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# Modeling Linearity

Discussion in 'Strategy Building' started by vanilla2, Nov 1, 2003.

1. ### vanilla2

Using tradestation's standard set of optimization parameters as building blocks, what is the best measure of linearity in an equity curve that somehow factors in the number of trades to determine a sort of efficiency measure?

Basically, I want to find the most linear curve with the fewest trades within a multi-dimensional matrix of strategy inputs and optimization outputs.

Would this be ROA / # of trades, like a sort of ROA per trade?

Or (Net Profit / max drawdown) / # of trades?

I tried working with net profit / # of trades, but realized this is simply a net profit per trade, which is biased toward fewer numbers of trades without really addressing the linearity issue.

2. ### bdixon619

answer this directly because I don't have TS. However, to measure the relative efficiency when comparing stocks to other stocks I did this:

Each day divide your gain or loss for the day by the stock's closing price. Divide the gain or loss for the day by the number of trades your system made that day. Add these two numbers together. Divide this number by the amount of commissions paid during the day. This will give you a measure of efficiency for the stock you are trading compared to other stocks you are watching. I would generally use three days worth of data for comparing anywhere from 12 to 20 stocks and update the three day block every evening then just watch the ones showing the best performance. As I built up a statistical record it became a little easier to find stocks to trade.

I have no idea how this would work for futures.

How about using Standard Error.

Take the equity curves total profit and divide it by the SE.
The higher the ratio the better the equity curve in terms of profit and linearity!

I actually use the Standard Error Band width.

So, for your use figure the standard error of the equity curves for the various opts, and divide the total profit for each by the SE. The highest ratio should be the best curve.

See the attached equity curve for an example

Bob

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4. ### vanilla2

excellent suggestions guys, thanks.

Bob, what platform are you using to calc standard error of an eq curve?

I know in TS, I could plot the eq curve as an indicator and apply standard error bands but this would become extremely tedious over a matrix of 75,000 input combinations. Are you using custom written software, or are you only performing this analysis on individual eq curves? If I had an easy way for TS to generate standard error, NP/SE sounds like an excellent metric. Thanks for getting me thinking in the right direction.

Basically the metrics I have readily available are # of trades, net profit, gross profit, gross loss, profit factor, % profitable, roa and max drawdown. I can manipulate these core figures in any manner in excel. Now that I need the functionality, I'm really surprised TS doesn't have more sophisticated DD analysis like standard error, average DD, or something ala Seykota's lake ratio which I believe compares the area under and over sections of the curve as drawdowns and new highs are made. Max DD leaves much to be desired.

thanks

any other ideas are welcome and appreciated.

I use Metastock
But for my simple systems it is sufficient and I can plot the standard error bands on each equity curve to aid in determining which of the systems is performing the best.

So, I do not use the equity output to curve fit my systems. I only use the equity output to determine which of several hundred systems I want to use in trading a specific market. From the equity curve it is possible with the standard error bands to determine the most linear systems. The equity curves that have the highest SW ratio are used for trading.

Bob

6. ### vanilla2

yes, curve fits are bad. i hesitate to trade more than two degrees of freedom, three max. what i'm working toward finding are the loci of efficiency across massive swaths of the input matrix. not for one specific best fit per se. the next step is to animate the data and observe how the efficient planes migrate over time. this could lead to an adaptive component. it's increasingly looking like a custom harness is required for this type of analysis.

Are there other good DD metrics, especially ones that can be abstracted from standard TS outputs?

7. ### Volker Knapp

No point in optimzing an equity curve of a single system on a single market. Believe me I have done it 10 years ago.

8. ### vanilla2

can you elaborate ... are you saying that arbitrary parameters are preferable?

hard core system people, how do you measure efficiency? since my initial post, i am coming to think MAR/#trades is decent. are there any mechanically focused boards anyone can perhaps point me to..