Risk Latte - Golden Ratios in the FX Markets

Golden Ratios in the FX Markets

Rahul Bhattacharya
Mar 28, 2006

The value of a golden ratio, also known as the divine proportion, is 1.618033......... This ratio is denoted by the Greek alphabet phi and has the striking property that it is exactly equal to one plus its reciprocal. .

The golden ratio, 1.618033ˇK.. is actually an infinite series and is the most "irrational" number in the universe because it has a continued fraction representation:

In terms of nested radicals one can express phi, the golden ratio, as:

On March 19, 2002 , the exchange rate (FX rate) for one Pound Sterling was one Euro and 61.8 cents (i.e. 1.618 Euros) and this meant that the reciprocal exchange rate for one Euro was 61.8 pence (i.e. 0.618 Pounds). This exhibited "a kind of symmetry" in the FX market. In fact, this symmetry, which exhibited the golden ratio, was very profound*.

See the excellent book A Mathematician Plays the Market by John Allen Paulos (Penguin Books, 2003).The above is referenced from that book as well as www.mathworld.wofram.com.

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