Predicting Bankrupty using Tabu Search in the Mauritian Context
Paper Presenter: Kawthur Lallmamode
Authors: Kawthur Lallmamode, Jayrani Cheeneebash, Ashvin Gopaul
In this paper we apply the Tabu search variable selection model (ref) to a group of both
public and private firms to predict bankruptcy. This algorithm is an extremely efficient
means for selecting a subset of variables from the whole set of explanatory variables
under consideration and it can be applied to problems in finance. Bankruptcy is the state
of a firm or corporation being unable to repay its debts whereby it legally declares its
inability to continue business. The occurrence of business failure all round the world is in
constant rise, whereby statistics shows that in US itself, there are more than thirty
companies which go out of business every week. Being able to predict bankruptcy, if ever
it is to occur, for any firm, is of great importance to the enterprise and other related
enterprises.
Different bankruptcy and scoring models have tried to better illustrate the concept of
predicting business failure since the literature about bankruptcy prediction and scoring
models is very extensive. Some of them is, the cash flow models, the Altman Z-score
models, the loss on default bank loans, the credit scoring and the Lehman Brothers
mortgage default model.
In order to predict bankruptcy the Tabu search method is applied. Tabu search is defined
as a meta-heuristic that guides a local heuristics procedure to explore the solution space
beyond local optimality. It is also viewed as a mathematical optimization method
belonging to the class of local search technique whereby it enhances the performance of a
local search method from the usage of memory structures. It is based on the premises that
problem solving in order to be qualified as intelligent must include both adaptive memory
and responsive exploration. The adaptive memory feature suggests the importance of
analyzing current alternatives in relation to previous ascents of similar situation allowing
the implementation of procedures that are capable of searching the solution space
effectively. On the other hand, the responsive exploration integrates the basic principles
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of intelligent search while exploiting good solution feature from exploring new promising
regions.
Tabu search has its application in many field namely, scheduling design,
telecommunications, logic and artificial intelligence, routing, graph optimization and
financial analysis. The Tabu search for multiple regression analysis requires seven
definitions and parameters elaborated below.
Firstly, one criteria for the selection of independent variables with the lowest significance
level for the correlation coefficient R 2 , for the subset selected from among all possible
subsets. The significance level can be calculated by the F-probability distribution using
the following formula
F p ,n  p 1 
R p2 p
(1  R p2 ) (n  p  1)
,
p being the number of
independent variables, n being the number of observations, R 2  R Rnp , where R is
the determinant of the correlation matrix including the independent variable and the
denominator represents the determinant of the correlation matrix of p independent
variables.
Secondly, a definition of the neighborhood is required. The neighborhood of the current
solution is defined as all subsets of the current solution with one additional variable, one
variable less and those subsets for which one current variable is swapped by one not in
the current solution set of variable. Given a total of k independent variable under
consideration and p  k , a current (solution) subset of p independent variable has a
neighborhood size equal to k  p possible additions, plus p possible removals plus
p(k  p) possible replacements equating to a total size of k  p (k  p ) subsets. Thirdly,
the starting solution is obtained by applying an algorithm, which resembles the maximum
R 2 improvement approach.
Following the starting solution, we have the tabu list and tabu size. The tabu list contains
a list of variables, which are not permitted to be used in a move, whereby a move is
adding, removing or swapping a variable. Whenever the length of the tabu list exceeds
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the tabu size, the original member of the tabu list is discarded in a First In First Out
manner.
We always start with an empty tabu list and with a new best solution obtained the tabu
list is emptied. Next to the tabu list, a move within the neighborhood is admissible if the
variables involved in the move are not in the tabu list, thus the admissible set. Finally we
have the search parameters and the stopping criterion. The search parameters are the tabu
size which is set in advance. The tabu size is calculated as being greater than 10% of the
neighborhood size, thus giving a tabu size of 7. The stopping criterion is set to a number
of 30 iterations. The procedure ends when 30 consecutive tabu search does not produce a
new best solution.
The prediction of bankruptcy using Tabu search is applied in the Mauritian context. Data
for twenty companies was collected from the Registrar of companies. For confidentiality
purpose neither the 20 company names, nor the years for which data was taken, will be
given. The data collected consisted of 10 bankrupt companies. The year of reference is
set to a general T value and data collected is done for T-1 and T-2 years, that is, for one
year prior to bankruptcy T-1 and two years prior to bankruptcy T-2.
The following information was required from each company’s annual report:
1.CURRENT ASSETS
2. CURRENT LIABILITIES
3. INVENTORIES
4. RECEIVABLES
5. INTESREST CHARGES
6. DEBT (LOAN)
7. SALES
8. RETAINED EARNINGS
9. CAPITAL
10. PRICE PER SHARES
11. NET PROFIT MARGIN
AFTER TAX
12. OPERATING EXPENSES
13. EARNINGS PER
SHARES
14. SHARE CAPITAL
15. RETURN ON TOTAL
ASSETS
16. DEBT DUE (LOAN WITHIN
ONE YEAR)
17. MARKET PRICE PER
SHARE
18. TOTAL ASSETS
19. BOOK VALUE PER SHARE
20. SHARES OUTSTANDING
21. MARKET VALUE OF
EQUITY
22. SHAREHOLDER'S EQUITY
23. RETURN ON EQUITY
24. NET FIXED ASSETS (NONCURRENT ASSETS)
25. EARNINGS BEFORE
INTEREST AND TAX
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The following panel represent the initial set of independent variable which is required as
to obtain those variable selected by the Tabu search needed to create the Tabu prediction
score equation.
The Tabu code is run for all the T-1 and T-2 years for both the bankrupt and nonbankrupt firms with 40 observations and the following two variables was selected:
(i) ALT5 = TOTAL ASSETS TURNOVER and
(ii) INV X = INVENTORY TURNOVER.
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SIZE : MARKET
VALUE OF EQUITY
2
ALT1
3
4
ALT2
ALT3 : BASIC
EARNING POWER
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6
7
ALT4
ALT5 : TOTAL
ASSETS TURNOVER
CR : CURRENT
RATIO
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9
10
11
12
QR : QUICK RATIO
INV X : INVENTORY
TURNOVER
DSO : DAYS SALES
OUTSTANDING
FAT : FIXED ASSETS
TURNOVER
CAP REQ : CAPITAL
REQUIREMENT
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14
15
16
DEBT : DEBT RATIO
TIE : TIMEINTEREST EARNED
NOPAT : NET
OPERATING PROFIT
(MARGIN) AFTER
TAXES
PM : PROFIT
MARGIN ON SALES
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ROA : RETURN ON
TOTAL ASSETS
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ROE : RETURN ON
EQUITY
SHARES OUTSTANDING *
PRICE PER SHARES
WORKING CAPITAL /
TOTAL ASSETS
RETAINED EARNINGS /
TOTAL ASSETS
EBIT / TOTAL ASSETS
MARKET VALUE OF
EQUITY / BOOK VALUE
OF DEBT
SALES / TOTAL ASSETS
CURRENT ASSETS /
CURRENT LIABILITIES
(CURRENT ASSETS INVENTORIES) /
CURRENT LIABILITIES
SALES / INVENTORIES
RECEIVABLES /
(ANNUAL SALES / 360)
SALES / NET FIXED
ASSETS
OPERATING CAPITAL /
SALES
TOTAL DEBT / TOTAL
ASSETS
EBIT / INTEREST
CHARGES
EBIT ( 1 - T) / SALES
EBIT / SALES
NET INCOME
AVAILABLE TO
SHAREHOLDERS /
TOTAL ASSETS
NET INCOME
AVAILABLE TO
SHAREHOLDERS /
COMMON EQUITY
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PE : PRICE EARNING
RATIO
CD OBL : CURRENT
DEBT OBLIGATION
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20
21
MB : MARKET-TOBOOK RATIO
PRICE PER SHARE /
EARNINGS PER SHARE
DEBT DUE IN ONE
YEAR / SIZE
MARKET PRICE PER
SHARE / BOOK VALUE
PER SHARE
We note that the dependent variable is a dummy variable set to 0 for non-bankrupt firms
and 1 for bankrupt firm. The same data set with T-1 under consideration for both
bankrupt and non-bankrupt with 20 observations for each variable produces the following
selected five variables:
(i)
ALT2 = RETAINED EARNINGS / TOTAL ASSETS,
(ii)
QR : QUICK RATIO,
(iii)
DSO : DAYS SALES OUTSTANDING,
(iv)
DEBT : DEBT RATIO, and
(v)
PE: PRICE EARNING RATIO.
For T-2 year of reference for both type of firms with 20 observations the following 5
variables was selected:
(i)
ALT1= WORKING CAPITAL / TOTAL ASSETS,
(ii)
ALT2 = RETAINED EARNINGS / TOTAL ASSETS,
(iii)
INV X = INVENTORY TURNOVER,
(iv)
DSO : DAYS SALES OUTSTANDING, and
(v)
DEBT: DEBT RATIO.
Through out this analysis the Tabu prediction score was compared with the Altman Zscore prediction value, and it proves to be a better predictor of bankruptcy. The Tabu
search proves to be an efficient and effective way of selecting variable for scoring and
bankruptcy models in corporate, personal and real estate finance. Moreover, the
attractiveness behind the use of Tabu search is that its implementation is quite
straightforward and the results are outstanding.
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