1. Superior University, Lahore.
Assignment
Of
“QUANTITATIVE TECHNIQUE IN BUSINESS”
Presented to: SIR AMIR BASHIR
Presented by: Group “Supereye”
MUBEEN ABDUR REHMAN MCE 12151
SALMAN ANJUM MCE 12157
HAFIZ ASHFAQ SALAMAT MCE 12155
ZOHAIB AHMAD MCE 12152
SHABAN CHEEMA MCE 12169
MUTAHIR BILAL MCE 12147
MEMONA JAVED MCE 12104
NADIA IZHAR MCE 12170
Class M.Com
Semester 1st Evening
Superior University
Kalma Chowk Campus,
Lahore.
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Table of contents
CHAPTER NO 01
1. Factor analysis ….……………………………………. 03
Types of Factor analysis ……………………………………… 03
Functions ……………………………………… 04
Binary logistic ……………………………………… 04
Explanation ……………………………….. 06
Reference ……………………………….. 07
CHAPTER NO 02
Probability of Default ……………………………………….. 08
Literature Review ……………………………………….. 09
CHAPTER NO 03
Data analyze and interpretation …………………………….. 10
Scree plot ………………………………………. 11
Logistic regression interpretation …………………….......... 13
CHAPTER NO 04
Probability of default …………………………………...... 15
Explanation ………………………………… 16
Graph …………………………………………………... 19
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CHAPTER 01
Factor Analysis
The main applications of factor analytic techniques are:
To reduce the number of variables and
To detect structure in the relationships between variables, that is to classify variables.
Therefore, factor analysis is applied as a data reduction or structure detection method
(the term factor analysis was first introduced by Thurstone, 1931).
1: Confirmatory factor analysis:
Structural Equation Modeling (SEPATH) allows you to test specific hypotheses about the
factor structure for a set of variables, in one or several samples (e.g., you can compare factor
structures across samples).
2: Exploratory analysis:
Exploratory analysis is a descriptive/exploratory technique designed to analyze two way
and multi way tables containing some measure of correspondence between the rows and
columns. The results provide information which is similar in nature to those produced by factor
analysis techniques, and they allow you to explore the structure of categorical variables
included in the table. For more information regarding these methods, refer to Correspondence
Analysis.
TYPES OF FACTOR ANALYSIS
There are basically two types of factor analysis: exploratory and confirmatory.
o Exploratory factor analysis (EFA) attempts to discover the nature of the constructs
influencing a set of responses.
o Confirmatory factor analysis (CFA) tests whether a specified set of constructs is
influencing responses in a predicted way.
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Function of factor analysis
o Data reduction tool
o Removes redundancy or duplication from a set of Correlated variables
o Represents correlated variables with a smaller Set of “derived” variables.
o Factors are formed that are relatively Independent of one another.
Combining Exploratory and Confirmatory Factor Analyses
o In general, you want to use EFA if you do not have strong theory about the constructs
underlying responses to your measures and CFA if you do.
o It is reasonable to use an EFA to generate a theory about the constructs underlying your
measures and then follow this up with a CFA, but this must be done using separate data
sets. You are merely fitting the data (and not testing theoretical constructs) if you
directly put the results of an EFA directly into a CFA on the same data. An acceptable
procedure is to perform an EFA on one half of your data, and then test the generality of
the extracted factors with a CFA on the second half of the data.
o If you perform a CFA and get a significant lack of ¯t, it is perfectly acceptable to follow
this up with an EFA to try to locate inconsistencies between the data and your model.
However, you should test any modifications you decide to make to your model on new
data.
o Factor analysis is a collection of methods used to examine how underlying constructs
influence the responses on a number of measured variables.
Binary logistics
In statistics, logistic regression (sometimes called the logistic model or legit model) is
used for prediction of the probability of occurrence of an event by fitting data to a logistic
function. It is a generalized linear model used for binomial regression. Like other forms of
regression analysis, it makes use of one or more predictor variables that may be either
numerical or categorical.
EXAMPLE
The probability that a person has a stroke within a specified time period might be
predicted from knowledge of the person's age, sex and body mass index. Logistic regression is
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used extensively in the medical and social sciences fields, as well as marketing applications such
as prediction of a customer's propensity to purchase a product or cease a subscription.
An explanation of logistic regression begins with an explanation of the logistic function,
which, like probabilities, always takes on values between zero and one:
Formula
f (z) =
A graph of the function is shown in figure 1. The input is z and the output is ƒ (z). The
logistic function is useful because it can take as an input any value from negative infinity to
positive infinity, whereas the output is confined to values between 0 and 1. The variable z
represents the exposure to some set of independent variables, while ƒ (z) represents the
probability of a particular outcome, given that set of explanatory variables. The variable z is a
measure of the total contribution of all the independent variables used in the model and is
known as the legit.
The variable z is usually defined as
Z= β0+ β1x1+β2x2+......................+βk × k
Lie between 0 and 1 figure 1
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EXPLANATION:
Where β0 is called the "intercept" and β1, β2, β3, and so on, are called the "regression
coefficients" of x1, x2, and x3 respectively. The intercept is the values of z when the value of all
independent variables is zero (e.g. the value of z in someone with no risk factors). Each of the
regression coefficients describes the size of the contribution of that risk factor. A positive
regression coefficient means that the explanatory variable increases the probability of the
outcome, while a negative regression coefficient means that the variable decreases the
probability of that outcome; a large regression coefficient means that the risk factor strongly
influences the probability of that outcome, while a near-zero regression coefficient means that
that risk factor has little influence on the probability of that outcome.
Logistic regression is a useful way of describing the relationship between one or more
independent variables (e.g., age, sex, etc.) and a binary response variable, expressed as a
probability, that has only two values, such as having cancer ("has cancer" or "doesn't have
cancer") .
The application of a logistic regression may be illustrated using a fictitious example of
death from heart disease. This simplified model uses only three risk factors (age, sex, and blood
cholesterol level) to predict the 10-year risk of death from heart disease. These are the
parameters that the data fit:
β0 = − 5.0 (the intercept)
β1 = + 2.0
β2 = − 1.0
β3 = + 1.2
X1 = age in years, above 50
X2 = sex, where 0 is male and 1 is female
X3 = cholesterol level, in above 5.0
The model can hence be expressed as
In this model, increasing age is associated with an increasing risk of death from heart
disease (z goes up by 2.0 for every year over the age of 50), female sex is associated with a
decreased risk of death from heart disease (z goes down by 1.0 if the patient is female), and
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increasing cholesterol is associated with an increasing risk of death (z goes up by 1.2 for each 1
mmol/L increase in cholesterol above 5 mmol/L).
We wish to use this model to predict a particular subject's risk of death from heart
disease: he is 50 years old and his cholesterol level is 7.0mmol/L. The subject's risk of death is
therefore
This means that by this model, the subject's risk of dying from heart disease in the next
10 years is 0.07 (or 7%).
REFANACES:
1) Names S, Jonasson JM, Genell A, Steineck G. 2009 Bias in odds ratios by logistic
regression modeling and sample size. BMC Medical Research Methodology 9:56
BioMedCentral
2) Peduzzi P, Concato J, Kemper E, Holford TR, Feinstein AR (1996). "A simulation study of
the number of events per variable in logistic regression analysis". J Clin Epidemiol 49
(12): 1373–9. PMID 8970487.
3) Agresti A (2007). "Building and applying logistic regression models". An Introduction to
Categorical Data Analysis. Hoboken, New Jersey: Wiley. p. 138. ISBN 978-0-471-22618-
5.
4) Jonathan Mark and Michael A. Goldberg (2001). Multiple Regression Analysis and Mass
Assessment: A Review of the Issues. The Appraisal Journal, Jan. pp. 89–109
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CHAPTER 02
PROBABLITY OF DEFAULT
Definition
“The Probability of Default is the likelihood that a loan will not be replayed and
falls into default. This PD will be calculated for each company who has a loan. The credit history
of the counterparty and nature of the investment will all be taken into account to calculate the
PD figures. Many banks will use external ratings agencies such as Standard and Poors.”
“Probability of default (PD) is the likelihood of a default over a particular time
horizon. It provides an estimate of the likelihood that a client of a financial institution will be
unable to meet its debt obligations.PD is a key parameter used in the calculation of economic
capital or regulatory capital under Basel II for a banking institution.”
Overview
o Under Basel II, a default event on a debt obligation is said to have occurred if it is
unlikely that the obligor will be able to repay its debt to the bank without giving up any
pledged collateral the obligor is more than 90 days past due on a material credit
obligation
o The PD is an estimate of the likelihood that the default event will occur over a fixed
assessment horizon, usually taken to be one year. The PD can be estimated for a
particular obligor which is the usual practice in wholesale banking, or for a segment of
obligors sharing similar credit risk characteristics which is the usual practice in retail
banking.
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Literature review:
Altman, E.I., 1968,
Aalen, O.O. and S. Johansen, 1978,
Altman, E.I. and D.L. Kao, 1992,
Andrews, D.W.K. and M. Buchinsky, 1997
Agresti, A. and B.A. Coull, 1998,
Brown, L.D., T. CAI and A. Dasgupta, 2001,
Cantor, R. and E. Falkenstein, 2001
Crouhy, M., D. Galai, and R. Mark (2001)
Bangia, A., F.X. Diebold, A. Kronimus and C. Schagen and T. Schuermann, 2002,
Federal Reserve Board, 2003,
Basel Committee on Banking Supervision, 2003,
Hamilton, D. and R. Cantor, 2004,
Christensen, J. E. Hansen and D. Lando, 2004,
References:
o FT Lexicon: Probability of default
o Basel II Comprehensive Version, Pg 100
o Issues in the credit risk modeling of retail markets
o A b BIS:Studies on the Validation of Internal Rating Systems
o Slides 5 and 6:The Distinction between PIT and TTC Credit Measures
o The Basel II Risk Parameters
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CHAPTER 03
DATA ANALYSIS AND ITERETATION OF FACTOR ANALYSIS AND BINARY LOGISTIC
o Descriptive statistics tell about the mean and std deviation of all ratioies
o Over all test is significant because p-vale is less than 0.05
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o 65%Variation or date explain in the date of net sale to total assets
o 70%Variation or date explain in the date of ebit to total assets
o 83%Variation or date explain in the date of total equity to total assets
o 75%Variation or date explain in the date of retained earning to total assets
o 53%Variation or date explain in the date of fund operational to total debts
o 66%Variation or date explain in the date of working capital to total assets
o 69.28% explain the first 2 components
Second and third step is Scree plot
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o 2 and 3 step is scree plot
From fist components select;
o total equity to total assets
o retained earnings to total assets
Form second component select’
o net sale total assets
o ebit to total assets
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H0: All the predictors are not jointly insignificant
H1: All the predictors are jointly significant
All the p-values are less than 0.05, therfore we accept our H1.
Model Summary
Cox & Snell R Nagelkerke R
Step -2 Log likelihood Square Square
a
1 36.336 .004 .228
a. Estimation terminated at iteration number 12 because
parameter estimates changed by less than .001.
o 22.8% of the variation is explained
by independent variables (Financial ratios)
H0: The overall fit is good
H1: The overall fit is not good
Here p-value>0.05, so the overall fit is good.
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o 99.9% overall classification check
o From this table we get the value of beta for calculated the probability of default
o If one is increasing and other is also increasing then correlation is positive
o If one is increasing and other is decrease then correlation is negative
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Explanations
0 % chance of default the total Client is 92
1 % chance of default the total Client is 215
2 % chance of default the total Client is 160
3 % chance of default the total Client is 118
4 % chance of default the total Client is 75
5 % chance of default the total Client is 72
6 % chance of default the total Client is 73
7 % chance of default the total Client is 60
8 % chance of default the total Client is 33
9 % chance of default the total Client is 34
10 % chance of default the total Client Is 40
11 % chance of default the total Client is 52
12 % chance of default the total Client is 50
13 % chance of default the total Client is 35
14 % chance of default the total Client is 33
15 % chance of default the total Client is 41
16 % chance of default the total Client is 29
17 % chance of default the total Client is 32
18 % chance of default the total Client is 32
19 % chance of default the total Client is 37
20 % chance of default the total Client is 29
21 % chance of default the total Client is 24
22 % chance of default the total Client is 28
23 % chance of default the total Client is 31
24 % chance of default the total Client is 21
25 % chance of default the total Client is 34
26 % chance of default the total Client is 20
27 % chance of default the total Client is 23
28 % chance of default the total Client is 18
29 % chance of default the total Client is 19
30 % chance of default the total Client is 25
31 % chance of default the total Client is 17
32 % chance of default the total Client is 29
33 % chance of default the total Client is 19
34 % chance of default the total Client is 31
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35 % chance of default the total Client is 21
36 % chance of default the total Client is 25
37 % chance of default the total Client is 10
38 % chance of default the total Client is 15
39 % chance of default the total Client is 17
40 % chance of default the total Client is 11
41 % chance of default the total Client is 25
42 % chance of default the total Client is 21
43 % chance of default the total Client is 17
44 % chance of default the total Client is 11
45 % chance of default the total Client is 13
46 % chance of default the total Client is 14
47 % chance of default the total Client is16
48 % chance of default the total Client is 13
49 % chance of default the total Client is 16
50 % chance of default the total Client is 15
51 % chance of default the total Client is 20
52 % chance of default the total Client is 8
53 % chance of default the total Client is 18
54 % chance of default the total Client is 9
55 % chance of default the total Client is 9
56 % chance of default the total Client is 15
57 % chance of default the total Client is 9
58 % chance of default the total Client is 19
59 % chance of default the total Client is 19
60 % chance of default the total Client is 19
61 % chance of default the total Client is 10
62 % chance of default the total Client is 18
63 % chance of default the total Client is 8
64 % chance of default the total Client is 13
65 % chance of default the total Client is 12
66 % chance of default the total Client is 15
67 % chance of default the total Client is 13
68 % chance of default the total Client is 14
69 % chance of default the total Client is 8
70 % chance of default the total Client is 13
71 % chance of default the total Client is 7
72 % chance of default the total Client is 6
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73 % chance of default the total Client is 10
74 % chance of default the total Client is 13
75 % chance of default the total Client is 15
76 % chance of default the total Client is15
77 % chance of default the total Client is 13
78 % chance of default the total Client is 11
79 % chance of default the total Client is 9
80 % chance of default the total Client is14
81 % chance of default the total Client is 21
82 % chance of default the total Client is 13
83 % chance of default the total Client is 7
84 % chance of default the total Client is 13
85 % chance of default the total Client is 5
86 % chance of default the total Client is 17
87 % chance of default the total Client is 16
88 % chance of default the total Client is 13
89 % chance of default the total Client is 6
90 % chance of default the total Client is 11
91 % chance of default the total Client is 18
92 % chance of default the total Client is 15
93 % chance of default the total Client is 24
94 % chance of default the total Client is 12
95 % chance of default the total Client is 30
96 % chance of default the total Client is 17
97 % chance of default the total Client is 19
98 % chance of default the total Client is 34
99 % chance of default the total Client is 58
100 % chance of default the total Client is 122
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Frequency of probability of default of shares from stock exchange
PDs
120%
100%
80%
60%
PDs
40%
20%
0%
1081
1405
1189
1297
1513
1621
1729
1837
1945
2053
2161
2269
2377
2485
2593
2701
1
109
217
325
433
541
649
757
865
973
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