QUANTITATIVE TECHNIQUE IN BUSINESS

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.

1


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

2


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

4


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

5


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

6


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

7


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.

8


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

9


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

10


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

11


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

12


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.

13


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

14


CHAPTER 04

Probability of default of Share of stock Exchange
percentage frequency Percentage Frequency Percentage frequency
0% 92 34% 31 68% 14
1% 215 35% 21 69% 8
2% 160 36% 15 70% 13
3% 118 37% 10 71% 7
4% 75 38% 15 72% 6
5% 73 39% 17 73% 10
6% 72 40% 11 74% 13
7% 60 41% 25 75% 15
8% 33 42% 21 76% 15
9% 34 43% 17 77% 13
10% 40 44% 11 78% 11
11% 52 45% 13 79% 9
12% 50 46% 14 80% 14
13% 35 47% 16 81% 21
14% 33 48% 13 82% 13
15% 41 49% 16 83% 7
16% 29 50% 15 84% 13
17% 32 51% 20 85% 5
18% 32 52% 8 86% 17
19% 37 53% 18 87% 16
20% 29 54% 9 88% 13
21% 24 55% 9 89% 6
22% 28 56% 15 90% 11
23% 31 57% 9 91% 18
24% 21 58% 19 92% 15
25% 34 59% 19 93% 24
26% 20 60% 19 94% 12
27% 23 61% 10 95% 30
28% 18 62% 18 96% 17
29% 19 63% 8 97% 19
30% 25 64% 13 98% 34
31% 17 65% 12 99% 58
32% 29 66% 15 100% 122
33% 19 67% 13 Total 2784

15


Explanations
 0 % chance of default the total Client is 92
 10 % chance of default the total Client Is 40

16


 47 % chance of default the total Client is16

17



18


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

19

QUANTITATIVE TECHNIQUE IN BUSINESS

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