modelul anghel

8/10/2019 Modelul Anghel

1/7

Constanta Maritime University Annals Year XI, Vol.14

PREDICTION ANALYSIS OF BANKRUPTCY RISK USING BAYESIAN NETWORKS

1CRACIUN MIHAELA-DACIANA, 2BUCERZAN DOMINIC, 3RATIU CRINA

1 ,2Aurel Vlaicu University of Arad, 3 Daramec srl Arad, Romania

ABSTRACT

The Bayesian probability, is widely misunderstood by the general public, as well as some economists. On the otherhand, bankruptcy risk can be estimated in the static and dynamic analysis of the financial balance that outlines theformer performance of the enterprise. A global evaluation of the enterprises future becomes interesting for themanagement of the enterprise and especially for its business partners: banks, clients, capital investors. Therefore, in this

paper we mould the Anghel Prediction Model for bankruptcy risk using the Bayesian probability. To this purpose, weuse Bayesian Networks (BN) and the AgenaRisk Tool. The result of this mould is a solution of bankruptcy risk

prediction using BN.

Keywords: Bayesian probability, Bayesian Network (BN), bankruptcy risk prediction, AgenaRisk Tool, Anghel Prediction Model

1. INTRODUCTION

A Bayesian Network (BN) is a way of describingthe relationships between causes and effects, and is madeup of nodes and arcs. The collection of nodes and arcs isreferred to as the graph or topology of the BN. Inaddition, in a BN each node has an associated probabilitytable, called the Node Probability Table (NPT). Thenodes represent variables. The arcs in a BN representcausal or influential relationships between variables. Thekey feature of BN is that they enable us to model andreason about uncertainty. The NPT for any node givesthe conditional probability of each possible outcomegiven each combination of outcomes for its parent nodes. Usually, there are several ways of determining the

probabilities in any of the tables. Alternatively, if nosuch statistical data is available we may have to rely onsubjective probabilities entered by experts. A key featureof BN is that we are able to accommodate bothsubjective probabilities and probabilities based onobjective data , as specified in [1].

Having entered the probabilities we can now useBayesian probability to do various types of analysis.Bayesian probability is all about revising probabilities inthe light of actual observations of events.When we enter evidence and use it to update the

probabilities in this way, we call it propagation . Intheory we can enter any number of observationsanywhere in the BN and use propagation to update themarginal probabilities of all the unobserved variables.This can yield some exceptionally powerful analyses thatare simply not possible using other types of reasoningand classical statistical analysis methods, as you see in[5].BN offer the following benefits, subject founded in [2]:- Explicitly model causal factors: this key benefit is in

stark contrast to classical statistics whereby prediction models are normally developed by purelydata-driven approaches.

- Reason from effect to cause and vice versa: A BNwill update the probability distributions for everyunknown variable whenever an observation is

entered into any node. So entering an observation inan effect node will result in back propagation, i.e.revised probability distributions for the causenodes and vice versa. Such backward reasoning ofuncertainty is not possible in other approaches.

- Overturn previous beliefs in the light of newevidence: The notion of explaining away evidence isone example of this.

- Make predictions with incomplete data: There is noneed to enter observations about all the inputs, asis expected in most traditional modelling techniques.The model produces revised probabilitydistributions for all the unknown variables when anynew observations (as few or as many as you have)are entered. If no observation is entered then themodel simply assumes the prior distribution.

- Combine diverse types of evidence including both subjective beliefs and objective data. A BN isagnostic about the type of data in any variable andabout the way the NPTs are defined.

- Arrive at decisions based on visible auditablereasoning: Unlike blackbox modelling techniques(including classical regression models and neuralnetworks) there are no hidden variables and theinference mechanism is based on a long-establishedtheorem (Bayes). This range of benefits, together with the explicit

quantification of uncertainty and ability to communicatearguments easily and effectively, makes BN a powerfulsolution for all types of risk assessment.

The first working applications of BN (during the period 1988-1995) tended to focus on classicaldiagnostic problems, primarily in medicine and faultdiagnosis. Intelligence Group at Aalborg University

produces the MUNIN system. Companies such asMicrosoft and Hewlett-Packard have used the early BNfor fault diagnosis, and in particular printer faultdiagnosis. There have also been numerous uses of BN inmilitary applications, for example the TRACS system for

predicting reliability of land vehicles. Another high-stakes application domain where BN have been used


2/7


extensively by commercial organizations is fault prediction; subject is founded in [4].

Because of historical limitation even Bayesianstatisticians have shunned BN for problems that involvecontinuous variables and complex stochastic models.Instead they have used tools like the WinBUGS software

package, which are based on intensive samplingalgorithms collectively known as Markov Chain MonteCarlo (MCMC) methods. Fortunately, there have beensome recent breakthroughs in algorithms for hybrid BN.Building on the work of Koslov and Koller, Neil havedeveloped and implemented a dynamic discretisationalgorithm which works efficiently for a large class ofcontinuous distributions.

Users of AgenaRisk Tool, which implements thisalgorithm, can simply define continuous nodes by theirrange and distribution. Without any of the complexitiesassociated with the MCMC approach, they can achieveresults of matching or greater accuracy for many classesof models, especially for models that include discrete

variables, as specified in [6]. On a wider scale, there isconsiderable research into how to model extremely large problems involving hundreds of data points, with manyvariables, over long periods of time, or involvingcomplex sequences of variables and data. A number ofextensions to BN beyond the classical inferencealgorithms are being used for this purpose, including:Relational BN, Statistical parameter learning, Sensitivityanalysis, Safety and reliability modelling, Operationalrisk in finance, Recommendation engines andinformation retrieval.

2. THE I. ANGHEL MODEL IN

BANKCRUPTCY RISK PREDICTION

Anghel has developed a model based ondiscriminatory analysis, starting from a sample of 276enterprises, grouped into non-bankrupt (60%) and

bankrupt (40%), and belonging to a number of 12

industries of the national economy. The analysis coveredthe period 1994 -1998 and has initially used a number of20 economic -financial indices.

After the selection stage, four financial rates have been established for the development of the scorefunction:- X 1 - earning after taxes / incomes;- X

2- Cash Flow / total assets;

- X 3 - liability / total assets;- X 4 - liability/ sales * 360All the above rates have been aggregated in thefollowing score function: A = 5.667 + 6.3718 * X 1 +5.3932 * X 2 5.1427 * X 3 0.0105 * X 4 , subject isfounded in [3].

Varying within the values established for thisfunction, enterprises are included in one of the followingthree situations:- When A < 0 , bankruptcy/failure situation;- When 0 A 2.05 , uncertainty situation demanding

prudence;

- When A > 2.05

, a good financial situation.The analysis of the previously presented models hasrevealed a certain facility in detecting bankruptcy intime.

Subject to bankruptcy risk prediction was beentreated with interest over the years. The use of BN forBP was study, as you see in [7], by Lili Sun and PrakashP. Shenoy.

3. THE ANGHEL PREDICTION MODEL (PM)FOR BANKRUPTCY RISK (BR) EXPLAINEDUSING A BAYESIAN NETWORK

Accepting the Bayes Theorem and the accuracy ofthe AgenaRisk software it is possible to explain theAnghel PM for BR without exposing the mathematicaldetails. The vehicle for doing this is a visual modelcalled Bayesian Network (BN) as shown in the Figure 1.

Figure 1 BN showing causal structure


3/7


In this structure we have four types of nodes: sample, probability, result and assumption nodes . The sample nodes represent the probability that X i is faulty (i= 1, 2, 3, 4). The probability nodes are X i faults innumber of trials, where number =20, 10, 15, 25. Theresult nodes are the following: Mediate Node1, Mediate

Node2 and A Z score. The Hypothesis node is theassumption node . As mentioned in the previous section, the Anghel PM for BR is based on the function score A= 5.667+6.3718*X 1+5.3932*X 2-5.1427*X 3-0.0105*X 4.In this case we are handling nodes with multiple parents.The initially model we built, was that all four samplenodes were parents for the result node. In this case thecalculation was very slowly and difficult. So weintroduce the two Mediate Nodes and so we reduce thenumber of parents node and of the calculation time, too.

Next we explain how we built the nodes.The sample nodes are simulation nodes, with

continuous interval type. The lower bound is 0.0 and theupper bound is 1.0. The NPT is a Uniform Expression

with lower bound 0 and upper bound 1. The graph typesassociated to this node are Histogram.The probability nodes are simulation nodes, with

integer interval type. The lower bound is 1 and the upper

bound is 9. The NPT is a Binomial Expression with 20,10, 15 and 25 trials and the probability of success given

by the parents node probability p_X i _faulty. The graphtypes associated to this node are Histogram.

The result nodes are simulation nodes, too. Theydivide in two categories. The Mediate Nodes and the AZ score node. The types of Mediate Nodes arecontinuous interval with values between -10 and 50. The

NPT is an arithmetic expression 6.3718*p_ X1_faulty+5.3932* p_ X2_faulty . The graph types associated tothis node are Histogram. The type of A Z score node iscontinuous interval with values between -20 and 100.The NPT is an arithmetical expression MN1+MN2. Thegraph type associated to this node is Histogram.

The assumption node Hypothesis is a simulationnode, with Boolean type. The state options arecustomised, with positive Outcome Good financialsituation and the Negative Outcome Bankruptcy /failure situation. The NPT is a comparison expression:if(zscore


4/7


Figure 3 - Risk graph of Hypothesis after evidence has been entered

The risk map for this model has attached thefollowing risk table, as shown in Figure 4.

Figure 4 Risk table of Hypothesis generated afterevidence has been entered

4. THE ANGHEL PREDICTION MODEL (PM)FOR BANKRUPTCY RISK (BR) USINGHYPOTHESIS TESTING WITH EXPERTJUDGMENT

The structure of the risk map described at the previously section, will be changed. We add a new nodeat the top of the risk map named Prior Type. This node is

a labelled type with Uniform and Beta label value. The NPT is a comparison expression with value 0. The graphtype associated to this node is Histogram. (see Figure 5).

Figure 5 - Hypothesis Testing with Expert Judgment


5/7


In this case the sample nodes are modified only bythe NPT. The NPT Editing Mode changes intoPartitioned Expression. We specify the distribution asfollows: for nodes X 1 and X 4 the uniform distribution isgiven by the function Uniform(0,1) and the betadistribution is given by the function Beta(1,9,0.0,1.0). So

we obtain the chance of failure of 1 to 10. For nodes X 2 and X 3 the uniform distribution is given by the functionUniform(0,1) and the beta distribution is given by thefunction Beta(2,8,0.0,1.0). So we obtain the chance offailure of 1 to 5.

Figure 6 - Complete Hypothesis Testing model with Expert Judgment

Next, we define two scenarios one type Uniform

and the second type Beta . The two scenarios will becorrelated with the risk map entering the observation that

the Prior Type is Uniform in the scenario that we have

named Uniform and Beta in the scenario that we havenamed Beta (see Figure 7).


6/7


Comparing the last two figures we observe thedifference of the results.

Combining Data and Prior Assumptions We change the probability nodes so that we

decrease 1/5 the trials: from 20 to 4, from 10 to 2, from15 to 3 and from 25 to 5.

For the both scenarios, Uniform and Beta, we willintroduce values as follow: for the probability nodes X 1 and X 4 Uniform and Beta receive the value 1,respectively the nodes X2 and X3 receive the value 0 forUniform and Beta. The results are shown in Figure 8.

Figure 8 - Results of hypothesis test after entering sparse sample data

Figure 9 Risk table of Hypothesis Testing with ExpertJudgment after entering sparse sample data

Changing the Simulation SettingsWe delete the Uniform scenario and we remove

from the probability nodes X 1 and X 4 the value 1 forBeta. After we calculate we obtain the mean 0.40 for X 1 and 0.50 for X 4 and the variance value 0.46 for X 1 and0.62 for X 4.

Next, we modify the properties for the definedmodel. The maxim number of iteration defined in thesimulation settings are 25. We work with 5 iterations.

Running the calculation we will obtain different valuesfor both probability nodes.

5. CONCLUSIONS

We have shown that, using BN and AgenaRiskTool, it is possible to show all of the implication andresults of a complex Bayesian argument withoutrequiring and understanding of the underlying theory ofmathematics. Economists can use the obtained analysisto predict the bankruptcy risk using Bayesian

probability.

6. REFERENCES

[1] JENSEN FINN V, GRAVEN-NIELSEN THOMAS - Bayesian Networks and Decision Graphs , Springer 2002[2] POURRET OLIVIER, NAIMS PATRICK,MARCOT BRUCE Bayesian Networks - A PracticalGuide to Applications , John Wily & Sons Ltd, 2008[3] ANGHEL ION Falimentul radiografie i

predic ie, Ed. Economic , Bucure ti, 2002[4] NEAPOLITAN RICHARD E. Learning Bayesian

Networks, Prentice Hall Series in Artificial Intelligence[5] HECKERMANN DAVID A Tutorial on Learningwith Bayesian Network , March 1995[6] Agena 2007, Press Release,http://www.agenarisk.com/agenarisk/case_13.shtml[7] SUN LILI, SHENOY PRAKASH P. Using

Bayesian Networks for Bankruptcy Prediction Some Methodological Issues , European Journal of OperationalResearch, 2007
http://www.agenarisk.com/agenarisk/case_13.shtmlhttp://www.agenarisk.com/agenarisk/case_13.shtml


7/7

Copyright of Analele Universitatii Maritime Constanta is the property of Analele Universitatii Maritime

Constanta and its content may not be copied or emailed to multiple sites or posted to a listserv without the

copyright holder's express written permission. However, users may print, download, or email articles for

individual use.

modelul anghel

Documents