Monday, February 03, 2014

Embracing Randomness

The investment industry can be defined in a number of ways, usually centered on its fiduciary role of managing and allocating capital. But fundamentally it is a data driven industry. Data is its lifeblood. Data is its nervous system. Data is what gives investment life. Without data capital cannot be managed or allocated. Without data capital is locked away, unproductive and hoarded.

Instinctively, we know this. Every investor makes decisions based on available data. Remember, data comes in many forms – much of it qualitative, unstructured, and fluid. Structured quantitative data is more readily recorded, warehoused and shared. It includes macroeconomic data, financial statements, capital stock changes, insider trading reports, industry market analysis, and – most importantly for market technicians - market trading data. In all its forms this data alerts the marketplace to investment channels and helps form our investment opinions. The magnitude of this data is impossible to quantify.

With so much data available how can we achieve optimally informed investment decisions? Is a truly informed position, one that is measured from all essential data, a realistic expectation? The way many investment professionals talk about their version of data analysis you would think it is. But there are too many alternate informed decisions to know which would be the best, the most profitable. Indeed, your quest to find the most profitable data analysis has likely led you to a numerous sources of investment information.

Of course, data can also tell us whether one version of analysis is superior to another. How can we know whose opinion to heed except for their past record measured in a response variable? What returns have been generated by a system of analysis? But what if the trading record of the analyst who has the best story supporting his or her opinion is not much better than results derived from investment decisions based on specious factors, like astrology or the Super Bowl winner? What if, for all the esteemed knowledge of the most brilliant market oracles, the result does not match the billing? These questions and the quest for a more rigorously-tested approach to investing bring many serious traders to the world of quantitative analysis. It is only by examining the trading results of informed decisions that we will know whether the data analysed to make those decisions holds the key to success.

So, we’ve arrived in the world of the ‘quant’ – a world of data variables and the dynamic nature of their relationships. It’s not easy stuff. But don’t let that scare you away. Like most things quantitative analysis can be broken down to simpler elements.

Stock Trends is an excellent data source for analysis. It provides a consistent set of variables – the Stock Trends indicators – that can be measured against a response variable. The response variable can be subsequent share price changes of any time parameter. However, we will focus on end-of-period price changes for 4-week, 13-week, and 40-week periods. These time periods represent trade time frames best executed by the Stock Trends indicator analysis. These would be most effective time frames for position or swing traders.

In fact, the average holding period for Stock Trends trading strategies based on changing trend categories (like the Dow Jones Industrials Bullish Crossover Portfolio trading strategy) is around 40-weeks, while the average holding period in more sensitive Stock Trends trading strategies tends to be lower – between 7 to 10 weeks. Typically, we will be focused more on the 13-week time frame (3-months) as the most pertinent time frame, but both the 4-week and 40-week time frames are of interest, too.

Regardless of time frame of our quantitative analysis of Stock Trends, we will be most interested in finding opportunities to trade where the probabilities of a market outcome are better than that exhibited by random selections. Why? Because regardless of how informed decisions are codified – every Stock Trends Pick of the Week or every Jim Cramer recommendation, for example – measured trading results of any prescribed period that follow will, given enough data, tend toward a normal distribution (bell-shaped). A normal distribution, like the one presented below, implies randomness. It has 50% of observations above its mean, and 50% below its mean.

This is an important understanding of trading. In an ideal trading system there would be a positive skew to the distribution of trading results, one with a fat tail on the right side of the distribution curve. This would represent a trading record with a significant number of ‘home runs’. For example, when you look at the published Stock Trends portfolios, in particular the Nasdaq 100 Bullish Crossover Portfolio, the positive skew is evident.



However, real world and model trading strategies can only be products of a sample of possible outcomes. No matter how successful a trading strategy appears in a sample, we know that the outcomes are not a complete representation of all outcomes – past, present and future. We cannot know precisely the shape of a population distribution, but it will tend toward a normal, bell-shaped, distribution. The shape may be “skinnier” (a higher kurtosis in statistical terminology) than the example standard normal distribution shown above, but the symmetrical aspect will be formed.

If even the best strategy, using the most essential, optimal data inputs, eventually develops a distribution of results that approximates a normal curve, and a normal curve is the expected distribution of results derived from random data inputs - what is the difference?  Certainly, anyone who has done capital markets quantitative work will confront this question. That is why it is important to embrace the randomness of markets. A key to success is in understanding it.

As an example of the distribution of returns we expect from random results, here is a distribution of the 13-week returns of 1,000 randomly selected North American stocks from randomly selected dates.

 

How do we turn the random nature of the market into a profitable trading plan? 

Stock Trends can help.

A key premise of technical analysis is that market valuations are subjectively determined. Buyer and seller – opposing forces – effect a market price based on the balancing of these subjective valuations. In classical market technician parlance, the market price discounts all available information. However, an interdependent set of variables add a dynamic feedback loop to this subjectively determined price – elements of time, and price change. We call this price momentum and it factors into much of the terminology of technical analysis. We’ll avoid elaborating on that, but suffice to say price change is a significant element in the subjective environment of every market and is an important variable for every buyer and seller. It results in the establishment of price trends, as well as the breaking of those trends.

The reason we study price trends – and the raison d'ĂȘtre for Stock Trends – is the self-fulfilling aspect of price movement. The Stock Trends indicators are variables that represent different aspects of price change, as well as time. The trend indicator categories – BULLISH and BEARISH – tell us about the relative price changes over a longer time frame. The Weak Bullish () and Weak Bearish () trend indicators tell us about possible changes in those long-term price trends. The Bullish Crossover () and Bearish Crossover () indicators tell us about changes in the trend categories.

Adding the element of time to the trend indicators is the trend counters (major and minor trends), both of which help characterize the assigned trends. They tell us how long a stock/ETF/index has been trending – an important variable that alerts us to concepts of trend fatigue and other psychological aspects of price movement. Market technicians use techniques that attempt to interpret time fractals; similarly Stock Trends trend counters also extend our trend analysis framework.

The Relative Strength indicator measures price momentum relative to the price movement of the benchmark market index over a thirteen week period, while the RSI +/- indicator gives a binary representation of the relative price momentum versus the benchmark index for a one week period. Finally, the Stock Trends volume indicators isolate unusually high weekly trading volume.

The Stock Trends variables – most specifically the combination of these variables – provide us with a dataset that is ripe for quantitative analysis. A very simple question we can pose: what are the statistical returns that the market generates after particular combinations of Stock Trends indicators? This is the concept being developed here, and introduced in recent editorials.

Let’s look at combinations (trend indicator, RSI indicator, RSI +/- indicator, volume indicator) from the current week ended Jan17.  Of over 8,000 N.A.-listed common stock, exchange-traded-funds and income trust issues (NYSE, Nasdaq, NYSE-Amex, and TSX) with Stock Trends trend indicators, there are 1,113 distinct ST indicator combinations this week. Some combinations are shared by multiple issues; some are unique. Some combinations are absent this week, but recorded in other weeks.

Each of these distinct combinations, for the most part, is repeated in the Stock Trends database of over thirty years of weekly reporting. In the database there are 16,668 distinct combinations recorded, with each combination representing a sample of what would be a larger population of distinct combinations possible. Not surprisingly, the most frequently recorded combinations are Bullish trends () centered around the market’s price momentum (Relative Strength Indicator near 100).

In order to more accurately find like combinations of the ST indicators, though, we add another two variables to the indicator combinations – the major and minor trend counters – and group RSI values within discrete ranges. In this manner we can attempt to group each combination in a meaningful way that reflects similar qualities of trend, price momentum, and volume.

By running a query for each of the current issues with a Stock Trends trend indicator to find like observations of these indicator combinations in the historical data (about 8.4-million records) and measuring the subsequent 4-week, 13-week, and 40-week returns we can determine the statistical mean and standard deviation of those returns for each sample. Then using statistical inference methods estimate an interval for the population mean. From those intervals we can rank each indicator combination.

That’s a lot to digest. Let’s try an example.

Cigna Corp. (CI-N) is a notable name in the health care sector. Its Stock Trends Bullish trend is now 67 weeks long and the stock is outpacing the S&P 500 index by 13% over the past 13-weeks. That’s a healthy trend.



But what does this kind of trend and price momentum tell us? What guidance do other examples give us?
A query to the Stock Trends database locates 311 other records with similar Stock Trends indicator combinations. Of those records 303 pre-date 13 weeks ago and consequently have 13-week price returns recorded. The distribution of those returns is illustrated in the graph below, represented by the green density curve. The blue lined plot is of the corresponding normal distribution of the sample.

Remember, the distribution presented represents a sample of returns. Indeed, all portfolio records are samples. Back-test to your heart’s desire – but every portfolio record is by definition only a sample of a much larger population of trades. Samples - especially relatively small samples - can be flattering, and they can be less flattering, but what we are really interested in is the population of trades that are represented by a trading strategy.

Obviously, we can never truly generate a record of this or any such population. However, using statistical inference methods we can extrapolate some important pieces of information about the population from the sample. We can estimate the mean and the standard deviation of the population from the sample.

The mean 13-week return of stocks in the CI sample is 5.43% and the standard deviation of those returns is 14.98. Those are two measurements of the distribution illustrated above that we can use to say something meaningful about the population.

For 13-week (closing price) returns estimation, with 95 % confidence, the mean (average) return of the population of stocks with a similar Stock Trends indicator combination to CI will be between 4.0 % and 6.85 %. This means we are pretty confident the mean is above the mean return of a randomly selected stock (2.19%). Also, if we accept the mean return as 5.4%, a normal distribution of the population of 13-week returns tells us that 58.6 % of returns will be above 2.19% (the 13-week mean return of randomly selected stocks).

Remember, this edge is relative to the random outcome we expect, which is a 50% probability of besting the mean market random outcome in the coming 13-weeks. In an exercise of chance, an edge in positive probable outcomes is an excellent foundation for relative success. Applied to the stock market it is also effective, although success will also be a function of trading practice. In this CI example there is still a 41.4% chance the 13-week return will be less than the mean return of random results, and a possibility that the loss could be substantial. It is imperative that investors learn proper trade setups to limit losses. This analysis, like all analysis in the investment business, is a starting point. Portfolio management tools are always the key to long-term trading profitability.

Stock Trends is working toward providing this quantitative analysis on all stocks, and editorials ahead will help bring a better understanding of how to use the information.
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