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^{rd}quartile (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.