I encountered this paradox a while back and there is less than meets the eye. It's just one of those tricks used to impress the gullible.
As for mixing a bunch of systems - I contend that the less fancy you are the better off. You are going to have to construct and reconstruct your portfolio all the time because - guess what, markets keep changing.
The key element of portfolio design is keeping the expectation as high as possible while keeping the risk of ruin as low as possible - the combination of the two being a function of your own risk tolerance.
It's obvious that having markowitz's assertion about diversification is incontroversial and correct - anyone who doesn't agree and can prove it should go collect their Nobel prize (or memorial Bank prize to be pedantic about it, since there is no Nobel prize for economics).
If I am playing a dice game that pays $20 on 6 and loses $10 on 1, my average expectation on each roll is $10/6. Risk of losing $10 is 1/6
If instead I can play a dice game where I roll 2 dice, each of which pay $10 on 6 and lose $5 on 1, my average expectation on each roll is still $10/6. But my risk of losing $10 is now 1/36.
Substitute strategy for dice and you get the picture.
We can extrapolate this - if my dice game now involves N dice, each of which pays $20/N on 6 and loses $10/N on 1. Make N arbitrarily large and your avg expectation is still $10/6.
But lo and behold, your risk of losing $10 can now be arbitrarily small. Each round of your game will in fact converge to a payout distribution that tightly focuses around $10/6 ..... creating a nice steady coupon like stream. That would be really nice ..... some call that the holy grail, but I prefer to think of it as medallion.
As for mixing a bunch of systems - I contend that the less fancy you are the better off. You are going to have to construct and reconstruct your portfolio all the time because - guess what, markets keep changing.
The key element of portfolio design is keeping the expectation as high as possible while keeping the risk of ruin as low as possible - the combination of the two being a function of your own risk tolerance.
It's obvious that having markowitz's assertion about diversification is incontroversial and correct - anyone who doesn't agree and can prove it should go collect their Nobel prize (or memorial Bank prize to be pedantic about it, since there is no Nobel prize for economics).
If I am playing a dice game that pays $20 on 6 and loses $10 on 1, my average expectation on each roll is $10/6. Risk of losing $10 is 1/6
If instead I can play a dice game where I roll 2 dice, each of which pay $10 on 6 and lose $5 on 1, my average expectation on each roll is still $10/6. But my risk of losing $10 is now 1/36.
Substitute strategy for dice and you get the picture.
We can extrapolate this - if my dice game now involves N dice, each of which pays $20/N on 6 and loses $10/N on 1. Make N arbitrarily large and your avg expectation is still $10/6.
But lo and behold, your risk of losing $10 can now be arbitrarily small. Each round of your game will in fact converge to a payout distribution that tightly focuses around $10/6 ..... creating a nice steady coupon like stream. That would be really nice ..... some call that the holy grail, but I prefer to think of it as medallion.
... I'm NOT disappointed... 
