Long ago, someone posed a question that ended up revolutionizing mathematics.

The question: “If we start with one pair of rabbits, how many pairs of rabbits will there be one year later if we assume that every month each pair reproduces and adds a new pair to the group?”

The answer? The number of rabbits in any given month is equal to the sum of the number of rabbits in the two previous months.

So if we start with one pair, in the second month there is still one pair, as they have not yet delivered any baby rabbits. In the third month, there are two pairs. In the fourth month, there are three pairs. And in the fifth month, there are five pairs of rabbits. But in the twelfth month, there would be 144 pairs of rabbits.

This is a demonstration of a number sequence known as the Fibonacci series. It was identified by mathematician Leonardo Fibonacci, and has been written about since the 13th century. They are widely used by traders in the 21st century — particularly Fibonacci ratios.

What Are Fibonacci Ratios?

The Fibonacci series is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, etc…

Three ratios are commonly associated with this series:

1. The ratio of a number to the next higher number in the series is about 0.618 for numbers above 5. For example, 34/55 is equal to 0.6182.

2. The ratio of a number to the next lower number in the series is about 1.618, the inverse of 0.618. For example, 55/34 equals 1.6182.

3. The ratio of numbers that are separated by one additional number (such as 5 and 13) is about 2.618, or its inverse 0.382. For example, 89/233 equals 0.382 and 233/89 equals 2.618.

Still with us? The important thing go know is that traders believe these ratios are often found in price data. Fibonacci ratios are applied to individual stocks and futures contracts, as well as indices, and can be used in any time frame.

The most common Fibonacci ratios to remember are 61.8% and 38.2%. After a sharp advance or decline, technicians will apply these numbers to determine resistance/support levels.

How Traders Use Them…

Here’s an example of how the Fibonacci ratios are applied.

After a significant price decline, traders generally look for at least a short rebound in price. And many traders will expect the price rise to stop, at least temporarily, at a Fibonacci ratio related to the decline. The Fibonacci ratio may also prove to be a long-term resistance level. This is shown in the chart of the Nasdaq 100 index below.

After the Nasdaq 100 crashed in 2000, the 38.2% Fibonacci ratio served as resistance. Prices did not advance past this level for another 12 years. The 38.2% level was finally broken decisively in the spring of 2012. Traders then looked at the 61.8% retracement as the next resistance level. The market moved easily through that level in 2013, and then served as support.

Why Fibonacci Ratios Matter To Traders

Fibonacci ratios are also used to define upside price targets and support levels. They can also help identify times when a stock or index is likely to turn.

No one knows why, but Fibonacci ratios seem to work in many markets. Traders are often aware of them on long-term and short-term charts. For example, they may become cautious as prices approach a Fibonacci ratio that is likely to be resistance.

Once the resistance level is broken, traders may become more bullish. Quick gains are often seen when prices break above a significant ratio. Traders will sometimes become more aggressive at a Fibonacci support level, since they expect prices to bounce higher from that price.

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