At the start of this thread, C3PO wrote:I am aware that people on this forum have warned against trading the optimal-f percentage. I am not debating that. I am asking about the mechanics of diversification with fixed fraction. I would very much appreciate it if someone can clarify this for me. Thank you.
I think you are asking a question that might have an answer but that your approach to the problem is flawed; further, that this flaw is so large that it makes the entire question irrelevant.
First, in order to arrive at an "optimal" figure, there need to be some inputs, namely expectation (aka expectancy), win/loss ratios, etc. These inputs are in turn the output of some process, either actual trading, paper trading, or simulation. Unless you've been trading or paper trading for many, many years and have been religiously applying a rigid and well-specified set of rules, the results from trading or paper trading are suspect. This, in turn, makes any derived values like optimal-f or Kelly fractions suspect.
So the best source of the information is a simulation of the underlying trading system across historical data, since that is the only way you will be able to practically test the approach across a variety of markets and get a sufficiently large number of trades so as to have a statistically valid basis for drawing any conclusions.
Second, you really should be looking at the combined expectation anyway. Otherwise, you don't get to see the effects of correlation.
For example, if you trade only currencies, you will find that the benefits of diversification are lower than if you trade a basket of diverse futures, Crude Oil, Soybeans, Coffee, Japanese Yen, Eurodollars, etc.
Any formula that simply combines results from single-market tests will be in error. This means that your simulations should be portfolio-level simulations in order to get values for expectation and win/loss ratios that reflect the effects of diversification.
Since, A) You need to run simulations to get the inputs anyway, and B) those simulations will be portfolio-level simulations, why not just simulate the effects of various bet sizes across the entire portfolio and then decide which levels have the type of equity curve you personally prefer?
I think you'll find that's what the more experienced (read profitable) traders actually do.
The more sophisticated of them run hundreds or thousands of simulations at any given level using Monte-Carlo simulations, varying the start dates, etc. in an effort to understand the range of possible equity curves that a given bet size might demonstrate.
- Forum Mgmnt
P.S. I think that much of the lore of trading reflects the constraints of the tools in common use. I suspect your question comes more from the limits of products like TradeStation that don't allow you to do portfolio-level simulation than because the approach you are attempting to take makes sense in an objective sense.
That is to say, if you can't do portfolio-level simulation, then your question is a good one. If you can, then it becomes meaningless because you can get the answer to your question much more directly.
Since, there are tools that allow portfolio-level testing at price points in the range of everyone; as a practical matter, we can all do portfolio-level simulation; some of us have just chosen not to.
The correct solution to the problem of not being able to do portfolio-level simulation, is to get better tools; not to come up with some formula to compensate for the poor quality of the tools you have.