We respond to Sornette and Johansen's criticisms of our findings regarding
log-periodic precursors to financial crashes. Included in this paper are
discussions of the Sornette-Johansen theoretical paradigm, traditional methods
of identifying log-periodic precursors, the behavior of the first differences
of a log-periodic price series, and the distribution of drawdowns for a
securities price.Comment: 12 LaTex pages, no figure