Average Absolute Deviation
Excel's Avedev() function is all I can afford to fully understand. Sharpe ratio is too complex for me, but I see that it might have added a different point of view on my systems' performances, that it can tell me things about my systems that Return On Account and Profit Factor alone cannot tell me.
Now, since it relies mostly on Standard Deviation, which is also too hard for me, but which has to do with average deviation, that is what I will try to focus on:
http://en.wikipedia.org/wiki/Average_absolute_deviation
During the weekend, I will plot a hypothetical system, with its own chart, and just 20 trades or so, and I will tweak it to see if all situations need to be described with those three ratios, or if I can do without the Average Deviation.
I will document my progress here, as long as I can edit this post, and later on another post. I do it all here, because it gives me more motivation to study in front of everyone, like in highschool's "study hall", where a professor checks on you if you are studying.
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Now let's first study in depth what this simple function does, so to avoid any misunderstandings. Indeed, I feel this function is more solid and reliable than that crap Sharpe Ratio. The simpler, the better. No squirt roots here.
This formula on excel corresponds to:
=avedev(range).
This formula:
1) first computes the average of a series of numbers, and
2) then measures the (absolute) distance of each number from that average.
3) Then it adds all these (absolute) distances together and divides them by how many items are on the list, thereby telling you the average distance of all items from the average value of all items. I think this is simple enough and good enough. I don't need any Sharpe Mother ****ing Ratios.
Let's move on.
Let's say I have two different systems that both make 20 points profit. One system achieves this by making 20 trades of 1 point each. And this guy will have an average deviation of:
1+1+1+.../20= 1 (average of values on the list)
|1-1|+|1-1|+|1-1|+|1-1|+|1-1|+...=0/20=0
Now. A system that makes 20 points by making 1 point per trade and never losing is the best system of all, ceteris paribus (all other things equal). So obviously a ranking of zero is the best ranking (for a profitable system). I wonder if we could go as far as dividing total net profit by average deviation, and obtain simply how good a system is, but then we'd make things more complicated, so for now let's at least postpone it.
Now let's look at another system, since by now it's totally clear what we mean by average (absolute) deviation. This system makes 20 points in 20 trades, but instead of making 1 point per trade and never losing, it makes these trades:
1
1
1
1
2
0
1
1
1
-1
2
3
1
-2
1
2
1
2
1
1
And achieves a AveDev of 0.60, which so far makes sense, because I was expecting such a higher number to rate a worse system.
Now, always with an overall profit of 20 points, let's compare a system that has 3 trades of 0, and three trades of 2 with another that has 3 trades of -1 and 3 trades of 3. There are no doubts that I prefer the first one, because it never has a loss. But let's see what their AveDev scores say. I will later attach the excel sheet for anyone's utility.
So, here I compare the first one:
DATE GAIN
04/01/2010 1
04/02/2010 1
04/03/2010 1
04/04/2010 1
04/05/2010 1
04/06/2010 1
04/07/2010 0
04/08/2010 2
04/09/2010 1
04/10/2010 0
04/11/2010 2
04/12/2010 1
04/13/2010 0
04/14/2010 2
04/15/2010 1
04/16/2010 1
04/17/2010 1
04/18/2010 1
04/19/2010 1
04/20/2010 1
total profit 20
average deviation 0.30
With the second one:
DATE GAIN
04/01/2010 1
04/02/2010 1
04/03/2010 1
04/04/2010 1
04/05/2010 1
04/06/2010 1
04/07/2010 -1
04/08/2010 3
04/09/2010 1
04/10/2010 -1
04/11/2010 3
04/12/2010 1
04/13/2010 -1
04/14/2010 3
04/15/2010 1
04/16/2010 1
04/17/2010 1
04/18/2010 1
04/19/2010 1
04/20/2010 1
total profit 20
average deviation 0.60
Ok!!! That's good. It even signals that it's bad, with its own ranking of 0.60, so twice as bad. But now that I look at it, it was also obvious that it would've scored a higher (thus worse) value, because 3 goes further from the average and so does -1.
So I am very happy with this new rating of my systems, and I feel that Return On Account and Profit Factor get close to this type of measurement but they're not the same. Yes, if I had to only rely on one of them, I would use ROA, followed by PF, but here's their limits.
1) ROA tells you how well it's done compared to how badly it scared you with its worst drawdown. Yet it definitely does not tell you how
often it scared you. So AveDev so far is useful.
2) Profit Factor tells you how often and how much it wins compared to how often and how much it loses. I realize that many of these performance indicators overlap: the average trade profit could tell you much of what PF tells you. For example, if you see a system that return a million dollars, you would think it's great. But what if they tell you that its Profit Factor is 1.01? This indicates that the system has a gross profit of 101 millions and a gross loss of 100 millions, which would suck. Unless of course we imagine unlikely hypotheses that such a systems trades 100 millions times a day and doesn't require any margin.
Now let's even say that this system achieved this (small) profit by each time winning 101 dollars and losing 100 dollars, one up, one down... until 101 millions of gross profit and 100 million of gross loss. Now this system would have an amazingly good ROA (1 million over 100 dollars), but luckily the PF tells you it still sucks. So this means we still need these two performance indicators together. Now let's see if PF overlaps too much with AveDev.
Thinking... walking around the house... indeed it seems quite hard to fool profit factor.
Ok... after being clueless and lost for half an hour, I've decided as usual to work on what could be done, rather than quitting, and here's the beautiful piece of excel art which I developed, on which I will run endless tests in the days to come, to appraise how different performance indicators actually do their job at appraising a system.
I'll make sure to post later versions in case I create any. But this is a real masterpiece, and I'll be able to get a good idea of how well ROA, PF, AD appraise a system's performance.
SEE BELOW FOR FILE
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Eureka
Before losing this inspiration... what do I want from my systems?
1) To make as much money as possible - also in terms of leverage
2) To have as little drawdown as possible
Let me elaborate on this:
For every loss and drawdown I am risking to blow out my account, that's what this is all about. And since the maximum loss and drawdown can always be underestimated, I have to select not the systems who make the most money but the systems who make the most money compared to how much they could lose.
I believe that % profit is already measured by profit over maximum loss, which is already in my ROA index (because I customized it). In the sense that usually a future that will need a big margin will also have a big loss. Also, since I have more capital than needed, I don't need to focus to return in terms of investment, because I can invest on how many contracts I want, but the problem is not blowing out my account. So capital is not a concern in terms of profitability of it, but in terms of its relationship to drawdown. I don't even make total sense to myself, but I sense this is the way to go, more or less, with my limited knowledge and intelligence.
So, forget about leverage. I will focus on profit / average(backtested dd, forwardtested dd, maximum loss)
And that's already in my systems.
But we also said that profit factor enriches the appraisal of my systems, in the sense that we don't care if a system makes 2k if they're coming from gross loss of 10k and gain of 12k. That system sucks, and the ROA will never tell us. Take a system that makes 10 dollars today and loses 8 dollars tomorrow. In the long run it will look great in terms of ROA, because it has a max loss of 2 dollars, and a huge profit, but Profit Factor will tell us that it sucks by rating it with a 1.2. So...
...so far we have established that a good appraisal is the average of ROA index with Profit Factor.
Let's just make sure of this by citing an opposite case (bad ROA and good PF). We have a system that got unlucky and one day it had just one huge loss of 3k, such as the CL. But then, not only did it recover from it, but it went on to make a profit of 12k, without any more losses. Now, this system will have a PF of 4, but its ROA index will look worse than the other one, and yet this system is better.
So, these two, which I use presently are good.
What does the AveDev add?
I'll plot these systems and see what happens... by sticking real data in them, precisely these examples I used (I have real systems in mind, CL_ID and ZN_ON). When theory fails, I resort to practice.
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Ok, I am done. I will implement the average profit / average deviation on my new Final Index formula, and it will be responsible for my money management. All automated. That's enough ingredients for now.
Here's attached the latest file. I am done with this stuff as well. I will just start automating everything, starting tomorrow.
What reassures me is that all three parameters give very similar ratings. All systems score equally well or bad on ROA, PF, AveDev.
On the other hand, all three performance indicators have Profit on the numerator so it's normal, even though they are not identical.
Roughly, they rate each system's profit matching it against:
ROA:
Max Loss and Drawdown, and therefore risk of the system:
it produces great money but how dangerous was it at its worst moment?
PF:
Total Losses, and therefore accuracy of system:
it produces great money but how many trades did it take them to do so?
Av.Prof./Av.Dev.:
Unpredictability throughout all of its trades, and therefore
general risk of systems:
it produces great money but how dangerous was it on average during all its trades?
