## 4 Experiment and Results
### Experiment Results
#### 4.3.2 Portfolio Performance Evaluation  
Secondly, we evaluated the constructed portfolios based on prediction models, including SVR, LR, and LSTM models. In order to optimize the performance of the constructed portfolio, MCS and MVO were employed to evaluate the impact of optimization on portfolio performances. In the majority of cases, expected returns showed a tendency to increase, while SRs tended to decline gradually over time, except in the SVR model, where they fluctuated significantly. It can be observed in Figures 7-9 that MCS and MVO techniques perform approximately the same in all built prediction models. As predicted by the SVR prediction model in Figure 7, expected returns fluctuated. Although SRs obtained by MCS and MVO methods were considerably higher than EQ, the performance of constructed portfolios showed poorer performance compared with the LR and LSTM models in both expected returns and SRs. For example, the highest expected return and SR were only 55% and 0.05 at \(P_{8}\) and \(P_{10}\), respectively. As shown in Figure 8, portfolios constructed by the LR model obtained the highest expected returns using the EQ method compared with MCS and MVO over periods. However, the constructed portfolios obtained higher SRs using MCS and MVO compared with the EQ method. This suggests that optimization methods can improve the performance of constructed portfolios by increasing the SR values; in other words, optimization techniques are not inevitably guaranteed to improve the return but can reduce the risk in trading. As reported in Figure 9, our constructed portfolios based on the LSTM prediction model obtained the highest expected returns as well as SRs in most of the predicted periods. EQ showed the effectiveness of returns, however, the gap between MCS and MVO was smaller than EQ, as shown in Figure 9. Therefore, the LSTM prediction model is more efficient than the SVR and LR models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{P} & \multicolumn{3}{c}{LSTM} & \multicolumn{3}{c}{GRU} \\ \cline{2-7}  & **Stock** & **MAE** & **MSE** & **Stock** & **MAE** & **MSE** \\ \hline \multirow{4}{*}{**8**} & **ABMD** & 0.00813 & 0.00014 & **ALGN** & 0.01011 & 0.00021 \\  & **ADBE** & 0.00756 & 0.00010 & **IPGP** & 0.00662 & 0.00008 \\  & **ALGN** & 0.00161 & 0.00000 & **NKTR** & 0.00186 & 0.00001 \\  & **AMZN** & 0.01258 & 0.00027 & **NDVA** & 0.01095 & 0.00021 \\ \hline \multirow{4}{*}{**9**} & **ALGN** & 0.00522 & 0.00006 & **ABMD** & 0.00847 & 0.00016 \\  & **IPGP** & 0.01104 & 0.00030 & **ADBE** & 0.01157 & 0.00025 \\  & **NKTR** & 0.01319 & 0.00027 & **ALGN** & 0.00919 & 0.00012 \\  & **TTWO** & 0.02046 & 0.00063 & **ATVI** & 0.01863 & 0.00055 \\ \hline \multirow{4}{*}{**10**} & **ALGN** & 0.00751 & 0.00013 & **ALGN** & 0.00672 & 0.00010 \\  & **IPGP** & 0.01134 & 0.00014 & **IPGP** & 0.00469 & 0.00005 \\  & **NKTR** & 0.00273 & 0.00002 & **NKTR** & 0.00505 & 0.00004 \\  & **TTWO** & 0.00969 & 0.00015 & **TTWO** & 0.01234 & 0.00027 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._Figure 8: Linear regression (LR) constructed portfolios’ performance. Figure 7: Support vector regression (SVR) constructed portfolios’ performance. Figure 9: LSTM constructed portfolios’ performance. Third, the constructed portfolios and weights for each portfolio in the prediction phase were tested in actual trading. The constructed portfolios' performance based on prediction models is presented in Figures 10-12. Actual returns and SRs based on the SVR prediction model fluctuated significantly on time periods. MCS and MVO weights showed effective improvements in the returns but showed less impact on SRs. Especially, the actual return and SR suddenly drop to negative in \(P_{8}\), as shown in Figure 10. The fluctuation can be the cause of low predicted accuracy. Therefore, predicted stocks and adjusted weights were ineffective.