(Fotis, Reason for Edit: Graphs)
Greetings to all,
I have been re-visiting the issue of the waiting time to re-enter the market, one a signal has been issued to exit from the current trade (e.g. when the current price drops below the entry price, in any of the two variations we have explored). Although in our code we have provided the option of a threshold parameter as a % of the entry price to fine-tune the exit strategy, we still have had questions about an approach that deals with “how many days should I wait before re-entering, if I do not want to wait until the next buy signal is issued and the standard moving average is still on?”
First, here is a reminder: if one looks at the price path itself then, once an exit signal is issued, the waiting time for a return to the origin (i.e. the last entry price) may be infinite – depending on certain assumptions underlying the nature of the random walk that prices follow. Therefore, once you exit you: (a) either wait for the next signal to re-enter or (b) you go short on the asset. How fast you exit is controlled by the threshold parameter.
Suppose now that instead of looking at the price we look at the intervals between signals, whether from the standard or the improved moving averages (in fact the following discussion applies to any signal variable). For concreteness consider the intervals you are out of the market and count the number of days per interval. Then, you generate a new time series of waiting times or durations which you can try to fit to an appropriate distribution. These durations correspond to the number of days you have to wait to have a new entry, whether this is issued by a new buy signal or be having the current price rise above the last entry price. It should be clear that the properties of such a series of waiting times is data and method dependent; however, can we draw some useful conclusions by modeling it?
The four figures below give a preview of some work-in-progress on this issue. They contain QQ plots of the durations for all 9 signals that our code returns benchmarked on the geometric distribution (which is suitable to this kind of analysis). Figures 1 and 1a are for SPY with the exponential and the weighted moving averages respectively, while Figures 2 and 2a are for EWJ again with the exponentiala and weighted moving averages. For both series the star date is 1993 and the look-back periods were 20 and 100 days; an exit threshold of 3% was also used.
The results show some consistencies that are surprising yet useful: (a) the fit of the geometric distribution is extremely good for both ETFs when the fast moving average is used, either in standard form or in the two improved forms (first vertical panel of three figures on the far left of each picture); (b) the fit decreases when we go to the slower moving average and decreases even more when we go to the moving average cross-overs; (c) the fit on (b) improves when we change from the exponential to the weighted moving average, again for both ETFs; (d) note that there appears to be a “kink” or discontinuity in the figures for the slower moving average and the moving average cross-over: this might imply that the waiting times cannot be modeled by a single probability in the geometric distribution but that probability might be dependent on the duration itself.
The above suggest two avenues of research that we are pursuing: first, how general is the result in (a) above and if it is how can we use it for more effective trading? For example, we could use the average waiting time implied by the geometric distribution to work out strategies for re-entry. Second, if the probability that determines re-entry depends on the duration itself how can we model it? I have made a modification to the standard geometric distribution that appears to be working and more results will be posted once we perform additional tests.
Hope you find this useful so please let us know of your thoughts.