A market portfolio is a portfolio in which each asset is held at a weight proportional to its market value. A swap portfolio is a portfolio in which each one of a pair of assets is held at a weight proportional to the market value of the other. A reverse-weighted index portfolio is a portfolio in which the weights of the market portfolio are swapped pairwise by rank. Swap portfolios are functionally generated, and in a coherent market they have higher asymptotic growth rates than the market portfolio. Although reverse-weighted portfolios with two or more pairs of assets are not functionally generated, in a market represented by a first-order model with symmetric variances, they will grow faster than the market portfolio. This result is applied to a market of commodity futures.
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