#### Fibonacci Numbers & Fibonacci Retracements by Attain Capital

Our friend Dana Lyons over at Yahoo always has the best charts, bringing to mind Jack Nicholson’s Joker in the original Batman movie saying the line: “Where does he get those wonderful toys.” And they usually have something in common: a 61.8% Fibonacci Retracement line:

Here’s the Fibonacci Retracement numbers in the Hong Kong Hang Seng (say that five times fast), but he’s also got them in the Belgium stock market, and Copper Futures, to name a few:

**What are Fibonacci Numbers?**

Just what are Fibonacci numbers, and what is this retracement stuff? Glad you asked. First, let’s start with the Fibonacci series. Some guy named, you guessed it, Fibonacci, came up with a nifty sequence of numbers (actually it has since been found that the sequence was in Indian texts predating his work), which roughly equal the preceding number in the sequence, plus the number preceding that number. So, 1+1 = 2, 1+2 = 3, 2+3 = 5, 3+5 = 8, 5+8 = 13, and so on into eternity.

But it’s simpler to just watch this video to understand it:

Some quant hedge fund needs to hire that girl, quick; if for nothing else but explaining models to investors on the whiteboard.

And here’s where things get interesting. Because while all this quant stuff may seem like advanced math, and much of it is. A lot of it isn’t all that advanced. A lot of it boils down to things as simple as Fibonacci numbers. Markets have been referred to as living, breathing organisms – and despite the rise of algorithmic trading, still have human beings hard earned money being won or lost in them. Is it all the weird to think that a market might find support at the 21 (Fibonacci number) or 34 day moving average, because investors have some innate, subconscious magnetism towards that number based on it being all round them. And for those coding systematic models, why not use the number of spirals found on pineapples, flowers, and more as the number instead of some static number pulled out of a hat.

**Fibonacci Retracements**

Which brings us to Mr. Lyons Fibonacci retracements on his clever charts. Where is 61.8 in the Fibonacci sequence. We looked, we can’t find it. We couldn’t find 38.2% or 23.6% either. What’s going on? Where do these numbers come from? How is this connected to the Fibonacci sequence? Well, 61.8% is what’s also referred to as “The Golden Ratio”, which sounds fancy, but is found by simply dividing a Fibonacci sequence number by the next number in the sequence. For example:

34/55 = 61.8%, 55/89= 61.8%, 89/144 = 61.8%, 144/233 = 61.8%

The other Fibonacci Retracement levels are 38.2%, which a number in the series divided by the number two places after it; and 23.6% – which is a number in the series divided by the number three places after it in the series. (Note, you’ll find these ratios don’t work with the lower numbers in the sequence (for example, 1/1 = 100%, 1/2 = 50%), and only kick in above lucky 13 for some reason).

So, like the quant who decides to use a Fibonacci number for a variable in his code; many traders ask themselves – why tempt natural law, and math, and go against these Golden Ratios derived from numbers in the Fibonacci sequence. While it may sound a little quirky; it is still math; and not quite basing your trades off planetary movement or the tides (some people do).

And there you have it. Billions of dollars around the world being traded by algorithms with a simple numerical sequence found on pine cones, likely somewhere in their code. Long live math!