# STGAT: Spatial-Temporal Graph Attention Neural Network for Stock Prediction
## 4 Experiments
### Experimental Results
#### 4.3.2 Performance of Portfolio Optimization Results
This suggests that STGAT is highly effective at identifying and exploiting \begin{table}
\begin{tabular}{l c c} \hline \hline
**Indicators** & **Formula** & **Meaning** \\ \hline Cumulative Return & \((1+R_{1})\times(1+R_{2})\times\cdots\times\) & Total return of the portfolio \\  & \((1+R_{n})-1\) & Fluctuation range of stock prices \\ Volatility (V) & \(\sqrt{\frac{\sum_{i=1}^{t}(R_{i}-R)^{2}}{n-1}}\) & Fluctuation range of stock prices \\ Sharpe Ratio & \(\frac{E(R_{p})-R_{f}}{V}\) & Additional return per unit of deviation \\ Maximum Drawdown (MDD) & \(\max_{t:\tau}\left(\frac{R_{f}}{P_{t}}-1\right)\) & Maximum loss from peak to trough before new peak \\ Calmar Ratio & \(\frac{E(R_{p})}{MDP}\) & Ratio of annualized return to maximum drawdown \\ Information Ratio & \(\frac{E(R_{p})-R_{p}}{\sigma_{p-b}}\) & Excess return per unit of tracking error \\ Treynor Ratio & \(\frac{E(R_{p})-R_{f}}{\beta}\) & Risk premium per unit of systematic risk \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Quantitative indicators of portfolio performance. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Model** & **\begin{tabular}{c} **\begin{tabular}{c} Cumulative** \\ **Return** \\ \end{tabular} \\ \end{tabular} & **Volatility** & \begin{tabular}{c} **Sharpe** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Max** \\ **Drawdown** \\ \end{tabular} & \begin{tabular}{c} **Calmar** \\ **Ratio** \\ \end{tabular} & \
\begin{tabular}{c} **Information** \\ **Ratio** \\ \end{tabular} &
\begin{tabular}{c} **Treynor** \\ **Ratio** \\ \end{tabular} \\ \hline CSI500 & \(-\)5.76\% & 0.1552 & \(-\)0.7878 & 13.68\% & \(-\)0.8069 & - & \(-\)0.1222 \\ GCN & 11.52\% & 0.2150 & 1.3166 & 10.99\% & 2.6832 & 0.4645 & 0.2363 \\ GRU & 7.28\% & 0.2198 & 0.8178 & 13.49\% & 1.4208 & 0.3365 & 0.1497 \\ LSTM & 11.51\% & 0.2230 & 1.2774 & 13.43\% & 2.2095 & 0.4328 & 0.2319 \\ MLP & 8.00\% & 0.1979 & 0.9689 & 11.02\% & 1.8476 & 0.4659 & 0.1698 \\ RNN & 18.78\% & 0.2096 & 2.2460 & 8.62\% & 5.5977 & 0.6108 & 0.4161 \\ TCN & 2.65\% & 0.2138 & 0.3266 & 14.35\% & 0.5695 & 0.2819 & 0.0556 \\ Transformer & 7.48\% & 0.2170 & 0.8471 & 11.94\% & 1.6391 & 0.4629 & 0.1399 \\ STGAT & 28.21\% & 0.2582 & 2.9279 & 10.10\% & 7.6034 & 0.5752 & 0.5771 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Performance of investment portfolios in fixed time interval on A-share test sets. market inefficiencies. The Treynor Ratio, which reflects the maximum excess return a model can achieve under the same market risk, demonstrates that the majority of models, including STGAT, efficiently manage systematic risk. This makes STGAT a robust choice for investors aiming to balance risk and return. These indicators collectively reveal that the STGAT model excels at identifying stocks whose expected returns exceed their risk-taking capacity while avoiding those highly sensitive to market volatility and offering limited contribution to returns. This strategic approach allows for better control of downside risks while ensuring consistent returns, enabling the model to achieve more excess returns with lower volatility. Overall, STGAT's performance highlights its effectiveness in navigating complex market dynamics and delivering superior risk-adjusted returns. To visually illustrate the returns of portfolios constructed by different neural networks, Figures 11 and 12 depict the cumulative returns over a fixed interval in the A-share and US stock markets, respectively. These figures present the cumulative return curves of the portfolios generated during the test period, demonstrating their performance in real market conditions. Notably, the STGAT portfolio exhibits divergent temporal patterns between the two markets: in the A-share market, its outperformance emerges earlier (during mid-2023), whereas in the US market, significant gains materialize later (during early-mid 2024).