are >6.45%

* Note: The Stock Trends Inference Model uses end-of-period closing price returns. See Variability of returns

What does this tells us? First, it is understood that generally we cannot precisely know the true population. We can only estimate it’s characteristics from a given sample. Equipped with two sample statistics – the sample mean (average) return and sample standard deviation (a standardized measure of variance of the returns) – we can estimate the population mean return and standard deviation (both known in statistical parlance as parameters). This magical property you can investigate further in many statistical books that introduce concepts of statistical inference.

In this example we can see that the lowest value of the interval estimate of the population mean is above the mean return of random returns in each of the three periods. This implies that we are pretty certain that the mean return of this population is higher than the random return benchmarks. If we assume a normal distribution of returns for the population – which we do because our assumption is that returns are random – then we can use another statistical method to give the probabilities that XRT will return above the random mean return.

The sample density distribution is filled in green. The assumed population distribution - a normal distribution - is outlined in blue. The vertical yellow line indicates the estimated population mean return. The vertical red line indicates the base return of a randomly selected stock.  

In the case of the 13-week period ahead, the Stock Trends inference model posits that there is a 65.5% chance that XRT will return above 2.19%. That is better than the 50% chance a random return will generate a 13-week return better than 2.19%, but we should always remember that unless a probability is 1 (100%) there is no certainty. You can always roll a negative outcome even if the probability of a positive outcome is 99%. However, a 65.5% chance is an edge a trader can use.

The ST-IM report gives us a weekly round-up of stocks that have at least a 55% probability of generating a 13-week return better than 2.19%. There are other indicator combinations that also share this property, but these are the ones that meet the criteria of having a confidence interval above the base mean return of each period (others may have lower estimates in the interval that fall below the base mean return). These are the ones that we are most certain will have a population mean return above the base return of every period.

Another important aspect of the Stock Trends Inference Model demands more attention. Each ST-IM report represents a sample of a new population, namely all stocks that fit the model criteria. The Central Limit Theorem states that the mean return of random samples from this population will be normally distributed (bell-shaped). We can also estimate that a portfolio of stocks randomly selected from the ST-IM reports will return above the base market return.

Let’s experiment. We can construct many randomly selected sample portfolios from the ST-IM Select stocks reports, with equal amounts invested in each stock or ETF. What kind of 13-week returns were generated?

There have been 5,905 ST-IM Select stocks in the past year that generated subsequent 13-week returns (ST-IM Select reports from April 4, 2013 to January 3, 2014). This sample can be summarized as follows:

The sample density distribution is filled in green. The vertical yellow line indicates the sample mean return. The vertical red line indicates the base return of a randomly selected stock.  

vars n mean sd median trimmed mad min max range skew kurtosis se 1 1 5905 8.75 19.89 6.4 7.11 12.6 -59.5 336.8 396.3 2.67 22.65 0.26

The mean (average)13-week return of these ST-IM Select stocks is 8.8%. The maximum 13-week return was 396%, the biggest loss 60%. Our inference model directs us toward stocks that have a higher probability of returns greater than the mean 13-week return of randomly selected stocks – 2.19%. The results confirm that – 64% of ST-IM Select stocks had a return greater than 2.19%. But how did these ST-IM Select stocks do in comparison to the benchmark market indexes? The following gives a summary of the Stock Trends RSI values of the select stocks 13-weeks after the selections:

vars n mean sd median trimmed mad min max range skew kurtosis se 1 1 5905 104.06 18.91 101 102.49 11.86 37 417 380 2.72 23.44 0.25

The mean Stock Trends RSI is 104. This tells us that had we invested in all of these ST-IM Select stocks our performance would have exceeded the market outcomes – we would have done better than trading simultaneously in a benchmark exchange traded fund like the SPDR S&P 500 ETF (SPY).

Obviously, it is not practical to look at the total of these numerous selections. We would have had to trade a much smaller number of ST-IM Select stocks. It’s difficult to isolate which subset of ST-IM Select stocks would have generated the best returns in this distribution (although I will try to do this in the future using data mining analysis techniques), but we can estimate the average or likely return attainable by random sampling.

How would have investor done if he randomly selected small portfolios of stocks from the ST-IM reports? For example, what results would have been attainable if we randomly selected five (5) stocks from the ST-IM reports and measured subsequent 13-week returns of these portfolios? Does the ST-IM model deliver superior returns for a retail trader?

If we take 1,000 random portfolios of 5 stocks from our sample, the following distributions of portfolio returns and RSI values is evident after the 13-week period for each portfolio:

The sample portfolio returns density distribution is filled in green. The vertical yellow line indicates the portfolio mean return. The vertical red line indicates the base return of a randomly selected stock.  

vars n mean sd median trimmed mad min max range skew kurtosis se 1 1 1000 8.53 7.72 7.72 8.11 7.03 -13.64 46.08 59.72 0.71 1.48 0.24

The mean 13-week return of these portfolios is 8.5%. That translates to an annualized return of 34%. Of these 1,000 random portfolios, 79% generated a 13-week return greater than the base period return of 2.19%.

Below is a summary of how these portfolios did relative to the benchmark indexes over these 13-week periods.

The sample portfolio post-trade 13-week RSI density distribution is filled in green. The vertical yellow line indicates the portfolio mean post-trade RSI. The vertical red line indicates the base benchmark index.

vars n mean sd median trimmed mad min max range skew kurtosis se 1 1 1000 103.83 7.49 103.2 103.44 6.82 82.4 140.2 57.8 0.66 1.31 0.24

The mean 13-week RSI is 104. This tells us that the random portfolios are outperforming the market, on average, by about 4% in these13-week trades. Take note that although transaction costs are not discounted here, we are comparing against an active trading of a market index, not a buy-and-hold strategy. A buy-and-hold strategy can be compared against the ST-IM portfolio annualized mean return of 34%. The S&P 500 index is up 20% in the past 12-months; the S&P/TSX Composite Index is up 17%. In this comparison the ST-IM annualized return should be discounted for transaction costs.

Subscribers to Stock Trends Weekly Reporter should feel quite confident in actively trading the highlighted stocks in the weekly ST-IM Select stocks report.

Learn more about the Stock Trends Inference Model at www.stocktrends.com