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Investor apathy to stock market: a study using discriminant analysis.


Financing is an integral function of any business organization. After firming up an investment decision, financing decision is an obvious next step. Capital structure decides how much financial risk a business organization is willing to take for their investments. Both main sources of financing, debt and equity, are complementary to each other. In a real world where taxes, flotation costs and agency problems are unavoidable and compulsorily present, the composition of capital structure becomes important (Modigliani and Miller 1958/1963; Miller 1977). Excessive reliance on borrowed capital leads to high risk and even makes the equity financing costly. Debt adds bankruptcy cost, agency cost and reduces flexibility for further financing. Especially in the early stages of business, high debt may become the biggest bottleneck for the survival of the business organization. Though, equity is costlier than debt, it reduces the reliance upon the financial institutions and on the economy to provide with debt financing. Equity financing adds confidence of the business organization and sends positive signal to the financial market which may be quite useful for the future financing requirements. In principle, a sound capital structure will have a healthy mix of both the main sources of financing but the households do not think alike.

These are the households who are the net savers in any economy among the three sectors of the economy a long with business organizations and government. The financial assets held by the households are skewed heavily towards the fixed income securities like bank deposits and other claims on the government. In India only 3.5 percent of the total financial assets is invested in the stock market directly as well as indirectly (NSE, 2013). The penchant of investors for fixed income securities is not limited to Indian investors rather this is found in other countries also. Literature has found that in USA less than 30 percent have invested in stock market (Haliassos and Bertaut 1995; Brav, Constantinides and Greczy 2002; Vissing-Jorgensen 2002b; Attanasio, Banks and Tanner 2002; Heaton and Lucas 1997; Bogan 2008). Statistics revealing the number of household who have invested in stocks directly as well as indirectly having more than $1000 investment is only 23.2 percent (Mankiw and Zeldes 1991; Biume and Zeldes 1994). This non-participation in the stock market is a world-wide phenomenon and besides US there are evidences from many other countries like Italy and other European countries for non-participation (Guiso, Haliassos and Jappelli 2003b; Gardini and Magi 2007; De Santis and Gerard 2006; Heaton and Lucas 2000; Gomes and Michaelides 2005). Deliberations on the stock market participation puzzle may provide with the necessary inputs for solving the equity premium puzzle given by Mehra and Prescott (1985). The issue of non-participation in stock market helps in explaining assets pricing too (Hsu 2012). This tendency of the investors of having limited participation in the stock market ultimately make equity financing difficult for issuers. Keeping this in view authorities also want that stock market participation should be increased. Lack of clarity on the causes of stock market participation puzzle despite so many studies and efforts has developed snag on the cause of increasing the stock market participation (Andersen and Nilesen 2011; Haliossos 2002). In India the capital market regulator, SEBI (Securities Exchange Board of India) has embarked upon many innovation and corrective measures to increase the participation of investors in the stock market. SEBI has amended some of the provisions in its regulations on primary market in Issue of Capital and Disclosure Requirement 2009 (SEBI, 2009). Some of the important measures are reducing the depository charges for small investors, minimum allotment of the shares to all the applicants irrespective of the bidding size and non-withdrawal of institutional investors from IPO bidding. It seems that SEBI is facilitating more and more participation of the investors in the stock market. The aforesaid discussion describes that equity financing is very important especially during the initial and growth stages of the firm. This lackluster response in the equities by the householders makes this issue fit for further exploration. The exploration should be for the causes of such distorted way of Investment towards the fixed income securities. This is the main motivation for having this study. In this paper the causes have been explored for such behavior of the investors. A multivariate tool, discriminant analysis, has been used to do the exploration and estimate the model to explore the causes for the non-participation of the investors in equities.

The paper has been further divided into five more sections. The next section talks about review of literature. The third section discusses the data and methodology followed by fourth section on results. Discussion has been the part of fifth section. The sixth and last section is on concluding observation on the paper.

2. Review of Literature

Non-participation in the stock market is an area which has widely been researched. The studies done in this field can further be divided into three sets. The first set hovers around cases of stock market non-participation. The second set studies talks about the financial causes of non-participation. The third set of studies deals with the non-financial causes of the non-participation.

There are studies which suggest that all the investors should invest in the stock market. But the first set of researches on the instances of non-participation, do not support such results. The standard finance theory especially propounded by Von Neumann and Morgenstern (1944) and Savage (1954) in Expected Utility Theory and Subjective Utility Theory respectively, observe that all the investors should invest in the stock market. The benefit of diversification and significant equity premium are good reasons for all the investors to invest in the stock market (Arrow 1971; Samuelson 1969, Merton 1969, Andersen and Nilesen 2011). Some studies have also opined that the investors who have participated in the Stock market have got high life-time income (Mankiw and Zeldes 1991). It has been expressed by Guiso Haliassos and Jappelli (2003a) that in the European countries large stock market return has not ensured increased stock market participation. There are many more studies which have reported stock market non participation like King and Leape (1987), Mankiw and Zeldes (1991), Blume and Zeldes (1994), Blume and Friend 1978 and Crockett and Friend (1963). It has been observed that getting data related to stock market participation is difficult in some cases (Kennickell 1 998, Campbell 2006, Juster and James 1997). Due to this reason different studies have used different sources to collect the data related with nonparticipation (Kopczuk and Emmanuel 2004, Grinblatt and Keloharju 2000).

Second set of studies are on the financial causes of non-participation. Participation cost is one of the main financial causes for non-participation in the stock market (Haliassos and Bertaut 1995; Hong, Kubik Stein 2004; Heaton and Lucas 2000; Williamson 1994; Faig and Shum 2002). The participation cost includes the entry cost, transaction cost, cost to get the required information and any other cost which may be involved due to participation in the stock market. This cost may be moderate but creates hindrance in the mindset of the prospective investor in the stock market (Vissing-Jorgensen 2002(b)/2003; Gardini and Magi 2007; Haliassos and Bertuat 1995; Haliassos 2002; Hong, Kubik Stein 2004; Hsu 2012). Allen and Gale (1 994) further explained and added liquidity costs besides participation cost as another financial causes for the non-participation in the stock market. Vissing-Jorgensen (2002b) quantified the contribution of participation cost in non-participation and expressed that more than three fourth of the non-participation in the stock market is due to ownership cost or participation cost. Hsu that for low-income group investors the ownership cost which may be moderate, causes the non-participation. Hsu (201 2) has als o reported the contradiction that young and retired both of high-skilled and high-income group people also do not invest in the stock market. These finding corroborate the fact raised by Haliassos and Bertaut (1995) and Gomes and Michaelides (2005) that participation and ownership cost may be the reason for the non-participation but do not fully explain the causes of non-participation (Gomes and Michaelides 2005; Vissing-Jorgensen 2002a; Haliassos and Bertaut 1995; Gardini and Magi 2007). Use of internet also support this contradiction. Because internet and Information Technology have reduced participation costs significantly and despite that the issue of nonparticipation has not gone down (Gardini and Magi 2007, C hoi 2002). But in some other studies by Bogan (2008) and Barber and Odean (2002) on internet and stock market participation, it has been expressed that the participation has gone up due to internet.

The third set of studies are on the non-financial causes for the non-participation. Andersen and Nielsen (2011) made the point that for the majority of households, non-participation is unlikely to be explained by financial constraints. It was explained that there are investors who are despite having high-income and education about the financial products do not invest in stocks. This may be due to the fact that they procrastinate the decision to invest in stock market. In terms of age it has been found in the literature that young people invest more in the stocks than the older people (Jagannathan and Kocherlakota 1996; Haliassos 2002). As the human capital in terms of age falls, elderly start reducing exposure to stock and move to relatively secure mode of avenues like bonds. Even the financial planners also suggest the same to their clients of age (Georgarakos 2005). The reason is logical that in the long run stock are less risky and can easily perform better than bonds but for elderly investors long-term horizon is a difficult proposition (Jannathan and Kocherlakota 1996). Among non-financial causes of the non-participation, disappointment aversion (Gul 1991) has also been reported as an important cause (Ang, Bekaest and Liu 2005).

It is the Kahneman and Tvers ky (1979) who started the work on loss aversion and different investment buying behavior (Benartzi and Thaler 1995, Berkelaar and Kouwenberg 2000, Ait-Sahalia and Brandt 2001 and Gomes and Michaelides 2005). Ang, Bekaest and Liu (2005) correlated the loss aversion behavioral bias with the nonparticipation. Some studies have proposed that the limited stock market participation can be explained by risk aversion (Gomes and Michaelides 2005, Haliassos and Michaelides 2003) also. Cao, Wang and Zhang (2005) explained that the lack of proper model of the stock market return distribution and behavior of the stock market are also deterrents for participation. Cao, Wang and Zhang (2005) described this as model uncertainty. The same has also been reported in the seminal work by Hariossos and Betaut (1995) but explained that non-participation is due to deviation from the expected utility theory. Before Cao, Wang and Zhang (2005), Dow and Werlang (1992) and Epstein (2002) have also proposed the model uncertainty as the reason for the limited participation in the stock market. It is Cao, Wang and Zhang (2005) who further explained model uncertainty into high and low uncertainty aversion and eventually they attributed high uncertainty aversion as the reason for the non-participation. Bogan (2008) showed that the stock market participation is low because of market friction. Business cycle risk, cultural bias and education have also been reported as the non-financial reasons behind nonparticipation by Hariossos and Bertaut (1995). Haliassos and Bertaut (1995) has enumerated following three nonfinancial reasons for stock market non-participation. They are deviation from the expected utility theory, inertia factors (which includes age, cultural issues and business cycle risk) and non-diversifiable income risk. Besides Haliassos and Bertaut (1995), Compbell (2006) also explained that the deviation from the expected utility theory as one of the reasons for the limited participation in the stock market. Some studies have shown that lack of knowledge about the financial products or financial literacy may also be the cause of the limited participation in the stock market (Haliossos 1995, Campbell 2006, Guiso and Jappelli 2005). Level of education besides, age and wealth have been expressed as the cause of the stock market non-participation by Gardini and Magi (2007). Naudon, Tapian and Zurita (2004) proposed Choquet expected utility theory to explain the information acquisition cost as the reason for non-participation. It is proposed in the paper that information acquisition cost cannot be explained well in Neumann's Expected utility theory framework as the reason for non-participation. There are findings which explain that the reason for non-participation is more of behavioral or social in nature (Hong, Kubik Stein 2004, Campbell 2006, Guiso and Jappelli 2005).

Non-participation can be explained well by behavioral finance than the standard financial theory (Barberis and Thaler 2003). Haliassos (2002) enumerated background risk as the reason for non-participation which include uncertain labor income and unpredictable health expenditure. Barber and Odean (2000) opined that it is the active portfolio management which has eroded financial wealth of many investors. The reason for the loss in the stock market may be overconfidence but investors have directly or indirectly lost the wealth (Odean 1998, Gervais and Odean 2001). Such instances are deterrent for the stock market participation. In a landmark article Guiso and Sapienza and Zingales (2008) has presented trust as the deciding factor to explain the stock market participation puzzle. Ang, Bekaest and Liu (2005) also shared the similar views earlier on the relationship between trust and stock market participation.

3. Data and Methodology

The study was conducted in Jaipur, State of Rajasthan, India. A convenient sampling of 300 sample size was taken for the study. The sample unit has been defined as an individual whose earning is more than 5 lakh per annum. Discriminant analysis is used to serve the objective of the study. A structured questionnaire has been used to collect the required information. The questionnaire is comprised of one categorical variable of two categories as dependent variable (Criterion variable) and eight independent variables (Predictor variables). The criterion variable is dichotomous variable having two choices. One choice is for the existing stock market participants and the second choice is for the stock market non-participants. The predictor variables in the questionnaire are combination of categorical variables and quantitative variables. A predictive model for group membership is formulated with the help of discriminant analysis. This model is comprised of a discriminating function which is based on the linear combinations of the predictor variables so as to generate the best discrimination between the groups. The discriminant function is evolved from a sample of cases with known group membership. For this purpose the sample has been divided randomly into two groups. One group is used to estimate the discriminant function and the other group is used to check the predicting accuracy of the discriminant function. The same function can be applied to predict the cases that have the values for predictor variable but do not have the known membership.

Discriminant analysis serves three purposes. The first purpose is to identify the variables useful in predicting the cases, the second purpose is how these variables are combined into a mathematical equation to predict the most likely outcome and the third purpose is to determine the accuracy of the derived discriminating equation. To serve the first purpose, stepwise method has been used to find out the variables, best used to discriminate the cases. The criteria used are to minimize the Wilk's Lambda. Wilk's lambda is the ratio of the within-groups sum of squares to the total sum of squares. This is the proportion of the total variance in the discriminating scores which is not explained by differences among groups. Therefore the lower lambda implies that group means are different. In our analysis the results have been arrived at second step. Minimum partial F is 1.15 to include the variable and maximum partial F to remove the variable is 1. To determine the second purpose of the Discriminant analysis, Discriminant functions also known as canonical Discriminant functions are estimated. A canonical Discriminant function is considered as a linear combination of the discriminating variables which are formed to satisfy certain conditions. To determine the third purpose, the prediction accuracy a classification table is established carrying two set of data. One set of data is used for the building of the model another set of data is used for the validation of the results. Predicting accuracy is calculated for both the set of data.

4. Results

Table-I reports the mean scores of all the predictor variable used in the study. To estimate the discriminant function, 70 percent of the respondent have been used. The remaining 30 percent cases have been used in finding the predicting accuracy of the estimated discriminant function. On the visual inspection of the table-1, it is found that 'belief in capital market', 'surplus cash' and 'mutual funds are better than the stock markets' variables have large differences in their mean scores for those who want to invest in the stock market and for those who do not want to invest in the stock market. It can be inferred from this, that the discriminant function should be comprised of three variables. For the rest of the predictor variables, the differences in the mean score for both the categories of the criterion variable are not large enough.

One of the important assumptions for using Discriminant analysis is that the variance-covariance matrices of population of both the categories of criterion variable should be equivalent. This assumption is tested with the help of Box's M results which has been reported in table-II. The null hypothesis of equality of variance-covariance matrices has been found to be insignificant as the p-value of the F-statistics is .653 which is more than .05 (at 5 percent level of significance). This result ensures the appropriateness of discriminant analysis for further analysis. To estimate the discriminant function, stepwise method has been used. Here it is found that out of eight predictor variables used in the analysis only belief in capital market and Surplus cash have the capacity to discriminate between those who are interested in the stock market and those who are not interested in investing in the stock markets. Further the estimated discriminant function has also been tested for its significance (Table-III). T he value of the Wilk's lambda is .975 which is small. The Chi-square test applied on the estimated discriminant function is coming out to be significant as the p-value of the chi-square test is .045 which is smaller than .05 (at 5 percent level of significance). For making the discriminant function and knowing the relative strength of the discriminant variables, unstandardized and standardized coefficients have been estimated and reported in table-IV. Out of both the estimated discriminant variables in the discriminant function, 'belief in the stock market' has larger impact as compared to the other discriminant variable 'surplus cash'. The standardized coefficient for 'belief in the capital market' variable is .789 which is higher than the standardized coefficient for surplus cash (standardized coefficient for surplus cash is. 496).

The discriminant function is used to estimate the predicting accuracy of the discriminant model for classifying the cases between both the categories of the criterion variable. Not only to know the predicting accuracy of the discriminant model but also the discriminant function can be used to classify cases between both the categories of criterion variable. It is helpful in deciding about the cases whether one would be investing in the stock market or not. For this purpose group centroids have been estimated. Group Centroid are the group means of the categories of the criterion variable, estimated with the help of discriminant function. The group centroids are also called the average discriminant scores. The values of the group centroid for the group of those who invest in the stock market is .089 and for the other group of those who do not invest in the stock market is -.292. With the help of group centroids, the cut-off score is calculated for classifying the cases. The cut-off score is average of the group centroids and in this study it is coming out to be -.102. A discriminant score of a case more than -.102 would classify the case in the category of those who would invest in the stock market and a discriminant score of less than -.102 would classify the case in the category of those who do not want to invest in the stock market. The classification table (Table-V) has been estimated with the help of discriminant function and cut-off discriminant score. There are three set of predicting accuracy which has been reported. The first set of predicting accuracy has been estimated by the cases which are used to estimate the model (70 percent of the cases). The second set of predicting accuracy has been estimated again by the selected cases which are used for estimating the model but in the cross-validated manner. In the cross-validation manner the predicting accuracy is estimated by excluding the case which is being predicted. The third set of predicting accuracy has been estimated by the cases (30 percent cases) which have not been used to estimate the discriminant function. The predicting accuracy for first set and second set is 76.6 percent and for the third set is 72.9 percent.

5. Discussion

Stock Market participation differs from country to country and it has been increasing also (Guiso, Haliossos and Jappelli 2003a; Giannetti and Koskinen 2010). De spite this, the stock market participation is less than what it should have been (Compbell 2006). These research papers support the motivation of doing the present study.

The method used in the study is discriminant analysis for studying the causes for the non-participation in the stock market. Similar approaches have also been used by different studies to establish the causes for non-participation in the stock market. Haliassos and Bertaut (1995), Guiso, Haliossos and Jappelli (2003a/2003b) and Gardini and Magi (2007) have used Probit regression to do the similar study on non-participation. Probit models are also probability models where dependent variable is categorical and in case of non-participation studies, it is dichotomous. Discriminant analysis is also similar type of model used in the study where dependent variable (Criterion variable) is dichotomous.

In this study two variables have been found to discriminate between stock market participants and non participant. The variables are surplus cash and belief on the capital market as the discriminating variables.

There are many studies which corroborate that the wealth or income induces stock market participation. There might be other reasons besides the wealth or income for non-participation but wealth or income has been found to be an important factor for the stock market participation (Hsu 2012; Haliassos and Bertaut 1995; Gardini and Magi 2007; Vissing-Jorgensen 2002/2003). It has been demonstrated that with increase in wealth and age, the stock market participation also increases (Mankiw and Zeldes 1991; Poterba and Samwick 2003). This further corroborates the finding of this study. Because surplus cash increases with age and wealth which is one of the discriminant variable found in this study.

Andersen and Nilesen (2011), Ang, Bakaert and Lui (2005), Barberis, Huang and Thaler (2006) and Puri and Robinson (2007) have expressed in one way or the other that non-financial psychological causes are responsible for non-participation in the stock market. In this study the second variable found as the discriminant variable is 'belief in the capital market' which is also non-financial and psychological. The variable 'belief on the stock market' has also been widely accepted as one of the main reasons for stock market participation. There are many studies which have observed many findings but none claimed to have fully explained the reason for non-participation. In such scenario this variable, belief in the stock market, contributes significantly in the knowledge of causes for the stock market non-participation. Guiso Sapienza and Zingales (2008) and Ang, Bekaest and Liu (2005) have strongly put forth this view that the trust in the stock market is one of the main reasons for deciding to participate in the stock market or not. Huberman (2001), Merton (1987) and Hong, Kubik and Stein (2004) have also supported directly or indirectly that the trust is related with the stock market participation.

6. Conclusion

The study has estimated two main reason for the stock market non-participation. The first and the main reason which has been found in the study is belief in the stock market. Belief in the stock market may come from the understanding the stock market. Lack of belief may come due to the ignorance about the stock market. The lack of belief about the stock market may also come due to miscommunication about the stock market. The second reason found in the study which differentiate investors between those who invest in the stock market and those who do not invest in the stock market is lack of surplus cash. This reason should also be explored further as these are instances in the literature that even those who have surplus cash they also do not invest in the stock market. Both the reasons found in the study for the stock market non-participation require further investigation which is the limitation of the study but ideas for future studies in the field of stock market non-participation.


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Shailesh Rastogi

Professor, School of Business and Management, Jaipur National University.


Comparison of Means of Predictor Variables

Criterion Variable: Stock                  Means    Standard    No. of
Market Investments                                  Deviation   Items

Yes     Knowledge of Capital Market        7.1030    1.65140      165
        Awareness                          6.7515    1.38108      165
        Surplus Cash                       6.3212    1.36144      165
        Risk Averse                        7.1636    1.42406      165
        Financial Backing                  6.3697    1.27463      165
        Belief in Capital Market           7.2303    1.19768      165
        Published Information              5.8061    1.33844      165
        Mutual Funds better than Stocks    7.3273    1.39757      165
No      Knowledge of Capital Market        7.0200    1.55826       50
        Awareness                          6.7200    1.60408       50
        Surplus Cash                       6.0000    1.27775       50
        Risk Averse                        7.0000    1.38505       50
        Financial Backing                  6.2000    1.32480       50
        Belief in Capital Market           6.8200    1.35059       50
        Published Information              5.6200    1.10454       50
        Mutual Funds better than Stocks    6.9600    1.32419       50
Total   Knowledge of Capital Market        7.0837     1.6270      215
        Awareness                          6.7442    1.43216      215
        Surplus Cash                       6.2465    1.34640      215
        Risk Averse                        7.1256    1.41357      215
        Financial Backing                  6.3302    1.28535      215
        Belief in Capital Market           7.1349    1.24384      215
        Published Information              5.7628    1.28780      215
        Mutual Funds better than Stocks    7.2419    1.38656      215


Box's M Results

Box's M                    1.653

F Value     Approx.        0.542
              dof1           3
              dof2       126200.874
          Significance     0.653

Tests null of equal population covariance matrices


Wilk's Lambda Table

                 Wilks' Lambda   Chi-square   dof   Sig.

Test of                 0.975        5.476     2    0.045


Canonical Discriminant Function Coefficient

Variables                  Unstandardized   Standardized

Surplus cash                   0.370           0.496
Belief in capital market       0.639           0.789
Constant                       -6.871            --

The unstandardized coefficients are estimated to develop
equation of the discriminant function. The discriminant
function equation is

Discriminant Score = 0.370[X.sub.1] + 0.639[X.sub.2] + (-)6.871


X1 = Surplus cash

X2 = Belief in Capital Market


Classification Table *

Invest in the Stock Market               Predicted     Total

                                          Yes    No

Cases        Original      Count   Yes     164     1     165
  selected                         No       50     0      50
                           %       Yes    99.4   0.6   100.0
                                   No    100.0   0.0   100.0
             Cross-        Count   Yes     164     1     165
               validated           No       50     0      50
                           %       Yes    99.4   0.6   100.0
                                   No    100.0   0.0   100.0
Cases not    Original      Count   Yes      62     0      62
  selected                         No       23     0      23
                           %       Yes   100.0   0.0   100.0
                                   No    100.0   0.0   100.0

* Selected cases have 76.6 percent predicting accuracy (for
both original and cross validated cases); not selected cases
have 72.9 percent predicting accuracy
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Author:Rastogi, Shailesh
Article Type:Report
Geographic Code:9INDI
Date:Jul 1, 2014
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