# Random Forest Prediction of IPO Underpricing
## 3 Results  
In this section we report the results of the experimental analysis performed to test the suitability of the random forest algorithm for the IPO underpricing prediction domain. The main experimental results are reported in Table 3. There, we provide the main descriptive statistics for the RMSE obtained in the 15 repetitions of the 10-fold cross-validation. For stochastic algorithms we report the average, median, variance, maximum, and minimum. The exception to this is SMO-Reg. Even though it has a stochastic component and we used different seeds, the 15 experiments converged to the exact same solution. The statistical significance of the differences reported in Table 3 was tested formally. Given the distribution of the prediction errors, we relied on the Mann-Whitney test [38]. The results of this analysis are reported in Table 4. There, we represent the fact that the algorithm in the row has median prediction error that is significantly larger than the one in the column at 1% by \"++\". In case a similar difference in the opposite direction is found, the symbol used is \"-\". If the disparity is such that the first one is significantly smaller at 5%, we use \"-\". Finally, if the possibility of equal predictive accuracy cannot be discarded at 5%, we report \"=\". Following [3], we complement the analysis based on predictive performance illustrating the potential economic benefits of using these techniques to price IPOs. In Table 5 we compare the actual observed underpricing with the initial returns resulting should we use forecasts of the models as the offering price. For each of the models, we provide the average value of the statistics on the 610-pattern test set over 15 experiments. That is, we report the average mean underpricing, average median underpricing, and the average of the standard deviations. All of the differences between the median mean observed underpricing and model-based ones were significant at 1%. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline  & **IBK** & **LMSReg** & **LWL** & **MSP** & **M5 Rules** & **MLP** & **RBFN** & **RForest** \\ \hline LMSReg & ++ & & & & & & \\ LWL & ++ & ++ & & & & & \\ M5P & ++ & – & – & & & & \\ M5 Rules & ++ & – & – & – & & & \\ MLP & ++ & ++ & – & ++ & ++ & & \\ RBFN & ++ & – & – & = & ++ & – & \\ RForest & – & – & – & – & – & – & – \\ SMO-Reg & ++ & – & – & ++ & ++ & – & = & ++ \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical significance of differences of median underpricing RMSEs on the test set according to the Mann–Whitney test. Positive signs indicate higher prediction errors for the algorithm in the columns vs. the algorithms in the rows. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & **Mean** & **Median** & **Std. Dev.** & **Min** & **Max** \\ \hline IBK & 0.331 & & & & & \\ LMSReg & 0.374 & 0.374 & 0.00001 & 0.371 & 0.376 \\ LVL & 0.396 & & & & & \\ M5P & 0.361 & & & & & \\ M5 Rules & 0.358 & & & & & \\ MLP & 0.386 & 0.389 & 0.00033 & 0.357 & 0.425 \\ RBFN & 0.361 & 0.361 & 0.00001 & 0.355 & 0.366 \\ RForest & 0.310 & 0.394 & 0.00001 & 0.306 & 0.314 \\ SMO-Reg & 0.361 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptive statistics of mean RMSE for underpricing on test set based on 15 experiments. Random forests can also be used in this context as an investment tool. A potential trading strategy would be investing in IPOs with the highest initial return potential according to the models. Even though the predictions for initial returns might not be completely accurate, the distribution of forecasts could provide very valuable insights. This is evidenced by Figure 4. There, we report the returns obtained investing in IPOs prioritized according to the forecasts of the models. The 610 IPOs that compose the test set were ranked by predicted return. Given that we repeated the experiments 15 times, we obtained as many ranks. The IPO Return series shows the average of the actual returns that correspond to the 15 IPOs that have the same rank. The series labeled Av. Cumul.