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The Geometric Index Revisited: A Rejoinder

The authors, Hodges and Schaefer, of the preceding paper [2], taking up where my own article [3] left off, have contributed to a better understanding of the geometric mean index of stock price relatives. Their basic point is that, if in any practical situation a portfolio were managed according to a policy of periodic reallocation, the wealth relative of the portfolio would not be approximated by the geometric index. This is demonstrated through simulation, using randomly generated price sequences as well as empirical data. In addition, they have presented a verbal characterization of the hypothetical portfolio policy whose wealth relative is measured by the mth-order power mean of price relatives discussed in my paper. This policy, as I had stated, is not an intuitively simple one like “maintain equal dollar amounts at all times” or “buy and hold.”