Apple Daily --- 8 Oct, 2000

In Technical Analysis, there was a set of numbers called Fibonacci Numbers or Magic Numbers? This set of numbers are 0.382, 0.5, and 0.618.

The Egyptians first used the Fibonacci Numbers to build the pyramid. Elliot was the first to apply these numbers to forecast stock price movements. The venerable Wave Theory invented by him relied extensively on these numbers to identify different phases of the wave cycle.

In a nutshell, the theory states that during an up trend, when price undergoes a significant correction, the correction usually ends at 38.2%, 50%, or 61.8% of the total up movement. Conversely, during a downtrend, subsequent significant rebounds usually terminates at 38.2%, 50%, or 61.8% of the total down movement.

These numbers really work and that is why they are called Magic Numbers? On hindsight, when you look at any chart, you will see that all the major highs or lows did occur levels which follow one of these ratios.

Figure 1 shows the Candlesticks chart of Hutchison Whampoa (0013). As can be seen, during the downtrend from A to B, subsequent rebound hit near exactly at 61.8% of AB (marked C in the figure) and then the market fell again. Similarly, after the market rose from B to C, the subsequent market correction caused price to fall first to 38.2% of BC at D and E. The market then rose for a while. Afterwards, it fell again to 61.8% of BC at F before it rebounded. These kinds of phenomena occur repeatedly to any stocks in any markets.

However, there are two problems with these magic numbers. First, how can we forecast beforehand which ratio to use? Secondly, to forecast retracement levels, we need to identify a major low followed by a major high, and to forecast rebound levels, we need a major high followed by a major low. However, which high or low to use is quite subjective. Professional traders can point it out to you confidently when they are given the charts. It takes experiences and training to acquire the skills.

Figure 2 shows the Prosticks chart of Dao Heng Bank (0023). As can be seen, after the uptrend from A to B, the market corrected 50% to C, then rebounded 61.8% of BC to D and then finally continued to dive 61.8% of AB to E before the market rallied significantly again. It seems that that market movements are guided by an invisible hand which follows these magic numbers.

Actually, we can use Prosticks to help increase the accuracy of our Fibonacci predictions. Consider Figure 2 again. Notice that all C, D, and E points not only lie on the Fibonacci levels, they coincide with some previous Modal Points or platforms also. Thus, when price rises to or falls on them, we can be sure that there are two kinds of support/resistance: one from the Fibonacci level and the other from the Modal Platform, and they occur at exactly the same price. In short, Modal Platform can serve to confirm whether the Fibonacci level is likely to be effective.

It is not advised to go long or short when price falls or rises to a particular Fibonacci level, even the level coincides with certain important Modal Platform. It is because the Fibonacci level only serves as a support or resistance. However, support or resistance does not necessarily hold. They may be broken. Two tactics may then be employed. One should wait for several days and see whether price really holds at the support or resistance level. Or, one should use technical indicators like RSI and Stochastics to evaluate the market momentum. If the market momentum is weak, then the probability that the support or resistance will hold is great.