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In the next chapter, we will present numerical results. In order to calculate this chapter, the data of 32 companies registered in the Tehran Stock Exchange market for 10 years (from 1392 to 1401) have been used. The investigated companies were selected from among the companies in the 50 most active companies index. A total of 2398 rows of data were used for different algorithms, of which 80% (equivalent to 1918 rows) were used for training algorithms and 20% (equivalent to 431 rows) were used for testing. Among the initial 32 companies, the 10 companies that had the highest ratio of average daily return to standard deviation of daily return during the training period were selected as the final 10 companies to form the portfolio. The content of this chapter includes the settings of algorithms, prediction results by different algorithms, and portfolio optimization results.
In this section, we will optimize the portfolio using Monte Carlo simulation and by applying the predictions of different algorithms.
Table 7-4 shows the descriptive statistics for cumulative returns obtained from portfolios formed based on different forecasting methods and different models. It can be seen from this table that the statistical values for different models (compared to daily returns) show different results. From this table, it can be seen that the highest average cumulative efficiency is related to the Omega model with the LSTM prediction algorithm. After this algorithm, Omega-DMLP and Omega-SVR algorithms have the highest average cumulative efficiency. Therefore, the Welch test has been used again. The null hypothesis of these tests is the equality of the average of all algorithms. The results are shown in Table 9-4. Based on this table, significance values smaller than 0.05 indicate that a significant difference has been observed between the cumulative efficiency of different algorithms. In addition, the comparison chart of average values of cumulative efficiency for different models is shown in Figure 2-4 (a) and (b). From these figures, it can be seen that the five methods have significant differences in obtaining cumulative efficiency compared to each other. Using the MV optimization model, the highest average cumulative efficiency is related to SVR and the lowest is related to RF. Using the Omega optimization model, the highest average cumulative efficiency is related to LSTM and the lowest is related to CNN.
In addition to the above graphs, Figure 4-4 (a) and (b) show the trend of changes in cumulative efficiency resulting from different models. It can be seen from Figure 4-4 (a) that almost until day 370, portfolios with equal weights generally have higher cumulative returns than other methods. However, after that, the model based on the CNN algorithm has surpassed all the models and has been able to have the best cumulative efficiency until the end of the examined period.
It can also be seen from Figure 4-4 (b) that using the Omega model, the portfolio with equal weights almost always has a lower cumulative return than some of the investigated methods. Another important point is that it is not possible to say which model has the best performance in the entire time period. For example, up to about day 70, the best performance is related to the RF method. From day 70 to day 360 for more than 1 year, the best performance corresponds to the LSTM method and from then on the best performance corresponds to the DMLP method.
In order to compare the proposed methods for portfolio optimization, Table 10-4 shows the descriptive statistics for the cumulative return of the portfolio with equal weights. This table shows that the average cumulative return of this portfolio is equal to 1.12, which only combined Omega models with DMLP, SVR, and LSTM have been able to have a higher average cumulative return. In addition, skewness and kurtosis indicate that this variable is not normal.
Due to the non-normality of the cumulative return values, various parametric and non-parametric tests have been used to compare the cumulative return of each of the proposed methods with the cumulative return of the portfolio with the same weights. The null hypothesis of all these tests is the equality of the average cumulative returns obtained from both investigated methods. The results of these tests are presented in tables 11-4 to 19-4. The results of these tests show that the significance level for all the models and all the examined tests is greater than 0.05. Therefore, the average cumulative return of the investigated models is not significantly different from the portfolio with equal weights. This issue comes from the fact that according to Figure 4-4, in different time periods, the performance ranking of different portfolio optimization algorithms changes, and it cannot be said that one algorithm is better than others in all time periods. has acted