Hi france, liftoff,
just a couple of citates from Ralph Vince (ISBN 978-0-471-75768-9) which seem relevant to this topic.
There is a gain from adding each new market system to the portfolio provided that the market system has a correlation coefficient less than one and a positive mathematical expectation, or a negative expectation but a low enough correlation to the other components in the portfolio to more than compensate for the negative expectation. There is a marginally decreasing benefit to the geometric mean for each market system added. That is,each new market system benefits the geometricmean to a lesser and lesser degree. Further, as you add each new market system, there is a greater and greater efficiency loss caused as a result of simultaneous rather than sequential outcomes. At some point, to add another market system may do more harm then good
Adding more and more market systems results in higher and higher geometric means for the portfolio as a whole. However, there is a trade-off in that each market system adds marginally less benefit to the geometric mean, but marginally more detriment in the way of efficiency loss due to simultaneous rather than sequential outcomes. Therefore, you do not want to trade an infinitely high number of scenario spectrums. What’s more, theoretically optimal portfolios run into the real-life application problem of margin constraints. In other words, you are usually better off to trade three systems at the full optimal f levels than to trade 10 at dramatically reduced levels.
Rather than trading at a fraction of OptimalF instead of full OptimalF, it's better to split the whole equity (e.g. 1000$) into passive part (800$) and active part (200$). OptimalF is then calculated after subtracting passive part from (hopefully increased over time) whole equity (e.g. after 100$ are earned, OptimalF is calculated based on 1100$-800$=300$; you do not reallocate after each trade or week or month - passive part remains the same in $ but gets hopefully less and less percentually).
Rule of thumb: Set your initial active equity at one half of the maximum drawdown you can tolerate. Thus, if you can take up to a 20% drawdown, set your initial active equity at 10% (however,if the account is profitable and your active equity begins to exceed 20%, you are very susceptible to seeing drawdowns in excess of 20%). Notice, that for portfolios, you must use the sum of all f in determining exposure
Rather than allocating a part of whole equity to each system, it's better to find OptimalFs in portfolio. This is what Ralph Vince calls "terrain peak". I think the coordinates of the peak will greatly depend on if systems are trading simultaneously or sequentially (like day birds and night birds never hunting together), and also on how corellated their equity curves are (if there are no worms for day birds, there are not any for night birds either).
Tomasini suggests an appealing rule for taking systems in to and out from portfolio - system's individual equity curve plunges below or goes above its own moving average; at the same time, suggestions about allocating partial equities to systems are more fuzzy.
Vince suggests to treat test results as a proxy for likely future results, and to look for "terrain peak": what should be each OptimalF in order to maximize the geometric mean of the portfolio (logically, this will maximize the return under re-investing). A zero value will tell me to take a system out of my portfolio.
Vince also suggests not to be fixed too much on maximum drawdown seen during the test. It's just a single outcome from a universe of possible ones and thus not worth beeing a measure for making position sizing decisions. Instead, OptimalF gives an esimate (theoretical, but reasoned) of what drawdown to expect. And yes, it will be huge when trading at OptimalF, that's why I ought split the whole equity into passive and active parts, as mentioned above.
Sorry for this citate-loaded long post. My secondary purpose is to gain better understanding of the topic by attempting to re-tell what I learned.
