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# Fortune Formulae: Money Management that Beats Kell's Formula

You know that money management is at the heart of trading systems in which one can lose for a given trade, but win on average.

Kelly produced his formula in Bell labs, which was essentially an entropy optimization method. It essentially says that you should bet an amount such that if you were to win the amount to be won is equal to the average (arithmetic return) return of a trade.

The question I posed to myself is: could one develop better than Kelly? This may seem strange as a question particularly given the fact that kelly's formula maximizes the geometric return.

At first sight one cannot do better. But there are hidden assumptions in Kelly -based systems which if looked at again one can design superior money management formulae.

An example of implicit assumptions in Kelly's formula is that one has no knowledge of the underlying distribution of trade returns.

Therefore, Kelly's formula is implicitely making the assumption of a particular type systems (bernouilli trial type of systems).

Here is a challenge to you. Could you do better than Kelly's formula? You can assume any distribution of trade outcomes or any particular knowlegde on this distribution such as type of distribution, moments of distribution, etc.

You would then start seeing that Kelly's money management formula can be suboptimal, either because it can lead to lower geometric returns, and/or one can get the same goemetric returns of Kelly, but with less variance.

Get to work, and show us what you got!

If you know of others who challenged Kelly's formula, let us know here.

The experts in money management: tell us what you know and what it is possible and what is not possible?

2. ### nonlinear5

Kelly's formula does account for the distribution of returns, as it contains terms such as average profit per trade, average loss per trade, and probability of a gain/loss.

I suppose if you have some weird distribution, it would be possible to improve Kelly's in a way that it finds a better maximum in geometric return. Analytic solution probably doesn't exist, but it shouldn't be too difficult to find one with a Monte Carlo simulation.

As a side note, I'll say that a more interesting problem is to maximize the return/risk ratio, not the return itself.

3. ### phattails

Why not look in academic publications. Find the original paper and look for publications that use that as a reference.

4. ### slacker

Good suggestion, the attached research paper describes using a fraction of Kelly to produce a 'never look back trading goal' to reach a point where your chances of giving everything back to the market is very small. It is one of the better papers I have seen on the subject.

However, using historical data to determine risk is not a low risk approach as your historical data probably does not include 'black swan' size adverse moves. (see Taleb's Black Swan for a full description.)

I think you can combine a Kelly Fractional approach as long as size does not exceed a 'max loss limit' based on non-historical data.

Good luck,

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5. ### slacker

Also on the subject, this month's edition (August) of Futures magazine has an article entitled "Minimizing your risk of ruin" which is very interesting. It does not tell you what position size to trade tomorrow, but does describe how much 'risk of ruin' a trader is carrying based on past trading results. Worth a read.

Good luck.

Past trading results cannot provide any information about future risk of ruin due to possible black-swans. I have not read the article but have stopped reading trading magazines long time ago because of the extremely low quality of most of the articles written essentially by newbie traders or people who do not trade. People who trade have no time to write articles and the marginal gain for them for such activity is nothing compared to trading profits. Have you ever seen an article by G. Soros in one of those magazines?

I can safely infer that only losers write trading articles, other than the ones that describe technological infrastructure, product characteristics or review software.

7. ### Martinghoul

I agree with nonlinear here...

While there may not exist a general Kelly-like framework with analytical solutions, all you need to do is define the appropriate parameters for your particular strategy and just apply Monte Carlo. If you do it sufficiently rigorously and your hypothesis is correct, you'll be able to define per-strategy criteria that will maximize whatever you seek to maximize.

8. ### acrary

Optimal F by Ralph Vince is a good way to find the optimal geometric mean for trading. The real question I found is whether to trade size at the geometric mean or a sub-optimal level using Monte Carlo sims for drawdowns. i.e. If I'm willing to suffer through a 30% drawdown should I place 70% of funds in T-Bills and risk the 30% at the geometric mean or risk say 1% of the total account that models to a 99% confidence level DD of 30%.

9. ### athlonmank8

Hmmm why optimize it?

10. ### Bernard111

We could ask Mr. Vince... he've been here @ ET a few weeks ago.

#10     Aug 16, 2009
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