# High-Frequency Direction Forecasting of the Futures Market Using a Machine-Learning-Based Method
## 5 Results and Discussion
### Results of Classifiers
#### 5.1.3 Trading Result Results  
In Table 8, we show the maximum drawdown results, while the Sharpe ratio results of the proposed method and benchmarks are reported in Table 9. The primary objective of adopting those two indicators is to measure the transaction risks of each method in determining the investment portfolio. The maximum drawdown results in Table 8 show that BAH yielded an average maximum drawdown result of 0.080 and an overall maximum drawdown result of 0.134 over four testing periods, which outperformed our proposed approach and other benchmarks. Nevertheless, as we discussed in Section 5.1.2, although BAH experienced no obvious retracement, the profit-making ability that market traders give much attention to is markedly worse than the proposed XGBoost-SMOTE-NSGA-II method. Similar conclusions can be drawn from the maximum drawdown results of SAH. Except for BAH and SAH, the proposed method generated an overall maximum drawdown result of 0.146 over the one-year testing period, while other benchmark methods ANN, SVM, RF, XGBoost, and XGBoost-SMOTE, respectively, generated values of about 0.838, 1.241, 1.575, 0.587, and 0.491, which were worse than the proposed method. Furthermore, although the proposed method obtained a larger maximum drawdown result than the XGBoost-based benchmark in testing period 2, it produced better results than the benchmarks in the other three testing periods. Experimental results demonstrate that the proposed method yielded a relatively \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Testing Period** & **BAH** & **SAH** & **ANN** & **SVM** & **RF** & **XGBoost** & **XGBoost-SMOTE** & **XGBoost-SMOTE-NSGA-II** \\ \hline Period 1 & 0.107 & 0.085 & 0.301 & 0.489 & 0.417 & 0.157 & 0.179 & **0.083** \\ Period 2 & 0.044 & 0.147 & 0.328 & 0.199 & 0.367 & 0.121 & 0.257 & 0.175 \\ Period 3 & 0.081 & 0.083 & 0.304 & 0.431 & 0.837 & 0.523 & 0.092 & 0.128 \\ Period 4 & 0.086 & 0.286 & 0.274 & 0.351 & 0.201 & 0.224 & 0.225 & 0.154 \\ Average & 0.080 & 0.150 & 0.302 & 0.368 & 0.456 & 0.256 & 0.188 & 0.135 \\ Overall & 0.134 & 0.367 & 0.838 & 1.241 & 1.575 & 0.587 & 0.491 & 0.146 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Maximum drawdown results of all methods for simulation trading. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **BAH** & **SAH** & **ANN** & **SVM** \\ \hline Excess Return & 0.0479 & \(-\)0.0621 & \(-\)0.1894 & \(-\)0.2733 \\ Standard & 0.1147 & 0.1147 & 0.0926 & 0.1672 \\ Deviation & 0.4176 & \(-\)0.5414 & \(-\)2.0454 & \(-\)1.6346 \\ \hline  & **RF** & **XGBoost** & **XGBoost-SMOTE** & **XGBoost-SMOTE-NSGA-II** \\ \hline  & \(-\)0.3599 & \(-\)0.0696 & \(-\)0.0839 & 0.3427 \\  & 0.2999 & 0.2743 & 0.0648 & 0.0937 \\  & \(-\)1.2001 & \(-\)0.2537 & \(-\)1.2948 & 3.6574 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Sharpe ratio results of all methods for simulation trading. stable and excellent return successfully, and the proposed method was remarkably superior to the other machine-learning-based methods, which suffered from large retracements. Furthermore, as we mentioned in Section 4.5, the risk-free interest rate set at 0.61% is used for the Sharpe ratio calculation. In Table 9, we report the excess returns and Sharpe ratio results of the benchmark methods and proposed method. In the trading simulation over the whole testing period of 2020, the proposed method generated the best Sharpe ratio result (3.6574), which was obviously superior to all the other benchmark methods. As for the trading strategy BAH, its excess return was about 0.0479, ultimately leading to a very small positive Sharpe ratio value of 0.4176. Additionally, it could be noticed that the Sharpe ratio of SAH, ANN, SVM, RF, XGBoost, and XGBoost-SMOTE were all negative with the values of \(-0.5414\), \(-2.0454\), \(-1.6346\), \(-1.2001\), \(-0.2537\), and \(-1.2948\), respectively, demonstrating that the integration of the parameter optimization method NSGA-II successfully promoted the profitability as well as lowering the volatility for the proposed method.