- Data for testing
- Point A
- Failed Point A
- Point C
- Pivot range
- W-pivot range -new
- Points A and C through the pivot
- Closing method -new
- Dynamics of Points A and C
- Significant time frames
- Entry and exit

Appendix

Testing, research and upgrade of Mark Fisher's ACD system, trading programs

- Data for testing
- Point A
- Failed Point A
- Point C
- Pivot range
- W-pivot range -new
- Points A and C through the pivot
- Closing method -new
- Dynamics of Points A and C
- Significant time frames
- Entry and exit

Appendix

According to the ACD theory, the opening range is most often the high or the low compared to any other time interval (see page 12 of The Logical Trader). If this were not so, then breakouts in the opening range in both directions would occur almost every day. But breakouts in only one direction occur much more often than might be expected according to the random walk theory. For example, for SBER stocks, the number of breakouts in the 20-minute opening range in one direction only is 1127 for 2422 trading days. If random walk theory were in effect, the number of breakouts in only one direction would be only 186. By the way, the number of trades from Point A is much larger than from Point C. And point C is established only in case of a breakout in both directions.

We can estimate the probability *P* that the opening range will be the high or the low during the trading day, as

*P=N1/N*x100%

where

*N1* – the number of breakouts in the opening range in only one direction during the trading day,

*N* – total number of days used in backtesting.

If there were never breakouts in the 2nd direction and breakouts in one direction occurred every trading day, then *P* would be equal to 100%.

Substituting the actual values, we get *P*=1127/2422x100=46.5%. Thus, for SBER stocks, the 20-minute opening range is the high or low during the trading day as often as 46.5% of the time. In the case of random walk theory, the 20-minute opening range will be the high or the low of only about 7.7% of the time, given that a trading day lasts an average of 517 minutes (2x20/517x100% = 7.7%. Coefficient 2 is present because the opening range can be both the high and the low. Trading day on the Moscow exchange began at 10-30 a.m. until August 31, 2011. Now it starts at 10 a.m. and for stocks ends at 19-40 p.m. After the calculation, we get 517 minutes for the average trading day).

Thus, the opening range is really statistically significant.

The above formula for *P* does not take into account the likelihood that the 2nd breakout will not occur, but the market will reach the corresponding border of the opening range one more time later during the trading day. In this case the opening range will not be the high or the low. However, such cases are very rare and affect the value of *P* little.

For accuracy, I developed a simple program that calculates *P* by comparing the high and the low of the opening range with the price levels of the remainder of the trading day. If the low and the high of the opening range is less than the low and the high of the remaining part of the trading day, or the high and the low of the opening range is greater than the high and the low of the remaining part of the trading day, then the opening range is considered the high or the low of the trading day.

The results of these accurate calculations are presented in Table A.12 in the Appendix for different opening range time frames and securities.

It follows from the table that the opening range is the high or the low during a trading day from 2.1-13.4 to 3.9-30.2 times more often than in the case of the theory of random walks depending on security (see the 2nd row in Table A.12 for each security). The less the opening range time frame, the more often the opening range is the high or the low compared to the theory of random walks, i.e. the lowest and the highest number (for example 3.9 and 30.2) correspond to 40- and 4-minute opening range respectively. Such a big difference between the lowest and highest numbers is extraordinary. At first I thought it was because at the very beginning of the trading day, the volatility was the greatest. I backtested how many times the difference between the high and low of the opening range is on average greater than that of other equal intervals during the trading day. It turned out that for the 4-minute opening range, this ratio was the largest. On the other hand, the difference between the high and low of the 4-minute opening range is greater than that of the other 4-minute intervals, only 2.7-5.7 times (not 13.4-30.2 times!) depending on the security (see the 3rd row in Table A.12 for each security). Thus, we see that the statistical significance of the opening range is determined not by the difference between its high and low, but by something else.

The fact that the opening range is most often the high or the low during the trading day seems to allow you to make a profit as follows. As soon as the market breaks through the upper or lower border of the opening range, a long or short position is opened, respectively. The position is closed at the end of the trading day. Profit and p/l for this strategy are presented in Table A.12 (see the 4th and 5th rows for each security). They are not impressive, in some cases the profit is even negative. Although the opening range is much more often the high or low during the trading day, making a profit in such a simple way is difficult. True, for stocks, profit is rising and positive for higher opening range time frames.

The Logical Trader also emphasizes the statistical significance of the first trading day of the month (see page 47). I backtested this idea for different securities. The program compares the high and the low of the first trading day of the month with the high and the low on the remaining days of the month. If the low and the high of the 1st trading day are less than the low and the high of the remaining part of the month, or the high and the low of the 1st trading day are greater than the high and the low of of the remaining part of the month, then the first trading day is considered the high or the low of the month.

The results of these calculations are presented in Table A.13 in the Appendix. As can be seen from the table, on the 1st trading day of the month there are 28.2-39.4% of the highs and lows of the month, depending on the security. In the case of random walk theory, the 1st trading day of the month will be the high or the low in only 10% of cases, given that there are an average of 20 trading days in a month (2/20x100 = 10%).

Thus, the 1st trading day of the month is really statistically significant.

It is possible that for trending markets some other trading day of the month can also be the high or the low as often as the 1st day. Therefore, it is better to consider stocks and futures that demonstrate an almost identical frequency of both highs and lows on the 1st trading day. These are RI, BR, ED, GAZP and VTBR, as can be seen from Table A.13. Although they grow and fall almost equally often, they have the high or the low on the 1st day of the month in 28.2-39.4% of cases. This proves that the 1st trading day of the month is statistically significant not only for trending markets, but also for flat markets.

For other trading days of the month, except the 1st day, I did not make calculations, because it is not clear how to do them - compare, for example, the 5th day with the remainder of the current month or until the 4th of the next month.

The question arises, how to use the significance of the 1st trading day of the month for profit? To do this, you can follow what happens on the following days of the month. As soon as the market rises above the high or falls below the low of the 1st trading day of the month, a long or short position is opened, respectively. Position is closed at the end of the last day of the month. Profit and p/l for this strategy are presented in Table A.13. The results are mixed. For futures, profit is positive, and for most stocks, it is negative. Perhaps before opening a position, you should wait for confirmation, for example, Point A.

As stated in The Logical Trader, plus and minus days are most often repeated in a 30-day trading cycle (see page 50). I checked this idea by backtesting different trading cycles for different securities. The program works as follows. First, it calculates the pivot range for each day based on the high, low and close for the previous day and identifies the plus and minus days. In the case of a 30-day trading cycle, the program checks, starting from the 31st day, where the opening takes place. If the opening is below the pivot and 30 trading days ago was a plus day, then the program checks if the 31st trading day is a plus day. If the opening is above the pivot and 30 trading days ago was a minus day, then the program checks if the 31st trading day is a minus day. This procedure is performed sequentially day after day until the current day. The program performed the calculation for trading cycles of 1, 2, 15, 29, 30, 31, and 45 days.

The results of these calculations are presented in Table A.14 in the Appendix. It turned out that for all trading cycles, the plus and minus days are repeated almost equally often, in about 30% of cases. In terms of repetition rate, a 30-day trading cycle is no better than, say, a 29- or 31-trading cycle.

Thus, a 30-day trading cycle is not statistically significant in terms of the repetition rate of plus and minus days.

It is noteworthy that in the case of a 1-day trading cycle, if the previous day was a plus (minus) day, then the next day, opening below (above) the pivot is rare. This is not surprising: for the plus (minus) days to follow each other, on the 2nd trading day there should be a gap down (up), which does not happen often. As can be seen from table A.14, the repetition rate of plus and minus days in the n-day trading cycle is slightly higher than the percentage of plus and minus days of the total number of days.

I did not take into account the additional condition indicated in The Logical Trader about the volatile session 30 trading days ago from the current day. Perhaps this would change the results. In fact, I don’t know how volatile the market should be, and even if I could take volatility into account, the plus and minus days would be repeated less frequently in the n-day trading cycle, and the results could be statistically unreliable.