The Fibonacci theory named so after a prominent Italian mathematician of the late twelfth and
early thirteenth centuries gives ratios, which play important role in the forecasting of market
movements. Fibonacci introduced an additive numerical series that has come to be called the Fibonacci sequence, which consists of following series of numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,4181, (etc.).
These numbers exhibit several remarkable relationships, in particular the ratio of any term in the
series to the next higher term. This ratio tends asymptotically to 0.618. In addition, the ratio of any term to the next lower term in the sequence tends asymptotically to 1.618, which is the inverse of 0.618. Similarly constant ratios exist between numbers two terms apart, three terms apart, and so on. The ratio 0.618, referred to as the Fibonacci ratio, or the “Gold Spiral” which is being observed in structures of many natural objects and events – from clam’s construction till the form of whirlwinds and hurricanes.
The financial markets exhibit Fibonacci proportions in a number of ways; particularly they are
powerful tools for calculating price targets and placing stops. For example, if a corrective wave is
expected to retrace 61.8 percent of the preceding impulse wave, an investor might place a stop slightly below that level. This will ensure that if the correction is of a larger degree of trend than expected, the investor
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will not be exposed to excessive losses. On the other hand, if the correction ends near the target level, this outcome will increase the probability that the investor's preferred wave interpretation is accurate (See also p.
4.1).