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fibonacci retracements are usually drawn with stock charting software...first, you need to identify two extreme points, for example, from the trough to the opposing peak.
Then, by drawing the fibo retracement between these two points, you should get nine horizontal lines at Fibonacci levels of 0.0, 23.6, 38.2, 50, 61.8, 100, 161.8, 261.8, and 423.6 percent.
The whole basis of fibo retracement is banking on that prices often return to their previous levels, and correct their initial movement. I don't know the exact maths behind it, but prices often face support/resistance at the level of Fibonacci Retracements or near them, when their prices do retrace, hence the name.
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