Computing the Probabilities of Closing of 10b-5 Securities Class Action Cases
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1 Computing the Probabilities of Closing of 10b-5 Securities Class Action Cases Steve Hillmer and Prakash P. Shenoy CBAR Seminar January 31, 2014 c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 1/ 49
2 Outline Problem Data Model and Results Limitations Future Work c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 2/ 49
3 Problem Given a new 10b-5 securities class-action case, filed in a Federal court, where lead plaintiff and lead plaintiff counsel have been appointed, and a consolidated amended complaint has been filed, what is the probability that the case will be dismissed? This problem is relevant to D&O insurance companies from a claims perspective. During , securities class action cases have settled for a total of $73 billion, not including $15 billion in plaintiff lawyers fees and an equivalent amount in defendant lawyers fees. c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 3/ 49
4 Problem This is part of a related problem from an underwriting perspective: Given a potential D&O customer, What is the probability that a class-action complaint will be filed? Assuming that a class-action complaint is filed, what is the probability that it will be dismissed? Assuming that it is not dismissed, what are the potential settlement amounts? c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 4/ 49
5 Outline Problem Data Model and Results Limitations Future Work c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 5/ 49
6 Data Closed 10b-5 securities class-action cases filed during ,150 such cases. c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 6/ 49
7 Data Why ? Sarbanes-Oxley Act of 2002 has changed the characteristics of 10b-5 cases. Many of the cases in the period 2011 onwards are still pending. c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 7/ 49
8 Data Sources of data: 1 Advisen s Master Significant Cases and Actions database (MSCAd) for case data 2 Stanford s Class Action Clearinghouse to verify case details 3 COMPUSTAT for financial information about securities c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 8/ 49
9 Data The class variable is CLOSING: with two possible values: dismissed or settled c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 9/ 49
10 Data Predictor variables (in our model): c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 10/ 49
11 Data Predictor variables we considered (but not in model): c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 11/ 49
12 Data Predictor variables we considered (but not in model): c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 12/ 49
13 Outline Problem Data Model and Results What are naïve Bayes (NB) models? How does one use a NB model? Why NB? What is our NB model? What are the predictors? What are the parameters? How good is our NB model? What are the relative influences of the predictor variables? Limitations Future Work c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 13/ 49
14 Model and Results We use a naïve Bayes model to compute posterior probabilities of CLOSING given observed values of a subset of variables What are naïve Bayes models? c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 14/ 49
15 Model and Results: What are NB Models? Let s construct a naïve Bayes model with, e.g., CLOSING, GAAP, and INST INV c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 15/ 49
16 Model and Results: What are NB Models? Adding GAAP: c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 16/ 49
17 Model and Results: What are NB Models? Adding INST INV: We are assuming that given CLOSING, probabilities of INST INV are independent of GAAP c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 17/ 49
18 Model and Results: What are NB Models? This model has only 5 parameters (instead of 7) A naïve Bayes model with 10 predictor variables would have only 21 parameters, instead of ,024 = 2,047 without the independence assumption. c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 18/ 49
19 Model and Results: How does one use a NB Model? Consider the model with CLOSING and GAAP: Multiplication of priors and likelihoods gives us joints that add to 1. c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 19/ 49
20 Model and Results: How does one use a NB Model? Suppose GAAP = 0. What is the posterior Pr(dismissed)? This way of computing posterior probabilities is not tractable when we have many predictors It is easier to use odds and likelihood ratios c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 20/ 49
21 Model and Results: Probabilities and Odds What are odds? Pr(dismissed) = 0.52 is equivalent to O(dismissed) = = 1.08 Probabilities are on a scale from 0 to 1. Odds are on a scale from 0 to O(dismissed) = 1.08 is equivalent to Pr(dismissed) = = O(dismissed) = 1, means Pr(dismissed) = 0.5 O(dismissed) > 1, means Pr(dismissed) > 0.5 O(dismissed) < 1, means Pr(dismissed) < 0.5 c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 21/ 49
22 Model and Results: Probabilities and Odds c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 22/ 49
23 Model and Results: How does one use a NB Model? Suppose GAAP = 0. What are the posterior O(dismissed)? Posterior O(dismissed) = = = O(dismissed) LR(GAAP = 0) = = Posterior Pr(dismissed) = c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 23/ 49
24 Model and Results: How does one use a NB Model? Suppose GAAP = 1. What are posterior odds of dismissed? Posterior O(dismissed) = = O(dismissed) LR(GAAP = 1) = = Posterior Pr(dismissed) = = c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 24/ 49
25 Model and Results: How does one use a NB Model? Suppose GAAP is unknown. What are posterior odds of dismissed? Posterior O(dismissed) = Prior O(dismissed) = LR(GAAP = unknown) = 1 1 = 1 c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 25/ 49
26 Model and Results: How does one use a NB Model? Easy to compute posterior odds (or probabilities) of dismissed: Posterior odds = Prior odds Likelihood ratio of evidence Suppose GAAP = 1, and INST INV = 0. Posterior O(dismissed) = O(dismissed) LR(GAPP = 1) LR(INST INV = 0) = = Pr(dismissed) = c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 26/ 49
27 Model and Results: Why use NB? Why use naïve Bayes? Provides probabilities of dismissed and settled; Can be used even if some predictor variables have missing values; Variables can be numeric or nominal; Simple has very few parameters (# parameters is linear in # predictor variables); Robust predicts well even if the independence assumption of the model is violated; c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 27/ 49
28 Model and Results: What are the predictors? Which subset of predictor variables provides the best naïve Bayes model? By best, we mean a model that has the lowest out-of-sample prediction errors Given 19 predictor variables, we have = 524, 287 non-empty subsets too many to enumerate We did a search using several methods: best first, random, etc. c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 28/ 49
29 Model and Results: What are the predictors? Which subset of predictor variables results in a good naïve Bayes model? Answer: The subset consisting of 1 GAAP (violations of generally accepted accounting procedures allegation) 2 SEC-11 (allegations of filing false claim with SEC) 3 INST INV (whether lead plaintiff is an institution or individuals) 4 RESTATED FIN (whether restated financials are involved) 5 BANKRUPTCY (case is related to bankruptcy filing) 6 ONE DAY DROP (discretized into 2 states: 40.5% and > 40.5%) c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 29/ 49
30 Model and Results: What are the parameters? Naïve Bayes Model (estimated from all 1,150 cases): with priors for CLOSING, likelihoods for GAAP and INST I NV : c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 30/ 49
31 Model and Results: What are the parameters? Adding likelihoods for SEC 11: c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 31/ 49
32 Model and Results: What are the parameters? Adding likelihoods for RESTATED FIN: c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 32/ 49
33 Model and Results: What are the parameters? Adding likelihoods for BANKRUPTCY : c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 33/ 49
34 Model and Results: What are the parameters? Adding likelihoods for ONE DAY DROP: c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 34/ 49
35 Model and Results: What are the parameters? c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 35/ 49
36 Model and Results: Using our NB model If all predictors are No: Odds for dismissed = = 2.22 Probability of dismissed = = 0.69 c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 36/ 49
37 Model and Results: Using our NB model If all predictors are Yes: Odds for dismissed = = 0.03 Probability of dismissed = = 0.03 c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 37/ 49
38 Model and Results: Using our NB model If predictors are as follows (e.g., Panera Bread Company, 2008, E. D. Missouri): Odds for dismissed = = 0.58 Probability of dismissed = = 0.37 c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 38/ 49
39 Model and Results: How good is our model? For each case, we compute the Pr(dismissed) based on a naïve Bayes model whose parameters are estimated from the other 1,149 cases (Lachenbruch procedure). We sort the cases by Pr(dismissed), highest to lowest, and divide the set of all cases into 5 groups of 230 cases each (quintiles). The characteristics of each quintile are as follows: c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 39/ 49
40 Model and Results: How good is our model? c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 40/ 49
41 Model and Results: How good is our model? How well can our NB model predict CLOSING?: This procedure is repeated with each case as a hold-out case (Lachenbruch) c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 41/ 49
42 Model and Results: How good is our model? Confusion matrix using the Lachenbruch procedure: # incorrect predictions is = 444 cases (39%) A naïve strategy of predicting all cases as dismissed would have an error of 557 (48%) So lift over marginal is = 113 cases (10%) The search method for identifying a good subset uses # incorrect predictions as an objective to be minimized c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 42/ 49
43 Model and Results: Relative influence of each predictor What is the relative influence of each predictor variable? For each variable, we removed it from the set of 6 predictor variables, and observed the increase in # incorrect predictions as a result. Results are as follows: c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 43/ 49
44 Model and Results: Relative influence of each predictor Relative influence of predictors depends on likelihood ratio, and frequency of occurrence: Smaller the likelihood ratio, higher the influence Higher the frequency of occurrence, higher the influence c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 44/ 49
45 Outline Problem Data Model and Results Limitations Future Work c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 45/ 49
46 Limitations History of past cases is used to predict the future, which assumes that future will be like the past Changes in accounting rules or litigation laws could change the filing and closing of securities class action cases We have too many (56%) missing values for ONE DAY DROP. Our model may perform better if we had fewer missing values Model built is only as good as the data errors in the data will result in errors in the model c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 46/ 49
47 Outline Problem Data Model and Results Limitations Future Work c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 47/ 49
48 Future Work For each case, we know the judge who made the judgment to dismiss/not dismiss. Judges have a history of ruling on civil cases. Also we know which president (Democrat or Republican) appointed the judges. Can we use such information to improve our model? Financial re-statements can be classified as core/non-core, materially significant or not. Can we take advantage of such classifications of financial re-statements to predict closing? c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 48/ 49
49 Future Work Are there other variables (not in Advisen data set) that we can use to predict closing? E.g., Stock options for CEO and board members that provide perverse incentives to ratchet up stock prices at exercise dates (C Shenoy) Conservatism of reporting earnings (Ettredge) Insider selling of securities based on insider information Short interest (Meschke) Notoriety of the class action case (Meschke) c 2014 Hillmer-Shenoy Prob. of Closing of 10b-5 Class Action Cases 49/ 49
On Computing Probabilities of Dismissal of 10b-5 Securities Class-Action Cases
Appeared in: Decision Support Systems, 94(C), 2017, 29 41. On Computing Probabilities of Dismissal of 10b-5 Securities Class-Action Cases Sumanta Singha a,, Steve Hillmer a, Prakash P. Shenoy a a University
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