That left me wondering why the above is statement is true, so I am hoping this is the time for the discussion.It's also fun to note that the maximum MAR ratio occurs at a betsize less than the optimal f. But that's another discussion for another time
Maximum MAR; optimal betsize
Maximum MAR; optimal betsize
I've been reading through some past threads and I came across viewtopic.php?p=17701&highlight=curvature#17701 which I found really interesting and clearly explained. Here is the part I am having trouble with:
For those who wish to run experiments and analyze data, let me offer a couple of suggestions:
Figure 2 shows the higher resolution Statistics in the results table. They have more digits of resolution, making it easier for you to find the absolute peak.
The system code is attached in a .zip file.
 Blox is an excellent tool to use for this kind of study, because it lets you change the betsize ("%Risk per trade") in a Stepped Parameter Run, and then save the results to Excel for further analysis. Once the data's in Excel you can make your own set of customized plots, overlays, etc.
 Blox prints CAGR, MAR, MaxDD, Sharpe with only two digits of precision after the decimal point. I suggest adding your own Statistics (or PRINT statements) in the AfterSimulation script, and forcing more digits of resolution. This makes it easier to discern the absolute peaks of the graphs.
 Run the simulation with a large Starting Equity (such as: $75 million) to be certain you'll take every trade, even at the beginning of the simulation, with a large enough position size so that rounding effects are negligible.
 Rightclick on the Blox output table and select Export to Excel.
Figure 2 shows the higher resolution Statistics in the results table. They have more digits of resolution, making it easier for you to find the absolute peak.
The system code is attached in a .zip file.
 Attachments

 hires.zip
 Donchian system code with high resolution Statistics
 (2.34 KiB) Downloaded 800 times

 Figure 2. Shows the high resolution Statistics (last 4 columns)
 fig2.png (11.55 KiB) Viewed 13644 times

 Figure 1: System parameter settings to study peakCAGR, peakMAR, etc.
 fig1.png (26.54 KiB) Viewed 13646 times
Sluggo,
I donâ€™t own TradingBlox, mostly because I don't want to go through the rigmarole of installing Windows on my Mac. Yet, I also appreciate your advice. Even more so because you make the reader work through the problem rather than drag them through it. So I think the course is fairly clear.
Thanks for the guidance. It will take me a few days to get everything purchased and set up on the computer, plus a bit to work through everything after I get it.
I donâ€™t own TradingBlox, mostly because I don't want to go through the rigmarole of installing Windows on my Mac. Yet, I also appreciate your advice. Even more so because you make the reader work through the problem rather than drag them through it. So I think the course is fairly clear.
Thanks for the guidance. It will take me a few days to get everything purchased and set up on the computer, plus a bit to work through everything after I get it.
Re: Maximum MAR; optimal betsize
Optimal F maximizes the growth rate yielding the highest terminal wealth. The MAR ratio is ((growth rate) / (max drawdown)). Solving for the maximum value of this fraction is quite different from simply trying to make as much money as possible.corvus wrote:I've been reading through some past threads and I came across viewtopic.php?p=17701&highlight=curvature#17701 which I found really interesting and clearly explained. Here is the part I am having trouble with:
That left me wondering why the above is statement is true, so I am hoping this is the time for the discussion.It's also fun to note that the maximum MAR ratio occurs at a betsize less than the optimal f. But that's another discussion for another time
Perhaps I can expand slightly on what Eric has just said: if my memory serves, Optimal f delivers the highest geometric rate of growth (translation: the most money that can be made) but while it does this it can incur epic drawdowns in the process. MAR, as Eric says, is CAGR/MDD and so while the CAGR may be huge while trading at Optimal f the MDD may be even bigger (huger?), hence the disparity. Does that help any?
... your results may resemble the image shown below.sluggo wrote:For those who wish to run experiments and analyze data ...
I have placed a dot at the peak of each curve. You may or may not be surprised to note that each dot appears at a different betsize. Thus the "optimal f" betsize (blue dot) does not maximize the MAR ratio (green dot) and vice versa.
When MaxDD approaches 100%, the CAGR and the MAR become the same number (since MAR = (CAGR/MaxDD) and MaxDD is very nearly 1.0000), so the green line and the blue line converge.
The crazy behavior of the black line alerts you that when system has completely wiped out (at the right side of the graph), the Sharpe ratio becomes unreliable. Jack Schwager remarked upon this in his 1996 book (link) on page 32.
 Attachments

 One picture is worth a thousand words
 1000words.png (19.97 KiB) Viewed 13387 times
Sluggo,
That is an outstanding chart. Excellent.
Sluggo replies: Nah, it's just the output of a Blox "Stepped Parameter" simulation run, plotted using Excel (to get all four curves on the same graph). Only took an hour from start to finish, including the chart. Blox did all the work. S. (see fig1.png above)
That is an outstanding chart. Excellent.
Sluggo replies: Nah, it's just the output of a Blox "Stepped Parameter" simulation run, plotted using Excel (to get all four curves on the same graph). Only took an hour from start to finish, including the chart. Blox did all the work. S. (see fig1.png above)