29 September 2011

Optimising Percentage Risk

I have been reading Vince, R. (1992), The Mathematics of Money Management: Risk Analysis Techniques for Traders, John Wiley & Sons, Inc. Interesting book. A little confusing, but interesting. The central theme of the book is determining what the author terms "optimal f". Now just what this quantity is remains somewhat mysterious, but I have gathered that it is what is normally thought of as percentage risk. That is, what percentage of your trading capital you risk on any one trade. I am going to denote this as r (and assume that it is equivalent f, but expressed as a percentage).

Now the conventional wisdom is that you never have r > 1. A string of losses with larger r can leave your trading account severely depleted. At the same time, using r < 1 means that you are risking very little per trade, and consequently stand to gain commensurately little.

I have always just assumed that your winnings would scale linearly with r. For example, if you make $100 in a month using r = 1, then in the same month you would have made $200 with r = 2. Seems reasonable, right? Apparently not. The author of the book illustrates this point very nicely with an example of a simple coing tossing game in which you stand to win $2 (heads) or lose $1 (tails). In this case, it turns out that the optimal f is 0.25 (equivalent to r = 25). In other words, each time you play you should risk 25% of your capital.

So I wondered whether something similar applied with one of my trading strategies. So I chose a reasonably good set of parameters and then varied the percentage risk.

Wow, isn't that interesting? As r increases the payoff (average nett winnings per trade) increases until it reaches a peak (at r = 2.75) then declines. For r > 5.75 the payoff becomes negative and then gets progressively worse. The percentage drawdown also increases with r. Well, that stands to reason: the more you risk, the more you are likely to lose at any given time!

So, why is the simple linear assumption wrong? Well, evidently trading is a little non-linear. Consider the following two plots which show the evolution in account balance with (top) r = 2.75 and (bottom) r = 8.00.

Initially the curves look rather similar. However, whereas r = 2.75 incurs a relatively deep depression during the losing streak and is able to recover, r = 8.00 is almost completely depleted and really doesn't bounce back.

I am not suggesting that we should trade with r > 1, but it is interesting to know that there is an optimal percentage risk. Perhaps this might in some instances be at r < 1? More research required.

17 September 2011

Quiz Night

Quiz night at Northlands Girls' High School. We have been on a team for the last few years, faring reasonably well: not at the bottom and not at the top, just somewhere in the middle. But this time we ripped the thing apart. Largely due to a few very clued up folk on our team!

Based on the last few years, things that are good to know for this quiz:
  • flags of the world,
  • all sorts of obscure quotes, and
  • what's going on in the news (obviously!).

16 September 2011

Crackpot Friday

I have to confess: I do a lot of reading on the toilet. This morning I dug a little bit deeper into my pile of literature and found something that looked really interesting:

Predicting the stock market. Hell yeah, been trying to do that for a couple of years. Maybe this guy knows the secret? But, hold on, what's this? His prediction technique has something to do with "planetary cycles". Hmmm. That's a little bit troubling. I do know that the solar cycle really does have an influence on the price of wheat, but the planets... surely not?

In the Foreword things immediately start to go wrong:
It is not the intention to promote stockmarket activity, but rather to show and to prove the correspondence between planetary operations and market responses.
So he is back pedalling immediately. Apparently the book is not about predicting the stock market after all... But then it all becomes clear:
Those who are already conversant with astrological principles...
Oh, it's astrology is it? Well then, since I was born on 16 June then surely GKX is right for me. No need to read any more: BUY, BUY, BUY!

PS. You can actually buy this drivel online for the princely sum of around $56.
PPS. But I might just be able to give you my pdf copy. Whoops, no, looks like I deleted it.

08 September 2011

PIC Dispersion Relation

My Phd student, Etienne Koen, is using Particle in Cell (PIC) techniques to simulate beam-plasma instabilities. This shows his most recent result. The black curves are the theoretical result.

Isn't that beautiful?