# Empirical Analysis of Automated Stock Trading Using Deep Reinforcement Learning
## 5 Empirical Analysis
### Dow Jones 30 Stocks  
This experiment with the Dow Jones 30 as its domain is an empirical analysis of the ideas and content of [10]. Therefore, the process of designing the model, building the environment, stock trading constraints, and the data employed are the same as in [10]. However, not only did we employ Remake Ensemble as a new trading agent, but there are also two main differences.  
The first is the number of experiments. For more objective experimental results, we conducted five experiments and for each agent, and we compared and analyzed the evaluation metrics obtained through each agent. Ref. [10] only shows the results of a single experiment. Since we believe that the results of a single experiment alone are not adequate for judging the robustness of an automated stock trading system, we ran five backtesting experiments on each trading agent. We calculated the average value of each based on the five evaluation metrics. The results are shown in Table 1. In particular, we considered the cumulative return as the main criterion among the five evaluation metrics because it is the final benefit obtained through stock arbitrage. Figure 3 visualizes this evaluation metric in a box chart to make it easier to compare each agent's experimental results and the DJIA.  
Second, the duration of the data employed for trading is different. There was no need to preprocess the data separately because we used the refined Dow Jones 30 data that [10] used. As in [10], we used data from 1 January 2009 to 30 September 2015 for training, and  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**EM** & **DJIA** & **A2C** & **DDPG** & **PPO** & **Ensemble** & **Remake** \\ \hline CR & 53.287\% & 47.717\% & 54.620\% & 48.919\% & 53.992\% & 48.217\% \\ AR & 9.957\% & 8.944\% & 10.033\% & 9.225\% & 9.995\% & 9.094\% \\ AV & 20.509\% & 8.125\% & 8.838\% & 7.384\% & 8.061\% & 8.270\% \\ SR & 0.57 & 1.094 & 1.154 & 1.236 & 1.216 & 1.108 \\ MD & \(-\)37.086\% & \(-\)7.88\% & \(-\)8.822\% & \(-\)8.413\% & \(-\)9.035\% & \(-\)7.865\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Average performance of five RL-based agents on Dow Jones 30 stocks from 4 January 2016 to 6 July 2020 (1134 days).  
validation data were from 1 October 2015 to 31 December 2015. However, we set the trading period from 1 January 2016 to 6 July 2020, while [10] set the trading period from 1 January 2016 to 8 May 2020. Currently, the number of days of stock market opening used in the test was 1071 days in the case of [10], and in our case, there were 1134 days in total. We fixed the validation window and rebalance window to 63 days as in the code provided and extended the trading period from the previous one, where rebalance window means the number of months to retain the model, and the validation window is the number of months to validate the model and select for trading. There is a 63-day difference between the number of stock opening days used in the current work and the number of stock opening days we used.  
We ran backtesting by changing the trading period to ensure that the automated stock trading system still showed strong results even if the trading period changed. However, as shown in Table 1 and Figure 3, each agent did not generate a higher cumulative return than the DJIA. In our experiments, only DDPG and the ensemble strategy among the five agents produced higher cumulative returns than the DJIA, and there were few differences between the DJIA and their cumulative returns. Moreover, the Remake Ensemble agent showed a lower cumulative return than the DJIA.