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.