other way to analyse the influence of the market evolution on the performance of our strategy consists of comparing the excess return to the evolution of the CAC40 index. The correlation is lower but still equal to 0.73, a reasonably high-level confirming our initial interpretation. Moreover, even if the two are not really comparable, it is worth noticing that our strategy always outperforms the CAC40 index. But this fact is not really significant because our analysis deals with 24 stocks among the 40 contained in the index.
For strategy BH2 in which all the cash is initially invested in the stock, the performance of the genetic strategy is lower but it still outperforms the BH2 strategy. However, the correlation between the excess return and the CAC40 performance is low, about 0.086. It is not surprising because the genetic portfolio starts with a large amount of cash; consequently when ‘sell’ or ‘do nothing’ signals are received from the experts, the difference between the genetic strategy and the BH2 portfolio remains considerable.
4.2. Are some stock returns easier to predict?
Assume that some stocks are easier to predict than others; if this were the case, we would observe important correlations between the results of different experiments. In other words, an easily predictable stock would experience, most of the time, a higher excess return than the mean performance. To analyse this point, consider the matrix M which gives the correlations of excess returns across experiments. More precisely, if we denote by Y i ¼ ðYji; j ¼ 1;...;24Þ the excess returns for experiment i; the correlation matrix contains the terms corðY i;Y kÞ; i;k ¼ 1;...;10:
21 3
6666666 00::04280:48 100;;1855 10;38 1 7777 M ¼ 6666600::3140:18 0:0300::124 00::14060:18 00::40240:04 10:240:04 10:01 1 7777777777777
66
66
666660:17 0:07 0:36 0:12 0:29 0:16 0:27 1 7777757
4660:3 0:24 0:31 0:03 0:05 0:14 0:16 0:28 1
0:32 0:1 0:18 0:17 0:51 0:08 0:25 0:18 0:24 1
The mean correlation is equal to
j5k¼1
that is to say, near 0.
It is in fact a result which can be interpreted in favour of the efficient market hypothesis; it means that the return on any given stock cannot be permanently predicted in a more efficient way than the return of another stock.
Nevertheless, the fact remains that the returns obtained from the genetic strategies outperform the classical buy-and-hold strategy for almost all the stocks and almost all the periods.
4.3. Are some trading rules more efficient?
The other important question for the technical analyst to consider is to know whether some trading rules give better results than others. Figure 2 presents for one experiment the number of times each rule is used by the four best experts in each stock, that is 96 experts. To be more precise, we constructed a matrix with 24 4 rows and 235 columns; each column corresponds to a rule and the vertical axis measures the number of experts who use the corresponding rule.
It is clearly evident that no rule consistently outperforms the others. The percentage of use of the different rules varies between 8.5 and 28.09%. This is at the same time both surprising and yet predictable. It may seem surprising because the returns presented above show that stock returns contain a non-negligible predictable component; hence, we could expect to identify the best rules which would allow us to point out this predictable return. However, rules are grouped in categories; it may be that some experts use the 5-days’ moving average while others use the 10-days’ moving average. These rules are different but express the same type of behaviour. It is then very difficult, probably even impossible, to define the ‘distance’ between two rules because the only thing we know is whether an expert uses a particular rule to take his decisions.
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