Sci. Rep. Kanazawa Univ.
Vol. 59, pp. 1–26, 2015

Bankruptcy Prediction on Margin Trading andApplications
T RISTIYANTO∗
Graduate School of Natural Science and Technology,
Kanazawa University, Kakuma, Kanazawa 920–1192, Japan(Received May 27, 2015 and accepted in revised form August 14, 2015)

Abstract Although bankruptcy and default are well known as critical factors leading tovarious ﬁnancial recessions or ﬁnancial bubbles, such as the Great Depression in the USA
that began in 1929 and the Lost Decade of Japan in the 1990s, predicting when they will
occur has not been studied sufﬁciently. In this paper, we propose a method that ﬁltersout risky investors and keeps good investors in a margin-trading simulation. Investors
are divided into three classes (bankrupt, surviving and proﬁtable) instead of the standard
two (bankrupt/bad and surviving/good). As a result, bubble bursting can be thwarted,since maintaining credit absorption for the qualiﬁed investors can prevent the collapseof prices. We expose the problems with using the minimum margin as the de facto toolfor controlling trading on the margin. We compare the results of four well-known dataclassiﬁcation methods (multiple discriminant analysis, neural networks, decision trees
and support vector machines) in order to determine the one that is most suitable forbuilding a credit-scoring schema. Of the methods considered, the C4.5 algorithm forbuilding decision trees was found to be the best. Our proposed strategy can successfully
use credit scoring to tame the bubble phenomenon.
Keywords. margin trading, credit scoring, bankruptcy prediction, stock market simulation, bubble bursting.

1

Introduction

Bankruptcy prediction is a challenging topic in business analytics because of the importance of precise and timely strategic business decisions and their impact on thecorporation, society and the country and even globally. In the United States, the Great
Depression that began 1929 and the 2008 ﬁnancial crisis when the housing bubble∗ Current address: Department of Computer Sciences, Faculty of Mathematics and Natural Sciences,
University of Lampung, Jalan S. Brodjonegoro no.1 Gedung Meneng, Bandar Lampung, Indonesia.
e-mail: trimsya@gmail.com

2

Bankruptcy Prediction on Margin Trading and Applications

burst and in Japan, the Lost Decade of the 1990s were ignited by the inability to accurately predict bankruptcy [6].
Following these recessions, various regulations were established to ensure the stability of the market and to prevent another collapse [31]. Because buying on the margin
is correlated with ﬁnancial distress, it can be used as an indicator for detecting an imbalanced ﬁnancial market [19]. Margin requirements are used to control price volatility
and to prevent investors from going into debt to engage in reckless speculation. It isalso used to ensure sufﬁcient liquidity in the market that prices are established fairly
and smoothly. Relaxing requirements for investing on the margin holds great appeal
for the investors, but it is a double-edged sword. Although it increases liquidity, it isalso likely to increase volatility [36]. On the other hand, tight requirements restrict
volatility, but the liquidity will be low, because many investors will default. Some of
the investors who will be defaulted or ﬁle to bankruptcy should be well predicted to
manage the risk as instructed on Basel II accord [15]. For a bank or lender, increasing the margin requirements is an effective tool for mitigating risk. However, goodinvestors may also be ﬁltered out since only investors who have sufﬁcient working
capital are retained, but, unfortunately, this tool cannot predict which investors will
perform well.
In this paper, we develop a new method for using credit scoring to predict an investors’ performance when trading on the margin. Compared to a margin requirementthat screens investors merely by their capital and collateral, credit scoring can extend
the scope of the evaluation to include the character, capacity and condition of the
trader. The simulation presented here was developed from the stock market simulationthat was studied by Nakatani et al. [23, 25] and Zhu [40]. The bank agent in that model
did not have intelligence and considered only the ratio of debt to working capital. We
implemented an artiﬁcial intelligence approach to credit scoring for granting loans. We
used a statistical method, multiple discriminant analysis [2] and artiﬁcial neural networks, decision trees and support vector machines to create our credit-scoring schema.
In the ﬁnancial industry, credit scoring is well known as a way to predict bankruptcy
and thus our research appears to be similar to that of others; however, to the best of
our knowledge, there have been no scientiﬁc studies of using credit scoring for margin
trading. Most of the related research considers ways to predict bankruptcy of companies [12, 14, 20, 22, 27, 32, 39]. However, Wang [35] used an analytical approach
to measuring the credit risk for margin trading and calculated the threshold-breaking
probability, the default probability and loss given default. In that study, ﬁnancial ratios were not used to predict bankruptcy, whereas we use the investors’ ﬁnancial ratios
and an artiﬁcial intelligence approach to predict the status of each investor. We developed a method for credit scoring that uses three classes (“bankrupt”, “surviving”
and “proﬁtable”), although most known methods use only two classes (“bankrupt”
and “surviving” or good and bad). The “proﬁtable” class is useful for maintaining

Tristiyanto

3market liquidity when a bubble occurs. Banks can deliver their loans to investors whowill help maintain market liquidity. We consider the impact of credit scoring on pricemovement and its effect on controlling bubbles.
We also present a new banking strategy for taming bubbles [24]. Most economists
use ﬁnancial regulations and macroeconomic policies in their attempts to tame thecrashes that follow bubbles. For example, Danthine [9] used capital buffers to mitigate systemic risk and Sornette [33] developed a method for detecting bubbles andpredicting crashes. In our bubble-taming strategy, we use artiﬁcial intelligence, credit
scoring, bubble detection and loan adjustments. We veriﬁed in our cases that if a bankuses our strategy, it can prevent the bubble from bursting.
The remainder of this paper is organized as follows. In Section 2, we explain
the use of the simulation model for discovering problems and ﬁnding critical factors.
In Section 3, we brieﬂy describe the theoretical background of various classiﬁcation
methods that are used to predict bankruptcy. In Sections 4 and 5, we discuss the resultof the simulations. In Section 6, we make some remarks and present our conclusions.

2

Model

2.1

Investor Behavior

We assume that there are two types of investors (or players) in the stock market, thatis, players with artiﬁcial intelligence (AI players) and players with random behavior(random players). AI players are big players who are smart and have large assets,
whereas random players are small, speculative traders. AI players create trends, while
random players create noise. AI players create price movement, since they make effective order decisions and are able to capitalize them. On the other hand, the decisions ofrandom players are made by a random walk with a Gaussian distribution. AI players
are given loans and this leverages their actions; random players are not given loans.
When AI players collapse, this will cause price movement and it may even cause prices
to crash, since AI players have large capitalization in the market. Therefore, in order
to avoid sinking prices, it is important that bank agents properly analyze the situation
before granting their loan applications.
The algorithm we used for the AI player’s decisions is based on the back-propagation neural network (BPNN) rules, which were developed by Nakatani et al. [23, 25]
and Zhu [40]. The BPNN is made up of three layers (input, hidden and output). The
input data consisted of 53 items, it learned from 51 historical transactions and theinformation includes the amount of cash and number of shares of stock possessed by
the investor being evaluated. The hidden layer contains 60 neurons and the transfer
function that is applied is a sigmoid function. The output of the BPNN are buying andselling signals and the result is the larger of the two. A market order occurs when the

4Bankruptcy Prediction on Margin Trading and Applications

buying or selling signal is greater than 0.99; otherwise, there is a limit order or a bid
order. In order to determine the signal to buy or sell, the BPNN evaluates the following
function as a measure of wealth in future:n

Q p = ∑ ΔVp+n γ n .
n=0

ΔV = V (t p+n ) −V (t p+n−1 ), γ is a future discount factor (0 < γ < 1) and V is an evaluation function of investor’s assets. Here, ΔV > 0 signiﬁes that the investor’s wealthincreases as the price rise and ΔV < 0 signiﬁes that the investor’s wealth decreases as
the price decline. A decreasing price is a signal for applying a short-sale strategy. The
teacher signal tip is determined by Q p as follows:
tip = σ (Q p ),where σ is a sigmoid function with α = 0.5 × 10−6
σ (x) =

2− 1.
1 + exp(−αx)

The random player’s orders are based on the normal distribution:(x − μ)2
1
exp −,f (x, μ, σ ) = √
2σ 2
2πσ 2

(2.1)

where μ is the mean order and σ is its standard deviation. We used a Gaussian distribution, because we believe that this best approximates the value of the price bids andasks of random players. We assume that the probability that they decide to invest all of
their money is smaller than the probability that they invest only a part. If the standard
deviation is equal to half of a player’s working capital, it means that the probability
that they invest half of their wealth is around 70%. A positive value indicates buying and a negative value indicates selling. When this value is less than the minimumtransaction, a hold results. The minimum transaction was set at 100 shares.
Some of the random players use a buy-and-hold strategy. This simple approach
attempts to create proﬁt by only selling shares when the price is higher than it waswhen the shares were purchased. This is a common strategy for the average investor.

2.2

Simulation Model

There are two main phases in the simulations: credit scoring and taming the bubble.
1. Credit Scoring
In the ﬁrst step, we will formulate a credit-scoring schema to describe how credit
scoring is developed and in the second part, we will explain how bank uses credit
scoring.

5

Tristiyanto(a) Credit Scoring Schema
A credit score is a model that predicts whether an applicant will be able torepay a loan [12]. It transforms the relevant data pertaining to the applicant
into numerical measures that are used to guide credit decisions [4]. Credit
scoring is used to predict the investor status, which is determined fromtheir working capital (w(t)), deﬁned asw(t) = cash(t) + price(t) × share(t) - debt(t),t: time.

The investor status is classiﬁed as bankrupt, surviving, or proﬁtable. Investors are said to be bankrupt if and only if their working capital is lessthan or equal to zero. Investors are said to be proﬁtable if and only iftheir working capital has increased by at least 40% in the previous month(22 days). Investors are said to be surviving if their working capital isgreater than zero and less than 1.4 times their working capital in the previous month:⎧⎪⎪⎨ bankrupt, if (w(t) ≤ 0)
status = surviving, if (0 < w(t) < 1.4w(t − 22))⎪⎪⎩ proﬁtable, if (w(t) ≥ 1.4w(t − 22)).
To predict the status of investors, we used four well-known methods to develop credit scores. These methods include multiple discriminant analysis(MDA) from statistics, C4.5 from the ﬁeld of decision trees, resilient propagation neural networks (RPNN) and the support vector machine (SVM)from the ﬁeld of machine learning. Each of these methods used the following eight ratios to predict the status of investors.
i. (market value)/(total assets) = v1
ii. (proﬁt or loss)/(total assets) = v2iii. (liabilities)/(working capital) = v3
iv. (cash)/(working capital) = v4
v. (market value)/(working capital) = v5
vi. (proﬁt or loss)/(working capital) = v6
vii. (liabilities)/(total assets) = v7
viii. (cash)/(total assets) = v8
In the AI approach, we use a vector-valued function f (v) with eight arguments (v1 , . . . , v8 ). The output data are normalized to be in the range[−1, 1].
Y= (y1 , y2 , y3 ) = f (v1 , . . . , v8 ),−1 ≤ yi ≤ 1 (i = 1, 2, 3).(2.2)

6Bankruptcy Prediction on Margin Trading and Applications

Each output (yi + 1)/2 (i = 1, 2, 3) can be regarded as the probability ofinvestor status which is bankrupt, surviving and proﬁtable. The maximum
output of the prediction indicates whether the investor is bankrupt, surviving, or proﬁtable. The status of each investor is determined by⎧⎪⎪⎨ bankrupt, if (y1 = maxY )g(Y ) =

surviving,⎪⎪⎩ proﬁtable,

if (y2 = maxY )if (y3 = maxY ).

In the AI approach, the training data included bankrupt data, which included the values of eight variables for one week (ﬁve days) before bankruptcy; proﬁtable data, which included the values of eight variables forone month (22 days) before the proﬁt exceeded 40%; and surviving data,
which included the data of any surviving investors.
(b) Credit Scoring Application
When a loan is requested, the bank agent will check the investor’s creditscore. If the investor status is surviving or proﬁtable, then their loan proposal will be granted. If an investor is identiﬁed as bankrupt, the bankthen checks whether that investor’s working capital > debt. If true, thenthe player is considered likely to default and the bank agent will send apayback request that forces the sale of all of their assets in order to repay
the loan. The function for the bank’s action based on the investor status isloan,
if g( f (v)) = proﬁtable or g( f (v)) = survivingΦ=request pay back, if g( f (v)) = bankrupt.
If the investor’s working capital ≤ debt, the investor will be liquidated
and removed from the market. Liquidated means that all of the investor’scapital and stocks are used to pay the debt; the stocks are sold through themarket. If a liquidated investor cannot recover his debt, the bank loses its
money. This threshold for checking bankruptcy is called the margin ratio
and it is deﬁned as the value of the collateral over the total liabilities:
R(t) =(working capital).
(debt) + (interest)

If this is equal to unity, or the maximum debt of the player is equal to theworking capital, bankruptcy can be deﬁned as(total cash) + (total stocks market value)≤ 2.
(total debt)

Tristiyanto

7

2. Taming The Bubble
In the ﬁnal phase, we consider how a minimum margin adjustment can be used
to control the price movement in a bubble and then we replace it with credit
scoring. We then perform a simulation and analyze the impact of credit scoring
and loan adjustments on the price movement. Finally, we explore a strategy for
maintaining a bank’s reserves.
(a) Minimum margin evaluation
Minimum margin is minimum payment or collateral that investor has toprovide at a margin trading transaction. We compared the minimum margin to the credit score as a tool for identifying bankruptcy. We carried out
an experiment to calculate how many investors had been correctly or incorrectly classiﬁed either using minimum margin or credit scoring. The
result is presented in the Experiment 3.
(b) Margin trading with credit scoring
We analyzed the impact of credit scoring and loan amount adjustmentson the price movement in the simulation. We will compare four methods
for developing credit scoring and discuss loan absorption in Experiment 4.
Figure 1 provides an overview of the simulation model.

Figure 1: Overview the simulation model8

Bankruptcy Prediction on Margin Trading and Applications

3. Bank’s Reserve
We created a strategy for taming bubbles by comparing the simulation of a smart
bank to a non-smart bank when there are both static and dynamic reserves. A
smart bank is one that has already been trained or uses AI to evaluate loan requests; a non-smart bank is one that is not trained or that does not use credit
scoring. In the simulation, the smart banks used the AI method which had thebest accuracy in Experiment 1 and 2; this was the C4.5 decision tree method.
Static reserves are the resources that maintain a constant monetary value. A
bank’s static reserves depend on the total credit extended to all investors. Dynamic reserves are resources which depend on the total market value, which is
total number of investor’s shares × the market price. We consider the dynamic
reserves because some banks have enormous amounts of reserve capital; theircapitalization is higher than the margin-trading capitalization market. Thus, they
can provide reserve money as the total market value to be used in margin trading
and gain proﬁt from the interest.
The smart bank has the functions of credit scoring, bubble detection and loan
adjustment.
(a) Credit Scoring
In the simulation, the smart bank uses the AI approach for determining
credit scoring. The initial data for training is generated by using the resultof Experiment 3. When the market is closed in midnight, the artiﬁcial
intelligence is updated.
(b) Bubble Detection
Denote by ti the noon of i-th day in the trading period. Let S(t) be thestock price at the time t and R(ti ) the daily logarithmic return, that is,
R(ti ) = log S(ti ) − log S(ti−1 ). As a simpliﬁcation of Sornette’s method forbubble detection [33], we identify the bubble when B(ti ) ≥ 2, whereB(ti ) =EMA(ti , 5)
EMA(ti−5 , 5)

and EMA(ti , n) is the exponential moving average for n days. It can becalculated by the following recurrence relation and suitable initial value:
EMA(ti , n) = αR(ti ) + (1 − α)EMA(ti−1 , n),

α=

2
.
n+1

(c) Loan Adjustment
The ﬁnancing frame is a measure of how much leverage an investor canhave from their working capital. If the ﬁnancing frame is equal to one, itmeans that the maximum loan is equal to the working capital or collateral.

9

Tristiyanto

If the ﬁnancing frame is equal to 0.5, it means that the maximum loan ishalf of the working capital.
RM(t) =

(reserve money)(total loans)

⎧
⎪
⎪
⎨1,
ﬁnancing frame = 0,⎪⎪
⎩ 10 (RM(t) − 0.1),
6(RM(t) ≥ 0.7)
(RM(t) ≤ 0.1)
(otherwise)

It is essential to adjust the frame when a bubble occurs, which happens
when the price movement follows a pattern that is similar to a power-log
distribution. Restricting the loan in a heating market is beneﬁcial for decreasing liquidity in the market. If a bubble is detected, the bank can restrict the average investor loan based on Y , as deﬁned in equation 2.2 andmaintain a proﬁtable investor leverage. That is, the previous ﬁnancing
frame is replaced by⎧⎪
1,(g( f (v)) = proﬁtable)⎪⎪⎪⎨ 1 (y − y ),(g( f (v)) = surviving and y1 ≥ y3 )21
ﬁnancing frame = 2 1⎪1 − (y2 − y3 ), (g( f (v)) = surviving and y1 < y3 )
⎪
2
⎪
⎪
⎩
0,
(g( f (v)) = bankrupt)
Here f (v) = (y1 , y2 , y3 ).

3Classiﬁcation Methods

In this section, we present a concise summary of the fundamental theory of each of thefour methods that we used to create our credit score. These methods are all commonlyused in current credit-scoring research [20]. One of these is a statistical method (multiple discriminant analysis) and the other three methods are from the ﬁeld of artiﬁcial
intelligence (the C4.5 algorithm, RPNN and support vector machines).

3.1

Discriminant Analysis

Multiple discriminant analysis is an extension of linear discriminant analysis (LDA),
which was invented by Ronald A. Fisher in 1936 [13] for classifying data into morethan two classes. LDA assumes a standard distribution of classes or that the classes
have equal covariance and it searches for the linear combination of variables that best
separates the classes. Fisher solved this problem by ﬁnding a linear function thatmaximizes the distance between the means of the various classes but minimizes the

10Bankruptcy Prediction on Margin Trading and Applications

variance of each class. The result of Fisher’s LDA is equal to that of a least-squares
problem or a linear regression classiﬁcation [38]. It was also shown by Duda et al. [11].
In 1968, Edward I. Altman discovered a formula that uses Fisher’s LDA to predict corporate bankruptcy. His work was developed from William Beaver’s researchon bankruptcy prediction, which used univariate analysis of an accounting ratio. Instead of using the t-test to evaluate each ratio, Altman applied discriminant analysis
to multiple variables concurrently [2]. He chooses ﬁve ratios, each from a different
category: liquidity, solvency, proﬁtability, leverage and activity; this combination wasshown to be able to predict bankruptcy with statistical signiﬁcance. The ﬁve ratios thatwere chosen as predictors are X1 : (working capital)/(total assets); X2 : (retained earnings)/(total assets); X3 : (earnings before interest and taxes)/(total assets); X4 : (market
value of equity)/(book value of total liabilities); and X5 : (sales)/(total assets). The
Z-score formula is Z = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4 + 0.009X5 . A scoreabove 3.0 means that it is unlikely that the company will go bankrupt and a score below
1.8 means that it is likely to do so. Although the initial test showed that the accuracy
is around 72% for the predicting bankruptcy within two years, Altman’s Z-score is theleading model. In 1999, further research by Altman considered more ﬁrms and used
more recent data and the accuracy was shown to have increased to approximately 80%90%. The improvement of the Z-score formula has resulted in its use as a bankruptcy
prediction tool in other business sectors, such as private ﬁrms, non-manufacturers andemerging markets [3].
Altman’s Z-score cannot be used for lending decisions for margin trading because
it is difﬁcult to calculate the Z-score for each investor; in particular, it is difﬁcult to
calculate X4 , the (market value)/(total liabilities). If the total liability is zero, then
X4 will be undeﬁned and if the total liability is much smaller than the stock market
value, X4 will be excessively large and will overwhelm all of the other information.
Moreover, for individuals, the variables X1 , X2 and X3 measure almost the same thing,namely, proﬁt per total asset. Although it can be calculated, the Z-score is not valid formaking predictions. However, its principle still can be implemented to create a creditscore for margin trading. Bankruptcy can be predicted by assessing ﬁnancial ratios
which have signiﬁcant correlation with the outcome.
Our Z-score function is deﬁned by a linear form of eight ﬁnancial ratios v1 , . . . , v8
as follows:
Z = α, v = α1 v1 + α2 v2 + · · · + α8 v8 ,where v = (v1 , v2 , . . . , v8 ) and α = (α1 , α2 , . . . , α8 ) . We classify samples into threeclasses those are bankrupt, surviving and proﬁtable. Then the coefﬁcients α for eachclass are determined by using Fisher’s LDA. Let μi be the mean and σi the standard
deviation for each class. The Z-score for each class can be interpreted to the probability

11

Tristiyantodensity of investor status as follows:
Ni (Z) =(Z − μi )2
exp −
2σi2
2πσi2
1


.

Hence, we can translate the Z-score function into the AI function f (v).

3.2

Resilient Propagation Neural Network

Recently, artiﬁcial neural networks have become a practical technology for ﬁnancial
industries [1]. Many ﬁnancial applications can exploit the strength of neural networks;
these include determining credit card fraud, evaluating mortgage applications, predicting bankruptcy and option pricing [14]. We developed a neural network which consistsof three layers: an eight-node input layer, a ﬁve-node hidden layer and a three-node
output layer (the three output nodes represent the three classes). A sigmoid transfer
function is used for each node. Because of its fast performance, we used the resilient
propagation neural network (RProp) as the learning algorithm; it was created by Martin Riedmiller and Heinrich Braun in 1992 [30]. RProp uses batch updates to obtain
the gradient of each weight. The sign of the gradient is then used to estimate the direction in which the weight is updated. The update value, delta, is not ﬁxed. Thechanging sign of the gradient is used to adjust delta so that the speed of the training
can increase [18].
The initial step size was 0.1, the coefﬁcients for changing Δ were η + = 1.2 and−η = 1.2 and the boundaries on delta were Δmax = 50 and Δmin = 10−6 .

3.3

C4.5

A decision tree is a graph-like structure which consists of nodes as test variables andbranches as test results; a leaf node is a class label [21]. The ﬁrst node is called the root.
A decision tree is a nonlinear discrimination method which uses a set of independent
properties to split data into progressively smaller subgroups [8]. Decision trees are
popular classiﬁcation algorithms because they can be intuitively explained [27]. In
this study, we used only C4.5, because it is free and it performs well, as shown in
a comparative study [27]. C4.5 was invented by Ross Quinlan [29] for generating
decision trees using a divide-and-conquer technique. In order to divide and conquer
the data, C4.5 uses the concept of information entropy; this entropy is used to quantify
how informative a variable is when it is used to separate the data. The gain principle
is used to select which attribute is to be split at any given node. However, when thiscriterion is used to determine the node splits, the algorithm tends to create leafs for
attributes with many distinct values. In order to rectify this, the C4.5 normalizes thedata and uses a gain-ratio criterion. To reduce the error, the tree continues to grow12

Bankruptcy Prediction on Margin Trading and Applications

bigger and this can lead to overﬁtting. To reduce overﬁtting, pruning is used. Pruning
is a technique for removing a leaf for which the power to classify has only a small
signiﬁcance. The threshold for pruning is called the conﬁdence factor and its value isbetween 0 and 1. Lowering the threshold results in more pruning and a more generaltree. We used a conﬁdence factor of 0.25 in this study.

3.4

Support Vector Machine

The support vector machine (SVM) was invented by Boser, Guyon and Vapnik in
1992 [5]. They combined the margin hyperplane and the kernel method for discriminating between two groups in the data. The margin hyperplane is used as a linear
classiﬁer when nonlinear data are treated by a kernel trick to manipulate the domainfunction into a higher-dimensional space. The essence of the SVM is to ﬁnd the best
hyperplane as a classiﬁer of two classes in the input space, for example, the surviving
class (+1) and the bankrupt class (−1). The best hyperplane between those classes
can be computed by ﬁnding their maximum margin hyperplane. The margin is theclosest distance between two classes. In some cases, it is hard to use a hyperplane toseparate samples completely. The samples must be transformed into a higher feature
space by a kernel function K(xxi , x j ) [17]. There are several types of kernel functions,
including linear, polynomial, sigmoid functions, exponential radial basis functionsand Gaussian radial basis function. We use a Gaussian radial basis function kernel,
K(xxi , x j ) = exp −γxxi − x j 2 , to implement our SVM credit scoring method, because the data are not linear and the classiﬁcation problem has three classes (bankrupt,
surviving and proﬁtable). We used the LIBSVM library created by Chang and Lin [7],with the default parameter settings and γ = 1/8.

4Credit Scoring

To avoid making risky loans, a bank must be able to identify appropriate investors. We
propose a credit-scoring method that ﬁlters out risky investors. We compare creditscoring methods to ﬁnd the best average performance. We then use the best method toprevent bubbles from bursting. In this ﬁrst part of the experiment, we implemented thefour methods (MDA, RPNN, C4.5 and SVM) to create a credit score. These methods
were then tested with several market conditions.
Let us assume we are assessing a credit proposal. The result of our evaluation canbe positive (approved) or negative (rejected). We will say that a correct prediction istrue and an incorrect one is false. An enhanced credit score should maximize the truecases and screen out the false ones [32]. We will use confusion matrix Table 1 to assess
the performance of our credit score:
We introduce basic terminology of confusion matrix as follows:

13

Tristiyanto

Table 1: Confusion Matrix [32]Approved
Loan Approval

Rejected

Survive Investor
True Positive(TP)
False Negative(FN)
Sensitivity= TP / (TP+FN)

Bankrupt Investor
False Positive(FP)
True Negative(TN)
Speciﬁcity= TN / (TN+FP)

True positive : number of investors correctly approved.
True negative : number of investors correctly rejected.
False positive : number of investors incorrectly approved.
False negative : number of investors incorrectly rejected.
Misclassiﬁed : number of investors assigned to wrong class; false positive + false
negative.
Sensitivity or recall : probability of being correctly approved, given that it is a goodﬁnancial investor [28]; (true positive)/(true positive + false negative).
Speciﬁcity : probability of being correctly rejected, given that it is a poor ﬁnancial
investor [28]; (true negative)/(true negative + false positive).
Accuracy : probability of being correctly predicted [28]; (true positive + true negative)/population.
Precision : proportion of correctly approved to total approved [28]; (true positive)/(true positive + false positive).
F-Score : it combines positive predictive value with the rate of true positives [28]; 2(precision × recall) / (precision + recall).
Experiment 1 (Credit scoring performance with various random normal settings). After creating our credit-scoring methods, it is necessary to test their robustness in various market conditions. Six scenarios were considered. Each scenario consists of 100
simulations; each of these was populated by 100 bankrupt investors, 100 surviving
investors and 100 proﬁtable investors. Ten-fold cross-validation was used for eachcredit scoring method in each simulation. All investors have 3 million JPY as their initial working capital. The basic assumption is that the scenarios are in a free market inwhich many players are able to trade. Thus, any one action by a player has no impact
on the equilibrium price. All decisions to buy, sell, or hold and their order volumes
are based on a normal distribution.

14

Bankruptcy Prediction on Margin Trading and Applications(a) μ = 0, σ = 3 million
JPY(b) μ = 0, σ = 1.5 million
JPY(c) μ = 0, σ = 4.5 million
JPY(d) μ = 0, σ = 6 million
JPY(e) μ = 1.5 million JPY,
σ = 3 million JPY(f) μ = −1.5 million JPY,
σ = 3 million JPY

Figure 2: Probability density function of order value for six different market behaviors

Figure 2 presents six different player behaviors and shows the probability density
functions (pdf) of the order values for each player in each scenario. Positive values
are buying orders and negative ones are selling orders. Both are shown in units ofone million JPY. The maximum purchase order is cash multiplied by leverage and the
maximum sell order is the amount of stock that the player owns. A hold occurs if theabsolute value of the order is less than 100 times the current stock price.
Figure 2a shows an example pdf for a player order decision with mean 0 and standard deviation 3 million JPY. This means that approximately 70% of the order value
is less than 3 million. The purchase order is greater than the leverage multiplied bytheir cash and it is set to buy the maximum possible for the given cash and leverage.
Note that a sell order that exceeded the stock value results in the sale of all the stocks.
Figure 2b shows the behavior of a player in a stressful market condition, so the order

15

Tristiyanto

is placed very carefully. The order is expressed as half a standard deviation of theworking capital and in this example, that is 1.5 million JPY. This means that 95% of
this order will not exceed their working capital. Figures 2c and 2d show a situation inwhich a player fully uses a loan and sells all their stocks, respectively. Around 70%of the transactions would be less than 4.5 million for Figure 2c and 6 million for Figure 2d. Figure 2e shows a player who tends to buy, while Figure 2f shows a player
who tends to sell.
Tables 2 and 3 show the average of each of the six scenarios. The results demonstrate that the artiﬁcial intelligence methods perform better than the statistical method
and among the artiﬁcial intelligence methods, there are only slight performance differences. The SVM had the highest accuracy, which exceeded that of the C.45 decision
tree by only by 0.148% in accuracy and 0.005 for the F-score. However, the C4.5
decision tree had the most success in predicting proﬁt; it had an average accuracy
69.547%, while the proﬁt accuracy of the SVM was 67.707%.

Table 2: Average Prediction Result for Normal Distribution

XXX
ActualXXX
BankruptXX
XXX
Predicted
X

MDA

C4.5

RPNN

SVM

Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable

96.988%1.523%
15.560%98.912%0.0%
0.0 %99.438%0.018%
0.200%
100%
2.703%
0.942%

Surviving

Proﬁtable

0.027%
72.643%34.263%0.740%
73.060%30.453%0.182%
72.878%32.267%0%75.133%31.352%2.980%
25.833%50.177%0.348%
26.940%69.547%0.380%
27.120%67.533%0.0%
22.163%67.707%

Accuracy
73.270%80.506%79.950%80.654%

Table 3: Average Performance of Credit Scoring with Normal Distribution
MDA
C4.5
RPNN
SVM

Sensitivity
0.733
0.805
0.800
0.810

Speciﬁcity
0.866
0.902
0.900
0.905

Precision
0.727
0.816
0.802
0.811

FScore
0.719
0.801
0.799
0.806

16

Bankruptcy Prediction on Margin Trading and Applications

Experiment 2 (Credit scoring performance with uniform probability random behavior). In order to evaluate the robustness of the credit scoring methods, we tested themin a market situation in which the investors trade randomly. We performed 300 simulations, each of which was populated by 100 bankrupt investors, 100 surviving investors and 100 proﬁtable investors. Each simulation was evaluated using ten-foldcross-validation. Using fewer investor and running only 300 simulations gave a morereliable result. All of the decisions in this experiment were randomly selected from a
uniform probability distribution.
The average percentages of the predictions are shown in Table 4. The C4.5 decision
tree had the highest score for accuracy (79.478%), followed by the SVM, the RPNN
and last, the MDA (78.645%, 76.499% and 71.874%, respectively). The harmonicmean of the true positive and true negative rates for the credit scoring methods areshown in Table 5 and these are not signiﬁcantly different from the results of the ﬁrst
Table 4: Prediction Result from 300 Simulations of Uniform Probability Random Behavior
XXX
ActualXXX
BankruptXX
XXX
Predicted
X

MDA

C4.5

RPNN

SVM

Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable

99.567%0.897%
0.183%
98.973%0.0%
0.0
99.753%0.046%
0.003%
99.16%
0.453%
0.036%

Surviving

Proﬁtable

0.107%
55.673%39.433%0.767%
59.423%19.963%0.143%
59.953%30.206%0.84%
55.183%18.37%

0.327%
43.433%60.383%0.26%
40.57780.0360.103%
40.0%
69.79%
0.0%
44.363%81.593%

Accuracy
71.874%79.478%76.499%78.645%

Table 5: Average Performance of Credit Scoring with Uniform Probability
MDA
C4.5
RPNN
SVM

Sensitivity
0.719
0.795
0.765
0.786

Speciﬁcity
0.859
0.897
0.882
0.893

Precision
0.720
0.812
0.769
0.799

FScore
0.716
0.789
0.763
0.782

Tristiyanto

17

experiment. The machine learning methods outperform the statistical MDA method.
The decision tree performed better in every aspect that was being measured: accuracy,
sensitivity, speciﬁcity, precision and F-score. The decision tree showed human-likereasoning, as did the MDA, while the RPNN and SVM worked like black boxes.

5

Taming the Bubble

Bubble prices burst because some players with signiﬁcant market wealth go bankrupt.
The market is then ﬂooded. As other players ask for lower prices, prices sink to lower
levels. To show the impact of bubble prices when credit scoring in not used, we constructed a simulation to demonstrate this event. We populated the simulation with ten
AI players, each of whom owned 10,000 shares, had 10 million JPY in cash and wasable to take out a loan. We also populated it with 100 random players, each of whom
owned 1000 shares, had 1 million JPY in cash and was not able to take out a loan.
Note that these settings were also used in Experiment 4 and 5.
Figure 5a illustrates a bursting bubble. In this simulation, nine of ten AI players
go bankrupt since they cannot repay their loans on their due dates. Since they haveaccumulated most of the market wealth, their bankruptcy bursts the price. As can beseen in Figure 6a, the total market value drops from 250 million JPY to 3 million JPY.
This simulation is based on Nakatani’s work [23], in which the bank agent checks only
the ratio of debt to the working capital; that is, if an investor’s debt is greater than theirworking capital, they are bankrupt and are liquidated from the stock market.
Regulators create a minimum margin in order to mitigate the risk, since the collateral value will drop as the price collapses. However, setting a minimum price also
creates a barrier for liquidity and maintaining the price, because some good investors
will have already stepped out of the market. We evaluate the effectiveness of thisminimum margin in Experiment 3. In Experiment 4, we analyze a simulation of margin trading that uses credit scoring and in Experiment 5, we create a bank strategy
for taming bursting bubbles. Again, ten AI players were used and they had the same
capitalization as the 100 random players. Because they can each receive a loan, thecapitalization of the AI players is double that of the random players. The bankruptcy
of an AI player will have a signiﬁcant impact on the price movement.
Experiment 3 (Minimum margin evaluation). We investigated the consequences ofadjusting the minimum margin in the market. We wanted to determine how many
investors would survive but be forced to liquidate. We simulated margin trading byusing n investors with random behaviors for the period [0, T ] and deﬁned the positionof i-th investor at t = T with respect to minimum margin as follows:

18

Bankruptcy Prediction on Margin Trading and Applications⎧⎪⎪⎨bankrupt, (wi (T ) ≤ β wi (0))
position = proﬁtable, (wi (T ) > β wi (0) and wi (T ) ≥ 1.4wi (T − 22))⎪⎪⎩surviving, (otherwise)
where wi (t) is the working capital of i-th investor at time t, the parameter β signiﬁes minimum margin ratio. The investor position and status coincide if β = 0. We
increased the parameter and counted positions of investors.
Put T = 300 days and n = 6347. Table 6 shows the number of investors that gobankrupt or other positions with various minimum margins. We also calculated the differences, which is called misclassiﬁcation, between investor position and status. Whenthe minimum margin increases, misclassiﬁcation also grows. In the USA, the margin
trading market has the minimum margin set at 50% and in Japan, the Tokyo Stock Exchange (TSE) market is set at 30%. In this experiment, 314 surviving investors and 215
proﬁtable investors were misclassiﬁed as bankrupt when the minimum margin was set
at 30%. On the other hand, 603 proﬁting investors and 660 surviving investors weremisclassiﬁed as bankrupt. By setting the minimum margin at 50%, the system alreadyscreens out 20% of the investors. It is almost half of the investors who likely gain
proﬁt more than 40% within a month. Of the total population, 9.5% was misjudged asbankrupt and it is equal to 38.97% of the proﬁtable investors.
Table 6: Number of Investor Position when Minimum Margin is Adjusted
βBankrupt
Surviving
Proﬁtable
Misclassiﬁcation

0
2400
2400
1547
0

0.1
2402
2398
1547
2

0.2
2417
2385
1545
17

0.3
2929
2086
1332
529

0.4
3329
1944
1074
929

0.5
3663
1740
944
1263

0.6
3847
1625
875
1447

0.7
3994
1542
811
1594

0.8
4098
1479
770
1698

For comparison, we developed a credit scoring and predicted investor condition.
Table 7 shows the prediction accuracy of each of the four methods. Ten-fold crossvalidation was used to measure the accuracy.
From Table 8, it can be seen that the SVM outperformed the other methods for proﬁt
and bankrupt predictions by 0.005 and 0.019, respectively (compared to the lowest).
Unfortunately, it was the worst at predicting surviving investors. The MDA was thebest at predicting surviving investors (by 0.034 over the lowest performance), but did
not perform well when predicting bankrupt and proﬁtable investors. There are only
slight differences among the predictions of the MDA, C4.5, RPNN and SVM when it
came to predicting bankruptcy in these experiments.
When credit scoring is used, there are fewer misclassiﬁcation of proﬁting investors;
the fewest misclassiﬁcations occurred with C4.5 and the SVM, with misclassiﬁcation

19

Tristiyanto

XXX

Table 7: Predictions when using Credit Scoring

ActualXXX
BankruptXX
XXX
Predicted
X

MDA

C4.5

RPNN

SVM

Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable

2047
761
13
2152
854
4
2213
928
13
2047
1013
0

Surviving

Proﬁtable

353
1634
14
248
1543
16
187
1471
15
110
1387
18

0
5
1520
0
3
1527
0
1
1519
0
5
1529

Accuracy
81.9442%82.2751%

81.9757%

82.023%

Table 8: Benchmarking Credit Scoring

MDA

C4.5

RPNN

SVM

Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable
Bankrupt
Surviving
Proﬁtable

Sensitivity
0.853
0.681
0.983
0.897
0.643
0.987
0.922
0.613
0.982
0.954
0.578
0.988

Speciﬁcity
0.891
0.909
0.911
0.783
0.933
0.999
0.762
0.949
0.999
0.743
0.968
1

Precision
0.726
0.817
0.997
0.715
0.854
0.998
0.702
0.879
0.999
0.693
0.916
1

FScore
0.784
0.743
0.989
0.796
0.734
0.993
0.797
0.722
0.991
0.803
0.709
0.994

of only 20 and 18 investors, respectively. By adjusting the minimum margin, misclassiﬁcation of 20 investors are between 20% and 30%. However, the error predictions
for bankrupt and surviving players varied quite signiﬁcantly. The best performance
was that of the SVM, which misclassiﬁed 110 bankrupt and 1013 surviving players. If
we combine the minimum margin regulation with credit scoring, we obtain a condition
where the minimum margin can be set to a minimal value, but the surviving and prof-

20

Bankruptcy Prediction on Margin Trading and Applications

itable investors are able to maintain the prices even in a bubble-bursting condition. To
test the effectiveness of the credit scoring method, we executed a simulation of margin
trading with credit scoring as Experiment 4.
Experiment 4 (Margin trading with credit scoring). To investigate the effectivenessof our credit-scoring method for controlling a bubble, we carried out a simulation inwhich our credit-scoring method was implemented by a bank agent. We created ten
AI players who each had 10,000 shares, 10 million JPY in cash and the ability toreceive a loan. We also created 100 random players who each had 1000 shares, 1
million JPY in cash and did not have the ability to receive a loan. We assessed theimpact on the price movement of credit scoring the loan applications. Credit scoring
evaluate investors by considering their working capital, their debts and their proﬁt
performance. This screens out risky players and seeks repayment from them at an
earlier time so they will not cause the market to collapse; at the same time, it gives
leverage to healthy proﬁtable investors. Figure 3 shows the results of some simulations
using various methods of credit scoring.
The results shown in Figure 3 conﬁrm that all of our credit-scoring methods had
similar accuracy. The least accurate method (MDA) failed to recognize one proﬁting
investor, and so its price movement is slightly lower than that of the other methods.
The RPNN, SVM and C4.5 had almost identical price movements.
Credit scoring also resulted in good credit absorption for the bank’s main business,
as shown in Figure 4. However, on some timelines, the reserve value exposed the bankto a lack of cash for ﬁnancing the players. The bank had negative cash at times 896
and 13,896. When there are inadequate reserves, banks can obtain loans from otherbanks and they can reject all new loans; they can also adjust the ﬁnancing frame tolimit the total debt owed to the players. The ﬁnancing frame will be explained in thenext experiment.
Experiment 5 (Bank’s reserves). We examined the impact on the price movement
when the bank’s reserves are controlled. In the previous experiment, we conﬁrmed thatloans will increase the stock price. By controlling the reserves, the bank can adjust theliquidity of the market. We wanted to ﬁnd out whether controlling the reserves would
inﬂuence the price movement. We performed some simulations to compare a smart
bank with a non-smart bank and with static and dynamic reserves.
Figure 5 illustrates some price movements for various bank reserve strategies andFigure 6 shows the bank reserves during a transaction. A non-smart bank with a static
reserve strategy will cause a price collapse and if it uses a dynamic strategy, the pricewill soar rapidly and then collapse. This shows that increasing either the cash invested
in the market or the liquidity of the market will increase the price and create a bubble.
Limiting the amount of cash will also have a tendency to cause a collapse. When thereserves are gone, the bank is in a dangerous position.

21

Tristiyanto(a) MDA(b) RPNN(c) SVM(d) C4.5 (Decision Tree)

Figure 3: Price Movement with Various Credit-Scoring Methods

Figure 4: Credit absorbing using credit scoring22

Bankruptcy Prediction on Margin Trading and Applications(a) Non-smart Bank with Static Reserves(b) Smart Bank with Static Reserves(c) Non-smart Bank with Dynamic Reserves(d) Smart Bank with Dynamic Reserves

Figure 5: Comparison of Price Movement between Smart and Non-Smart Banks with
Static and Dynamic Reserves

A smart bank can maintain the price movement. When the reserves are limited, theloans will be restricted. Thus, the prices will decrease slightly. After the reserves are
reﬁlled by credit repayments, the bank can relax the loans and the prices will increase.
This runs in a continuous cycle. When the bank has large cash deposits, the prices
increase steadily. The bank maintains market liquidity by assessing the credit scoresof investors.
When the reserves are unlimited, it depends on the total value of the stock market.
It is called the money creation. In this case, the smart bank can also predict the bubble
phenomena and maintains market liquidity by assessing the credit scores of investors.

23

Tristiyanto(a) Non-smart Bank with Static Reserves(b) Smart Bank with Static Reserves(c) Non-smart Bank with Dynamic Reserves(d) Smart Bank with Dynamic Reserves

Figure 6: Comparison of Reserves between Smart and Non-Smart Banks with Staticand Dynamic Reserves

6

Conclusion

We have developed a new method for ﬁltering credit requests. The accuracies of thepredictions are above 80% and thus our method for credit scoring for margin trading
can be used to manage and quantify risk. We also implemented credit scoring in our
simulation program. The results of the experiments show that credit scoring can prevent the market crashes by allowing good investors to maintain credit absorption. The
ﬁnancing frame can be adjusted to slow the rate of price increases, since it can be used
to detect bubbles and to monitor the bank’s reserves. In general, prices rise when there
is growing demand and they drop when there is excess supply. Restricting the entire
market heightens the effect of a crash, since the market needs capital in order to maintain the price. In this study, we investigated four methods for creating a credit score;24

Bankruptcy Prediction on Margin Trading and Applications

one of these methods was from statistics (discriminant method) and the other threewere from the ﬁeld of artiﬁcial intelligence. The accuracy of the artiﬁcial intelligence
methods was better than that of the statistical method, but the statistical method gave
more logical reasons for approving loans.
We have created a new strategy that banks can use to tame price bubbles. We
investigated several strategies for managing reserves and we investigated how each ofthem inﬂuenced price movement. We found that a smart bank with a dynamic reserve
policy can prevent a price collapse and maintain market liquidity.
Future research should aim at improving the accuracy of predicting good investors
and quantifying the risk of bankrupt investors. Risk management by hedging potential
defaulted loans is another potential area of study.

Acknowledgements
The author would like to express his deep gratitude to Professor Katsuyoshi Ohara forhis support, encouragement and guidance. The author also would like to thank the
Directorate General of Higher Education, Ministry of Education and Culture of the
Republic of Indonesia (DIKTI) for ﬁnancial support.

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