Forex Automaton

3. The entry parameter: how often should one place new trades?

The entrance sensitivity threshold, t_en is applied as a filter to the forecast of the next price difference d. (E.g., d=0.01 means that tomorrow's close will be 1% above today's -- we are talking about day time scale). Values of d below t_en by absolute magnitude are ignored by the decision making process, which means that if something is done to the position on that particular day, it's not going to be caused by the need to catch (or dodge) the predicted trend. When t_en is low, trades are entered easily. On the contrary, when t_en is high, the robot is reluctant to enter trades, it takes a forecast signal of very large amplitude to lure the robot into the market. Fig.3.1 shows a simulation of what t_en, the ENTRY quantity on the horizontal axis, does to the new trade frequency, expressed in inverse days. (When an simulated algo trader is adding to an existing position, this is not considered a new trade).

The dynamics of the annualized return in Fig.3.2 is understandable: lack of selectiveness in the trade ideas (the lower settings of the entry threshold parameter) leads to decreased returns. The extreme conservatism, on the other hand, leads to the situation when trades are made so seldom that it is hard to expect returns. Thus, a maximum is to be expected; it seems that it is located in the range of the ENTRY values in the 0.009-0.010 neighbourhood. We begin to move down the right-side tail of falling returns with more conservative ENTRY values.

Curiously, what looks like the optimum value of ENTRY, is seen in Fig.3.1 to correspond to new trade frequency of 0.05, which means one new trade idea once in 20 days! Recall that the system currently under study monitors the market daily, that is, it digests the information and makes a decision once a day. The decision may very well be to do nothing new today, in which case the day will count as a "no new trade" day for the purpose of constructing Fig.3.1. I wonder if the optimum for someone who checks this 24-hour a day market hourly will turn out to be selecting one trade idea per day, and for someone who looks at the screen every 10 minutes -- one trade idea every 3 hours or so. What's behind these guesses is the hypothesis of scaling, namely that as you "rescale" the market, as if by re-binning your bar chart, things stay in some statistical sense "the same" in the new time unit -- the thing that matters is the number of new time bins, not the actual astronomic time. (This scaling idea is frequently talked about by Mandelbrot.) Such a pattern of reasoning can be extended in the direction of wider time bins as well. Take Warren Buffet who, not being a forex trader, is said to make "one big decision a year". If the 1:20 (0.05) number holds, and the "decision" in this context implies buying or selling in some market, this means it takes Buffet 12 business days to complete each round of looking at things on his "big picture" scale of analysis.

Fig.3.3. Collection of profile histogram fragments following the same format as Fig.3.1 (return vs entry parameter), but for the individual markets. Compare the trends in the distributions of the points. Click on any panel to get to the report with the full information.

Fig.3.2 is effectively an average of the individual panels presented in Fig.3.3. Those latter ones show considerable similarity in shapes. AUD/USD is again an exception, as it seems to require more conservatism in trade idea selection than any other market shown -- seen from the fact that its maximum is shifted to the right along the t_en axis.