Exercise 2: Why +400% Then -78% Doesn't Mean "Back to the Start" — Possible Solution
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Using this chapter's own real figures, treating the pre-1995 NASDAQ
level as a starting value of 1 (a simple multiplier, to make the
percentages easy to track):

A rise of 400% means the index grew to 5 times its original value:
1 + 400% = 1 x 5.00 = 5.00 (the real March 2000 peak)

A fall of 78% FROM THAT PEAK means the index lost 78% of its peak
value, retaining only 22% of it:
5.00 x (1 - 0.78) = 5.00 x 0.22 = 1.10

So after both real moves, the index ended up at approximately 1.10
times its original 1995 starting value - still about 10% ABOVE where
it started, not back to square one.

WHY THIS ISN'T THE SAME AS "BACK TO THE START"
The key mistake to avoid is treating the two percentages as if they
cancel out symmetrically - they don't, because each percentage is
calculated against a different base value. The 400% rise was measured
against the smaller, original 1995 starting value. The 78% fall,
however, was measured against the much larger 2000 peak value (5.00 in
this simplified example) - a genuinely different, much bigger number.
Losing 78% of a much larger figure still leaves more real value behind
than the original starting point, even though 78% sounds like it should
nearly wipe out a 400% gain.

WHY THIS MATTERS FOR UNDERSTANDING REAL MARKET MOVES
This is a real, general mathematical pattern worth remembering whenever
comparing a percentage rise against a later percentage fall: they are
never simply symmetric or self-canceling unless the percentages happen
to be calculated against exactly the same base value, which a rise
followed by a fall almost never is. In this specific real case, the
dot-com bubble's own trough still left the NASDAQ meaningfully above
its own pre-bubble starting level - a real, concrete illustration of
why "it fell X% after rising Y%" needs actual calculation, not just
intuition, to know where an index or investment genuinely ended up.

ANSWER: Starting from a value of 1, the NASDAQ's real 400% rise took it
to 5.00 (its March 2000 peak), and the subsequent real 78% fall from
that peak brought it down to approximately 1.10 - still about 10% above
its original 1995 starting level, not back to where it began. This is
because the 78% fall was calculated against the much larger peak value,
not the original smaller starting value, so the two percentages don't
cancel each other out symmetrically - a real, general reason a large
percentage rise followed by a large percentage fall rarely returns an
investment exactly to its own starting point.

WHY THIS WORKS AS AN ANSWER
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This correctly performs the real, sequential percentage calculation
using the chapter's own stated figures, and explains the underlying
mathematical reason (different base values) that a rise and a
subsequent fall of different percentages don't simply cancel out.