Research On Two Types Of Loss Functions For Factor Investment Models In Deep Learnin

IC(information coefficient)and RankIC(rank information coefficient)indicators are employed by a large percentage of articles on financial prediction with deep learning(in particular,cross-section prediction)to evaluate the performance and show the effec-tiveness of the proposed algorithm.IC and RankIC are originally used to measure the effectiveness of financial factors,thus in fact these kinds of articles regard the output of the model as a factor unintentionally.However,they usually use mean square error as the loss functions of the network and do not optimize IC and RankIC indicators directly,which means the loss function is not consistent with the evaluation metrics.Thus,the main purpose of this article is to derive and introduce the loss function that can be used for deep learning to maximize IC and RankIC.Neither IC nor RankIC can be directly embedded into the training of the neural network as the target loss.If IC is used as the target loss function of the neural network,gradient disorder will occur in the training process.If RankIC is used as the target loss function,the network cannot be effectively trained because the Rank operator is not derivable.Thus,we need to derive a trainable loss function equivalent or approximate to IC or RankIC and apply it to the neural network to ensure that the evaluation metric is consistent with the loss function.For maximizing IC,deriving from the relationship between mean square error and IC,this research finds that if the output value of the neural network can meet that the mean value and the variance are consistent with the true value,then the problem of maximizing IC is equivalent to the problem of minimizing mean square error.By adding the Batch Norm mechanism to the training model,the equivalent conversion between IC and mean square error is achieved in this paper.In the real financial model training process,this method is significantly higher than other losses in IC indicators and has better strategy performance,which show the effectiveness of the proposed method.For maximizing RankIC,this paper equates this problem to the optimal sorting problem and borrows two loss functions corresponding to the classical models Rank Net and List MLE in the method of Learn2Rank to optimize RankIC.However,the calcu-lation complexity of the loss function corresponding to Rank Net is?(n~2),and the loss function corresponding to List MLE pays too much attention to the top and ignores the bottom samples,resulting in ignoring the return of the short part in the long-short strat-egy.This paper improves the two loss functions respectively from the perspective of long-short strategy,deducing two novel methods called APloss and LSloss.APloss re-duces the complexity of the loss function in Rank Net from?(n~2)to?(n)while LSloss improves the”top-heavy”problem of the loss function in List MLE.With the real train-ing data,APloss achieves the same effect as the Rank Net loss,while LSloss significantly outcomes the problems of the List MLE method.The ultimate goal of the factor is to use this factor to build a strategy,and it is generally believed that factors with higher RankIC and IC values can perform better in the long-short strategy.However,the relation between the performance of long-short strategy and IC or RankIC is still approximate and is not completely equivalent.To better fit the relationship between them,the weighted long-short strategy is introduced.Due to the randomness of the neural network training process and the low signal-to-noise ratio of financial data,the outputs of the network are of great fluctuation,and the strategy constructed is with little practical value.Therefore,this paper proposes a group mechanism,which can be treated as an attention module without introducing redundant parameters,so that similar samples can get similar prediction results.Compared with the Adaboost method using a similar group mechanism,our proposed strategy performs better.