It appears to me most if not all trading books I read so far would be probably produced mainly for promoting certain trading related services by the writers of the books. I wouldn't expect the writers to disclose (m)any of the secrets they learned/ discovered from their (painful? experiences, imo.
Is there ever an optimal position sizing ( money management ) rule? ONLY if you know for sure what is the absolute worst black swan loss in the future, which we will never know. So, if you have a postive expectancy system according to your research, the best money management strategy trades a position size that generates the greatest return for you and tries to ensure you are not taken out by any future black swans. You can increase return by increasing leverage or position size, but it increases your risk of ruin.(risk of taken out of business) Hence, to me, position size or m.m. is a personal preference and also depends on what stage you are in as a trader. If you are still young, you can afford to take on more risk and vice versa. There is no absolute answer.
This is an excerpt about options trading money management from another forum. Michael is an experienced options trader that is always ready to give an insightful advice. He's great at explaining clearly even the most complex things.
In most cases it is probably good enough to rely on a general consensus for position sizing: i.e. the total risk of your open positions to be about 5-6% of your account (risk being the amount you lose if all your stop losses are hit). You should also make sure that you know your maximum risk and are comfortable with it. If not, back down your sizes until you feel comfortable. If you take time to analyze your trading history to calculate your percentage wins/losses, your average win and your average loss you can better optimize your sizing for better profits. On the other hand there is always the danger that your historical data is too small and it hasn't yet encounter adverse streaks, so you might draw too optimistic conclusions about your trading performance and get too aggressive.
Perhaps one of the key elements in deciding optimal bet size, imo, would be the (dynamic?) correlations among the assets (providing keeping/ trading the same assets with same weighting all the times). I guess the correlations based on historical data might be sometimes not good enough to measure/ define/ predict the "you know your maximum risk" in the future trading environment, using whatever available tools/ calculations such as Kelly, Terminal Wealth Relative, VaR, double summation, etc. Using "Average" for problems such as MaxDD/ MaxConsecutiveLoss/ etc. and how to define them could be another interesting issue for me to learn. Just my 2 cents.
Q As already mentioned, the major flaw of the Kelly formula is it assumes two outcomes only - a winner of a certain magnitute and a loser ... For a better approximation of the optimal trade size, one should determine what is popularly known as the optimal f, which requires a slightly more complex calculation. --- Chapter 24 The Kelly Formula, Trading Systems and Money Management (Thomas Stridsman) UQ
I read Van Tharp's "Trade Your Way ..." and a few of his reports. I found a lot of good information in them, although I'm not a trend follower per se. I also read Van's weekly newsletter.
Here there is a probability analysis that justifies using 1/4 to 1/6 Kelly for sizing your positions (risk). The table shows the probability of "never being unhappy" as the author names it, for different combinations of maximum drawdown (a) and Kelly fractional (x=1/k of Kelly): "We look more closely at some special cases of the formula to see how Kelly fractions affect risk. In the sequel, we introduce the variable x=1/k, the inverse of the Kelly fraction. Thus x=1 and x=2 correspond to full Kelly and half-Kelly, respectively. In the table below we tabulate the function f(x)=1-a**(2x-1), which is the risk that you never reach the value a, as a varies from .5 to .8. For a=.5 it appears that this risk of being halved gets very small and doesnât change much as x increases above 4. This indicates (quite subjectively of course) that there is little reason for blackjack players to be more conservative than quarter-Kelly. Some futures traders suggest k=1/6, a conservative fraction perhaps due to the fact that traders are not usually sure of their edge (among other infelicities). The risk of never being unhappy (the probability of never reaching a=.5 to .8 for x=1/k=1 to 6): Code: x: 1 2 3 4 5 6 a 0.5 0.500 0.875 0.969 0.992 0.998 1.000 0.6 0.400 0.784 0.922 0.972 0.990 0.996 0.7 0.300 0.657 0.832 0.918 0.960 0.980 0.8 0.200 0.488 0.672 0.790 0.866 0.914 " You may find the whole document here.