to consider a brand new instance of financial numerology. An
email from a British correspondent apprised me of an interesting
connection between the euro-pound and pound-euro
exchange rates on March 19, 2002.
To appreciate it, one needs to know the definition of the
golden ratio from classical Greek mathematics. (Those for
whom the confluence of Greek, mathematics, and finance is a
bit much may want to skip to the next section.) If a point on
a straight line divides the line so that the ratio of the longer
part to the shorter is equal to the ratio of the whole to the
longer part, the point is said to divide the line in a golden ratio.
Rectangles whose length and width stand in a golden ratio
are also said to be golden, and many claim that rectangles of
this shape, for example, the facade of the Parthenon, are particularly
pleasing to the eye. Note that a 3-by-5 card is almost
a golden rectangle since 5/3 (or 1.666 . . . ) is approximately
equal to (5 + 3)/5 (or 1.6).
The value of the golden ratio, symbolized by the Greek letter
phi, is 1.618 ... (the number is irrational and so its decimal
representation never repeats). It is not difficult to prove
that phi has the striking property that it is exactly equal to 1
plus its reciprocal (the reciprocal of a number is simply 1 divided
by the number). Thus 1.618 ... is equal to 1 + 1/1.618
This odd fact returns us to the euro and the pound. An announcer
on the BBC on the day in question, March 19, 2002,
observed that the exchange rate for 1 pound sterling was 1
euro and 61.8 cents (1.618 euros) and that, lo and behold,
this meant that the reciprocal exchange rate for 1 euro was
61.8 pence (.618 pounds). This constituted, the announcer
went on, "a kind of symmetry." The announcer probably
didn't realize how profound this symmetry was.
In addition to the aptness of "golden" in this financial context,
there is the following well-known relation between the
golden ratio and the Fibonacci numbers. The ratio of any Fibonacci
number to its predecessor is close to the golden ratio
of 1.618 ..., and the bigger the numbers involved, the closer
the two ratios become. Consider again, the Fibonacci numbers,
1, 2, 3, 5, 8, 13, 21, 34, 59, The ratios, 5/3, 8/5,
13/8, 21/13, . . . , of successive Fibonacci numbers approach
the golden ratio of 1.618 ... !
There's no telling how an Elliott wave theorist dabbling in
currencies at the time of the above exchange rate coincidence
would have reacted to this beautiful harmony between money
and mathematics. An unscrupulous, but numerate hoaxer
might have even cooked up some flapdoodle sufficiently plausible
to make money from such a "cosmic" connection.
The story could conceivably form the basis of a movie like
Pi, since there are countless odd facts about phi that could be
used to give various investing schemes a superficial plausibility.
(The protagonist of Pi was a numerologically obsessed
mathematician who thought he'd found the secret to just
about everything in the decimal expansion of pi. He was pursued
by religious zealots, greedy financiers, and others. The
only sane character, his mentor, had a stroke, and the syncopated
black-and-white cinematography was anxiety-inducing.
Appealing as it was, the movie was mathematically nonsensical.)
Unfortunately for investors and mathematicians alike,
the lesson again is that more than beautiful harmonies are
needed to make money on Wall Street. And Phi can't match
the cachet of Pi as a movie title either.
Read More : The Euro and the Golden Ratio
