 # Understanding "Fibonacci Retracement Levels"

Recently while reading some analysis on mortgage backed securities (Mortgage Bonds) the author mentioned the “Fibonacci Retracement levels” in his analysis. I knew of Fibonacci numbers but wasn’t sure what “Fibonacci Retracement levels” were in relation to understanding movement of securities in the free market. So I did some investigation. Below is a summary of the article I read to get an understanding of this concept. The original article can be reached at: http://daytrading.about.com/cs/charts/a/fibonacci.htm

What Are Fibonacci Numbers

The original problem Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances. Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so at the end of its second month a female can produce another pair of rabbits. Suppose our rabbits never die and the female always produces one new pair (one male, one female) every month from the second month on.

How many pairs will there be in one year?

At the end of the first month, they mate, but there is still one only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs.

The number of pairs of rabbits in the field at the start of each month is 1, 1, 2, 3, 5, 8, 13, 21, 34, … The next number in the Fibonacci sequence is arrived at by adding the previous two values together. Thus, to get the next value after 34 add 21 to 34 and arrive at 55.

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Fibonacci numbers are used in calculating retracement patterns. Many securities, after making long sustained moves in one direction, will eventually retrace a portion of the move before continuing on to extend it. The most popular retracement amount used is 50%. Meaning, if on its latest move, a stock went from 50 to 100 and then started backing off, a 50% retracement would bring it to \$75 before it turns around.