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Jonathan E. Ingersoll, Jr., Jeffrey Skelton, Roman L. Weil, Duration Forty Years Later, The Journal of Financial and Quantitative Analysis, Vol. 13, No. 4, Proceedings of Thirteenth Annual Conference of the Western Finance Association, June 20-26, 1978 (Nov., 1978), pp. 627-650
Ingersoll et al. (Wed,) studied this question.