When the price of a stock or a similar investment is steadily rising, it usually doesn't do so in a straight line. It rises for a while, then dips, then resumes rising. What's happening is "profit taking" -- investors are locking in profit by selling their shares, causing the price to fall. Other shareholders see the decline and sell their own shares, pushing prices down further. Eventually, though, investors come to view the stock as underpriced, they rush in to buy it, and the price rises again. A similar phenomenon works in the other direction. When the price of a stock is steadily falling, there will come a point where many investors believe it's undervalued, and they buy shares, pushing up prices. When those investors then sell to take their profit, the price resumes its downward slide. These temporary reversals of the prevailing price trend are known as "retracements." Financial analysts have developed many strategies to try to predict -- and therefore profit off of -- retracements. One of the most widely used methods is through Fibonacci retracements, which are derived from the series of numbers identified in the 13th century by mathematician Leonardo Fibonacci.

## Discovering the Fibonacci Ratios

Write out the Fibonacci sequence. The sequence starts with 0 and 1, and each successive number in the series is the sum of the two numbers that precede it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597 and so on.

Select one of the larger Fibonacci numbers -- anything from 89 up will do.

Divide your chosen number by the next number in the series. If you'd chosen 144, for example, you'd divide 144 by 233. Regardless of the number you chose, your result should be approximately 0.618. This is the first Fibonacci ratio.

Divide your chosen number by the number that comes two places after it in the series. So if you're working with 144, divide 144 by 377. Whatever numbers you're working with, your result should be approximately 0.382. This is the second Fibonacci ratio.

Divide your chosen number by the number that comes three places after it. If you'd chosen 144, you'd divide 144 by 610. Whatever numbers you're working with, your result should be approximately 0.236. This is the third Fibonacci ratio.

Subtract the third Fibonacci ratio from 1. The result is approximately 0.764. This is the final Fibonacci ratio.

Add 0, 0.5 and 1.0 to your list of ratios. While not actually derived from the Fibonacci numbers, traders typically include them when examining "Fib retracements," because prices show similar behavior around these ratios as they do around the true Fibonacci ratios. You should now have a list of seven ratios.

## Calculating the Fibonacci Retracements

Identify recent price extremes -- the highest recent price and the lowest recent price -- for the stock or other investment you're analyzing. Prices of securities and other investments naturally fluctuate from day to day, but over time, many show a clear upward or downward trend. You're looking for a movement from a higher price to a significantly lower price, or vice versa.

Subtract the low price from the high price. For example, if you're looking at a stock that recently went from $10 a share to $14, your math would be: $14 - $10 = $4.

Multiply the price difference by the seven Fibonacci ratios: 0, 0.236, 0.382, 0.5, 0.618, 0.764 and 1. In the case of a $4 price difference, this would give you Fibonacci values of $0, $0.94, $1.53, $2, $2.47, $3.06 and $4.

Add the Fibonacci values to the previously identified low price to get the retracement levels. In this example, the low price was $10, so the retracement levels are $10, $10.94, $11.53, $12, $12.47, $13.06 and $14.

Watch the price for signs of change as it approaches any Fibonacci retracement, either on the way up or the way down.

#### Tips

- Different traders work with different definitions of "recent" when looking for recent price extremes. Time frames could be as short as a few hours or as long as a year or more. Generally, the shorter the time frame, the smaller the dollar values between retracements.
- Fibonacci retracements apply when the price of an investment is currently between its recent extremes. A stock that's reaching new highs or sinking to new lows is outside the frame of reference required to calculate Fib retracements -- it's quite literally in uncharted territory.

#### Warning

- There's no guarantee that a price trend will reverse at a particular Fibonacci retracement level -- or at any time. Fib retracements are simply points that traders have identified as being more likely to produce a shift than others.

### Items you will need

- Caculator
- Recent price data on the investment you're analyzing

#### References

- Investopedia: What Is Fibonacci Retracement, and Where do the Ratios Come From?
- "Fibonacci Trading: How to Master the Time and Price Advantage"; Carolyn Boroden; 2008
- Ball State University: Fibonacci Numbers and Their Application in Trend Analysis

#### Photo Credits

- Duncan Smith/Photodisc/Getty Images