Fibonacci Ratios, Price Retracements and Binary Options

A well known “strategy” for assessing likely market moves when trading binary options (or indeed placing any kind of bet on currency or stock markets) is the use of so-called Fibonacci indicators to plot price retracements.

Simply put, a retracement is when a clearly established price movement up or down pulls back for a while before continuing its original trend (a “projection”). The key point is that a retracement is a temporary reversal rather than a full blown reversal as such.

What happens visually (see graph on next page) is that the general trend hits a point where the price “bounces” and retraces its steps before resuming its projection. For a downward movement the switch back up is termed a price support point (the price is temporarily propped up) and the equivalent switch back down is termed a resistance point (the price cannot break through a ceiling).

It’s quite common to see repeated attempts for the price to “test” these points of support/resistance before finally breaching. It is also common to observe that a previously breached resistance point becomes a new support, below which the price will no longer retrace in a rising market (obviously the reverse also holds true in falling markets).


Clearly, being able to spot price trends and tell the difference between retracements and reversals significantly improves your chances of calling the market correctly and profiting from trades based on these predictions.

Or put another way, might protect you from losing your shirt because you didn’t see what was coming.

If a price reverses it’s recent trend direction you need to know whether that reversal is going to continue and become the start of a new trend or fizzle out fairly quickly. Get it wrong and you could find yourself holding or buying into a losing position, or conversely staying or selling out of a winning position.

A regular trader (one who actually buys and sells at a given price rather than simply betting on the movement of the price) needs to carefully gauge whether to hold, buy or sell in response to a price movement.

He or she must factor in trading costs (which may totally negate any possible advantage) and lost opportunity.

If you sell rather than hold and a reversal in a bull market turns out to be a very temporary retracement then you will incur two sets of trading costs for having both sold and bought back in at less then optimal prices.

A binary options trader doesn’t have quite the same concerns, but nevertheless needs to correctly assess how things are moving so as to trade on both short and longer term price movements.

But enough already – how the fuck does Leonardo Pisano Bigollo a.k.a. Fibonacci fit into all this?

Fibonacci and the Golden Ratio

Well… as you probably know, the eponymous Fibonacci sequence is where each ascending number is the sum of the previous two numbers. It goes like so:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc

It describes many natural phenomena such as phyllotaxis (you already knew that one, surely?), the arrangement of flower petals, the geometry of pentagons and shit loads else besides.

But it’s not the sequence itself that’s the really interesting thing; it is the ratio between the numbers.

Obviously in order for the Fibonnaci sequence to work, the ratio between each pair of numbers has to be very close, otherwise you wouldn’t see smooth transitions in, for example, the spirals of sea shells.

But it’s better than that even… As the sequence grows, the ratio between each pair of numbers both oscillates around and converges very tightly on 0.6180339887… And what’s so special about that? Well it’s the Golden Ratio for one thing.

That’s where the ratio between a pair of numbers is identical to the sum of both numbers to the larger of the two, such that b/a = a+b/b. This might seem like dull and irrelevant math but it is worth knowing so stick with it…

So for example, taking a=1597 and b=2584 we establish that 2584/1597 = 1.618033 which is very close to the Golden Ratio and likewise 1597+2584/2584 = 1.618034 which is again damn close and actually completely the same up to 4 decimal points. And as the sequence goes on, both results converge ever more tightly.

But even more intriguingly, this ratio has another surprising symmetrical property. Normally for example, 52/97 = 0.536082 whereas 97/52 = 1.865384. As Alexandr Orlov might put it, “don’t even sound same”.

With Fibonacci pairs however, 1597/2584 = 0.618273 while 2584/1597 = 1.618033. Sound familiar? The Golden Ratio has the unique property that 0.6180339887…:1 = 1:1.6180339887… – spooky or what?

Anyway, back to the point, which is that the key ratio between any adjacent pair on a Fibonacci sequence approximates extremely closely to the Golden Ratio, which for all practical purposes is 61.8 percent. There are a whole bunch of similar ratios that use numbers separated by increasing amounts and the standard set are:

61.8%, 38.2%, 23.6% and for good measure 50% even though it’s not a Fib ratio.

So now that we have these “magic numbers” we can dump old Fibonacci and set to work, because the scope of a retracement is highly likely to be pegged to one of these particular percentages. Or so the theory goes…

Magic Numbers and Self-Fulfilling Beliefs

Take a look at the sample graph taken at random from some or other currency exchange rates. The main upward trend is indicated by the green arrow and within that we see a clear retracement starting at about the 145 mark. If we take the peak at that point to be 100% then the scope of the retracement occurs at more or less 61.8% – bingo, it works!

Except that it doesn’t really because I’ve been careful to only select those specific points.

It’s extremely difficult to map any of the other very clear retracements to any of the magic numbers, despite the fact we have plenty of both to pick from.

And so it is with pretty much any graph you could choose at random.

Specifically the retracement immediately before the annotated one goes no where remotely close to it’s own 61.8% mark or any other magic percentage. I also cannot predict whether the final downward movement marks a reversal or another retracement based on analysis of what has gone before.

So why do so many traders (and trading strategies) put so much store by the predictive powers of Fibonacci ratios?

In a nutshell, it’s because as a group they tend to act on their own expectations and thus trigger reversal trades when prices approach the support and resistance levels that map to their magic ratios.

In effect, a self-fulfilling prophesy… but not a very good one since it sometimes pans out but more often doesn’t. Partly because different traders favor different pet ratios but mostly because the math just doesn’t stack up here.

In terms of hard evidence supporting the idea that there is a fundamental mathematical mechanism at work here, there is none whatsoever and if you’re so inclined you can read this academic study to find out why “magic numbers” and analysis of past behavior provide no reliable guide to the future.

That said, most academics are wedded to the notion of an efficient market that values assets openly and accurately and is populated by rational investors. The reality is that the market is not efficient, asset prices are often hopelessly wide of the mark and there is nothing remotely rational about the bi-polar herd instincts of the players.

Many corporations (especially large American ones) quite clearly appear to operate principally in the interests of the senior executives. Valuations are far from transparent and either manipulated to serve vested interests or reflect the mood swings of twitchy traders addicted to “risk”.

This makes for a highly erratic market driven by opaque and seemingly irrational factors that is difficult to predict over any relatively short time frame. But it also makes for a target-rich environment for those who pay no heed whatsoever to charts, volatility, moods, trends, magic numbers or any of the other technical analysis voodoo so beloved by so many “professional” traders.

The legendary investor (not to be remotely confused with “trader”) Warren Buffet described a decade back in this short essay The Superinvestors of Graham-and-Doddsville exactly how he and fellow investors got to be so spectacularly wealthy by avoiding risk and ignoring market sentiment.

Warren’s advice boils down to “buy dollar bills for forty cents apiece”. You could probably adapt the underlying strategy, which is to spot assets that are in reality far more valuable than the market presently values them, to binary options trading. But honestly, why would you? Why not just do as Warren does – investigate and invest? It’s not very immediate or exciting, but it will make you money. A fuck of a lot of money if Warren and his pals are any example.

Fib Lines, Ley Lines, Coke Lines, Take Your Pick

Anyway, back to the original point… Are Fibonacci retracements a useful tool for the binary options trader? Sure they are – but only about as much use as a lucky rabbit’s root or a four leaved clover.

People tend to see what they want to see (or go looking for) and traders are right up there with would be mystics and class A, certifiable fruit-bats. David Icke anyone? You can check this particular nutter out on your own time, but this little gem is not a million miles from folk scouring for price swings that can be molded to fit as near as possible to a 61.8% ratio.

Yes, it is (to quote Miranda’s mother) what I call the Fearsome But Wholly Fictitious Pentagram of Blood. It’s absolutely amazing isn’t it – that anyone should not only believe such utter toss, but go to such trouble to “prove” it! I do wonder, given the shape of the pattern, whether David perhaps harbors beliefs about Jewish conspiracies, but that’s just speculation. Unlike his pentagram of course, which is irrefutable evidence, apparently.

Anyway, not to be outdone I’ve “discovered” the ancient, secret (you know, the one THEY don’t want you to know) and thoroughly Diabolical Pentagram of New York Metro Stops. Granted, it is a little bit skewed – as if viewed from an angle suspiciously close to a minor Fib ratio…

The point is that you can find patterns in absolutely anything and as it happens random noise is among the very best places to find beguiling patterns and spooky coincidences. The world has no fewer folk trying to unravel the secret code behind winning lottery numbers than it once had alchemists searching for gold in pots of piss (yes, they really did try that one).

And so it is with Fibonacci and financial data. The occasional chance alignment but nothing more than that. But it’s your money and if you want to put it all on lucky 61.8 then no-one’s getting in your way.

But before you leave can I interest you in any other sure fire trading strategies?