Diversification Return, Portfolio Rebalancing, and the Commodity Return Puzzle

If you have access to FAJ, and care about the benefits of diversification: there’s an interesting paper in the latest issue. Pointing out that diversified portfolios are also assumed to be regularly rebalanced, the author finds that in fact it’s the rebalancing that drives the excess risk-adjusted return of diversified portfolios (and not the reduction in variance). from http://www.cfainstitute.org/learning/products/publications/faj/Pages/faj.v67.n4.1.aspx : “The diversification return of a rebalanced portfolio is often ascribed to a reduction in variance. I have shown that the underlying source of the diversification return is the rebalancing, which forces the investor to sell assets that have appreciated in relative value and buy assets that have declined in relative value, as measured by their weights in the portfolio. Although a buy-and-hold portfolio generally has a lower variance than the weighted average variance of its assets, it does not earn a diversification return. A buy-and-hold portfolio, however, can benefit from the fact that the best-performing assets become a larger fraction of the portfolio over time. This outcome changes the risk profile of a buy-and-hold portfolio, unlike a rebalanced portfolio, which maintains a constant risk profile.”

Yeah, it’s only the market portfolio that can be bought and held and not rebalanced. That’s where the confusion tends to lie. If you are a CAPM person (which few of us are, but that’s what they teach), then you conclude that the market portfolio is 1) the optimally diversified portfolio, and 2) can just be bought and held. After hearing that, people tend to think that all diversified portfolios can be bought and held, but no, they must be rebalanced; not needing to rebalance is a special property of the market portfolio. Any other portfolio needs to be periodically rebalanced or it will drift away from the optimal allocation over time. Optimal rebalancing is basically when the transaction costs of rebalancing reduce the Sharpe ratio by less than by letting the portfolio continue at its current allocation (though the mathematics of making that decision turn out to be more complex than it would seem on the surface).

Could you please help me understand this paragraph as well?

Rebalancing earns a diversification return. The compound growth rate of a portfolio is greater than the weighted average compound growth rates of the component portfolio holdings (given positive expected returns and positive asset weights). Given sufficiently low transaction costs, this effect leads to what has been called a diversification return to frequent rebalancing to a well-diversified portfolio.44