So, who is trading with Shannon? There must be another bettor taking the "tails" side of the proposition. The "tails" bettor must also be making money at the same rate if he rebalances according to Shannon's logic. But, somebody has to be losing. Even if you extend it to a large pool of bettor/rebalancers (some betting "head" and others betting "tails"), it still cannot work. Shannon is somehow assuming an idealized source of money that just does not exists in the stock market where aggregate behavior of bettors set prices. The problem with Shannon's mythical stock market is:rmelvey wrote:Rebalancing brings your portfolio's geometric return closer to the weighted average arithmetic return of its components. Momentum need not have anything to do with it. It is a function of diversification reducing steep losses, which we all know kills compounding.
I made a post awhile ago that shows it using an extreme example devised by Claude Shannon:
http://www.stableinvesting.com/2013/04/ ... demon.html
This example is interesting because obviously there is no momentum. Also there is no "buy low" and "sell high" because valuations have nothing to do with random coin flips. The real takeaway is that the individual coin flip games have a positive expected arithmetic return, but a an expected geometric return of 0. However, diversification can help close the gap between the arithmetic and geometric returns.
(1) Events (coin flips) are impacting prices with no buying or selling whatsoever, whereas in the real world events cause investors to buy and sell and that buying and selling sets prices.
(2) All buying and selling is rebalancing and it's having no impact on prices, whereas in the real world rebalancing would be the only thing that impacted prices if all buying and selling was rebalancing.