INTRODUCTION <ul><li>You may remember hearing something about the name Fibonacci in 2006, when the movie “ The Da Vinci Code ” appeared in theatres. When Jacques Sauniere was found murdered at the Louvre museum in Paris, the strange position that his body was placed in mimicked the famous painting of the Vitruvian man by Leonardo da Vinci. </li></ul>This painting illustrates how Fibonacci ratios appear in the human form. The film also piqued the curiosity when some characters started talking about Fibonacci numbers as a part of one of the clues. The Vitruvian Man by Leonardo Da Vinci
THE FIBONACCI NUMBERS <ul><li>The Fibonacci number series and the properties of this series were made famous by Italian mathematician Leonardo de Pisa . The Fibonacci number series starts with 0 and 1 and goes out to infinity, with the next number in the series being derived by adding the prior two. (e.g. 0 + 1 = 1, 1 + 1 = 2, 2 + 3 = 5, and so on). </li></ul><ul><li>0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 …up to infinity. </li></ul>What is most fascinating about this number series is that there is a constant found within the series as it progresses towards infinity. In the relationship between the numbers in the series, you will find that the ratio between consecutive numbers after 13 is 1.618, which is called the golden ratio, golden mean, or the Divine Proportion. Leonardo de Pisa, who was known as Fibonacci
FIBONACCI PRICE RETRACEMENTS <ul><li>Fibonacci price retracements are run from prior low to high swing using the ratios .382 (1-.618), .5 (1/2), .618 (the golden ratio), .786 (square root of .618 the golden ratio). </li></ul><ul><li>236 is also used in some cases to identify possible support levels as the market pull backs from a high. Retracements are also run from prior high to low swings using these ratios, looking for possible resistance as the market bounces from the low. </li></ul><ul><li>Though most basic technical analysis packages will run the ratios for you but to understand the math behind it, multiply the length of the swing (from low to high or high to low) by the retracement ratios and then subtract the results from high if you are running low to high swings and add to low if you are running high to low swings. </li></ul>1.618, the approximate value of the Golden Ratio.
EXAMPLES OF FIBONACCI PRICE RETRACEMENTS <ul><li>Now let's go through certain examples using the Fibonacci retracements, in the diagram below we ran the Fibonacci retracement from 04/10/06 low to 1/12/06 high, which was an 86.9 point swing looking for potential support. Note that this contract found support only around the .618 retracement of this prior swing. None of the other ratios provide meaningful support. </li></ul>
The next retracement is daily chart of Microsoft. Here we retraced from 15/11/04 highs to 29/03/05 lows. Notice that resistance was mostly around .618 retracement levels.
CORRECT RETRACEMENT <ul><li>One of the ways to create Fibonacci price cluster is by running retracements on multiple swings on the chart, the important point is to select the right swings which can be demonstrated with the help of figures below- </li></ul>INCORRECT WAY <ul><li>CORRECT WAY </li></ul>
CONCLUSION <ul><li>Thus we can see that Fibonacci retracements can provide important resistance and support levels but one very important thing to consider over here is unlike other studies in technical analysis support does not become resistance or vise a versa. The more accurate way is to find new support and resistance levels. </li></ul>
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