Fibonacci in Finance

The Fibonacci sequence shows up in the strangest place: stock trading. Fibonacci retracement levels — 23.6%, 38.2%, 61.8% — are drawn on price charts by traders every day to guess where prices will find support and resistance. (Charts usually add a 50% line too, but that one comes from Dow Theory's "markets retrace about half a move" idea, not from the Fibonacci sequence.)

Do they work? Partly, through self-fulfilling prophecy. When enough traders watch the same levels, they place buy and sell orders at those prices, which actually creates the support and resistance. The math generates the belief, and the belief shapes the reality.

The 61.8% level comes straight from the golden ratio: each Fibonacci number divided by the next one approaches 0.618, the inverse of phi.