I do not understand at all what is being covered in Page 435-436 of Book 4 Schweser. I can’t see how the average returns for BOTH portfolios = 0… And in the CFAI text (Page 115) the following is written: " Therefore the geometric return of a rebalanced portfolio is larger than the average return of its constitutents" Isn’t it always the case that geometric returns > average returns regardless of whether or not the portfolio is rebalanced? Would be great if you all can shed some light on this.
geometric return of each asset on the portfolio is 0. Asset A -> moves up 100% then down 50% so start with 1 * 2 * .5 = 1 Asset B - stays with 0% move - so remains at 1. Now when you have a two asset portfolio, equal weighted - if no rebalancing would have been done -> A 50->100->50 B 50->50->50 so Portfolio earned 0. Now with rebalancing A->50->100->75->37.5 B->50->50->75->75 Total return = 112.5 / 100 -> 6.07%
and in response to your CFAI text question - even if you took the average geometric return of constituents - as has been done in the example above - you have rebalanced portfolio giving you a better return than the individual constituents.
ah i see it now. 
thanks for your help cpk123
this is essentially the strategy that INTECH (quant shop) utilizes – of course, with much more sophistication including the capture of relative volatility (i.e. correlation matrix of their securities) and incorporating the capital distribution curve. They conjecture that in the short-term, a security has an equal probability of moving up or down and that if it reaches a threshold price, they will rebalance it back to a predetermined allocation. this mechanics effectively captures alpha by taking advantage of the newly rebalanced portfolio. if you’re interested in reading some of their white papers: https://ww4.intechjanus.com
of course this sounds great on paper – implementing it (with transaction cost accounted for) is another issue.