Rebeco: using machine learning to predict stock crash risk

1. Preface

Major developments in big data and machine learning are driving the frontier of quantitative investment . The enhancement of computing power promotes the deployment and use of machine learning models . Compared with the rule-based model , These models adopt a completely data-driven approach , Be able to model complex nonlinear relationships . It can potentially reveal systematic and repetitive patterns that simple linear models cannot capture .

for example , Some variables may only be when they exceed a certain threshold , Or when they are combined with other variables , Or they may only be able to predict underperforming stocks , To predict stock returns . In this white paper , We explored in depth how to use ML Technology can drive quantitative modeling to the next level . Let's also look at a specific example , Using machine learning model to predict individual stock price collapse .

The different uses of machine learning technology in quantitative investment are increasingly recognized by the academic literature . These models include relatively simple variable selection models , And a model that can identify the lead lag relationship between different asset returns . Machine learning technology has also been used in the complex depth learning model of statistical arbitrage . Overfitting has always been a key problem in quantitative strategy . When the amount of data and the number of variables increase , This is a bigger problem .

The risk here is , One can find the coincidence relationship between the variables observed in the past , And use it as a signal to build the portfolio , But in fact , This relationship will not be repeated in the future , Because there is no real underlying phenomenon . However , The machine learning toolkit contains solutions to avoid over fitting , Like regularization （ Variable selection ）, Model averaging and cross validation .

2. Forecasting companies facing financial difficulties

Avoid investing in companies that will later encounter financial difficulties , It can help investors win the market . in other words , It is far from easy to find the companies that are most likely to face difficulties in the future . Although there are many features that can help predict this result , But they may do this most effectively in a non-linear way or in a particular combination . Fortunately, ,ML Technology is designed to meet this challenge .

One way to mark troubled companies is to look at bankruptcy filings or credit downgrades . However , There may be a fall in share prices before these events occur . For stock investors , It is more meaningful to predict stock price decline than to correctly predict bankruptcy filing or credit rating downgrade , Because these events may have been digested at the time of occurrence . therefore , We define a crash as a sharp fall in a company's share price relative to other stocks . This indicator captures Special risks , Not the turbulence of the whole market , We think it is very suitable for stock selection model , It is not used in asset allocation or factor timing models .

According to our definition of financial distress , chart 1 Show , The identified distress events are not concentrated in a few industries , But across multiple industries . in other words , The more troubled the industry , The more events that usually happen . in general , The number of share price crashes changes over time , Because cross-sectional fluctuations are usually higher in times of crisis .

If we want to use ML Model to identify companies facing financial difficulties , We need to provide it with a set of variables that may contain predictive information about the collapse of stock prices . stay ML In terms of , These predictors are called characteristics , The predicted variables are called targets .

Select the feature set as input to the algorithm , The purpose is to find the predictive relationship with the target , This is an important modeling step for any predictive model . For our purposes , The variables we choose include the classic financial crisis indicators , Such as distance-to-default, volatility, and return on equity. however , because ML The model aims to select the most important features from a larger set of variables , We also decided to obtain more granular features from the financial statements , Such as operating cash flow and short-term and long-term debt .

In our model , We only include features that we believe may be relevant to the identification of companies with the risk of share price collapse . for example , The initials of the company name or the color of the logo are not included , Because we can't relate them to economic principles , To explain why they might be able to predict crash risk . Because many company characteristics are only snapshots of a certain point in time , For example, profitability , We also include some characteristic time series in the model . In our view , This allows the algorithm to identify a series of events , If profitability declines , How to affect the risk of distress .

majority ML The algorithm is designed to filter out uncorrelated predictors from a large number of features , This process is also useful in avoiding over fitting . We believe that , Fewer redundant features reduce the opportunity to make investment decisions based on noise data . Besides , Reducing the number of features can speed up the training process of the algorithm . For our application , We trained three statistical models ： Regularized logistic regression 、 Random forest and gradient enhanced tree .

Regularized logistic regression is a method based on classical linear regression model , But through logical transformation ( Measurements on a linear scale are converted to probabilities ), The probability used to predict binary results : In our case , Whether a company is in financial trouble . Regularization is ML Terms selected in the model , in other words , The technique selects only those variables that help predict binary results .

meanwhile , Random forest classification is based on multiple decision trees ( So there is the term forest ) The nonlinear model of , Take randomly selected features as nodes , Most of them voted to classify （ Determine which group an observation belongs to ）, In our application, it is a binary decision . Last , Gradient enhanced tree algorithm is also based on decision tree , But it does not depend on a majority vote , Instead, change the weight of the feature , To reduce the number of false predictions .

These three prediction models are retrained annually according to their cross validation indicators . After retraining the model , We build signals for the coming year based on data we haven't seen before . When setting up this training test configuration , It is extremely important to ensure that there are no data leaks . This refers to the process of model training , When there is a data leak that has not been seen before , It will happen . Data leakage will lead to better backtracking test results , This is impossible to achieve in practice , Because the information that can be accessed in the future is obviously not available .

Each model makes independent predictions , These predictions are then combined into a set of predictions . In our view , A set is ML The only free lunch , This is similar to diversification in investment . chart 2 It shows the stock price of American financial stocks , And the overall distress risk predicted over time . In this case , We see 2007 After the middle of the year , Its probability of crisis is higher than 75%, And in the following months, it surpassed 90%. We also observed that , The company's share price is at 2007 year 1 Monthly peak , But from 2008 year 3 The month began to fall sharply , until 2008 year 9 In June the company filed for bankruptcy .

We use this method to generate 2000 - 2020 The probability of financial distress for a separate sample of developed and emerging market stocks during the year . For comparison , We also consider other predictors of distress risk , Such as stock return volatility 、 The stock market beta And default distance . For each subsample , We form according to the ranking of the probability of stock price collapse 20 Portfolio , And calculate their return over the next period of time .

chart 3 Describe the performance of the market , And the portfolio with the highest probability of financial distress among the four distress risk measures . For developed markets , The average market return during this period is 10.0%. meanwhile , be based on ML The bottom portfolio yield of the method strategy is only 2.3%. This is much lower than based on other traditional variables ( from 4.2% To 5.0%) The highest predication of the plight of the constructed portfolio yields .

In the case of emerging markets , We see even greater improvements . The average market return is 11.6%, The return rate of the portfolio based on other traditional crisis prediction indicators is 4.5% to 7.0% Between . On the other hand , be based on ML The portfolio of methods produces 1.5% The loss of , Therefore, it produces better results than the other three schemes .

This shows that , advanced ML Technology can potentially help us identify stocks with high distress risk . let me put it another way , If we avoid investing in these stocks , It is possible for us to improve the return of the quantitative stock portfolio .

 

3. The interpretability of the model

Just to understand ML How to help predict financial distress , We first examined 5% Industry classification of the riskiest stocks . Although we hope ML The method can automatically identify the industries that may encounter difficulties , But we don't want it to be dominated by industry choices . For our ML Model , We have no such restrictions on it , Because we do not include sector information in its feature set .

chart 5 Shows the industry distribution of the stock subset over time . We observed that , Most distressed stocks appear in 21 The information technology sector at the beginning of the century , And then there was 2008 - 2010 The financial sector during the year , The second is 2015 - 2019 Energy sector during the year . Although over time , There is a clear preference for these troubled industries , But we noticed that , The identified distress events are not just concentrated in a few industries . therefore , We believe this makes our ML Technology is a good candidate for use in the stock selection process .

It is also important to assess the importance of each selected feature .SHAP Value is the average value of the marginal contribution of the feature when predicting the target . This approach enables us to understand the economic principles behind our forecasts .

In the figure 6 In this example , Our prediction model contains only three features ： Volatility 、 P / E ratio （PE） And stock turnover . Without considering any features , We assume that the model will predict the average probability of distress of the training sample as 10%. then , If only volatility is considered 、 P / E ratio or stock turnover information , We will see the probability of a stock's distress rise to 15%、12% or 11%. Besides , We show that when two variables are included at the same time , When all three characteristics are considered , Predict changes in probability .

The average marginal contribution of each feature , or SHAP value , Calculate on the right . In this case , Stock volatility contributes the most , by 4.5%. This includes adding to the baseline 5% The average increase in , As the next line 9 When adding the second feature of 4.5% The average increase in , And as the bottom section 3 When adding variables 4% Increase of . Again , P / E ratio SHAP The value is 1.5%, The marginal contribution of turnover rate is the smallest ,SHAP The value is 1.0%. in general ,SHAP The values add up to 7%, Constitute the predicted value of the model 17% And the baseline value 10% Differences between . In this way , We can deconstruct the importance of each feature to each observation .

our ML The importance of features in the model is shown in the figure 7 Shown . The color of each point indicates the size of the feature , Red indicates high characteristic value , Blue indicates low characteristic value . These characteristics are ranked from top to bottom in importance . for example , features 25 Is the most important , This shows that it is SHAP There is the biggest difference in the value .

As the red dot shows , features 25 A high value of will lead to a substantial increase in the probability of financial distress , Because these points are more to the right than any other feature . On the other hand , Lower value , As highlighted by the blue dot , It means that the probability of financial difficulties is reduced , Because the blue dot is on the negative side of the scale . by comparison , features 4 The minimum value of is on the far left , So these values may be better than the characteristic 25 The minimum value of has a greater negative impact on the probability of distress . features 5 The effect of is nonlinear , Because high values have a great positive effect on probability , Low values have only a small negative effect .

In order to better understand the nonlinear and interaction effects between characteristics and the probability of financial distress , We looked at the figure 8 Partial dependency graph in . These graphs show the marginal effect of a single feature on the predicted probability of distress .

chart 8 The chart on the left side of the middle shows , Lower Distance-to-default Will increase the probability of distress . But the overall shape is convex to the origin Distance-to-default Reduced pair of SHAP The greater the marginal contribution . This is a clear example , Explain why nonlinear models are useful , Because the cross-sectional values of the whole range are unequal information .

up to now , We have shown the relationship between characteristics and the probability of financial distress （ It could be nonlinear ） Relationship , This helps us understand the behavior of input based prediction models . However , It is also possible to go deep into what seems to be a black box to explain individual disaster predictions . Deep mining of raw data enables us to clearly understand why a stock is or is not recognized as a low-priced stock .

For every observation , We can all show exactly which features increase the probability of distress , Which features reduce the probability of distress . chart 9 In, we describe the situation of a certain stock in our investment field .

For each relevant feature , We describe the input values and their impact on the estimated probability of distress . The red bar chart contains eigenvalues that increase the probability of distress , The blue bar chart contains eigenvalues that reduce the probability of distress . By using these visualizations , We can ensure that our ML The application is a glass box, not a black box , And we can drill down to the source data , To better understand the ruin probability of each stock in our stock pool .

 

4. be based on ML The future of stock selection

We have officially run several ML Model . for example , We use naturallanguageprocessing technology to interpret a large number of news , To test emotions , Or analyze the information disclosed by the company , To determine the possible contribution of the company to the United Nations sustainable development goals . This is a comparison of the method described in this paper to predict the risk of stock price collapse ML Technology supplement . We believe that these tools can help us better identify companies that may perform poorly in the future . Avoiding investing in such stocks may improve investment performance .

In our view , New quantitative research techniques —— Such as ML—— It challenges the traditional wisdom in the field of quantitative investment , And it is possible to improve the investment results . In this paper , We explained ML How to deal with difficult events in developed and emerging markets ( For example, bankruptcy filing or credit rating downgrade ) Help investors find troubled enterprises before they happen . We have evaluated ML The added value of the model , Because they can consider the complexity of nonlinearity and interaction , Especially compared with the simpler traditional linear model .

ML A key advantage of the algorithm is , We can provide them with economically reasonable and well performing input parameters , And analyze in detail whether their choice is logical over time . Because we are still aware of the risk of over fitting , We used a cross validation framework , We believe that , as time goes on , Prudent data-driven changes can be made in terms of predictability . Besides , We have the ability to scrutinize the source data , This enables us to explain why a stock in our portfolio has a specific probability of distress risk . In short , We are based on ml The application of distress risk prediction and Robeco The concept of quantitative investment is consistent .

There is a high possibility that future innovative research projects will reveal complex prediction relationships or lead to better interpretation of unstructured data . The downside of financial market data is , The stock price may be affected by many known and unknown factors , And over time , The relationship between enterprise characteristics is complex and unstable . This makes it difficult to predict stock returns .

therefore , Standard statistical methods may not be able to find complex patterns , Or the complex patterns in the data may be random , So it may not be repeated in the future . We are in the crisis prediction ML The application shows that ,ML The toolbox may contain methods to reveal the true signals of future financial crises , At the same time, the noise data in asset prices and company characteristics are ignored .

When moving from a rule-based model to a rule-based model ml The model of , The role of researchers has changed from a mentor to a coordinator . In the traditional way , The researchers instructed the computer to test certain rules of input data , See if they help predict output . stay ML aspect , The researchers input and output data into the computer , Let it evaluate what the best rules are . This is in ML In terminology, it is called supervised learning .

This change in role enables researchers to deal with more complex problems . But people need to be cautious , And pay attention to the interpretability and over fitting of the model . That's the only way , Quantitative researchers can sit in the driver's seat , layout ML The process , Instead of instructing the algorithm how to behave . therefore , We believe that ML Technology can drive quantitative modeling to a new level within the scope of our proven investment philosophy . in fact , Evidence based research 、 Economic rationality and prudent investment are ML Key factors that play a role in the investment environment .