### Sphinxes, pyramids and pharaohs! What do these have  in common with the financial markets? By Sunil Mangwani.

In the early 1200s, an Italian mathematician Leonardo Pisano Fibonacci uncovered a secret about this ancient civilisation that would revolutionise the entire mathematical world... including the financial markets.

While studying the Great Pyramid in Egypt, Fibonacci made a startling discovery and uncovered a unique mathematical sequence of numbers that changed several theories of trigonometry, algebra and geometry.

He developed the famous Fibonacci sequence of numbers, which simply says that the third number is effectively the sum of previous two numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on.

But the real value of this sequence lies in the fact that the ratio of any number to the next higher number is approximately 0.618, and the ratio to the lower number is 1.618.

• For example, 55/34 = 1.6176; 144/89 = 1.6179 etc.
• Also 34/55 = 0.6181; 89/144 = 0.6180 etc.
• The key Fibonacci ratio of 61.8%, also referred to as ‘the Golden Ratio’ or ‘the Golden Mean’, is thus 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 the 38.2% ratio is found by dividing one number in the series by the number that is found two places to the right. For example: 55/144 = 0.3819.
• The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example: 8/34 = 0.2352.

These ratios developed by Fibonacci actually go back thousands of years to the time of the ancient Egyptians and the ancient Greeks. In addition to mathematics, they also used the ‘Golden Mean’ in architecture and music.

Subsequently, these ratios have become the foundation of many effective trading systems, but the truth is they are seldom used properly. And ironically, though it is one of the most effective tools of technical analysis, it is also the most misunderstood.

These Fibonacci ratios can accurately anticipate when the market makes a major turn and identify key turning points for tops and bottoms... but only if you know how to read it correctly. If you can learn to use them correctly, you can increase the probability of profitable trades and minimise potential losses.

These numbers are often more effective in the forex markets, since forex is a highly trending market. Prices are constantly changing in an oscillatory pattern, thus following the Fibonacci ratios quite precisely. These Fibonacci levels act as strong indicators of resistance and support levels, which helps to improve the accuracy of the entry and exit point for every trade.

One of the immense advantages of trading with Fibonacci numbers is that besides setting profit objectives, one can define stop losses to exit a market as well.

The different Fibonacci ratios are the cornerstone of price structure and go hand-in-glove with effective chart patterns like Elliott waves, Harmonic patterns, Divergence etc.

The Fibonacci ratios can be separated into four main groups:

• Retracements/Expansions.
• Fans.
• Arcs.
• Time zones.

In this first article on Fibonacci ratios, we will concentrate on the Retracements, Fans and Expansions and understand the basic concepts behind them. The next article will cover the different situations/patterns, where we should ideally use these ratios.

Using the Fibonacci ratios
The Fibonacci ratios play an important role in the financial markets, just as they do in nature, and can be used to determine critical points that cause price to reverse.

Price has an uncanny way of respecting Fibonacci ratios, often quite precisely. Hence one can use them to ascertain the correct technical levels.
Price action is never random, and every wave leaves behind clues for the next move. We can thus use previous price action to anticipate the subsequent price movement.

Most traders tend to use the standard Fibonacci retracement tool for all kinds of situations, with the standard values of 38.2, 50.0 and 61.8. But every trading situation demands an appropriate Fibonacci ratio with different values.
Using these ratios in a proper way gives us a tremendous advantage over the crowd and we will attempt to identify the correct situations to apply the appropriate ratio.

The basic rules for plotting  Fibonacci ratios
Let us start by laying down the basic rules of plotting Fibonacci ratios. As mentioned, even though these ratios are used extensively, most traders are not aware of the basic rules, which tend to give an incorrect picture.

The following rules apply to all the Fibonacci ratios:

• The Fibonacci ratios should always be plotted from the left side to the right of the chart.
• They should always be plotted on pivot points (swing highs/lows). Visually identify the levels from where price changes trend. In short, identify the waves of the price movement.
• They cannot be plotted on swing points in the middle of a wave.
• They should always be plotted on the wicks of the candles and not on the real body.
• On the other hand, if we are looking at the support/resistance levels of any Fibonacci ratio, we should consider the close of the real body of a candle. (For example, we plot the Fibonacci retracement ratio and see that price finds support at the 61.8% Fib level. A wick of the candle can go below the Fibonacci 61.8 level, but we cannot have a close of the real body below this level, or the support is invalidated.)…

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