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Flabbergasted by Fibonacci


Vinod Sharma writes on the Magic of Fibonacci Numbers (Business Standard)

Though the Fibonacci series was first explained by Pingala, the ancient Indian mathematician in 200 BC, the credit for the present day knowledge is attributed Leonardo Fibonacci, a 13 th century Italian mathematician who discovered a simple series of numbers that created ratios describing the natural proportions of things in the universe. The ratios arise from the following number series

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

Each number in this sequence is simply the sum of the two preceding numbers and the sequence continues infinitely. One of the remarkable characteristics of this numerical sequence is that each number is approximately 1.618 times greater than the preceding number.

The key Fibonacci ratio of 61.8 per cent – also referred to as “the golden ratio” or “the golden mean” – is found by dividing one number in the series by the number that follows it. For example: 8/13 = 0.6153, and 55/89 = 0.6179.

Similarly we have 76.4 per cent, 50 per cent, 38.2 per cent and 23.6 per cent retracement ratios, derived from the Fibonacci series.

Fibonacci Retracement levels are used to identify major support and resistance levels in an uptrend, as well as in the downtrends. For applying a Fibonacci retracement study on the chart, there must be an existence of a trend, i.e the study is not advisable for being used in the range-bound price movements, where there are higher chances of getting whipsaws.

UPTREND: This is the daily chart of Aban Offshore. Here we plotted the Fibonacci Retracement Levels by clicking on the Swing Low at 224 made on March 9 and dragging the cursor to the Swing High at 1,311 made on June 8, 2009. You can see the levels plotted by the software. The Retracement Levels were 1063 (23.6 per cent), 902 (38.2 per cent), 772 (50 per cent), and 642 (61.8 per cent). Now, the expectation is that if the Aban Offshore price retraces from this high, it will find support at one of the Fibonacci Levels, because investors would be interested to get entry at these levels as the market pulls back.

Now let’s look at what actually happened after the top of 1,311 formed on June 8 in Aban offshore. The stock price started to fall and did not take a support at 23.6 per cent, 38.2 per cent and 50 per cent retracement levels and kept on plummeting. Thereafter, around 61.8 per cent retracement was placed at 639, it took support and bounced back. At that time, another indicator favouring the reversal was the sudden rise in volumes on the day when price had taken support at 61.8 per cent retracement. So, this observation could have been the key trigger for entering into a long position, and cutting off the short ones. However, in this kind of scenario, other retracement levels like 23.6 per cent, 38.2 per cent, and 50 per cent do not go in vain, as they might act as a crucial resistance to levels going forward.

The image isn’t on the website – so I made one at

The stock is “supposed” to follow fibonacci patterns, but on the way down, ditches three key points – the 23.6%, the 38.2% and the 50% points. Then it finds support at a fourth point, which was the 61.8% level. Note that the first “support” was somewhere between two fibo levels – which is ignored because it didn’t follow the fibonacci number strategy. Going this way you can find ANY fibonacci number that matches something because at some point in life the stock is likely to stop at a point close to a fibonacci number. This one just got very lucky at the end.

If the stock craps out now, the next funda will be that the next retracement – the new high of 1300 minus the low at 640 – will have a fibonacci retracement at – voila – 61.8% near the 1050 level, which is where we are today. (and on the way up it has violated all the other fibo levels). If it goes up, no one will analyse this stock – who cares if a stock DIDN’T meet fibo numbers, no?

Elliott waves go one step further – it’s impossible to get any two analysts to concur on which wavelet of which sub-wave of which real wave and which’th fibonacci number we are at now. If the theory is wrong they start counting again, from a different point. The theory isn’t wrong, so let’s fudge the numbers.

And remember if enough traders believe in the fibonacci theory, they will sell or buy at those levels, which makes the chart show “support” or “resistance” because of THEIR transactions – thus proving the theory. It’s like saying buy apples today, the price will go up – if enough people listen to me, they will all buy and the price WILL go up.

You can always find a point that will match some number based strategy. Fibonacci numbers are an interesting mathematical phenomenon, but when you apply them randomly to trading you get no real answers. In fact, you’re wrong more often than you’re right; but no one cares to highlight the “wrong” part of the play.

This is why there is back-testing – you test evenly, on all stocks, with the same formula. If the odds show that it works then it *might* continue – i.e. there’s no guarantee it will. But if it does not work in the past, it’s a dud theory and you might as well toss a coin.

Oh wait, tossing a coin has 50% odds. And 50 is a fibonacci retracement number. Wow.


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