Why Successful Traders Use Fibonacci and the Golden Ratio

Support and resistance levels on bar charts are a major component in the study of technical analysis. Many traders, including myself, use support and resistance levels to identify entry and exit points when trading markets. When determining support and resistance levels on charts, one should not overlook the key Fibonacci percentage "retracement" levels. I will detail specific Fibonacci percentages in this feature, but first I think it's important to examine how those numbers were derived, and by whom.

Leonardo Fibonacci da Pisa was a famous 13th century mathematician. He helped introduce European countries to the decimal system, including the positioning of zero as the first digit in the number scale. Fibonacci also discovered a number sequence called "the Fibonacci sequence." That sequence is as follows: 1,1,2,3,5,8,13,21,34 and so on to infinity. Adding the two previous numbers in the sequence comes up with the next number.

Importantly, after the first several numbers in the Fibonacci sequence, the ratio of any number to the next higher number is approximately .618, and the next lower number is 1.618. These two figures (.618 and 1.618) are known as the Golden Ratio or Golden Mean. Its proportions are pleasing to the human eyes and ears. It appears throughout biology, art, music and architecture. Here are just a few examples of shapes that are based on the Golden Ratio: playing cards, sunflowers, snail shells, the galaxies of outer space, hurricanes and even DNA molecules. William Hoffer, in the Smithsonian Magazine, wrote in 1975: "The continual occurrence of Fibonacci numbers and the Golden Spiral in nature explain precisely why the proportion of .618034 to 1 is so pleasing in art. Man can see the image of life in art that is based on the Golden Mean."

I could provide more details about the Fibonacci sequence and the Golden Ratio and Golden Spiral, but space and time here will not permit. However, I do suggest you read the book "Elliott Wave Principle" by Frost and Prechter, published by John Wiley & Sons. Indeed, much of the basis of the Elliott Wave Principle is based upon Fibonacci numbers and the Golden Ratio.

Two Fibonacci technical percentage retracement levels that are most important in market analysis are 38.2% and 62.8%. Most market technicians will track a "retracement" of a price uptrend from its beginning to its most recent peak. Other important retracement prcentages include 75%, 50% and 33%. For example, if a price trend starts at zero, peaks at 100, and then declines to 50, it would be a 50% retracement. The same levels can be applied to a market that is in a downtrend and then experiences an upside "correction."

The element I find most fascinating about Fibonacci numbers, the Golden Ratio and the Elliott Wave principle, as they are applied to technical analysis of markets--and the reason I am sharing this information with you--is that these principles are a reflection of human nature and human behavior.

The longer I am in this business and the more I study the behavior of markets, the more I realize human behavior patterns and market price movement patterns are deeply intertwined.

Why Successful Traders Use Fibonacci and the Golden Ratio

Support and resistance levels on bar charts are a major component in the study of technical analysis. Many traders, including myself, use support and resistance levels to identify entry and exit points when trading markets. When determining support and resistance levels on charts, one should not overlook the key Fibonacci percentage "retracement" levels. I will detail specific Fibonacci percentages in this feature, but first I think it's important to examine how those numbers were derived, and by whom.

Leonardo Fibonacci da Pisa was a famous 13th century mathematician. He helped introduce European countries to the decimal system, including the positioning of zero as the first digit in the number scale. Fibonacci also discovered a number sequence called "the Fibonacci sequence." That sequence is as follows: 1,1,2,3,5,8,13,21,34 and so on to infinity. Adding the two previous numbers in the sequence comes up with the next number.

Importantly, after the first several numbers in the Fibonacci sequence, the ratio of any number to the next higher number is approximately .618, and the next lower number is 1.618. These two figures (.618 and 1.618) are known as the Golden Ratio or Golden Mean. Its proportions are pleasing to the human eyes and ears. It appears throughout biology, art, music and architecture. Here are just a few examples of shapes that are based on the Golden Ratio: playing cards, sunflowers, snail shells, the galaxies of outer space, hurricanes and even DNA molecules. William Hoffer, in the Smithsonian Magazine, wrote in 1975: "The continual occurrence of Fibonacci numbers and the Golden Spiral in nature explain precisely why the proportion of .618034 to 1 is so pleasing in art. Man can see the image of life in art that is based on the Golden Mean."

I could provide more details about the Fibonacci sequence and the Golden Ratio and Golden Spiral, but space and time here will not permit. However, I do suggest you read the book "Elliott Wave Principle" by Frost and Prechter, published by John Wiley & Sons. Indeed, much of the basis of the Elliott Wave Principle is based upon Fibonacci numbers and the Golden Ratio.

Two Fibonacci technical percentage retracement levels that are most important in market analysis are 38.2% and 62.8%. Most market technicians will track a "retracement" of a price uptrend from its beginning to its most recent peak. Other important retracement prcentages include 75%, 50% and 33%. For example, if a price trend starts at zero, peaks at 100, and then declines to 50, it would be a 50% retracement. The same levels can be applied to a market that is in a downtrend and then experiences an upside "correction."

The element I find most fascinating about Fibonacci numbers, the Golden Ratio and the Elliott Wave principle, as they are applied to technical analysis of markets--and the reason I am sharing this information with you--is that these principles are a reflection of human nature and human behavior.

The longer I am in this business and the more I study the behavior of markets, the more I realize human behavior patterns and market price movement patterns are deeply intertwined.

Switch Time Frames For Better Exits

I just returned from a weeklong Trader's Camp hosted by Dr. Alexander Elder in a beautiful island nation in the South Pacific called Vanuatu. When I studied geography in school many years ago, Vanuatu was known as the New Hebrides islands. Vanuatu is located about 1,000 miles west of Fiji.

If you have read Elder's excellent book, Trading For A Living, you will recall that Dr. Elder is an advocate of using multiple time frames for trading both stocks and futures. For example, he suggests looking at the weekly chart to make sure that the weekly trend is firmly up before trading the long side of a market based on the daily chart patterns. This approach makes good sense and I highly recommend his book and his strategy.

While listening to Dr. Elder explain his multiple time frame strategy for entries, my thoughts wandered to the application of his ideas to my favorite subject - exits. One of my goals in trading is to find exit strategies that do a good job of protecting open profits. One method of accomplishing this goal is to simply move the daily stops closer once a specific profit objective has been reached. However, it might also make sense to simply switch to a chart with a shorter time frame once we have reached a reasonable profit objective.

Here is an example of how such a strategy might work. Let's say that we have been trading XYZ stock on an intermediate term basis using daily charts. The trade is working out very well and we now have six ATRs of open profit. (See previous Bulletins for an explanation of how to use Average True Range to set profit targets). Up to this point we have been using our well-known Chandelier trailing stop placed at 3 ATRs below the high point of the trade.

However, now that we have reached our primary profit objective we want to tighten up our stop to protect more of our profits. We could reduce our Chandelier stop from 3 ATRs to 2 ATRs and continue using the daily bars or we could switch our chart to one hour bars and continue to trail the Chandelier exit at 3 ATRs based on the intraday one-hour bars. The basic idea is to switch to a chart with a shorter time frame once we have reached our profit objective. This procedure should allow us to let our profits continue to run but we would be protecting our open profits with much closer stops by using the chart with a much shorter time frame.

Combining our exit strategy with Dr. Elder's entry strategy would provide the following sequence: for entries we first examine the weekly chart and then use the daily chart to trigger the trade. Once we are ready to exit our trade we examine the daily chart and then trigger our exit using the hourly chart.

Of course this strategy would require some extra work as well as the use of intraday data. The alternative would be to simply reduce the number of ATRs used to hang the Chandelier exit on the daily chart. Either way we do it, the logic is to move our stops closer once we have achieved a worthwhile trading profit.

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Notes On Bear Markets

One of the best ways to gauge a bear market is to observe the reaction to good and bad news. In a bear market the averages go down even when the news is good. (For example, look what happened the last time the Fed cut interest rates.) We will know that the bear market is finally over when we observe the market reacting favorably to good news. In the meantime, we can take some consolation in the fact that at the present rate of decline we will soon be at zero. At least at that level we should be able to safely resume trading stocks from the long side.

Doubly Adaptive Profit Objectives

Having well-planned profit objectives is the best way to maximize closed-out profits. The tendency is to either take profits too soon or too late and most traders tend to err on the side of taking profits too soon. Taking a quick profit always feels good and helps to maintain our winning percentage because these "nailed-down" profits will never turn into losses. However, taking profits too soon can be one of the most costly of all possible mistakes.

It has been argued that profits in trading (especially in futures) are possible because the distribution of prices is not normal and is not a typical bell-shaped curve. The tail on the right hand side tends to be surprisingly thick indicating that unexpectedly large profits are possible. The opportunity for large profits comes our way more often than one might expect. However if we went for big profits on every trade we would also be making a big mistake. Major profit opportunities are the exception not the rule.

In very general terms there are two ways of having an advantage or "edge" in trading. One is to have gains much larger than losses and the other is to have more winners than losers. To succeed as traders we need to do our best to maximize both the percentage of winners and the size of the winners. These two worthy goals appear to be mutually exclusive. If we take the quick small profits we can have a good winning percentage but we eliminate any possibility of more substantial profits. However, if we fail to take some of the small profits they may well turn into losses.

Wouldn't it be ideal if we could know when it was best to take small profits and when it was best to hold patiently for big profits?

In previous Bulletins we have discussed the advantages of using profit objectives expressed in units of Average True Range. To quickly summarize that discussion, the ATR expands and contracts with the volatility of the market. In a quiet market a profit objective of 2 ATRs might bring us a profit of $600. In a very volatile market, two ATRs of profit might be $1400 or more. By expressing our profit goals in terms of ATRs instead of fixed dollar amounts we make them highly adaptive to what is going on in the market in terms of variations in volatility. However, what we will propose in this Bulletin goes a big step beyond that highly recommended procedure.

We have done a great deal of research using the Average Directional Index (ADX) that leads us to believe it is possible to vary our exit strategy to stay in tune with the trendiness of the market as well as the volatility. By having a doubly adaptive profit-taking strategy we can happily accept small profits when that is the best the market has to offer or we can change the strategy and hold out for unusually large profits when those opportunities are known to be present.

Volatility as measured by ATR is obviously important but daily volatility does not always relate to direction and trendiness. It is quite possible that we can have lots of big ranges in a market that is merely going sideways or we could have small ranges in a market that is highly directional. It is the correct combination of directional price movement and volatility that will allow us to maximize our profits in relation to what is happening in the market at any given time. For the best possible results we want to combine our knowledge of ATR and ADX.

As we have described in previous Bulletins, ADX tells us the underlying strength of any trend. When the trend is strong the ADX will rise. When the trend is weak the ADX will decline. This is true in stocks as well as in futures. It also applies in downtrends as well as in uptrends. A rising ADX means a strengthening trend and a declining ADX means a weakening trend.

Let's go back to our earlier example where our plan was to take our profits at the 2ATR level. With this adaptation to volatility we are counting on the changes in volatility to produce large profits and small profits based on a constant target of two ATRs of profit. However we can go a step further and get even better results. Under our new plan, when the ADX is declining we will reduce our expectations and accept profits of only 1.5 ATRs instead of two. And when the ADX is rising we will double our expectations and wait for profits of 4 ATRs instead of 2. Now we are adapting our exit strategy to both the current volatility and to the amount of trendiness in the market we are trading. As you might expect the difference in results is dramatic because our profit-taking strategy is doubly adaptive.

The logic of this strategy should be obvious. When the market is not trending strongly we improve our results by reducing our profit expectations and maintaining our winning percentage. When the market is trending strongly we know it is time to abandon our small profit targets and time to take advantage of some unusually large profit opportunities.

The examples of 1.5 ATRs as a profit target in a non-rending market and 4 ATRs as a profit target in a strong trending market are just broad guidelines and we need to vary these parameters depending on the particular market and type of system we are operating. Short-term systems may require smaller objectives and long-term systems may require much larger objectives.

We suggest you start with a 20 day ATR and a 14 to 18 day ADX. Play around with the units of profit and see what a dramatic improvement you can make in your trading results by combining ADX and ATR.

Moving Average Crossovers May Not Be The Best Entry Signals

There are many ways of using moving averages to trade but by far the most common method is to trade when a short-term moving average crosses over a longer term moving average. For example, if the 10-day MA crosses above the 30-day MA we typically assume that we have a new buy signal.

Let's stop for a minute and think about what exactly is occurring at the point of a crossover. When the 10-day MA and the 30-day MA are at the same price, the trend is not nearly as clear as it should be. What we are really observing at the crossover point is that the average of the last 30 prices is exactly the same as the average of the last 10 prices. If we are looking for trends to trade, this equal relationship of the two moving averages is not a reliable or logical indication of a trend. In an upward trending market the average prices over the last 10 days should be much higher than the average of the last 30 days. By implementing new trades at crossover points we are limiting our trading to points that may not clearly reflect what we should be doing. For best results in a trend-following system we want to be trading when the trend is clear and reliable; not when the trend is confused and questionable.

Instead of trading at crossovers we should be implementing our trades when the moving averages are parallel or when the short-term moving average is moving farther away from the longer-term moving average. Perhaps the short term MA should remain a minimum of some units of Average True Range above the longer term MA for several days. I believe that this procedure would give us more reliable and more frequent entry signals in the direction of the prevailing trend, which is exactly what we want. To identify the most reliable trends we want to see the slopes of various moving averages all moving steadily in the same direction and not crossing back and forth.

Take a look at a chart of any market with a strong trend. You will see that the moving averages are not crossing back and forth repeatedly. They will be moving in the same general direction in a more or less parallel fashion. Now look at a chart of a non-trending market. As this market moves sideways the moving averages will be crossing back and forth very frequently. Look at the implications of this simple examination of the charts. If we are trading the crossovers we will be trading most frequently in non-trending markets and trading most infrequently in strongly trending markets. Is that what we want? No, it's obviously not what we want. We want just the opposite. We want frequent entry opportunities in trending markets and we want to avoid as many trades as possible in non-trending markets.

The error in the logic of trading moving average crossovers also extends to some interpretations of MACD (Moving Average Convergence and Divergence) and DMI (Directional Movement Indicator). If we are looking at MACD we want to see both lines (each line reflects a moving average relationship) moving in the same direction. We don't want to see them crossing. When looking at DMI we want to see the Plus DI lines and the Minus DI lines moving in opposite directions and definitely not crossing. Remember, when the Plus DI and the Minus DI lines intersect it is telling us that the market is in balance and has no direction; the amount of upward and downward directional movement are exactly equal. What makes our favorite indicator, the ADX, so effective is that it rises only when the Plus DI and the Minus DI are moving in opposite directions and the distance between the two indicators is widening.

With a little thought and effort I'm sure we can design some reliable entry signals that are based on moving averages but avoid the typical crossover signals. For example we could measure the slope of several moving averages and when all the averages slope upward we would have a buy signal.

We could also measure the distance between several moving averages and implement our trades when the averages are all headed in the same direction but start getting farther apart. This procedure would give us a series of entry signals within the same original trend. This should provide an excellent entry and re-entry strategy.

Contradictions in using ADX

In our last article we described how the ADX works best when a move develops out of a basing pattern. Someone sent us a very courteous email questioning this strategy and reminded us of our "25 X 25"Bond system where we want the ADX to be above 20 before looking for an entry. He commented that by the time the ADX gets to 20 any move out of a base pattern may be over. He is absolutely right and I can see how there may appear to be some confusion on how the ADX should be applied. But there really isn't any contradiction if you understand that what we are trying to do with the ADX is very different in the two examples.

In the "25 X 25"strategy the ADX is used as an important "setup"condition that tells us when the trend is strong enough that we can confidently buy on weakness. However, when we describe the basing pattern strategy we are using the ADX as the actual entry trigger to buy on strength. There is a big difference in the buy on strength and buy on weakness strategies. In the basing pattern strategy a low level of the ADX is preferred because the rise in the ADX is the trigger. If the ADX is at 12 and starts rising we very well could miss the majority of the move if we waited for it to reach 20. With the ADX already at 20 or higher it might only be safe to buy on dips and of course that is exactly what the "25 X 25"bond strategy does.

To sum things up: there is no contradiction. To catch a move out of a base you should enter as soon as the ADX starts rising. Just compare today's ADX with yesterday's ADX and the faster it is rising the better. At this point the the lower the level of the ADX the better because we are buying on strength and the ADX is our entry trigger.

System Results Update

By the way, our bond strategies have been making lots of money this year. Hope you are all trading them with real money. Back in February I had lots of critics calling and asking why we were offering long only bond systems when bonds were at 115 and that had to be the top. They said that they couldn't possibly go much higher than that and our long only results could not hold up in real trading. Now that the bonds are over 130 I am glad that we have the Serendipity system that does trade the short side because I suspect that we really are near the top. (Doesn't take a genius to make a dumb statement like that. I apologize.)

The Big Dipper system has been long since July and has huge open profits even after having to be rolled forward from the September contract into December. The "25 X 25"system is not doing bad either. When is the last time you had a free system make that much money for you? And last but not least, lets not forget the "Little Dipper". According to my recollection the last seven trades were all winners and it could be more because I can't remember the last loser. Not too bad for out of sample trading results. REMEMBER: PAST RESULTS ARE NOT NECESSARILY INDICATIVE OF FUTURE SUCCESS. I'm not just saying that because I have to. I really believe it and so should you. The bull market in bonds has made us look smarter than we really are. Bull markets do that.

Combining RSI and ADX

Now that I am spending seven hours a day doing trading for the new hedge fund I haven't had much time for research or writing new Bulletins. However a comment in one of the trading newsgroups that I monitor got me thinking about the potential benefits of combining our knowledge of RSI and ADX into a simple system. Both the ADX and RSI are valuable trading tools and a combination of the two would seem to offer some interesting possibilities. I like to use the RSI primarily as an indicator for buying on dips in an uptrend. The ADX is my primary indicator of trend strength.

Here are a few ideas on how the two indicators might compliment each other in a system that "knows" when to enter on strength and when to buys on dips. (I'm only going to use the long side for examples but the logic should apply to short trades as well.)

When the ADX is rising it usually indicates that a strong trend is underway. In many cases waiting for any sizeable dip would be costly because the market could run away and the dip entry would be too late to maximize our profits. In this case we must enter on strength. To make this idea into a simple trading rule we might state that if the ADX is rising (and we have some indication it is rising because an uptrend is underway) we will buy whenever the RSI is below some very high threshold like 85. This rule would give us a very prompt entry in most cases and the result would be almost identical to simply trading whenever the ADX is rising which seems to be a good idea. The RSI has little, if any, benefit in this situation except it might occasionally keep us from buying into an extremely overbought market where the RSI was above 85. In this case a slight delay on the entry might be prudent.

The RSI, however, can play a much more important role when the ADX is flat or declining. In this case the rule would be that when the ADX is not rising we should postpone our entry until the RSI is below some more typical threshold like 45 or 50. Since the ADX is not giving us a signal that the trend is unusually strong we would need some additional indicator to show that the market has some minimal amount of upward direction. Otherwise we would not be buying a dip within the framework of an uptrend. Something simple like an upward sloping 20-bar moving average might work in this application.

Now that we have combined the ADX and RSI for our entries we might also want to combine them for our exits. When a market is rising but the trend is not particularly strong any spike in the RSI represents a good opportunity to take a profit. For example when trading in stocks the 9-bar RSI rising above 75 or 80 often signals that a correction is imminent. If the market trend is not unusually strong we would probably be happy with taking our profit on strength rather than waiting to get stopped out on weakness. However if the ADX is rising we might want to risk a correction in hopes of riding the trend even further. In this case when the ADX was rising we would ignore the RSI signal to take our profit. However, once our patience has allowed us to accumulate a very substantial open profit we might be best served by acting on the next RSI signal and nailing down the big winner. Also, when the ADX is rising it would not make much sense to be buying at a high RSI level and also selling at a high RSI level. We would be in and out of our trades almost immediately. Therefore we need to ignore the RSI extremes until our profit has had a chance to accumulate.

In summary, the important concept to remember is that our knowledge of the ADX can make the RSI a much more useful trading tool. When the ADX is rising the RSI tends to get overbought and it can often remain overbought for a surprising length of time. On the other hand when the ADX is flat or declining any spike to the upside in the RSI is an opportunity to nail down a profit. Conversely, any spike to the downside can be a potentially profitable entry point.

Here is the logic of a simple little system based on this discussion. (Just the rules in text form, you will have to do your own coding.) The parameters selected have not been tested or optimized. For example the 20-day moving average is just a number I picked out of the air. This is enough information to get you started and you can vary the rules to make the system trade over whatever time frame you prefer.

Long Entries:

1. The 20-bar moving average must be rising.
2. If the ADX is rising (ADX today is 0.20 or more higher than yesterday) then buy if the 14 bar RSI is less than 85.
3. If the ADX is not rising (ADX today is not 0.20 higher than yesterday) then buy if the 14 bar RSI is less than 50. Here is where you can influence the frequency of trading. For more trades use a higher threshold like 60. For fewer trades use a lower threshold like 40.

Long Exits

1. If the ADX is not rising (ADX today is not 0.20 higher than yesterday) then sell (long exit) if the 9-bar RSI is greater than 75.
2. If the ADX is rising (ADX today is 0.20 or more higher than yesterday) and the open profit is greater than (pick some amount - maybe 4 ATRs or some unit of price) then sell if the 9-bar RSI is greater than 75.
3. You need some additional exit rule for the losing trades. Use your favorite loss-limiting exit or you might want to exit when the price goes below the 20-dat moving average or when the 20-day moving average turns down. (See entry rule 1.)