QUANTITATIVE TECHNIQUE IN BUSINESS

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1. Factor analysis

1. Factor analysis

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  • 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. 1
  • 2. Superior University, Lahore. Table of contents CHAPTER NO 01 1. Factor analysis ….……………………………………. 03 Types of Factor analysis ……………………………………… 03 Functions ……………………………………… 04 Binary logistic ……………………………………… 04 Explanation ……………………………….. 06 Reference ……………………………….. 07CHAPTER 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
  • 3. Superior University, Lahore. CHAPTER 01Factor 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 thefactor structure for a set of variables, in one or several samples (e.g., you can compare factorstructures across samples).2: Exploratory analysis: Exploratory analysis is a descriptive/exploratory technique designed to analyze two wayand multi way tables containing some measure of correspondence between the rows andcolumns. The results provide information which is similar in nature to those produced by factoranalysis techniques, and they allow you to explore the structure of categorical variablesincluded in the table. For more information regarding these methods, refer to CorrespondenceAnalysis.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. 3
  • 4. Superior University, Lahore.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) isused for prediction of the probability of occurrence of an event by fitting data to a logisticfunction. It is a generalized linear model used for binomial regression. Like other forms ofregression analysis, it makes use of one or more predictor variables that may be eithernumerical or categorical.EXAMPLE The probability that a person has a stroke within a specified time period might bepredicted from knowledge of the persons age, sex and body mass index. Logistic regression is 4
  • 5. Superior University, Lahore.used extensively in the medical and social sciences fields, as well as marketing applications suchas prediction of a customers 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). Thelogistic function is useful because it can take as an input any value from negative infinity topositive infinity, whereas the output is confined to values between 0 and 1. The variable zrepresents the exposure to some set of independent variables, while ƒ (z) represents theprobability of a particular outcome, given that set of explanatory variables. The variable z is ameasure of the total contribution of all the independent variables used in the model and isknown as the legit. The variable z is usually defined asZ= β0+ β1x1+β2x2+......................+βk × kLie between 0 and 1 figure 1 5
  • 6. Superior University, Lahore.EXPLANATION: Where β0 is called the "intercept" and β1, β2, β3, and so on, are called the "regressioncoefficients" of x1, x2, and x3 respectively. The intercept is the values of z when the value of allindependent variables is zero (e.g. the value of z in someone with no risk factors). Each of theregression coefficients describes the size of the contribution of that risk factor. A positiveregression coefficient means that the explanatory variable increases the probability of theoutcome, while a negative regression coefficient means that the variable decreases theprobability of that outcome; a large regression coefficient means that the risk factor stronglyinfluences the probability of that outcome, while a near-zero regression coefficient means thatthat risk factor has little influence on the probability of that outcome. Logistic regression is a useful way of describing the relationship between one or moreindependent variables (e.g., age, sex, etc.) and a binary response variable, expressed as aprobability, that has only two values, such as having cancer ("has cancer" or "doesnt havecancer") . The application of a logistic regression may be illustrated using a fictitious example ofdeath from heart disease. This simplified model uses only three risk factors (age, sex, and bloodcholesterol level) to predict the 10-year risk of death from heart disease. These are theparameters that the data fit:β0 = − 5.0 (the intercept)β1 = + 2.0β2 = − 1.0β3 = + 1.2X1 = age in years, above 50X2 = sex, where 0 is male and 1 is femaleX3 = cholesterol level, in above 5.0The model can hence be expressed as In this model, increasing age is associated with an increasing risk of death from heartdisease (z goes up by 2.0 for every year over the age of 50), female sex is associated with adecreased risk of death from heart disease (z goes down by 1.0 if the patient is female), and 6
  • 7. Superior University, Lahore.increasing cholesterol is associated with an increasing risk of death (z goes up by 1.2 for each 1mmol/L increase in cholesterol above 5 mmol/L). We wish to use this model to predict a particular subjects risk of death from heartdisease: he is 50 years old and his cholesterol level is 7.0mmol/L. The subjects risk of death istherefore This means that by this model, the subjects risk of dying from heart disease in the next10 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
  • 8. Superior University, Lahore. CHAPTER 02 PROBABLITY OF DEFAULTDefinition “The Probability of Default is the likelihood that a loan will not be replayed andfalls into default. This PD will be calculated for each company who has a loan. The credit historyof the counterparty and nature of the investment will all be taken into account to calculate thePD 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 timehorizon. It provides an estimate of the likelihood that a client of a financial institution will beunable to meet its debt obligations.PD is a key parameter used in the calculation of economiccapital 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
  • 9. Superior University, Lahore. 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
  • 10. Superior University, Lahore. CHAPTER 03 DATA ANALYSIS AND ITERETATION OF FACTOR ANALYSIS AND BINARY LOGISTICo Descriptive statistics tell about the mean and std deviation of all ratioieso Over all test is significant because p-vale is less than 0.05 10
  • 11. Superior University, Lahore. 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 componentsSecond and third step is Scree plot 11
  • 12. Superior University, Lahore.o 2 and 3 step is scree plot From fist components select;o total equity to total assetso retained earnings to total assets Form second component select’o net sale total assetso ebit to total assets 12
  • 13. Superior University, Lahore. 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
  • 14. Superior University, Lahore.o 99.9% overall classification checko From this table we get the value of beta for calculated the probability of defaulto If one is increasing and other is also increasing then correlation is positiveo If one is increasing and other is decrease then correlation is negative 14
  • 15. Superior University, Lahore. CHAPTER 04 Probability of default of Share of stock Exchangepercentage 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
  • 16. Superior University, Lahore.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 16
  • 17. Superior University, Lahore.  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 17
  • 18. Superior University, Lahore.  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 18
  • 19. Superior University, Lahore.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