# Stock Portfolio Management in the Presence of Downtends Using Computational Intelligence
## 5 Experiments
### Results  
The proposed approach uses components that exploit randomness to explore the search space. Here, we intend to discard the effects produced by such randomness by running our approach many times; particularly, each stochastic component runs twenty times for each of the thirty back-testing periods mentioned in Section 5.1. Doing it this way sheds light on the robustness of our approach and allows us to reach sound conclusions. By following the recommendations in [88], the performance of our approach is evaluated by using the quantiles \(Q_{10}\), \(Q_{20}\), \(Q_{50}\) (median), \(Q_{80}\) and \(Q_{90}\) (see Figure 1). As is noted in [88], distribution solutions of stochastic optimization algorithms are often asymmetrical; hence by using quantiles, we could obtain more insights into our approaches. However, Figure 1 shows that, in our case, \(Q_{50}\) and the mean are almost always overlapped. Furthermore, (\(Q_{10}\), \(Q_{20}\)) and (\(Q_{80}\), \(Q_{90}\)) are symmetrical with respect to the mean. This behavior indicate that the performance of our approach is practically normally distributed. Therefore, in this study, the average returns of our approach is used to be compared with several benchmarks, as shown in Table 1 and Figure 2. For simplicity, the results are discussed hereafter as if the returns were not averages. In order to validate our approach,in this section, we have included several benchmarks to measure the effectiveness of our proposal. These benchmarks are: (a) the market index S&P500, (b) the approach of [10], (c) the approach of [12] and (d) our approach without including downtrends. From Table 1 and Figure 2, we can see that, in terms of the expected value, the worst overall return was produced by investing according to the S&P500 index, while the best overall return was achieved by investing in a portfolio produced by the proposed approach that takes advantage of both positive and negative trends. Figure 2 shows that the portfolio that considers negative trends is almost always in the top two from all the approaches. Furthermore, the returns obtained using this approach show that this model is not affected by the downtrends in the market as the benchmarks, as seen in the fall of all approaches from Jan 2020 to Mar 2020. Remarkably, this behavior did not prevent the proposed approach from exploiting the clear overall uptrend produced from Apr. 2020 to Apr. 2021, as can be clearly seen in Table 1.  
From Table 2, we can see that the proposed approach outperforms the benchmarks at the end of the thirty periods: the sum of returns is approximately 41% better than [PERSON] et al. 2019 ([PERSON] et al. 2019), 25% better than [PERSON] et al. 2019 ([PERSON] et al. 2019), 48% better than the one that only considers positive trends and more than 90% better than the market index. Moreover, the cumulative returns of our proposal is 63% better than [PERSON] et al. 2019 ([PERSON] et al. 2019), 35% better than [PERSON] et al. 2019 ([PERSON] et al. 2019), 75% better than the one that only considers positive trends and 141% better than the market index. This performance can be seen in Figures 3 and 4. Both Figures 3 and 4 describe the evolution of the portfolio returns in an aggregate way throughout the whole time lapse (i.e., November 2018 to April 2021). However, Figure 3 shows this evolution from the perspective of the sums of the returns, while Figure 4 shows the cumulative returns. Both figures can be relevant to the practitioner. The former shows the overall performance of the approach without considering the exact period where the return was obtained, while Figure 4 allows one to ponder the impact of the period where such a return was obtained. Let us unfold the latter. Figure 4 shows the amount that the investor would obtain if he/she takes their investment in a given period. For instance, an investment of USD 1000 at the beginning of November 2018 using the proposed model would have become USD 992 (i.e., \(-0.80\%\)) if the investor would have withdrawn the investment at the end of May 2019.