The Italian Monk and his Procreating Rabbits

Once upon a time, in the 12^th century, there was a monk named Leonardo Fibonacci, though his friends knew him as Leonardo di Pisa.  While studying the procreation of rabbits, he noticed an elegantly simple number sequence that explained the rate of increase in their population. 

Figure 1

The sequence starts with zero and one, then ads the latest two numbers to get the next one.  So zero plus one equals one, one plus one equal two, one plus two equal three, two plus three equal five, three plus five equal eight, and so on.

This sequence can be used to describe an amazing variety of basic growth patterns of nature, from the distances of the planets from the Sun to the rings of a tree to the proportions of the human body to the branches of the Sneezewort Plant.

Figure 2

Just why this simple sequence describes so many different processes of nature has been the subject of debate among philosophers and mathematicians alike for the past seven hundred years.  Perhaps even more mysterious is how the same Fibonacci sequence also pops up, with astounding regularity, in the financial markets.   Indeed there are many other sequences, formulas and numerical tea leaves that traders use to tell them when to buy and when to sell – you will learn some of them right here in this Handbook – but none describe the market so universally, and none portend it so regularly, and none translate its chaos into clear meaning so simply, and elegantly, as the Fibonacci sequence. 

If you think about it – if you really sit down and noodle it - perhaps the leap from the ordered chaos of nature, to the chaotic order of the financial markets, is not such a great one.  After all, what is the market but a most basic interaction between people, so primal that it precedes language in the development of human intelligence and even today is largely independent of language?  I mean, ever been to Marrakech?  Perhaps it is not a surprise that the ebb and flow of the financial market mirrors that of nature itself.  It certainly is no coincidence that we measure price waves in the same way that a surfer instinctively measures the swell of the ocean, and the same way that a school of fish flows with the invisible currents underneath.  And just as a forest is made up of trees of every possible size, each unique but each also coming from the same source, so we recognize that the market is made up of financial fractals – geometric patterns that are repeated at ever smaller scales to produce shapes that are unique on the one hand, but which can be defined using the simplest of mathematical sequences.

Lastly – and perhaps most importantly – there is another common thread connecting nature with the markets, and that is the notion of the “seed.”  Virtually all of the patterns in nature that are described by the Fibonacci sequence, have seeds of one kind or another.  There is no question that Leonardo’s rabbits had plenty.   Trees and the sneezewort plant all come from seeds.  In exactly the same way, all growth in the financial markets also comes from seeds.  It is no coincidence that in this Handbook you will frequently come across such words as “seeds” and “fractals.” And perhaps, at some point down the line, when you reach the trader’s equivalent of nirvana, in a sudden flash of enlightenment you will understand that seeds and fractals are indeed the same.

So how does it all relate?

To see how Leonardo’s mindlessly procreating rabbits can tell us when to buy and when to sell 500 shares of Microsoft for a profit, let’s look at the first numbers in the Fibonacci series:

1   2    3   5   8   13   21   34   55    89    144    233    377

There are an intriguing number of interrelationships between these numbers. For instance, any given number is approximately 1.618 times the preceding number and 0.618 times the following number.  (Note that these constants do not apply to the first several numbers in the sequence; however, the further along you move in the sequence, the closer the ratios get to 1.618 and 0.618.)

Just as 1.618 and 0.618 describe the relationship between one number and the next in the Fibonacci sequence, so they also describe the relationship between one “surge” in prices and the next, in the stock market.  So if prices surge from 5 to 8, then you can multiply the 8 x 1.618, to estimate that the next surge in prices will be to 13.     Likewise if they retrace from 13 to 8, by multiplying 8 x 0.618 you can estimate that the next retracement will be to 5. 

Continuing that logic, just as the ratios between any two successive numbers in the Fibonacci sequence are important, so are the ratios between any three successive numbers, and any four successive numbers:

1   2    3   5   8   13   21   34   55    89    144    233    377

1   2    3   5   8   13   21   34   55    89    144    233    377

This gives us additional ratios of secondary importance (0.382 and 2.618), and tertiary importance (0.236 and 4.682), as summarized in the next table.

The table also shows two other numbers that are important in the Fibonacci sequence, 0.5 and 1.382.  0.5 is an important retracement ratio because, well, it is halfway between 0.382 and 0.618.  Need more reason?  The midway point is always important in any growth cycle; just ask anyone who has reached that age!  In the financial markets, when prices drop to the midpoint of a previous trading range, the buyers and sellers will notice this and, collectively if not consciously, take pause to decide whether to move back up again, or to continue on down.  As for 1.382, I cannot explain why it is also an important growth number, other than to say that it inherently relates to 1.618 just as 0.382 relates to 0.618.

No, prices do not move in a straight line

Before we apply the ratios in Table 1 to the market, let’s look at the relationship between growth and retracement, because this is important to understanding how prices move in the markets.  Luckily for traders, prices do not move in a straight line.  The “dips,” or retracements, are what provide us with the opportunity not only to enter the trade, but also to estimate when to get out of the same trade.

Generally, when buyers outnumber sellers, the price goes up.  This, of course, attracts more buyers – and more willing sellers – until the buying pressure is spent.  Then what happens?  Prices usually collapse, or retrace, in the direction from which they came.  Why?  Because the buyers have “switched sides” to become sellers in order to take profits.  These sellers now outnumber the buyers and are chasing the price back down.   In a trending market, this tends to have a rubber band effect; each advance is met by a retracement.  After the sellers have taken their profits, if the overall uptrend is still intact, the retracement will then be met by another advance. 

The combination of an advance, a retracement, and another higher advance forms a wave pattern, as shown in Figure 3.  Note how the wave pattern is made up of a MSL, followed by a MSH, followed by a higher MSL.  This is the basic building block of any wave: MSL, MSH, Higher MSL.  For a downward wave, the pattern is simply the reverse:  MSH, MSL, and Lower MSH. The first wave in a sequence is known as the seed wave because it is the seed from which the subsequent waves grow. 

Figure 3

As you will see, the ratios that we derived from the Fibonacci sequence can be used to both gauge the retracement of one wave and predict the advance of the next.   All we need to know is the size of the first “seed.”

 Figure 4 shows the same wave pattern as Figure 3, but in the slightly more chaotic context of the real world:  an actual chart of Microsoft.

• Note again the pattern of MSL, MSH, and Higher MSL. 
• Note also that this Wave Pattern is the beginning of a reversal from a down trend to an uptrend (from short to long), so it is a seed wave.

Figure 4

You may also have noticed that (1) is a MSH and (2) is a higher MSL.  Why not use these as the “seed”?  There are many different ways to determine a wave.  Strict observers of the Fibonacci sequence contend that there should be between eight and thirteen time periods between the first MSL and the next higher MSL.  This gives the wave a “reasonable” amount of time to develop.  Strictly speaking, then, the MSL labeled (2) occurs before the eighth candle and so is not counted.

Using Fibonacci to forecast waves

Now that we have identified a seed wave, we can use the Fibonacci growth ratios to estimate how high the next wave(s) will be.  This is useful because it tells us when to exit the trade.   Note that the ratios do not tell us that there will be a subsequent wave.  They only tell us what to do if there is another, higher, wave.

Figure 5 shows the same 13-minute chart of Microsoft, with the Fibonacci growth targets and retracement pivots drawn in.

Figure 5

(1)  This is the beginning of the wave, as determined by the MSL.  Because it is also the low point of the previous trading range, it is the start of a seed wave.

(2)  This is the end of the first wave, as determined by the MSH.  Subtract the bottom of the wave from the top of the wave to get the range.  In this case, the range is 55.76 – 54.55 = 1.21.  Note how this range is shown in the drawing tool on the chart, with (1) as 0% and (2) as 100%.

(3)  This is the higher MSL.  It also represents the retracement back down from the initial advance to the MSH.  Typically, if prices are moving upward with strength, the retracement will be to about 50% of the range of the previous wave.  This is the “what shall we do now” point that I mentioned earlier, where buyers and sellers take a pause and, collectively, try to decide what to do next.  As you can see in this example, the main candle bodies of the MSH found support at the 50% retracement pivot.

(4)  This is the end of the next advance.  Once prices retrace to point (3), and once we see them pivot and move on up, we can then use the Fibonacci targets to estimate where the top of the next wave will be, like magic!  The calculation is easy.  Take the range of the seed wave, which we already know is 1.21.  Multiply that by the Fibonacci ratio of 1.618 to get 56.5.  That is the target for the growth of the next wave up.   As you can see, prices rose exactly to that target before falling back. 

This was an ideal example. On any given day in the market, the trading action is such that you rarely witness a retracement to exactly 50% of the previous wave, followed by a growth to exactly 161.8% of that wave.  But you will find that in strongly trending markets, this ideal is the rule more than it is the exception.  Shortly, I will take you through some trades that are not quite as ideal.

A word about Pivots

Let’s take a closer look at that retracement from the MSH down to the higher MSL.  Figure 6 shows a close-up of the same range as Figure 5, but with the key Fibonacci retracement pivots drawn in.

Figure 6

It is important to note that when prices come down to the 50% point, there is absolutely no guarantee that they will go back up.  Indeed, if you think about it, if there were a guarantee that prices would go back up, they would not have retraced as far as this “what shall we do now” point in the first place!  That is why they are called pivots.  You do not know what will happen at a retracement pivot.  What you do know is that at one or more of the Fibonacci pivots (0.618, 0.50, 0.382 and 0.236), prices will pause.  Like a basketball player, they will pivot, then either shoot or run on.

In Figure 6, you can see that the main body of the MSL candle found support at the 0.50 pivot (shown in the chart as 50%).  You can also see that the shadow of that candle reached down to the 0.382 pivot.  What that tells us is when the price dropped to 50% of the range of the seed wave, buyers and sellers started to hesitate.  A couple of bold bears pushed further down but met ultimate resistance at the 0.382 pivot before finally “giving up” when the candle closed at the 0.50 pivot.  During the next period, the bulls took over.  As soon as that happened, the pattern of the procreating bunnies told us that the price could go to 56.5 before the next major retracement.

Incidentally, if you had bought 1,000 shares of MSFT at the trigger point of $55.76 (a standard MSH-failure long trigger), and sold at the target of $56.50, you would be able to pay for this book and buy a round-trip ticket to Hawaii with the change.

What comes after that?

Once the seed wave is complete and you have taken your profit, you may have some questions.  “What do I do next?  Will there be another wave up?  What happens if prices reverse back down?  How do I tell the difference between a retracement and a reversal?”

During the Great Depression, a market speculator by the name of R.N. Elliot (no relation to T.S. as far as we know) used his spare time to come up with a method of quantifying and classifying the seemingly random undulations of mass psychology that we call the financial markets.  In a nutshell, a cyclical pattern often exists in which, when prices are trending upward, they normally move five waves upward and three waves downward. If the uptrend remains intact, it will then resume with another five waves upward, followed by three waves downward, and so on. To clarify, "Five waves upward" is actually a five-wave swing pattern made up of three successively higher peaks (MSH’s) with two successively higher troughs (MSL’s) in-between. When a stock is down trending, the reverse pattern is true, i.e., five waves downward followed by three waves upward. An up-trending pattern is shown in Figure 7:

Figure 7

In Figure 7, that first wave extending from “0” to “1” is called W1.  The correction wave down is called W2.  Waves 1, 3, and 5 are always the main waves in the trend, whereas waves 2 and 4 are always the counter-trend correction waves. The waves a, b, and c are correction waves against the greater trend.  Wave 1 is the “seed” for the subsequent waves, upon which the Fibonacci growth ratios are applied to come up with targets for potential waves 3 and 5.

These patterns have forecasting value - when five waves upward have been completed, quite often three waves downward will follow, and vice versa.  By integrating the Fibonacci ratios into the five-wave pattern, price goals can be calculated.  I call this pattern “eWaves” in deference to the man named Elliot, who knows a lot more about these things than I do.

Another Example

Now that we have seen some wave theory, let’s look at the structure and identify the waves on a chart of the S&P E-mini futures (which I will call ES from now on).

Figure 8 shows the retracement pivots drawn on the range of the first wave.  As you can see, prices retrace to 61.8% of the range before continuing on up.  This indicates a strong up-trend.  Note that there were several failed attempts to go down to the 50% pivot. 

Figure 8

 From Figure 8: 

(1)  Prior downtrend indicates that any reversal back up will be a seed wave.

(2)  MSL forms the potential reversal.

(3)  MSH forms the top of the potential seed wave

(4)  Prices retrace to the 0.618 pivot, which is the higher MSL.  Again, note that Fibonacci “purists” say that there should be no less than eight, and no more than 13, candles between the MSH (2) and the higher MSH (4).  Therefore technically, this is not a seed wave, even though I am going to confuse you by saying that it is. 

(5)  At the point where prices then move up above the previous MSH (3), the wave pattern is triggered.  We can now take the range of the seed wave, 1173.25 – 1158.25, and multiply that times 1.618 to get the growth target of the next wave.

 Refer to the wave count in Figure 7, and apply those to the pattern in Figure 8:

(2) is the “0” point of the first (seed) wave.

(3) is the top of the first wave, W1.

(4) is the bottom of the second (retracement) wave, W2.

(5) is the confirmation of the third wave, W3.

Figure 9  shows where W3 actually ended up. It also shows the retracements from W1 and the Fibonacci targets of 1.382 and 1.618. Note how nicely they match up.  Waves 1, 2 and 3 are shown as (1), (2) and (3) respectively.

Figure 9

It is important to understand that after a W2 retracement, prices do not always extend beyond the top of W1 to form a W3.  In such a case, the wave pattern is not registered.  Instead, prices are bound within the previously determined trading range.  Even if a W3 does register, there is no guarantee that it will reach the 1.618 target.  For example, there may be important price levels just below that 1.618 target that would impede prices from reaching higher.  You should always be aware of important points near a Fibonacci target, and always err on the side of caution when fine-tuning your exit target.  Also be aware that statistically, the 138.2% Fibonacci target will get hit more often than the 161.8% target. This is common sense, since it is a smaller target.

Whether the 138.2% target gets hit sufficiently more than the 161.8% target to make up the difference in potential profit, is of course an important question.  It is a constantly changing variable and the serious trader will keep careful notes of all trades in order to keep tabs on which of the Fibonacci targets is a better fit for which equity or instrument, over which time period.  Chapter 15 deals with this question in more detail.
 

What about that 8-13 wave count thing?

When you try to identify growth waves on your own, you will quickly discover that it is not as simple as it may appear; indeed, sometimes it seems as if there are as many different interpretations as there are traders.  Do not let this discourage you! The magic of Fibonacci is that in most cases, the Fibonacci ratios will apply to whatever your interpretation is.    For example, Figure 10 shows that a different interpretation of the same chart can also yield a profitable trade. 

Figure 10

In Figure 10, Point (3) is what we called W1 in Figure 9.  But notice that there is a MSH before point (1) in Figure 10, followed by a higher MSL (2).  This is the first sign of a 123 reversal.   Note also that there are eight candles between the first MSL (0) and that next higher one (2).    

(0)    This is the same bottom as in Figure 9.

(1)     This is the first actual MSH, and so becomes an alternate interpretation of the W1 seed.

(2)    A higher MSL forms here, signaling an earlier entry than in my trade in Figure 9.  Notice that there are eight candles between (0) and (2), which qualify this as a seed wave amongst strict observers of the Fibonacci sequence.  This becomes W2.  Once prices then turn up, confirming the seed wave structure, we can use the Fibonacci ratios to target the top of W3.

(3)    In this case, prices almost reach the 161.8 target but not quite.  This illustrates one reason why 1.382 is also an important Fibonacci ratio.  If prices move past 138.2 but do not quite reach the 161.8 target, then you can use 138.2 as a stop exit on the way back down.  As I said in the previous example, it is important to look at other price points that may be acting as resistance just below the Fibonacci target.   Any point within the 1.382 – 1.618 range is a good place to take profits.

(4)    Now here’s where it gets interesting.  In this interpretation point (4) is the W4 retracement and so we will have already made one successful trade before we even recognized the three wave pattern in the Figure 9 interpretation.  After the MSH is formed here we can re-enter the long, and can use the next higher Fibonacci ratio of 2.618 to target the high of this W5.  Note how this 5-wave pattern fits the eWave diagram shown in Figure 7.

(5)    Sure enough W5 is reached at the Fibonacci target of 2.618 x the range of the seed wave.

A note on fractals and different time frames

Just as Fibonacci growth targets and retracement pivots work in these examples, they also work across all time frames.  The two examples shown above are on a 13-minute chart.  If you looked at a three-minute chart over the same time period, you would see smaller wave patterns embedded within. Likewise, if you zoomed out to a 30-, 60-, or 120- minute chart, you would see that this three-wave pattern (or five-wave, if you saw it that way) is but a “jiggle” on larger scale wave patterns.

Review

If you’ve never looked at what Fibonacci can do, I image you are pretty impressed at this point. Quite possibly your head might also be spinning at all of the new terms.  So before I go on, let’s highlight what we already know.  Important terms are highlighted in bold.

o       The Fibonacci sequence is 1, 2, 3, 5, 8, 13, 21, 34, etc.

o       Prices do not move in a straight line.   They tend to move in undulations, or waves.  The combination of an advance, a retracement, and another higher advance forms a wave pattern.  This is indicated by a MSL, a MSH, and then a higher MSL.

o       The first wave in a sequence is known as the seed wave because it is the seed from which the subsequent waves grow.

o       Many Fibonacci traders believe that there should be no less than eight, and no more than thirteen candles, making up the seed wave (counted from the first MSL to the next, higher, MSL).

o       The key Fibonacci retracement pivot ratios are 0.236, 0.382, 0.50, and 0.618.  (These can also be expressed as percentages 23.6%, 38.2%, 50%, and 61.8%).  When prices retrace after establishing a range, they will usually “pivot” at one or more of these points.  If prices are going to move back up, ideally they will pivot near the 0.50 retracement level.

o       A retracement pivot will act as support until prices break below it, at which point it will then act as resistance against prices trying to move back up. Think of “The King is dead, long live the king.”

o       The key Fibonacci growth target ratios are 1.382, 1.618, 2.618 and 4.236.  Typically 161.8 is used as the target for W3, and 261.8 as the target for W5.

o       The eWave pattern shows that when prices are trending upward, they normally move five waves upward and three waves downward. If the uptrend remains intact, it will then resume with another five waves upward, followed by three waves downward, and so on.  These are fractal in nature and so one large wave up in a daily time frame will be made up of five smaller waves on a 30- or 13-minute time frame, etc.