In this study I will be using all US Stocks and studying over a period from September 15, 1998 to September 15, 2009. This time period captures the behavior of multiple bull and bear markets, as well as showing very little return on the SP500 for a buy and hold investor.
Since I have a day job that does not permit me to trade actively during the day, I would have to enter my orders in the morning and review my positions in the evenings. I would rely on stops to limit my risk during the day. Thus my shortest holding period for a position is about a day. Long holding periods over a month don't sit well with me, so I am limiting my holding periods to 4 weeks. I split the returns for stocks into 5 days, 10 days, 15 days, and 20 days. I counted the number of stocks exceeding a return threshold for each period of time. This analysis only looks at return on price and does not limit the stocks by any other criteria such as volume, float, etc.
I created an indicator that counts the number of US stocks that are up greater than a specified percentage from X days ago. This was a rolling indicator for the time frame. For example, the indicator could say that there are 20 stocks up greater than 30% in 15 days on Day 1, then on Day 2 it could also say 20. The 20 stocks on Day 2 may be the same stocks as Day1, or there could be a few that are different. I am not interested on whether or not the stocks are different from day to day. I am only concerned with how many stocks have exceeded the return for the start date for the time period.
I summarized the data using several statistics. The statistical summaries are shown in the chart below:
I began analyzing the data by looking at the average and median number of stocks for each period.
The bars represent the average number of stocks (over the entire 11 years) that exceed the return threshold each day. The data table is included below the chart for each bar value. In order to interpret the chart, take the first value in the data table, 710 (upper left), as an example. There are 710 stocks on average each day that have returned greater than 5% in the past 5days. Look at the last value in the data table, 55 (lower right), as another example. On the average day, there are 55 stocks that are up greater than 50% in the past 20 days. The chart shows the average number of stocks exceeding the return threshold decreases as the threshold increases, no big surprise.
The bars represent the median number of stocks (over the entire 11 years) that exceed the return threshold each day. Using the first value in the data table, 50% of the days during the 11 years had at least 591 stocks that had a return greater than 5% in the past 5 days. The median values are considerably lower than the average values due to the distribution in the results. The results are heavily skewed, as indicated by the chart below:
The average will be larger than the median because the distribution is skewed to the right, yielding a long tail. For this analysis, the median is a better metric for the number of stocks compared to the average. The median will indicate the number of stocks that exceeded the return on 50% of the 11 year test period. To get a feel for the extremes of the period, I plotted the maximum number of stocks to exceed the return in the chart below:
There is a significant difference between the max values and the average/median values. For example, on one day during the 11 year look back period, 4301 stocks exceeded a 5% return in 5 days. This is over half of the US stock market (about 7000 stocks) and 4301 is over 7 standard deviations above the mean. I would not use a normal distribution to model these results. Whats more incredible is that on November 28, 2008, there were 419 stocks exceeding a 50% return in 5 days!
I calculated the percent of days during the 11 year look back period that exceeded each return threshold. This will help to define the distribution of results better than a single number like the average or the median. Below is the chart for the stocks exceeding returns in 5 days:
The bars indicate the number of stocks that exceeded the return threshold in 5 days. I calculated the number of stocks that exceeded the return threshold for 90%, 75%, 50% (median), 25%, and 10% of the days during the 11 year look back period. I also included the maximum and average number for stocks exceeding the return threshold for the entire look back period. Using the first column of the data table, 90% of the days had at least 276 stocks that exceeded a 5% return in 5 days, 75% of the days had at least 390 stocks exceeding a 5% return in 5 days, 50% (which is also the median) of the days had at least 591 stocks, 25% of the days had at least 869 stocks, and 10% of the days had 1224 stocks exceeding 5% in 5 days. Below are the charts for 10, 15, and 20 days:
How are these numbers helpful? They can be used to determine what to expect in terms of returns on any given day. Let's say I was trying to pick a stock that I thought would increase in price by 50% in the next 5 days. From the charts, I know that 90% of the time there is only going to be about 1 stock that will return >50% in the next 5 days. Even on the best days (top 10%), there are only about 20 stocks that will return >50% in the next 5 days. These charts provide a feel for what to expect from the market in the coming 4 weeks.
Future exercises will determine how to separate between most days (90%) and the best days (10%). If I can develop a filter to identify the 10% of days that see the best chances of stock picking, I will certainly improve the odds of success. I can also use these results to identify groups of stocks based on the opportunity how long I want to hold a trade, what return I can expect, and the number of stocks that would fit those criteria. Finally, once a target group of stocks is selected, I can then study the characteristics of that group to help improve the chances of selecting the correct stocks.
No comments:
Post a Comment