martedì, maggio 29, 2007

Elliot e Fibonacci

Sto preparandomi per una certificazione; ho fatto quindi un piccolo lavoro basandomi sulle onde di Elliot e i numeri di Fibonacci. I risultati sono abbastanza deludenti, ma lo condivido ugualmente con voi. Mi spiace ma l'ho scritto in inglese, non ho avuto tempo di tradurlo.

A beginner’s application of Elliot’s Wave Theory and Fibonacci’s Numbers

I am not an expert of Elliot’s Waves Theory, nor I’ve ever considered it particularly interesting: I think it’s too subjective. However I’m starting to study it a bit deeper, since I am preparing the second exam of the CFT certification. As an exercise, I try to apply some basic principles of Elliot’s theory as I learned them from the famous Murphy’s book “Technical Analysis of the Financial Markets” and, more importantly, from Fischer’s book “Fibonacci Applications and Strategies for Traders”. The latter offers many some hints about calculating objectives, preferring Fibonacci’s ratios to simple wave count.
I consider two markets (Eurostoxx 50 and S&P 500) on a monthly horizon.

Eurostoxx 50

Event Time Price
Bottom March 2003 1845
First Wave Top March 2004 2970
Second Wave Bottom August 2004 2560
Third Wave Top April-May 2006 3900
Fourth Wave Bottom June 2006 3380

We want to calculate a price objective for the fifth wave of the upside trend. I follow three methods, as suggested by Robert Fischer.

1) I multiply the height of the first wave by 1.618; then I add the result to the first wave top.

(2970-1845)*1.618 = 1820.25

Target= 2970 + 1820.25 = 4790.25

2) I take the height of the first three waves, I multiply it by 0.618 and I add the result to the third wave top.

(3900-1845)*0.618 = 1270

Target= 3900+1270 = 5170

3) I draw a channel which touches the second and fourth wave bottoms. According to Elliot, the return line should be a target for the fifth wave, when it’s drawn on an arithmetic scale. If the return line is broken, you should again create a channel, but using a semi-log chart. The resulting objective is about halfway between the two targets calculated at points one and two, depending on the speed at which the rise will continue (please, see the attached chart).




S&P 500
Event Time Price
Bottom April 2003 790
First Wave Top March 2004 1164
Second Wave Bottom August 2004 1060
Third Wave Top June 2006 1327
Fourth Wave Bottom July 2006 1218

Using the same methods as before, I reach the following results.

1) (1164-790)*1.618=605.13. Target is 1164+605.13=1769.13
2) (1327-790)*0.618=331.87. Target is 1327+331.87=1659
3) The channel has been broken also on semi-log scale!







The resulting targets are ambitious (upside of 7.3% and 16% for Eurostoxx 50, according to the first and second methods; 16.8% and 9.5% for the S&P 500 from today’s levels, respectively 4463 and 1515). The difference in the results of the two methods is quite high and it’s interesting to see that while for the European index is the second one to give the higher target, the opposite is true for the American market.


Some backtesting…

Now, let’s try a simple back testing. I consider the downside movement of the S&P 500 index between 2000 and 2002, as if we were in the middle of 2002 (fifth downside wave just started).

S&P 500 (downtrend)

Event Time Price
Top March 2000 1553
First Wave Bottom March 2001 1081
Second Wave Top May 2001 1316
Third Wave Bottom September 2001 945
Fourth Wave Top January 2002 1180
Fifth Wave Bottom October 2002 770

Applying the same operations as before, we reach the following results:

1) (1553-1081)*1.618= 763.7 Target is 1081-763.7= 317
2) (1553-945)*0.618= 375.75 Target is 945-375.75= 569
3) The channel was broken only partially and gave targets not far away from the effective one.

With the benefit of hindsight, we can say that these results are very bad. The true low point of wave five was 770, so the two targets missed it by 142% and 35%! Only the channel gave a good indication (albeit not very precise).

Reaching conclusions after such a simple exercise is not correct: one should perform a deeper backtest. However, the methods used don’t seem able to offer a reliable source of targets for 5-wave movements. Of course, if another person saw different tops and bottoms for the waves, also the results would change: however in Fischer’s mind, the application of Fibonacci Numbers should also address this problem, at least partially.