387

Dutta, Bandopadhyay, and Sengupta 105

Volume 7, Number 1, June 2012

Prediction of Stock Performance in the

Indian Stock Market Using Logistic Regression

Avijan Dutta

Associate Professor & Head

Department of Management Studies

National Institute of Technology, Durgapur, India

[email protected]

Gautam Bandopadhyay

Associate Professor

National Institute of Technology, Durgapur, India

Suchismita Sengupta

Associate Professor

IES Management College and Research Centre

Mumbai, India

[email protected]

ABSTRACT

The authors use logistic regression (LR) and various financial ratios as

independent variables to investigate indicators that significantly affect the

performance of stocks actively traded on the Indian stock market. The study

sample consists of the ratios of 30 large market capitalization companies over a

four-year period. The study identifies and examines eight financial ratios that can

classify the companies up to a 74.6% level of accuracy into two categories –

“good” or “poor” – based on their rate of return. The paper asserts that the model

developed can enhance an investor's stock price forecasting ability. Macro-

ecomonic variables, which also can influence the share price, were not taken into

account, however. The paper dicusses the practical implications of using the LR

method to predict the probability of good stock performance. The authors state

that the model can be used by investors, fund managers, and investment

companies to enhance their abilty to select out-performing stocks.

Keywords: Classification of stock performance, Indian stock market, logistic

regression, market rate of return, financial ratios, NIFTY

mailto:[email protected]

mailto:[email protected]

106 Prediction of Stock Performance in the


International Journal of Business and Information

1. INTRODUCTION

Global crashes do not occur all of a sudden but are headed by local and

regional crashes in emerging economies. Even when the investors are not

exposed to emerging stock markets, they should pay attention to these markets,

as local crashes can affect developed markets. Moreover, the interdependence is

relevant as well, in that interest rates, bond returns, and volatility also affect the

probabilities of the different types of stock market crashes.

It is important for shareholders and potential investors to use relevant

financial information to enable them to make good investment decisions in the

stock market. Predicting stock performance is certainly very complicated and

difficult. In the history of stock performance literature, no comprehensive,

accurate model has been suggested to date for predicting stock market

performance.

A stock’s performance can, to some extent, be analyzed based on financial

indicators presented in the company’s annual report. The annual report contains a

vast amount of information that can be transformed into various ratios. Previous

literature suggests that financial ratios are important tools for assessing future

stock performance. Analysts, investors, and researchers use financial ratios to

project future stock price trends. Ratio analysis has emerged, therefore, as one of

the key parameters used by fund managers and investors to determine the

intrinsic value of stock shares; thus, financial ratios are used extensively for the

valuation of stock. The study of financial ratios emerged as a new discipline after

stock market crashes in the 1990s and early 2000s in the United States and parts

of Europe and southern Asia. Today, ratios are used extensively in fundamental

analysis to predict the future performance of a company. Various new ratios,

such as book value and price/cash earnings per share, have been included in this

discipline for share valuation. Financial ratios help to form the basis of investor

stock price expectations and, hence, influence investment decision making. The

level of importance given to financial ratios differs from industry to industry and

from one country to another. Thus, selecting appropriate ratios is very crucial in

increasing the prediction success rate.

The objective of this paper is to apply statistical methods to survey and

analyze financial data in order to develop a simplified model for interpretation.

This study aims to develop a model for classifying stocks into two categories



(good or poor), based on their rate of return. A company’s stock is classified as

“good” if its share returns perform above the market returns provided by the

National Stock Exchange composite index of India; i.e., the NIFTY. In this

study, the logistic regression (LR) method has been used to classify selected

companies, based on their performance. The LR method is used to predict the

probability of good stock performance by fitting the variables to a logistic curve.

Thus, LR is used to classify a set of independent variables into two or more

mutually exclusive categories. It involves finding a linear combination of

independent variables that reflect large differences in group means.

2. REVIEW OF LITERATURE

In stock performance literature, little attention has been given in the past to

the Indian stock market. In recent years, however, there has been a greater focus

on the market because of its rapid growth and its increasing potential for global

investors. In light of the market’s growing importance, more attention has been

directed to studies concerning different classification techniques for measuring

stock performance. A number of research papers predict stock performance as

well as pricing of the stock index across the globe. Harvey [1995] observes that

emerging market returns are usually more predictable than developed market

returns because emerging market returns are more likely to be influenced by local

information than developed markets.

In recent literature, artificial neural networks (ANN) have been successfully

used for modeling financial time series [Cheng, 1996; Van and Robert, 1997]. In

the United States, several studies have examined the cross-sectional relationship

between fundamental variables and stock returns. Fundamental variables such as

earnings yield, cash flow yield, book-to-market ratio, and size are demonstrated

to have some power in predicting stock returns [Fama and French, 1992]. Studies

based on European markets also demonstrate similar findings. Ferson and Harvey

[1993] observe that returns are predictable, to an extent, across a number of

European markets (e.g., UK, France, and Germany). Jung and Boyd [1996], in

their study of forecasting UK stock prices, suggest that the predictive strength of

their stock performance models is quite significant. In the Japanese stock market,

studies carried out by Jaffe and Westerfield [1985] and Kato et al. [1990] also

demonstrate some evidence of predictability in the behavior of index returns.




Logistic regression (LR), which is helpful for predicting the presence or

absence of a characteristic or outcome based on values of a set of predictor

variables, is a multivariate analysis model [Lee, 2004]. The applications of LR

have repeatedly been used in the area of corporate finance, banking, and

investments. Multivariate discriminant analysis (MDA) has been used by many

researchers for the default-prediction model. Altman [1968] was the pioneer in

this work, whereas Ohlson [1980] later used LR to construct the default-

prediction model. The early research on default prediction focuses on classifying

firms as either defaulters or non-defaulters. Ohlson [1980] identifies this

assumption of default prediction as an equal payoff state. Clearly, misclassifying

a defaulted firm as a non-defaulted firm would have repercussions that are more

severe for an investor or a loan officer than would be true in the the opposite

case. This research focuses, therefore, on the ability of the models to accurately

rank defaulted and non-defaulted firms, based on their default probability. In

predicting financial distress and bankruptcy, which have been widely applied as

evaluation models providing credit-risk information, Ohlson [1980] used LR, and

was then followed by several authors such as Zavgren [1985]. Subsequently, the

same trend was used by Zmijewski [1984] for probit analysis.

Öğüt and Aktaş [2009] found that data-mining techniques (ANN and SVM)

are better suited to detect stock-price manipulation than multivariate statistical

techniques such as discriminant analysis or LR, because the performances of

data-mining techniques in terms of classification accuracy are better than those of

multivariate techniques. They proposed a new binary classification method for

predicting corporate failure based on genetic algorithm, and proposed to validate

its prediction power through empirical analysis.

Min and Jeong [2009] compared prediction accuracy with other methods such

as multi-discriminant analysis, logistic regression, decision tree, and artificial

neural network, and showed that the binary classification method they proposed

can serve as a promising alternative to existing methods for bankruptcy

prediction.

Bildirici and Ersin [2009] proposed an ANN-APGARCH model to increase

the forecasting performance of the APGARCH model. The ANN-extended

versions of the GARCH models improved forecast results.



Mostafa [2010] showed that neuro-computational models are useful tools in

forecasting stock exchange movements in emerging markets. Their results also

indicated that the quasi-Newton training algorithm produces fewer forecasting

errors, compared with other training algorithms. Because of the robustness and

flexibility of modeling algorithms, neuro-computational models are expected to

outperform traditional statistical techniques such as regression and ARIMA in

forecasting price movements on stock exchanges.

Li et al. [2010] used LR as a comparative method in order to build a better

model for predicting stock returns effectively and efficiently. A 30 times hold-

out method was used in the assessment, along with the two commonly used

methods in the top 10 data mining algorithms (the support vector machine and k

nearest neighbor) and the two baseline benchmark methods from the statistical

area (MDA and LR).

Li and Sun [2011] observed that multiple classifiers outperform single

classifiers in terms of prediction accuracy and returns on investment. They

showed that there is no significant difference between majority voting and

bagging in prediction accuracy, but that the former has a better prediction

accuracy for stock returns than the latter. Finally, the homogeneous multiple

classifiers using neural networks by majority voting perform best when

predicting stock returns. The two classical statistical methods (MDA and logit)

have assumed a key role in the area of business failure prediction (BFP).

Chen [2011] carried out studies at the Taiwan Stock Exchange Corporation

(TSEC) to improve the accuracy of the financial distress prediction model and

collected 100 listed companies as the initial sample. The empirical experiment

included 37 ratios comprising financial and other non-financial ratios, and used

principal component analysis (PCA) to extract suitable variables. Decision tree

(DT) classification methods (C5.0, CART, and CHAID) and LR techniques were

used to implement the financial distress prediction model. The experiments

produced a satisfying result, verifying the possibility and validity of the proposed

methods for the financial distress prediction of listed companies.

Guresen et al. [2011] evaluated the effectiveness of neural network models,

which are known to be dynamic and effective in stock market predictions. The

models analyzed are multi-layer perceptron (MLP), the dynamic artificial neural

network (DAN2), and hybrid neural networks that use generalized auto-




regressive conditional heteroscedasticity (GARCH) to extract new input

variables. The comparison for each model is presented in two viewpoints.

Swiderski et al. [2012] demonstrated the new approach to the automatic

assessment of the financial condition of a company and developed the

computerized classification system, applying WOE representation of data and

LR, and using support vector machine (SVM) as the final classifier. The applied

method is a combination of a classical binary scoring approach and SVM

classification. The application of this method to the assessment of the financial

condition of companies, classified into five classes, has shown its superiority

with respect to classical approaches.

At the time of prediction, with the help of MDA, it was assumed that the

groups were of similar size as while predicting the default and non-default firms

in the prediction carried out by Altman [1968] and subsequent researchers. It

was shown that the number of non-default firms was never more than twice the

number of default firms. However, default or bankruptcy being a rare event, a

very high proportion of the non-defaulters was excluded from the analysis.

Besides being used to predict corporate fiascos, ratios are also used for scaling

or grouping industries according to the degree of risk. Horrigan [1965] found

financial ratios to be successful predictors for bond rating. Metnyk and Mathur

[1972] used ratios to classify corporations into similar risk groups and attempted

to relate them to the companies’ market rates of return; but, they did not report

favorable results. Conner [1973] studied five ratios – namely, (1) total liabilities

to net worth, (2) working capital to sales, (3) cash flow to number of common

shares, (4) earnings per share to price per share, and (5) current liabilities to

inventory – but found them to be poor indicators of return on common stock.

Different methodologies and financial ratios are used by various authors to

classify the performance of firms. Kumar and Ravi [2007] carried out a

comprehensive review of various work related to bankruptcy prediction problems

and found that neural network is the most widely used technique, followed by

statistical models. McConnell, Haslem, and Gibson [1986] have indicated that

qualitative data can provide additional information to forecast stock price

performance more accurately.

The LR technique yields coefficients for each independent variable based on a

sample of data [Huang, Chai, and Peng, 2007]. Logistic regression models



(LRM) with two or more explanatory variables are widely used in practice

[Haines et al., 2007]. The parameters of the LR model are commonly estimated

by maximum likelihood [Pardo, Pardo, and Pardo, 2005]. The advantage of LR is

that, through the addition of an appropriate link function to the usual linear

regression model, the variables may be either continuous or discrete, or any

combination of both types, and they do not necessarily have normal distributions

[Lee, 2004].

The predictor values from the analysis can be interpreted as probabilities (0 or

1 outcome) or membership in the target groups (categorical dependent variables).

It has been observed that the probability of a 0 or 1 outcome is a non-linear

function of the logit [Nepal, 2003]. Logistic regression is useful for situations in

which it is required to predict the presence or absence of a characteristic or

outcome based on values of a set of predictor variables. Logistic regression is

similar, therefore, to a linear regression model, but is proficient to models where

the dependent variable is dichotomous. Logistic regression coefficients can be

used to estimate odd ratios for each of the independent variables in the model.

Logistic regression helps to form a multivariate regression between a dependent

variable and several independent variables [Lee, Ryu and Kim, 2007]. It is

designed to estimate the parameters of a multivariate explanatory model in

situations where the dependent variable is dichotomous, and the independent

variables are continuous or categorical.

Existing literature indicates that LR has been rarely used to build a model for

predicting out-performing shares. Logistic regression has been used mostly for

predicting financial distress and business failure. It has not been used for

predicting share performance in India. In terms of investment destination in

share, India is a top performing emerging market. In this context, the present

study will provide useful information to shareholders and potential investors to

enable them to make good decisions regarding investments.

3. RESEARCH OBJECTIVE AND METHODOLOGY

In this study, the relation between financial ratios and stock performance of

the firms has been analyzed with the help of binary logistic regression. The

earlier studies mentioned above have generally indicated that logistic regression,

as used in the finance discipline, can be an effective tool for decision makers. It




has also been recognized that financial ratios can enhance an investor's stock

price forecasting ability.

The objective of this study is to build a model using financial ratios of the

firms for the purpose of predicting out-performing shares in the Indian stock

market. This study aims, therefore, to answer two questions: (1) Can the yields

of stocks be explained with the help of financial ratios? (2) Can we analyze stock

yields using a logistic regression model? The study also examines the efficacy of

ratios as predictors of stock performance.

3.1. Analysis of Model-Logistic Regression

Regression analysis is used to determine the magnitude of relationships

between variables as well as to model relationships between variables and for

predictions based on the models. Simple linear regression or multiple linear is

applicable when this relationship is assumed to be linear [Davis, 2005]. However,

a number of non-linear techniques could be used to obtain a more accurate

regression if the relationship between variables is not linear in parameters.

Logistic regression is preferred in case the response variable can take only binary

values (yes or no). The outcome of logistic regression is a function that describes

how the probability of the event (yes or no) varies with the predictors

[Tabachnick and Fidell, 2001].

Logistic regression could predict the likelihood, or the odds ratio, of the

outcome based on the predictor variables, or covariates. The significance of

logistic regression can be evaluated by the log likelihood test, given as the model

chi-square test, evaluated at the p < 0.05 level, or the Wald statistic. Logistic

regression has the advantage of being less affected than discriminant analysis

when the normality of the variable cannot be assumed. It has the capacity to

analyze a mix of all types of predictors [Hair, 1995]. Logistic regression, which

assumes the errors are drawn from a binomial distribution, is formulated to

predict and explain a binary categorical variable instead of a metric measure. In

logistic regression, the dependent variable is a log odd or logit, which is the

natural log of the odds.

Logistic regression allows one to predict a discrete outcome, such as group

membership, from a set of variables that may be continuous, discrete,

dichotomous, or a mix of any of these. Generally, the dependent or response



variable is dichotomous, such as presence/absence or success/failure. In instances

where the independent variables are categorical, or a mix of continuous and

categorical, logistic regression is preferred.

Since the probability of an event must lie between 0 and 1, it is unrealistic to

model probabilities with linear regression techniques, because the linear

regression model allows the dependent variable to take values greater than 1 or

less than 0. The logistic regression model is a type of generalized linear model

that extends the linear regression model by linking the range of real numbers to

the 0-1 range.

In the logistic regression model, the relationship between Z and the

probability of the event of interest is described by this link function.

pi= ezi

= 1

1+ezi 1+e

-zi

Figure 1. Logistic Regression Model

Here the y-axis is the predicted variable pi and the horizontal axis denotes the

explanatory variable zi.

or




zi=log(pi/1−pi)

where

pi is the probability the ith case experiences the event of interest, and

zi is the value of the unobserved continuous variable for the ith case.

The z value is the odds ratio. It is expressed by

zi= β0+β1xi1+β2xi2+…+βpxip

where

xij is the jth predictor for the i

th case,

βj is the jth coefficient, and

p is the number of predictors.

Logistic regression analysis does not require the restrictive assumptions

regarding normality distribution of independent variables or equal dispersion

matrices nor the prior probabilities of failure [Ohlson, 1980; Zavgren, 1985].

Rather, logistic regression is based on two assumptions; (1) it requires the

dependent variable to be dichotomous, with the groups being discrete, non-

overlapping, and identifiable; and (2) it considers the cost of type I and type II

error rates in the selection of the optimal cut-off probability. βs are the

regression coefficients that are estimated through an iterative maximum

likelihood method. However, because of the subjectivity of the choice of these

misclassification costs in practice, most researchers minimize the total error rate

and, hence, implicitly assume equal costs of type I and type II errors [Ohlson,

1980; Zavgren, 1985].

3.2. Application of Logistic Regression

We begin this section with a discussion of data sources. In this context, the

companies with large market capitalizations have been considered, of which,

most of these companies are part of the NIFTY index. The financial data used in



this analysis was collected from the Web link www.moneypore.com. The sample

of the study was drawn from the 30 companies that are most actively traded on

the Indian stock exchange as given in Appendix 2. Financial ratios and stock

prices for calculating return were then collected. In this research, a sample period

consisting of four years (2005-2008) was selected for classification purposes.

For the purpose of carrying out logistic regression analysis, first a method is

required for classifying a company as a “good” or “poor” investment choice for a

given year. Although there is no definitive method for defining a market

investment as “good” or “poor,” in this study we use a method that is simple and

objective – namely, if the value of a company’s stock over a given year rose

above market return, it is classified as a “good” investment option; otherwise, it

is classified as a “poor” investment option. Here, the NIFTY (Index of National

Stock Exchange) return has been taken as proxy for market return. To obtain the

return at the end of each financial year, the March ending prices were used for

each year.

The return was calculated using the following formula:

Return of stock = Χ 100

where,

Pt= Price at the T year

Pt-1= Price at the T -1year

Market return = Χ 100

Similarly, NIFTY(t) = NIFTY at the t year, and NIFTY(t-1) = NIFTY at the (t-1)

year.

The sample in this study is based on the selection of 30 companies for a four-

year period (2005 through 2008). The study consists of a sample size of 118

distinct companies’ year-wise observations. As discussed, we have used twp

dependent variables (“good” or “poor”) and six independent variables. Initially,

http://www.moneypore.com/




16 financial ratios were taken for analysis. A normality test was conducted on all

these explanatory variables. The results of the test are summarized and presented

in Table 1, which shows that six variables are normal. The normality test was

used to give a better prediction result. The table also shows that the P-value for

all six variables is greater than 0.05, which implies that these variables are

normal.

Table 1

One-Sample Kolmogorov-Smirnov Test

%

Increase

in Net

Sales

Earning

per share

Book

Value

Price/cash

Earning

per Share

PBIDT/

Sales

Sales/Net

Assets

N 118 118 118 118 118 118

Normal Parametersa Mean .2653 47.1581 230.8910 17.8159 31.7651 1.2439

Std.

Deviation .18741 35.20981 167.75761 9.36982 18.71652 0.88254

Most Extreme

Differences

Absolute 0.112 0.113 0.109 0.115 0.119 0.123

Positive 0.112 0.113 0.100 0.115 0.119 0.123

Negative -0.062 -0.113 -0.109 -0.071 -0.105 -0.094

Kolmogorov-Smirnov Z 1.220 1.231 1.181 1.253 1.288 1.333

Asymp. Sig. (2-tailed) 0.102 0.097 0.123 0.087 0.073 0.057

The variables were also tested using a Q-Q plot, as shown in Appendix 1. The

variables that were not normal were not considered for further analysis. The six

independent variables considered for final analysis are presented in Table 1. The

six ratios are mostly the valuation ratios, which generally determine the value of

share in the stock market. As a matter of fact, the dependent variable or outcome

is a dichotomous one, and, hence, has been rated GOOD = 1 and POOR = 0 to



signify the investment choice. Out of to 118 samples, 68 have been classified as

poor and 50 as good.

Table 2

Dependent Variables

Type of Company

(based on stock market return)

GOOD Return above Market return; i.e.,

NIFTY

POOR Return below Market return; i.e.,

NIFTY

Table 3

Dependent Variable Encoding

Original Value Internal Value

Poor 0

Good 1

Table 4

Independent Variables

Name of the Variable Description of the Variable

NS Percentage Increase in Net Sales

CEPS Cash Earnings per Share

BV Book Value

PECEPS Price/Cash Earnings Per Share

PE Price/Earning

PBIDTS Profit Before Interest

Depreciation and Tax/Sales

SNA Sales/Net Assets

PEBV Price/Book value




4. EMPIRICAL RESULT AND ANALYSIS

The estimated results of the logistic regression model of the stock price return

performance, along with the whole sample, are summarized in Table 5. The final

logistic regression equation is estimated by using the maximum likelihood

estimation for classifying a company:

Z= -3.425 + 1.064 * NS + 0.001 * BV + 0.004 * CEPS+.069*PECEPS + 0.014

* PE + 0.006 * PBIDTS + 0.393 * SNA+0.0288*PEBV ,

where

z= log (p/1-p),

and ‘p’ is the probability that the outcome is GOOD.

In the above equation, it is possible to classify a company by calculating Z

values. P values can be obtained from Z values. If the P value is higher than 0.42,

then the stock was classified as good; and, if it is lower than 0.42, then the stock

was classified as poor.

Table 5

(Using SPSS)

Variables in the Equation

1.064 1.212 .771 1 .380 2.898

.001 .003 .054 1 .816 1.001

.004 .010 .207 1 .649 1.004

.069 .044 2.424 1 .120 1.072

.014 .015 .828 1 .363 1.014

.006 .016 .157 1 .692 1.006

.393 .374 1.106 1 .293 1.482

.028 .131 .046 1 .830 1.029

-3.425 1.168 8.594 1 .003 .033

NS

BV

CEPS

PECEPS

PE

PBIDTS

SNA

PEBV

Constant

Step

1a

B S.E. Wald df Sig. Exp(B)

Variable(s) entered on step 1: NS, BV, CEPS, PECEPS, PE, PBIDTS, SNA, PEBV.a.

The ratio of B to S.E., squared, equals the Wald statistic. It provides the

statistical significance of each estimated coefficient. If the logistic coefficient is

statistically significant, we can interpret it in terms of how it impacts the



estimated probability and thus the prediction of group membership. Several

authors have identified problems with the use of the Wald statistic. Menard

[1995] warns that, for large coefficients, standard error is inflated, lowering the

Wald statistic (chi-square) value. Agresti [1996] states that the likelihood-ratio

test is more reliable for small sample sizes than the Wald test. Maximization of

Wald statistics indicates minimizing the standard error of the corresponding

parameter. Wald statistics actually provide the significant test of the β-

coefficients.

4.1. Classification Accuracy

The following classification table helps to assess the performance of the

model by cross-tabulating the observed response categories with the predicted

response categories.

For each case, the predicted response is the category treated as 1, if that

category's predicted probability is greater than the user-specified cutoff. The

cutoff value is taken at 0.5.

Table 6

Classification Tablea

51 17 75.0

13 37 74.0

74.6

Observed

POOR

GOOD

Perf

Overall Percentage

Step 1

POOR GOOD

Perf Percentage

Correct

Predicted

The cut v alue is .410a.

This table shows the comparison of the observed and the predicted performance

of the companies and the degree of their prediction accuracy. It also shows the

degree of success of the classification for this sample. The number and

percentage of cases correctly classified and misclassified are displayed. It is clear

from this table that the poor companies have a 75% correct classification rate,

whereas good companies have a 74% correct classification rate. Overall, correct

classification was observed in 74.6% of original grouped cases.




The plot of the distribution of the firms against the probability is shown above.

The graph shows another method to evaluate right and wrong predictions by

plotting POOR (P) and GOOD (G) status.

The cutoff probability for the decision taken is 0.42 (or 42%). Thus, using

this cutoff value, any company whose score is higher than 0.42 would be

predicted to be a good performing company, and any company with a score less

than 0.42 would be classified as a poor performing company. However, there

may be times when one would want to adjust this cutoff value. Neter et al.

[1996] suggest three ways to select a cutoff value for predicting:

Use the standard 0.42 cutoff value.

Determine a cutoff value that will give the best predictive fit for

the sample data. This is usually determined through trial and

error.

Select a cutoff value that will separate the sample data into a

specific proportion of the two states, based on a prior known

proportion split in the population.



4.2. Tests of Goodness of Fit

The Hosmer-Lemeshow [1989] goodness of fit test is well known when

data are obtained from a simple random survey. The procedure involves grouping

the observations based on the expected probabilities and then testing the

hypothesis that the difference between expected and observed events is

approximately zero for all the groups. Hosmer-Lemeshow [1989] proposed a

statistic that they show through simulation. It is distributed as chi-square when

there is no replication in the subpopulations. This test is available only for binary

response models. The Hosmer-Lemeshow [1989] statistic evaluates the

goodness-of-fit by creating 10 ordered groups of subjects and then compares the

number actually in the each group (observed) to the number predicted by the

logistic regression model (predicted). Thus, the test statistic is a chi-square

statistic with a desirable outcome of non-significance, indicating that the model

prediction does not significantly differ from the observed.

The present study also estimated the Hosmer and Lemeshow statistic,

which provides useful information about the calibration of the model. The

observed significance level for chi-square value is found to be 0.217 (Hosmer

and Lemeshow test), which indicates acceptance of the null hypothesis of the

model, meaning there is not much difference between observed and predicted

values. This result shows that the model appears to fit the data reasonably well.

The chi-square value (10.737) of this model at the 0.01 significance level

indicates that logistic regression is very meaningful, in accordance with the

dependent variable relating to each specified independent variables.

Table 7

(Using SPSS)

Hosmer and Lemeshow Test

10.737 8 .217

Step

1

Chi-square df Sig.




The omnibus tests are the measures of how well the model performs. They

test whether the explained variance in a set of data is significantly greater than

the unexplained variance, overall.

Table 8

(Using SPSS)

Omnibus Tests of Model Coefficients

21.757 8 .005

21.757 8 .005

21.757 8 .005

Step

Block

Model

Step 1

Chi-square df Sig.

If the step were to remove a variable, the exclusion makes sense if the

significance of the change is large (i.e., greater than 0.10).

If the step were to add a variable, the inclusion makes sense if the

significance of the change is small (i.e., less than 0.05).

5. CONCLUSION

This study used the binary logistic regression model to determine the factors

that significantly affect the performance of a company in the stock market. The

binary logistic regression method helps the investor to form an opinion about the

shares to be invested. It may be observed that eight financial ratios can classify

companies up to a 74.6% level of accuracy into two categories (“good” or

“poor”), based on their rate of return. The eight financial ratios are:

Percentage change in net sales (NS)

Sales/net assets (SNA)

Price/cash earnings per share (PECEPS)

Price/book value (PEBV)

Price/earnings per share (PE)

PBIDT/sales (PBIDT)

Cash price/earnings per share (CEPS)

Book value (BV)



When evaluated from the investors’ point of view, we conclude that it is

possible to predict out-performing shares by examining these ratios. Various

methods are available for data processing for analysis, but in this study, we

conclude that ratio methods have the capability to reveal maximum information

content, if variables are chosen very carefully with regard to the purpose at hand.

Ratios enjoy remarkable simplicity and, in spite of the problem of multi–

collinearity, the information revealed by them is so direct to a particular decision-

control situation that movements of ratio give a picturesque representation of the

movement of an actual business process.

In this study, data for 12 months were taken into consideration, and, at the end

of 12th month, stock share prices were compared with those of the previous year

to determine performance. In further studies, data for each three-month period

can be used, and different criteria can be defined, for evaluating stock

performance. This study used financial ratios as the only factor affecting share

prices, but there may be various other economic and management factors that

may also influence share prices. McConnell, Haslem, and Gibson [1986] have

shown that qualitative data can provide additional information to forecast stock

price performance more accurately.

Further studies can use qualitative data for improving forecasting ability. In

the current study, only logistic regression was considered to build the model.

Therefore, for further development, this study proposes to investigate and use

various approaches such as the genetic algorithm, rough set approach to increase

the prediction ratio.




Appendix 1



Appendix 2

Sample Data Set (118 Observations)

Year Perf Company NS EPS BV PECEPS PBIDTS SNA

2008 POOR Tata motor 0.04 50.52 202.68 9.24 11.11 2.33

2007 POOR Tata motor 0.34 47.1 177.57 11.68 11.16 2.91

2006 GOOD Tata motor 0.17 37.59 143.93 18.22 12.11 2.8

2005 POOR Tata motor 0.33 32.44 113.64 9.22 11.51 3.06

2008 GOOD Tata Steel 0.12 61.06 298.7 9.56 39.79 0.49

2007 POOR Tata Steel 0.15 69.95 240.22 5.35 37.1 0.84

2006 POOR Tata Steel 0.08 61.51 176.19 7.1 36.11 1.43

2005 POOR Tata Steel 0.33 60.91 127.51 5.56 38.72 1.66

2008 POOR TCS 0.24 43.69 111.43 16.76 29.49 1.68

2007 GOOD TCS 0.33 36.66 82.35 30.65 30.23 1.84

2006 POOR TCS 0.4 53.63 114.64 32.5 29.69 1.99

2008 GOOD Sterlite 0.09 12.75 185.82 48.51 10.48 0.82

2007 GOOD Sterlite 0.6 13.48 79.82 29.52 9.94 1.7

2006 GOOD Sterlite 0.87 44.84 366.97 31.06 11.99 1.26

2005 POOR Sterlite 0.35 9.25 324.09 36.41 7.4 0.69

2008 GOOD Tata Power 0.26 38.26 352.27 22.79 24.15 0.54

2007 POOR Tata Power 0.03 33.59 291.77 10.54 22.62 0.49

2006 POOR Tata Power 0.16 29.66 267.76 13.25 26.06 0.55

2005 POOR Tata Power -0.07 26.8 248.36 7.95 33.27 0.49

2008 POOR Satyam 0.31 24.99 109.71 14.59 25.63 1.1

2007 POOR Satyam 0.34 20.77 86.65 20.7 27.47 1.07

2006 GOOD Satyam 0.34 37.22 133.57 20.71 33.91 1.07

2005 POOR Satyam 0.36 22.85 100.77 15.65 28.05 1.07

2008 GOOD SBI 0.31 103.94 776.48 13.94 66.15 0.3

2007 POOR SBI 0.03 83.91 594.69 10.41 59.83 0.29

2006 POOR SBI 0.1 81.77 525.25 10.05 56.99 0.26

2005 POOR SBI 0.04 80.01 457.38 6.97 57.62 0.2

--Continued




Year Perf Company NS EPS BV PECEPS BIDTS SNA

2008 GOOD

Reliance

Industries 0.18 131.97 542.83 13.7 20.78 1.2

2007 GOOD

Reliance

Industries 0.33 84.28 439.67 11.51 17.34 1.29

2006 GOOD

Reliance

Industries 0.22 63.7 324.11 9.04 16.81 1.24

2005 POOR

Reliance

Industries 0.3 53.3 270.43 6.82 19.49 1.24

2008 GOOD

Reliance

Energy 0.1 44.97 430.21 22.99 26.45 0.4

2007 POOR

Reliance

Energy 0.46 34.16 374.19 11.09 23.62 0.38

2006 POOR

Reliance

Energy -0.05 29.92 327.54 13.2 33.42 0.33

2005 POOR

Reliance

Energy 0.18 27.4 267.3 11.5 25.3 0.44

2008 POOR ONGC 0.06 72.65 330.16 12.39 44.38 0.73

2007 POOR ONGC 0.18 68.4 289.51 11.57 44.45 0.74

2006 POOR ONGC 0.03 94.89 378.42 11.85 49.93 0.73

2005 POOR ONGC 0.44 85.61 328.53 9.87 43.35 0.83

2008 GOOD NTPC 0.14 8.4 65.5 17.92 38.38 0.46

2007 POOR NTPC 0.22 7.85 59.73 14.44 39.51 0.45

2006 POOR NTPC 0.18 6.67 55.06 14.65 39.65 0.41

2005 POOR NTPC 0.2 6.72 51.07 9.43 43.06 0.38

2008 POOR Maruti 0.22 59.03 291.19 10.54 14.89 2.26

2007 POOR Maruti 0.17 53.29 237.16 13.08 15.05 2.3

2006 GOOD Maruti 0.11 40.65 188.67 17.3 13.93 2.67

2005 POOR Maruti 0.21 29.25 151.52 9.34 13.48 2.85

2008 POOR

Mahindra

&Mahindra 0.15 44.54 181.44 12.76 13.47 1.86

2007 GOOD

Mahindra

&Mahindra 0.21 43.1 148.72 15.03 14.73 2.16

2006 GOOD

Mahindra

&Mahindra 0.21 35.26 124.06 14.31 14.35 2.45

2005 POOR

Mahindra

&Mahindra 0.3 44.02 176.64 8.22 12.14 2.54

2008 GOOD L&T 0.41 71.73 325.95 38.56 13.98 1.92

2007 GOOD L&T 0.2 47.65 202.67 30.38 12.83 2.29

2006 GOOD L&T 0.12 70.58 335.57 31.04 11.08 2.47

2005 GOOD L&T 0.35 71.94 256.98 12.65 11.18 2.58

--Continued




2008 POOR Jaiprakash 0.06 72.65 330.16 12.39 44.38 0.73

2007 POOR Jaiprakash 0.18 68.4 289.51 11.57 44.45 0.74

2006 POOR Jaiprakash 0.03 94.89 378.42 11.85 49.93 0.73

2005 POOR Jaiprakash 0.44 85.61 328.53 9.87 43.35 0.83

2008 POOR Infosys 0.19 72.5 235.84 17.43 36.2 1.16

2007 GOOD Infosys 0.46 64.35 195.14 27.74 35.15 1.18

2006 POOR Infosys 0.32 81.41 249.89 30.98 34.85 1.31

2005 POOR Infosys 0.44 68.96 194.15 28.55 36.41 1.31

2008 GOOD ITC 0.11 7.68 31.85 23.32 23.58 1.74

2007 POOR ITC 0.19 6.65 27.59 19.75 22.31 1.81

2006 GOOD ITC 0.22 5.58 23.97 30.15 22.05 1.77

2005 GOOD ITC 0.13 83.92 315.63 13.92 25.4 1.64

2008 POOR ICICI 0.37 36.02 417.64 18.68 69.68 0.34

2007 GOOD ICICI 0.5 32.88 270.35 21.91 67.23 0.3

2006 POOR ICICI 0.5 27.35 249.55 17.15 62.67 0.26

2005 POOR ICICI 0.07 25.99 170.34 11.56 66.23 0.24

2008 GOOD HDFC 0.5 81.53 420.64 29.03 96.63 0.11

2007 GOOD HDFC 0.38 58.33 219.42 25.76 95.86 0.09

2006 GOOD HDFC 0.26 47.58 179.05 27.65 95.02 0.08

2005 POOR HDFC 0.11 39.19 155.87 18.19 94.81 0.08

2008 GOOD HDFC BANK 0.5 43.42 324.39 25.84 52.24 0.25

2007 GOOD HDFC BANK 0.45 34.55 201.42 22.92 52.42 0.26

2006 POOR HDFC BANK 0.49 27.04 169.24 23.63 49.22 0.19

2005 POOR HDFC BANK 0.26 20.84 145.86 21.35 51.8 0.19

2008 GOOD Hindalco 0.06 23.01 141.02 5.93 18.71 0.81

2007 POOR Hindalco 0.61 24.34 119.03 4.4 21.82 1

2006 POOR Hindalco 0.19 16.49 97.46 8.4 23.34 0.84

2005 POOR Hindalco 0.57 140.43 826.32 6.8 24.65 0.9

2008 POOR Bharti Airtel 0.44 32.9 106.34 16.66 41.72 0.96

2007 GOOD Bharti Airtel 0.59 21.27 60.19 22.66 40.7 1.07

2006 GOOD Bharti Airtel 0.42 10.62 38.71 21.97 36.23 0.93

2008 GOOD Grasim 0.21 239.03 887.12 9.28 31.43 1.03

2007 POOR Grasim 0.26 163.68 679.19 10.54 27.64 1.05

2006 GOOD Grasim 0.06 91.36 543.01 16.71 20.96 1.1

2005 POOR Grasim 0.17 94.34 471.65 9.68 23.98 1.14

--Continued




Year Perf Company NS EPS BV PECEPS PBIDTS NVA

2008 GOOD BHEL 0.14 55.82 220.1 33.23 21.92 2

2007 POOR BHEL 0.29 94.86 359.06 21.32 21.31 2.14

2006 GOOD BHEL 0.4 66.57 298.31 29.33 19.46 1.88

2005 POOR BHEL 0.19 37.86 246.24 16.4 17.82 1.61

2008 POOR Sun Pharma 0.39 47.16 203.15 24.69 34.68 0.74

2007 GOOD Sun Pharma 0.32 31.57 126.58 31.03 30.21 0.65

2006 GOOD Sun Pharma 0.39 24.06 78.8 33 31.04 0.54

2005 POOR Sun Pharma 0.26 15.94 59.51 26.62 29.34 0.43

2008 GOOD SAIL 0.16 17.62 55.84 8.96 28.17 1.77

2007 GOOD SAIL 0.21 14.54 41.92 6.53 27.78 1.85

2006 POOR SAIL 0.02 9.44 30.51 6.74 22.58 1.96

2005 GOOD SAIL 0.33 16.06 24.95 3.35 34.8 2.03

2008 POOR Dr Reddy -0.15 27.62 286.11 15.86 22.05 0.65

2007 POOR Dr Reddy 0.92 69.45 260.44 9.4 38.35 0.86

2006 GOOD Dr Reddy 0.29 26.82 294.93 34.36 18.99 0.66

2005 POOR Dr Reddy -0.07 7.85 271.05 37.07 9.19 0.69

2008 POOR Wipro 0.28 19.94 79.05 18.44 22.89 1.14

2007 POOR Wipro 0.34 18.61 63.86 26.49 25.75 1.44

2006 GOOD Wipro 0.41 13.47 45.03 35.99 25.67 1.59

2005 POOR Wipro 0.4 20.55 69.54 28.94 26.77 1.47

2008 GOOD Asian Paints 0.21 36.23 96.8 29.48 15.18 3.99

2007 POOR Asian Paints 0.21 26.51 77.57 24.55 13.86 3.89

2006 GOOD Asian Paints 0.19 17.72 64.87 28.67 12.77 3.93

2005 POOR Asian Paints 0.15 16.81 59.66 17.96 13.75 3.58

2008 POOR Shree_Cement 0.51 73.38 193.11 5.12 36.84 1.22

2007 GOOD Shree_Cement 0.96 49.96 130.47 5.29 39.3 1.12





Appendix 3

Evaluation Data Set (22 Observations)


2008 GOOD

TATA

Tea 0.076155 44.64 288.19 17.81 40.68 0.45

2007 POOR

TATA

Tea 0.089039 49.26 257.81 11.6 39.22 0.46

2006 GOOD

TATA

Tea 0.085851 31.57 202.67 24.78 27.49 0.71

2005 POOR

TATA

Tea 0.149453 21.53 182.69 20.62 22.19 0.74

2008 GOOD

India

Infoline 1.345285 21.52 173.35 30.9 37.16 0.6

2007 GOOD

India

Infoline 4.789984 9.97 56.88 26.84 34.98 0.78

2008 GOOD

Unitech

Ltd 0.119135 6.31 13.21 43.42 63.07 0.27

2007 GOOD Unitech 2.832803 12.03 14.3 32.04 61.62 0.53

2006 GOOD Unitech 0.282665 53.93 179.78 49.38 22.71 0.72

2005 GOOD Unitech 0.362027 23.43 139.24 13.41 13.24 1.02

2008 POOR

Berger

Paints 0.150905 2.8 10.91 10.67 9.87 3.24

2007 POOR

Berger

Paints 0.184275 2.45 8.61 12.15 9.84 3.38

2006 GOOD

Berger

Paints 0.178203 3.25 11.45 20.75 10.35 4.1

2005 GOOD

Berger

Paints 0.230131 2.42 10.2 13.02 9.07 3.52

2008 POOR Pidilite 0.319534 7.15 25.28 15.32 16.65 1.49

2007 POOR Pidilite 0.235473 4.5 19.33 19.84 14.99 2.06

2006 GOOD Pidilite 0.173607 3.34 16.34 23.74 15.56 2.24

2005 POOR Pidilite 0.177303 27.48 141.62 10.87 15.41 2.13

2008 POOR

TVS

Motors -0.17658 1.22 34.59 6.72 3.84 2.57

2007 POOR

TVS

Motors 0.198751 2.68 34.07 9.36 4.77 3.23

2006 GOOD

TVS

Motors 0.123598 4.74 32.26 16.1 7.59 3.44

2005 POOR

TVS

Motors 0.018785 5.61 28.58 7.35 8.98 4.15




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Web Links

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-risk+models:...-a0160166497

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ABOUT THE AUTHORS

Avijan Dutta is a faculty member in the Department of Management studies, National

Institute of Technology, Durgapur, India. He obtained his post-graduate degree in

management from IIM-Ahemdabad, and received his Ph.D. from Jadavpur University. He

has published several articles in leading journals. He was awarded the Silver Medal for

the Best Research Paper at the Association of Indian Management Schools convention

held at Hyderabad in 2005. He was also awarded 2nd

place in the Best Case Writing

competition at AIMS Western Region conference in 2005. He has conducted in-company

training programs for Indian companies such as Reliance and Sterilite Industries. His

areas of research interest are capital market and investment management.

Gautam Bandyopadhyay is an associate professor in the Department of Management

Studies, National Institute of Technology, Durgapur. He has extensive experience in

http://en.wikipedia.org/wiki/Logistic_regression

http://www.moneypore.com/

http://www.thefreelibrary.com/3+Investigating+the+performance+of+alternative+default-risk+models:...-a0160166497

http://www.thefreelibrary.com/3+Investigating+the+performance+of+alternative+default-risk+models:...-a0160166497

http://en.wikipedia.org/wiki/Omnibus_test

http://userwww.sfsu.edu/~efc/classes/biol710/logistic/logisticreg.htm




teaching and research activities. He received his Ph.D. from the Department of

Mathematics at Jadavpur University. He is also a fellow member of the Institute of Cost

& Works Accountants of India, and has presented several research papers at international

conferences in India and elsewhere. He is the author of many research papers in peer-

reviewed journals of national and international repute. He is now guiding several Ph.D.

students, and has advised others who have completed their Ph.D.

Suchismita Sengupta is an associate professor at the IES Management College and

Research Centre, Mumbai, India, and has 16 years’ experience in teaching, research, and

consultancy. She has a M.Com, MBA, a master’s degree in international business

operations, and a Ph.D. in finance. She is actively involved in research and in the

publication and review process of a few international journals. She has published nine

papers in refereed national and international journals and has contributed book chapters

published by Allied Publishers, Deep and Deep, and McMillan Advance Research Series.

She has provided consulting services to clients on business operations and has carried out

various projects on a collaborative basis. She has experience in training and development,

identification of training needs with competency mapping activities, and conducting

training programs to enhance the efficiency in overall business operations. She has also

reviewed research papers for foreign journals.

387

Documents

stock market performance

indian stock market

future stock performance

emerging stock markets

performance of stocks

stocks performance

various financial ratios

various ratios