## Maximum MAR; optimal betsize

Discussions about Money Management and Risk Control.
corvus
Senior Member
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Joined: Sat Sep 01, 2007 11:41 pm

### 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:
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
That left me wondering why the above is statement is true, so I am hoping this is the time for the discussion.

sluggo
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For those who wish to run experiments and analyze data, let me offer a couple of suggestions:
1. 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.
2. 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.
3. 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.
4. Right-click on the Blox output table and select Export to Excel.
For example, the experiment outlined in Figure 1 will let you observe the positions of the peaks in CAGR, MAR, MaxDD, and SharpeRatio. Before running it, make a prediction: Will (maximum MAR) occur at the same betsize as (maximum CAGR)? At a smaller betsize? A larger betsize? Then when you run the simulation (which takes less than an hour), check to see whether your prediction was correct.

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
Figure 2. Shows the high resolution Statistics (last 4 columns)
fig2.png (11.55 KiB) Viewed 13508 times
Figure 1: System parameter settings to study peak-CAGR, peak-MAR, etc.
fig1.png (26.54 KiB) Viewed 13510 times

corvus
Senior Member
Posts: 31
Joined: Sat Sep 01, 2007 11:41 pm
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.

ecritt
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### Re: Maximum MAR; optimal betsize

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:
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
That left me wondering why the above is statement is true, so I am hoping this is the time for the discussion.
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.

Roscoe
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Location: Houston TX
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?

sluggo
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sluggo wrote:For those who wish to run experiments and analyze data ...
... your results may resemble the image shown below.

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 13251 times

ecritt
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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)

LeviF
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If the scale of that chart was adjusted, the blue line would resemble the "rightward-facing whale" that Eckhardt describes in Market Wizards.

Eckhardt states one should stay to the left of the [blue dot]. Which is probably close to the green dot.