Divergence is a phenomenon in technical analysis that states that the underlying security is probably poised for a reversal after a specific type of price action with respect to an oscillator. All indicators (including oscillators) are just a derivative of the price and/or volume and therefore they move in tandem with it.
However, there are a few times when we see a disagreement between what the price is doing as compared to what its indicator is depicting. This mismatch is popularly called a divergence. More precisely, when the price makes a higher high (or lower low) and the corresponding oscillator fails to make a higher high (or lower low) is called a divergence.
This instance depicts a slowdown of the ongoing bullish/bearish momentum which is generally an early warning of a trend reversal, at least temporarily.
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