Leonardo Fibonacci, an Italian mathematician, is credited for introducing Fibonacci sequence in his book (year 1202). However *Virahanka*’s work in 700 AD seems to have discussed the series pretty clearly.

## Share trader should know Fibonacci Retrenchment

The sequence starts from 1 & 1 and next digit is sum of last 2 digits. The sequence goes as follows:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…

**Golden ratio** is the ratio of the 2 quantities if the ratio is same as ratio of their sum to the larger of the two quantities.

The ratio of the Fibonacci number with the penultimate number as we tend towards end of the series is called “Golden Ratio”. The golden ratio is roughly equal to 1.618.

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Fibonacci number or the golden ratio has strong **presence in the nature**. A starfish has 5 arms, a Fibonacci number. Humans have 8 fingers in total, 5 digits on each hand, 3 bones in each finger, 2 bones in 1 thumb, and 1 thumb on each hand. The ratio between the forearm and the hand is the Golden Ratio. Many flowers have petals which are Fibonacci numbers. So number of petals in a flower would either be 3 or 5 or 8 but almost never 4.

It is this natural presence of Fibonacci series which attracted technical analysts’ attention. Fibonacci numbers are primarily used for either predicting support/resistance levels or to identify price targets/stops. Fibonacci numbers’ accuracy in finding important levels in any widely tradable market is fabulous.

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Fibonacci retracement is primarily based on the idea that markets will retrace a predictable portion of any move. Following Fibonacci ratios are used for the purpose of technical analysis:

**0% and 100%** are extremes of any directional price-move on which Fibonacci is to be applied.

**0.618** is golden ratio [(34-21)/21 = 0.618]

**0.382** (38.2%) is found by dividing any Fibonacci number by the number that is found two places to the right in the series. [(34-21)/34 = 0.382]

**0.236** (23.6%) is found by dividing any Fibonacci number by the number that is found three places to the right. [(34-21)/55 = 0.236]

**0.764** (76.4%) is the result of subtracting 0.236 from the number 1.

Applying Fibonacci retracement/extension requires defining 2 key anchor points. These points define a unidirectional move which is regarded as primary move on which Fibonacci series is applied.

Fibonacci numbers can be used on charts in following ways. (Charts below are sourced from Bloomberg and the Fibonacci is applied on India’s benchmark equity index SENSEX)

**Fibonacci retracement**is the potential retracement of a financial asset’s original move in price. Applied on SENSEX it suggests first key support on any correction in the index should be around 24805 (23.6% Fibonacci retracement of rally since Feb-lows).

**Fibonacci extension**consists of technical-levels drawn beyond the standard 100% level and are used by many traders to determine areas where they will wish to take profits. Applied on SENSEX for the bull-run between 2008-2010; next key resistances is expected around 26232 (138.2% Fibonacci extension) and 27814 (150% extension).

**Fibonacci projections**are the Fibonacci levels of a historical move projected from a third point. In the chart below we can clearly see how well projection levels have worked. Next key resistance comes around 28547.

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**Fibonacci fans**are consisting of three diagonal lines that use Fibonacci ratios to help identify key levels of support and resistance. In the chart below on SENSEX, Fan-Lines have worked as decent supports in 2011.

**Fibonacci Projection channel**provides levels within or outside of a trend-channel, when markets are trending in a particular direction.

**Conclusion**

Fibonacci retracement, projection and extensions are most common used Fibonacci tools. We suggest applying Fibonacci on multiple historic price moves. Then price-zones with dense cluster of Fibonacci lines can be considered as better support/resistance.

A general rule of thumb is to enter in the direction of prevailing trend at a retracement of between 50% and 61.8%. Such a trade normally has a target of ~123.6% in the direction of trend. Such trades should have stop at 76.4% of the prevailing move, providing a very good Risk:Reward ratio for the trade.

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