Do stock prices reflect Fibonacci ratios?
by Herbert H.J. Riedel
The claim has been frequently made that Fibonacci ratios occur in stock market data. A Fibonacci ratio
is the ratio between any successive numbers of the Fibonacci sequence — the Fibonacci sequence
1,1,2,3,5,8... produces the ratios 1, 1/2, 2/3, 3/5, 5/8....
After the first four numbers in the Fibonacci sequence, the ratios approximately equal 0.618, known as
the Golden Ratio or phi (f). Comparing one number in the sequence to the next lower number (8/5,5/3,
2/1. . .) produces ratios that approximate 1.618, the inverse of the Golden Ratio, f
In their book, Elliott Wave Principle, Key to Stock Market Timing, A. J. Frost and Robert Prechter cited
Dow theorist Robert Rhea's study of nine Dow Theory bull markets and nine bear markets . Of the 13,115
calendar days reviewed, bull markets were in progress for 8,143 days and bear markets for 4,972 days,
giving a ratio of 0.611, a value close to the Golden Ratio, f = 0.618.
In another Rhea study, the sum of the "primary swing" advances during a particular bull market divided
by the advance of the bull market was 1.621, a value close to 1/f.