# Random Forest Prediction of IPO Underpricing
## 4 Discussion  
As we can in Table 3, random forests provide the best results, followed by IBK. In addition to the relatively low mean and median RMSE, we should highlight the fact that the approach seems to \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Mean** & **Median** & **Std. Dev.** \\ \hline Observed & 0.17570 & 0.074 & 0.379 \\ IBK & 0.01125 & \(-\)0.020 & 0.331 \\ LMSReg & 0.08757 & \(-\)0.003 & 0.364 \\ LWL & 0.02264 & \(-\)0.003 & 0.395 \\ M5P & 0.00186 & \(-\)0.032 & 0.362 \\ M5 Rules & 0.00253 & \(-\)0.029 & 0.359 \\ MLP & 0.00035 & \(-\)0.029 & 0.385 \\ RBFN & \(-\)0.00255 & \(-\)0.069 & 0.361 \\ RForest & 0.00083 & \(-\)0.045 & 0.326 \\ SMO-Reg & 0.07406 & \(-\)0.005 & 0.354 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison between model-based and actual underpricing on the test set. Model-based underpricing is based on the forecasted first-day close price instead of the offer price. Average values are of the statistics on the test data over 15 runs. Figure 4: Return obtained investing according to the priorities set by the random forests (average over 15 runs on the test set). IPOs are ranked by the forecasted initial returns. Average cumulative return for rank \(n\) averages are the actual initial returns of the \(n\) highest ranking IPOs. be the second-most reliable one among those with a stochastic component. The range of variation for the prediction error is narrow and its variance is relatively low. It was only beaten by SMO-Reg. This algorithm offered an intermediate performance in terms forecasting ability, but converged to the same solution across the 15 experiments. On the opposite side of the spectrum, LWL and MLP offered the worst results. Even though multi-layer perceptrons have been successfully used in many regression tasks, their sensitivity to the presence of outliers drags its performance in this domain. Conversely, random forests handle this difficulty with much more efficacy. MLP showed the highest dispersion of results, including the worst prediction error in one of the executions. If we consider the potential economic implications of the potential of using random forests in this domain, the results lay down two interesting applications: IPO pricing, and investing. On the first front, random forests offered the lowest average difference between the actual closing price and the predicted one. This reduced model-based underpricing, where offer price is replaced with the output of the model, came together with the smallest average standard deviation. The implication is that the use of this algorithm to support the pricing decision is likely to have the potential to reduce the amount of money left of the table. On the second front, Figure 4 makes it apparent that there could be room for profitable trading based on the output of the models. Even though we cannot claim that random forests make perfect initial return predictions based on the variables discussed, they show good capabilities ranking them. IPOs that are predicted to offer the highest initial returns suffer significantly higher underpricing than the expected bottom performers. As we can see by the spikes of the IPO Return series, the models do not have the ability to rank perfectly. The highest initial return does not correspond to the first element of the series, and it is far from smooth. In addition to that, the 15 experiments do not result in the same rank (that is, the reason why the maximum value of the series is lower than the highest initial return). Having said that, as the highest values clearly tend to be at the beginning of the series and the lowest at the end, if we invested if the n most promising ones we would be very likely to gain excess returns. That would happen as long as the average return, shown in the Average Cumulative Return series, is higher than the IPO market return, Average Return, and the difference is enough to cover the transaction costs.