How many contract to trade? Strategy allocation.

[the hare]

Why will I lose all my money?

Because if you are trading at optimal F (rather than some watered down version), you are on the very right hand edge of the curve, just before it drops to zero. The slightest change in the distribution of returns can tip you over the edge (and frequently does if you try any type of walk forward optimisation).

The practical difficulties of dealing with a method which involves such massive varience are too much for most people. Lets assume you have an account balance of 10 million, and you witness a drawdown to 700 thousand, (which is a perfectly reasonable thing to expect when trading at optimal f), most people start to worry that perhaps the underlying distribution in returns has shifted, and the value of f that they are currently using was perhaps too agressive (maybe it is, and maybe it isnt but you wont know until you risk your last 700K to find out)

I wouldnt totally discount optimal f, particularly If someone has a small account that they dont mind taking a punt on its probably a fun thing to do, but I wouldnt like to see 100% of my assets at risk under those kind of circumstances.

Ironically, although optimal f has such high drawdowns, 95% of the time even if you quit after the drawdown you'd still be better off than trading at 1-2% fixed fraction, but in my experience, the derivation of f is just too problematic, and you end up with values that are too agressive. As I said previously, if you water down f to a fraction, you lose the growth, and its really no different to trading any other fixed fraction method (which is absolutely fine)

 

[Joey25]

Nice thinking. I usually do this analysis of randomly reorderin the trades. This is done out of the box by certain software apps. The question I always bring on the table is that this analysis is not valid for mechanical strategies because I beleive that one trade is not independent from the last. So this renders this random reorder useless imho.

Monte Carlo analysis is also a good way to go following your way of thinking about the expected DD. But I like yours more (providing we accept randomly reordering trades as valid). I'll do a couple of test tomorroww and see what I get.

Thanks for your interesting reply.

H

The sampling-with-replacement method you refer to is the bootstrap. The way to get around the problem of autocorrelation in trades is to sample "blocks" - this way your simulated series retain any dependencies. You are quite right to suspect that the simple bootstrap is incorrect - this "whitens" the series.

One problem you get by sampling blocks is as follows:

1,2,3,-2,4,5,6,8

In the above sequence there are 8 trades (or returns). If we are sampling blocks of size 3 at a time then this means that we sometimes start at the 6. The answer is then to circle round to the beginning of the sequence, so that the draw in this case is {6,8,1}.

The optimal block bootstrap is right at the cutting edge of research and unfortunately involves spectral density estimation, but the answer is to play around with different block sizes and to check your results are robust to changes in this parameter.