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68 HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 2.15 The Normal and Lognormal Distributionsshould in theory become progressively more difficult for the item to get
lower. For example, consider the price of a hypothetical stock at$10 per
share. If the stock were to drop$5, to$5 per share, a 50% loss, then ac-
cording to the Normal Distribution it could just as easily drop from$5to
$0. However, under the Lognormal, a similar drop of 50% from a price of
$5 per share to$2.50 per share would be about as probable as a drop from
$10 to$5 per share.
The Lognormal Distribution, Figure 2.15, works exactly like the Nor-
mal Distribution except that with the Lognormal we are dealing with per-
centage changes rather than absolute changes.
Consider now the upside. According to the Lognormal, a move from
$10 per share to$20 per share is about as likely as a move from$5to
$10 per share, as both moves represent a 100% gain.
That isn’t to say that we won’t be using the Normal Distribution. The
purpose here is to introduce you to the Lognormal, show you its relation-
ship to the Normal (the Lognormal uses percentage price changes rather
than absolute price changes), and point out that it usually is used when
talking about price moves, or anytime that the Normal would apply but be
bounded on the low end at zero.