First steps toward quantitative trading

Finding the right combination of indicators is an important launching point for technical traders. Fine tuning different charting constructs, different momentum and trend indicators and back-testing results - that's the life of many market timers. Indeed, optimizing indicators and trading systems is a growing part of the investment business, as much with wealth management institutions as among the many retail traders who live by the success of their algorithms. In its own way, Stock Trends is part of this movement toward quantitative trading.

Most quantitative trading runs through finely tuned statistical models that guide both trading systems and portfolio management. The Stock Trends analysis is more static in terms of the indicators used, but seeks to optimize applied trading systems within the given parameters. The toolset used here is basic: a moving average study, a momentum indicator, and a volume trigger. But together these elements provide a powerful - and simple - means of engaging the market on a quantitative level. Each report Stock Trends publishes can be used within the framework of a trading system.

Optimizing results through statistical modelling is a multi-step process. The first thing that must be achieved is to understand your data. It is important to be able to describe its characteristics and to determine the independent and dependent variables. I have started that process in recent editorials by generating some statistical output of the Stock Trends data. The next step is to break down those descriptive statistics by category. Each subset of data that is pulled from the data history can be grouped and assessed for differences in results of the output variable - namely, the post-observation performance of individual stocks or ETFs, or the probable outcomes based on statistical predictive models.

With a given combination of Stock Trends variables, for instance, are there sub-groups that have different characteristics. We can seek to ask questions like: what are the differences in central tendencies and the distribution of results for low priced stocks compared to high priced stocks? Does price momentum propel small cap stocks higher compared to large cap stocks? Do certain sectors perform better for the momentum trader? There are many of similar questions we can evaluate, and all would be important ones to answer when developing a trading model.

Building on last week's editorial, let's take another sample of the Stock Trends data and see what it can tell us about different categories of stocks. Of particular interest is whether we can identify any divergence of performance statistics between stocks based on their share price and the Relative Strength indicator. The Stock Trends Picks of the Week report (available to subscribers of Stock Trends Weekly Reporter) provides an interesting sample of the data for discovery of important relationships between the variables. Last week we looked at statistics of the entire sample; here we group the data and compare results.

Again taking a sample of Picks of the Week selections since the beginning of 2012 until February 8,2013 we can create new categories for the share price and Relative Strength indicator and group by ranges.

Share price ranges
$2.00 - $4.99
$5.00 - $9.99
$10.00 - $19.99
$20.00 - $49.99
$50 - max($800)

Relative Strength Indicator (RSI) ranges:100-104
105-109
110-119
120-149
150-max(800)

These groupings are arbitrary, and not based on any statistical method to create bins (groups). Nevertheless, they help us categorize the data in terms or ranges that are easy to understand.
So how do the statistics for the percentage change in price (to the current end date, February 22, 2013) break out for these groupings?

Below is a table, ranked by median percentage change of the groups (median represents the middle value of observations). It gives us a breakdown of the number of observations, as well as some important metrics of central tendency and distribution of results.

price group($)	RSI group	number	mean	standard deviation	median	trimmed mean	min	max	range	skew	kurtosis
(20,50]	(150,800]	29	15.57	40.68	14.70	14.50	-69.60	117.10	186.70	0.27	-0.22
(50,800]	(99,105]	380	8.40	14.55	8.25	8.24	-71.80	102.20	174.00	0.39	8.74
(20,50]	(110,120]	698	8.70	22.40	7.40	8.05	-70.10	172.40	242.50	0.97	6.46
(10,20]	(120,150]	404	9.46	31.83	7.30	8.03	-75.90	138.20	214.10	0.65	1.43
(50,800]	(105,110]	264	6.99	16.82	6.90	7.51	-49.60	58.00	107.60	-0.29	0.69
(20,50]	(105,110]	561	7.88	17.68	6.80	7.53	-57.00	110.30	167.30	0.60	4.30
(20,50]	(99,105]	701	8.40	15.95	6.50	7.59	-50.00	101.00	151.00	0.67	3.85
(50,800]	(110,120]	311	7.95	19.35	6.30	7.54	-44.70	106.80	151.50	0.49	2.09
(10,20]	(110,120]	420	7.15	26.35	6.10	6.55	-98.30	156.80	255.10	0.59	3.68
(5,10]	(105,110]	118	6.37	30.66	5.75	4.66	-91.20	150.00	241.20	1.26	5.40
(50,800]	(120,150]	110	7.53	25.55	5.75	7.38	-55.90	62.50	118.40	0.00	-0.07
(10,20]	(105,110]	287	6.96	21.31	5.20	6.57	-64.00	104.10	168.10	0.36	2.43
(10,20]	(99,105]	323	6.65	20.78	4.80	5.97	-98.30	96.40	194.70	0.14	4.63
(5,10]	(110,120]	269	9.23	34.14	4.30	7.39	-92.00	127.10	219.10	0.61	1.08
(5,10]	(99,105]	123	5.41	18.46	4.10	4.83	-58.00	89.40	147.40	0.84	4.67
(20,50]	(120,150]	390	6.68	30.64	3.75	4.49	-71.00	168.10	239.10	1.30	4.43
(5,10]	(120,150]	336	3.46	33.31	1.20	1.38	-89.40	142.60	232.00	1.02	2.96
(1.99,5]	(105,110]	59	6.96	34.59	0.00	3.97	-65.10	114.70	179.80	1.01	1.21
(1.99,5]	(99,105]	59	5.85	32.02	-1.10	1.87	-41.70	120.20	161.90	1.60	3.13
(1.99,5]	(110,120]	147	4.31	44.33	-1.80	0.84	-85.60	277.70	363.30	2.05	9.51
(5,10]	(150,800]	77	5.65	66.87	-2.00	-3.09	-79.90	352.40	432.30	2.38	8.75
(1.99,5]	(120,150]	289	7.89	53.54	-3.00	1.69	-88.80	228.10	316.90	1.33	2.46
(10,20]	(150,800]	54	0.31	61.09	-4.50	-3.51	-95.10	176.40	271.50	0.68	0.30
(1.99,5]	(150,800]	170	6.12	62.25	-4.70	-1.92	-84.90	501.80	586.70	3.43	22.18
(50,800]	(150,800]	8	14.75	58.73	-14.05	14.75	-38.60	109.20	147.80	0.59	-1.58

See full table and article at www.stocktrends.com

As with most tables, the first thing that jumps out is the extreme values. In particular, at the bottom half of the rankings are stock picks that had share prices between $2 and $5, across RSI values. The Picks of the Week report during the period was least populated by stocks in this price range. It is clearly the most variable price group, and also the poorest performing as shown by the low values for the median and trimmed mean (trimmed mean here excludes the top and bottom 10% of observations).

However, with variability also come the outliers - those observations we trim in statistical analysis. In the statistical world outliers are problematic. For some traders, it's their holy grail. It's the grand slam home run they celebrate. Here it would include the 500% gain on the November pick of Novogen Ltd. (NVGN), or the 277% gain of the January 2012 Santarus Inc. (SNTS) pick - among a number of other very profitable trades.

Nevertheless, when modeling a trading system it is always most important to understand the risk-reward balance. Attempting to capture higher returns on individual trades can be self-defeating. It is far better to model a system that keys on more predictable results, with low variability and a distribution that offers the best chance of long-term profits. The groupings in the top half of the table presented here would represent the more controlled parameters.

Below is a plot that compares the mean (average) percentage change in price for Picks of the Week in the sample (with a 95% confidence interval represented by the vertical bar). Also presented are Box Plots that give a visual representation of the distributions of the percentage change in price by Stock Trends RSI category range for each share price grouping.

Based on this sample of data we could focus on certain price and RSI ranges when evaluating the Picks of the Week report. For instance, we notice that relatively higher priced shares with high price momentum (high RSI values) performed better. More generally, though, it seems that stock picks with a share price above $20 provide the most consistent results. If we take a subset of the Picks of the Week sample with share price >= 20, we find the following distribution:

If we limit our analysis to Picks of the Week with a share price of $20 or greater, what kind of performance could we expect? Assuming that an investor could randomly select 5 different Picks of the Week over the period, the statistical breakdown is as follows:

This distribution is for 1000 random samples of 5 Picks of the Week, share price >= $20. Here we can see that the distribution is closer to a normal, bell-shaped distribution.

Minimum	1st Quartile	Median	Mean	3rd Quartile	Maximum
-19.5	5.845	12.77	13.52	20.76	58.70

number	mean	standard deviation	median	trimmed mean	minimum	maximum	range	skew	kurtosis
1000	13.52	12.01	12.77	13.11	-19.50	58.70	78.20	0.39	0.75

 See full table and article at www.stocktrends.com

These descriptive statistics of categories are just a starting point. We should also take other samples of the Picks of the Week data. This simple analysis is presented to show that the RSI indicator can be modeled in different ways to optimize on specific variables. In order to develop a trading model we need to delve deeper into the variance and correlation of the Stock Trends indicators as well as other market data variables like trading volume.

This particular exercise, though, helps us look at the Picks of the Week report (which is a specific sample of stocks that exhibited a particular combination of Stock Trends indicators) more constructively in terms of quantitative trading. Although there are levels of charting analysis that help pinpoint technically attractive trades within the Picks of the Week report, systematic traders should understand the importance of discovering the variable constraints that correlate with minimizing variance in trading results. In particular, we can learn how the Stock Trends indicators can guide us toward developing effective trading systems.

Stock Trends Picks of the Week: a statistical look

The primary action matrix published here is the Stock Trends Picks of the Week report. These reports are groups of stocks, organized by exchange, that match a defined criteria or combination of variables. Each of these observations are results (roughly stated here) of the following query: select stocks and ETFs, valued over $2, that have a Stock Trends Weak Bearish () or Bullish Crossover () trend indicator, a minimum level of trading volume, and a Relative Strength indicator of at least 100. Those that are Weak Bearish must also have a high probability of being a Bullish Crossover within three weeks.

This weekly screen focuses on Weak Bearish and Bullish Crossover stocks and ETFs for a simple reason: this is the transitional trend moment where issues are theoretically primed to begin a new bullish trend. Although the parameters of Stock Trends are by definition lagging, the assumption is that the long-term trend has or will change category. Sometimes arriving late to the party, these selections still arrive in time to have the forces of trend work for the trade. That is the modus operandi for the Picks of the Week report.

However, the report does not filter down to deeper levels of categorizing observations, and as a result the list is too extensive to use without additional filtering. It is really up to the investor to match the trend qualities that are presented and the technical merit of each potential trade. That is an important question: how do you isolate the best trading opportunities from the Picks of the Week report?

 

The answer to that question does not come easy, and I won’t attempt to answer it in this editorial. Instead, let us just say for now that one way is to draw at random from the Picks of the Week report. Before we assign value to the report itself – never mind finding the optimal trade within the report – it is important to know how outcomes of the report stack up against random outcomes more generally. Will random selections from the Picks of the Week report yield better results than random selections from the broader population – namely, all stocks and ETFs? Surely, there should be a statistically significant difference in the two probable outcomes, otherwise the Picks of the Week report lacks credibility.

 

Before we look at comparisons between random sample performance of the Stock Trends Picks of the Week and from a broad sample of the data population, we can get an understanding of the central tendencies and distribution of random samples of the Picks of the Week report. For instance, if an investor simply bought 5 different random Picks of the Week selections – what would be the statistical representation of those choices? This kind of mean analysis of random samples is a common statistical method in probability models.

 

Let’s take a sample of the Picks of the Week report: all selections, across all exchanges, since the beginning of 2012. The sum of the weekly picks during this period is 6,599. That’s a big grouping and includes all picks right up to February 8, 2013. The inclusion of very recent Picks of the Week (those in the last month, for instance) is problematic in that it does affect central tendency and distribution of the positive returns, but not in a more significant fashion than the use of “end-of-period” returns.

 

There are obvious problems in measuring results for a given period. For instance, stocks may reach a high and subsequently retreat, thereby under-reporting possible results if a simple end-of-period statistic (based on the most recent closing price) is used. Also, in practical terms, stocks that have hit stop levels may have been sold before the end period, thereby reducing the amount lost on the trade. Nevertheless, we’ll simplify this analysis to make the evaluation on a very crude level. We are asking: if an investor blindly picked 5 different stocks/ETFs from the Picks of the Week reports at any point during the time frame and held them to the end-point (February 15, 2013), what is the mean return and what would the distribution of those average returns look like?

 

First, here is a summary table and histogram of these Picks of the Week returns (% change since selection):

 

 

 

 

Minimum value (PSN-T)	1st Quartile	Median	Mean	3rd Quartile	Maximum value (SNTS-Q)
-98.3	-4.0	6.4	8.678	20.0	274.3

 

 

 

 

 

number	standard deviation	median absolute deviation	range	skew	kurtosis
6599	28.75	17.64	372.6	1.33	7.51

 

 

When we present the Stock Trends Picks of the Week, though, our expectation is not that every trade will be successful. However, we would like to see that the distribution of results is favourable. In practical terms, an appealing distribution will be asymmetrical, skewed positively with a fat tail to the right. While we can describe data with mathematical determinants that tell us of likely results, including simple measures of central tendency such as the mean and the median, in the end each pick represents a random sample of this subset of the larger population. We would want to see how these descriptive terms compare to the population itself.

 

We won’t make an attempt to calculate the population distribution now, but we can estimate that it would be close to a normal distribution, which would be symmetrical and possibly centered at the zero value, depending on the market’s overall direction. However, we can see that the distribution of the Picks of the Week sample is asymmetrical, that it is skewed positively – a long tail to the right. Half of the results fall with the 1^st and 3^rdquartile (the interquartile range)– between -4% and 20%. If an investor were to buy just one of the many selections in the Picks of the Week report since the beginning of 2011 their trade would have a greater than 95% chance of resulting in a return between -29 and 42%, which represents all those picks within 2 median absolute deviations (remember that the actual results obtained may be different in a real world scenario – profits booked at higher prices, losses capped at higher prices when a stock holding begins to retreat).

 

But putting all your eggs in one trade is not a trading plan sensible investors would endure. It is presumed that an investor would spread risk across trades. We should then be more interested in the distribution of average returns on samples of several picks. Let’s again assume that the investor makes a handful of trades in the period based on random selections from the reports (again, across all exchanges), and holds them until the end period. These mini-portfolio results should tell us something about the effectiveness of the Picks of the Week report.

 

A basic statistical method often used is sampling. By taking a random sample multiple times – actually many, many times over – we can estimate probable outcomes. Generally, this kind of resampling tends to prove a basic statistical truth: regardless of whether a statistic shows a non-normal distribution, as the sample sizes increase the statistic will tend toward a normal distribution. This is called the central limit theorem. However, let us take a first step and keep the sample size consistent with money management constraints and estimate that an investor’s portfolio would consist of at least 5 positions.

 

Bootstrapping 1,000 random samples (with replacement, since each of these samples is an independent portfolio) of those 5 selections from the Picks of the Week report generates the following histogram representation of the sample mean (average return of the 5 selected picks) distribution, as well as a summary table:

 

 

 

Minimum Value	1st Quartile	Median	Mean	3rd Quartile	Maximum Value
-25.08	8.11	17.77	18.9	28.06	90.4

 

 

 

 

 

number	standard deviation	median absolute deviation	range	skew	kurtosis
1000	15.91	14.83	115.48	0.58	0.84

 

 

Now we see that the measures of central tendency have moved up – the mean (of the sample means) is 19% - and the distribution is closer to a normal distribution. More importantly, most of the sample means are above 3% (one absolute deviation below the median). The following box plots of the sample returns and the sample means returns give us a good graphical representation of the data.

 

 

Differences in the kernel density plots are also represented by the horizontal shape of the violin plots.

 

 

Overall, this analysis indicates the Picks of the Week reports have a good record of delivering trades with above average performance. This analysis does not go deeply enough in the data to indicate optimization and does not accurately compare against random sampling of the broad population of stocks. Nevertheless, it gives us an idea of the statistical metrics behind the performance of this particular subset of Picks of the Week selections.

 

I’ll be digging further into the Picks of the Week report and try to isolate various combinations of the Stock Trends variables and trading stats that change the returns distribution significantly from the sample’s distribution. There are some things we can learn about price momentum and how it delivers different results based on the sector, market capitalization or the price of the stock, and other variables. Applying more rigorous statistical analysis of the Stock Trends indicators will be the primary goal of editorials. Also, while there may be room for a return to market commentaries, I am the first to recognize there are many, many sources of “opinions” about the market direction. I’ll try to stick to quantitative trading analysis, and statistical meat here. In the end, the decision about trading is up to the investor. The best any information service can do is provide a framework for understanding the risk and rewards at hand. There is no certainty - but it’s a lot better to know your odds.