Acceptable Max Drawdown

benji · Post by **benji** » Sat Jul 21, 2007 12:36 am

you're welcome. Actually the kelly here won't be the standard kelly but more the leverage that optimizes your capital growth under the drawdown constraint. You don't have to be scared of your higher moments, you can just feed the histogram of returns for obtaining your results numerically.

And i really think you need to give us the drawdown you don't want to see so that one can comment on the leverage, because that's the one relevant parameter (unfortunately all these kelly-like optimizations are strongly dependant on some elusive risk aversion parameter)

BTW *all* the details to solve that problem are in the paper posted by goldorak in this thread.

Tradenator · Post by **Tradenator** » Sat Jul 21, 2007 1:54 am

1.5 leverage gives me a worst month (in the sample Jan2000 - Mar2007) of -7.7%. I can leverage up to 195.5% to get a -10% worst month. This is different than the DDM discussed in the paper you mention (DDM is the chart posted earlier), but it does give an indication. And finally, yes, I'll try the empirical distribution approach.

FoF managers out there: your thoughts on worst month?

Tradenator · Post by **Tradenator** » Sun Jul 22, 2007 11:13 am

I get a Kelly optimum position of 7, ie 700% leverage (blue in the plot below.) I assume I did it right...the lines are a just a "best eyeball fit" approximation.

[img]/User%20Files/1915/KellyLeverage.jpg[/img]

I think this is too much heat. And it is evident that my DDM values aren't Gaussian. Looking at the negative months, those aren't Gaussian either, but are maybe a little closer, though.

[img]/User%20Files/1915/DDMdistribution.JPG[/img]

So I have taken the following approach, which I believe to be conservative enough. Reporting is done monthly, and so I just consider the stats of the monthly returns. The backtest shows a 6-sigma event as the worst month (these are commodity futures, in case you didn't guess.) If I can risk a -15% month as a 10-sigma event, then 150% leverage is reasonable.

[img]/User%20Files/1915/WorstMonthLeverage.JPG[/img]

ra · Post by ra » Mon Jul 23, 2007 6:53 am

Any opinions on Seykota's "Lake Ratio" as an alternative to a simple max drawdown? Seems pretty sensible to me.

http://www.seykota.com/tribe/risk/index.htm

Baltazar · Post by **Baltazar** » Mon Jul 23, 2007 10:27 am

you also migth want to take a look at

http://moving-averages.technicalanalysis.org.uk/Ande99.pdf

the author takes a known model, the turtle trader one, and check for a betting scheme. it is more detailled in his phd thesis but that paper is a good start.

Tradenator · Post by **Tradenator** » Mon Jul 23, 2007 10:57 am

Baltazar, thanks for the link.

ra, you can think of D(t) from the Maslov and Zhang paper that goldorak posted as the depth of Seykota's lake. The authors used a similar type of plot to illustrate their method.

NIP247 · Post by **NIP247** » Tue Jul 24, 2007 12:04 am

Baltazar, nice pdf. I don't agree with him that this is the turtle system though. AFAIK, the turtle system was a channel breakout system with pyramiding, stoploss and portfolio sizing rules. That's however all beyond the point.

1) Regarding chosing a size of trades, I'm not very comfortable intuitively with the optimal f & Co. If we look at the strategy described in the pdf, a natural "stoploss" is actually the exit level, which is the 70d MA. If you size the trade as to max lose a dollar amount = x% of your portfolio, you respect most of money management rules of not risking more than a certain portion of your portfolio on any single trade. The problem is how to chose that level. Anecdotally, Market Wizards talk of anything between 1% to 3%

2) This doesn't help you when it comes to correlation between your positions. To account for that, should you calculate some value of historical portfolio behaviour to obtain some VR and then size up/down the whole portfolio based on a target value at risk? what I don't like about that is that you end up diminsihing exposure to let's say corn whereas what is really the source of your concentrated risk is that you just obtained the same signal on Oil and on Gas, or on EUR and CHF, and therefore diminishing just that position would actually diminsh your VR. Any suggestions?

3) Finally, how do you account for the composition of your portfolio changing when stop-losses in certain positions are hit, which by defintion change the (historical) VR of your portfolio. Do you continuously resize according to target VR? How does that affect total trading costs? Conversely, how do you leave room for new positions that could be included on any day but are not today and which would require resizing whole portfolio to accomodate a target VR?

So main portfolio selection idea: (1) size up trade to lose x amount of money max at stoploss level. (2) size up or down whole portfolio according to vR, calculating what the max vr jump might be if you drop 1 random position, 2 random positions etc... (3) resize portfolio when trades are added or dropped.

All comments and suggestions are welcome

Tradenator · Post by **Tradenator** » Wed Jul 25, 2007 2:25 pm

Just in case anyone is interested in where I ended up with my leverage issue, it was decided to propose 125% leverage, with scope to run up to 150%. More heat can be put into separate mandates on a case by case basis.

EDIT: I don't like the VaR approach. To me, risk is about the downside tail. VaR is about the body of the distribution and relies too heavily on assumptions about its form. You are better equipped to survive if you use max acceptable drawdown, which is nonparametric, easily quantified and easy to conceptually think of. In both approaches, you can underestimate the true risk by not having captured the true nature of drawdowns with any given sample, though.