# Fibonacci Numbers & Fibonacci Retracements

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:

(Disclaimer: Past performance is not necessarily indicative of future results)
Data Courtesy: Dana Lyons Tumblr

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!

1. The correct term is actually “apophenia”.

2. “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.”

Why not Pi? After all, there was a movie about it. Or how about tea leaves? Chicken entrails? Or Financial Astrology? It’s an actual thing, you know. http://en.wikipedia.org/wiki/Financial_astrology

Oh, I get it. When you say, “Our friend Dana Lyons over at Yahoo always has the best charts,” you’re saying it because “best” is a subjective term, and by “best” you mean “most pseudoscientific.” You’re actually trolling us here, right?

Disclaimer
The performance data displayed herein is compiled from various sources, including BarclayHedge, and reports directly from the advisors. These performance figures should not be relied on independent of the individual advisor's disclosure document, which has important information regarding the method of calculation used, whether or not the performance includes proprietary results, and other important footnotes on the advisor's track record.

Benchmark index performance is for the constituents of that index only, and does not represent the entire universe of possible investments within that asset class. And further, that there can be limitations and biases to indices such as survivorship, self reporting, and instant history.

Managed futures accounts can subject to substantial charges for management and advisory fees. The numbers within this website include all such fees, but it may be necessary for those accounts that are subject to these charges to make substantial trading profits in the future to avoid depletion or exhaustion of their assets.

Investors interested in investing with a managed futures program (excepting those programs which are offered exclusively to qualified eligible persons as that term is defined by CFTC regulation 4.7) will be required to receive and sign off on a disclosure document in compliance with certain CFT rules The disclosure documents contains a complete description of the principal risk factors and each fee to be charged to your account by the CTA, as well as the composite performance of accounts under the CTA's management over at least the most recent five years. Investor interested in investing in any of the programs on this website are urged to carefully read these disclosure documents, including, but not limited to the performance information, before investing in any such programs.

Those investors who are qualified eligible persons as that term is defined by CFTC regulation 4.7 and interested in investing in a program exempt from having to provide a disclosure document and considered by the regulations to be sophisticated enough to understand the risks and be able to interpret the accuracy and completeness of any performance information on their own.

RCM receives a portion of the commodity brokerage commissions you pay in connection with your futures trading and/or a portion of the interest income (if any) earned on an account's assets. The listed manager may also pay RCM a portion of the fees they receive from accounts introduced to them by RCM.

Disclaimer
The performance data displayed herein is compiled from various sources, including BarclayHedge, and reports directly from the advisors. These performance figures should not be relied on independent of the individual advisor's disclosure document, which has important information regarding the method of calculation used, whether or not the performance includes proprietary results, and other important footnotes on the advisor's track record.

Benchmark index performance is for the constituents of that index only, and does not represent the entire universe of possible investments within that asset class. And further, that there can be limitations and biases to indices such as survivorship, self reporting, and instant history.

Managed futures accounts can subject to substantial charges for management and advisory fees. The numbers within this website include all such fees, but it may be necessary for those accounts that are subject to these charges to make substantial trading profits in the future to avoid depletion or exhaustion of their assets.

Investors interested in investing with a managed futures program (excepting those programs which are offered exclusively to qualified eligible persons as that term is defined by CFTC regulation 4.7) will be required to receive and sign off on a disclosure document in compliance with certain CFT rules The disclosure documents contains a complete description of the principal risk factors and each fee to be charged to your account by the CTA, as well as the composite performance of accounts under the CTA's management over at least the most recent five years. Investor interested in investing in any of the programs on this website are urged to carefully read these disclosure documents, including, but not limited to the performance information, before investing in any such programs.

Those investors who are qualified eligible persons as that term is defined by CFTC regulation 4.7 and interested in investing in a program exempt from having to provide a disclosure document and considered by the regulations to be sophisticated enough to understand the risks and be able to interpret the accuracy and completeness of any performance information on their own.

RCM receives a portion of the commodity brokerage commissions you pay in connection with your futures trading and/or a portion of the interest income (if any) earned on an account's assets. The listed manager may also pay RCM a portion of the fees they receive from accounts introduced to them by RCM.