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Rebalancing strategy

In schweser concept checkers we have question 3 p 48 vol 5 which states 

You expect the stock market to be relatively volatile over the next year. You also expect that the annual holding period return will be roughly zero. Recommend and justify a portfolio investment strategy given your forecast .

Of course we think of CM (constant mix) BUT because of 0% return I thought BH might be better given cost and tax efficiency as owing to transaction costs we would be negative with CM for sure .

Why would this be wrong in this case? 

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^ I think this belongs to CFA L3 not CAIA L1.

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