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Chapter 9 Final Data Analysis &

Interpretation

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CHAPTER 9

FINAL DATA ANALYSIS AND INTERPRETATION

The primary data analysed by way of Factor Analysis above in Chapter 8 and

the secondary data analysed (High Performer / Low Performer with the

benchmark as returns of BSE Sensex) in Chapter 6 was subjected to

Discriminant Analysis in order to generate the Z score for developing the

discriminant model towards the factors affecting the performance of Open

Ended Equity Scheme.

SPSS Output :

Analysis Case Processing Summary

Unweighted Cases N Percent

Valid 78 100.0

Excluded

Missing or out-of-range group codes

0 .0

At least one missing discriminating variable

0 .0

Both missing or out-of-range group codes and at least one missing discriminating variable

0 .0

Total 0 .0

Total 78 100.0

The Analysis Case-processing Summary gives us the dataset in terms of the

valid, excluded cases and the total cases. If the cases are excluded the

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SPSS output gives the reasons for such exclusions. It also gives the

percentage wise statistics of the valid, excluded and the total cases

processed by SPSS.

SPSS Output :

Group Statistics

PERFORMANCE Valid N (listwise)

Unweighted Weighted

1 FACTOR_1 41 41.000

FACTOR_2 41 41.000

FACTOR_3 41 41.000

FACTOR_4 41 41.000

2 FACTOR_1 37 37.000

FACTOR_2 37 37.000

FACTOR_3 37 37.000

FACTOR_4 37 37.000

Total FACTOR_1 78 78.000

FACTOR_2 78 78.000

FACTOR_3 78 78.000

FACTOR_4 78 78.000

The group statistics gives the distribution of observations into different groups.

Since, in the present research we have categorized into two groups viz High

Performer as ‘1’ and Low Performer as ‘2’, the SPSS has grouped the data

into two groups. The total numbers of 78 observations group, which represent

100% of the observations, have been grouped for the Discriminant Analysis.

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The function indicates the first canonical linear discriminant function. The

number of function depends on the discriminating variables. Since in the

present research we have used two discrimination variables, one function has

been calculated by SPSS. The function gives the projection of the data that

best discriminant between the groups.

Eigen Values

The Eigen values are related to the canonical correlations and describe how

best discriminating ability the functions possess. The % of variances is the

discriminating ability of the 2 groups. Since there is only one function, 100%

of the variance is accounted by this function. The cumulative % of the

variance gives the current and preceeding cumulative total of the variance. As

mentioned above, as there is only one function in the present research we

have 100% of the cumulative variance.

The canonical correlations of our predictor variables viz high performer or low

performer and the grouping of the job is given in the below analysis.

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SPSS Output :

Eigenvalues

Function Eigenvalue % of

Variance Cumulative % Canonical Correlation

1 1.275(a) 100.0 100.0 .749

First 1 canonical discriminant functions were used in the analysis.

The Eigen value gives the proportion of variance explained. A larger

Eigenvalue explains a strong function. The canonical relation is a correlation

between the discriminant scores and the levels of these dependent variables.

The higher the correlations value, the better the function that discriminates the

values. 1 is considered as perfect. Here, we have the correlation of 0.749 is

comparatively high.

Testing hypothesis regarding discriminating power of the variables

Null Hypothesis H0 : There is no significant discriminating power in the

variables.

Alternate Hypothesis H1 : There may be a significant discriminating power in

the variables.

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SPSS Output :

Wilks' Lambda

Test of Function(s) Wilks' Lambda Chi-square Df Sig.

1 .440 60.831 4 .000

Assuming 95% level of Confidence α = 0.05

p value (Sig value of the above output) = .000

Rule : Reject Null Hypothesis H0 and accept Alternate Hypothesis H1

Here 0.000 < 0.05, therefore we reject null Hypothesis H0 and accept

alternate Hypothesis H1 and conclude that based on the sample data, there

may be a statistically significant discriminating power in the variables included

in the model. Hence, we can proceed to develop the Discriminant Equation.

The test of the functions as mentioned earlier is the test with the null

hypothesis. The Wilks Lambda is one of the multivariate statistics calculated

by SPSS. The lower the value of Wilks' Lambda, the better. In the present

case the value is 0.440. The Chi-square is 60.831 with 4 degree of freedom,

which is based on the groups present in the categorical variables. A Wilks

Lambda of 1.00 is when the observed group means are equal, while a small

Wilks Lambda is small when the within-groups variability is small compared to

the total variability. This indicates that the group means appear to differ.

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At 95% level of significance with α = 0.05 we are rejecting the Null Hypothesis

H0 and accepting the alternate hypothesis H1 and proceeding further with the

Discriminant Analysis.

Checking for relative importance of each independent variable

On comparing the standarised coefficient, it is possible to identify which

independent variable is more discriminating than the other variables. The

higher the discriminating powers the higher the standarised discriminant

coefficient.

The SPSS output of the Standardised Canonical discriminant function

coefficient is given in the below table. The Existing Returns of the scheme

has the highest discriminating power due to the highest discriminant

coefficient of .542 followed by Excess Returns over Benchmark, Stock

Selection & Timing and the Risk Management. This indicates that the

existing return of the scheme has a best predictor of whether the scheme will

be a high performer or a low performer.

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SPSS Output :

Standardized Canonical Discriminant Function Coefficients

Function

1

Stock Selection & Timing .146

Risk Management .010

Existing Returns of the Scheme .542

Excess Return over Benchmark .524

The standardized canonical discriminant function coefficient is used to

calculate the discriminant score. The score is calculated as a predicted

value from the linear regression using the above standardized coefficients and

the standarised variables.

Based on the coefficient above we can rank the relative important predictor

variables as summarized below: -

Table 10 : Ranking of the Variables

Ranking of the

Variable

Predictor Variable

1 Existing Returns of the Scheme

2 Excess Return over Benchmark

3 Stock Selection and Timing

4 Risk Management

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Formulating the Discriminant Function

The standard form of the Discriminant Function is

Z = a + b1x1 + b2x2 + b3x3 + b4x4

Where

Z is the dependent variable

‘a’ is the constant term from the SPSS output, which is in the following table

viz ‘Canonical Discriminant Function Coefficient’.

b1, b2, b3 & b4 are the corresponding unstandarised discriminant function

coefficient from the SPSS Output

x1, x2, x3 and x4 are the independent variables, here we have Four predictor

factors viz Existing Returns of the Scheme, Excess Return over Benchmark,

Stock Selection and Timing and the Risk Management.

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Since the predictive equation is being constructed, the unstandardised

canonical coefficient will be used to construct the discriminant function as

follows: -

Z = -2.544 + 0.002(Stock Selection & Timing) + 0.000(Risk Management) +

.080(Existing Return of the Scheme) + .078(Excess Return over the

Benchmark)

SPSS Output :

Canonical Discriminant Function Coefficients

Function

1

Stock Selection & Timing .002 Risk Management .000 Existing Return of the Scheme .080 Excess Return over Benchmark .078 (Constant) -2.544

Unstandardized coefficients

Thus the Canonical Discriminant Function Coefficient indicates the

unstandardised scores of the independent variables.

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Formulation of the Decision Rule

SPSS Output :

Functions at Group Centroids

PERFORMANCE Function

1

1 1.059

2 -1.173

Unstandardized canonical discriminant functions evaluated at group means

The Function of the Group Centriod gives the average discriminant score of

the two groups. These two scores are equal in absolute values but have

opposite sign discriminating the score.

The centroids are the extreme point to formulate the decision rule and are

represented below: -

-1.173 0.000231 1.059

Since the 2 groups viz the High Performer and Low Performers are not equal

(37 Low Performer and 41 High Performer), we use weights on the centroids

to find the dividing point.

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The dividing rule will therefore be

= (n1)(Lower Centriod) + (n2)(Higher Centriod) ___________________________________________ n1 + n2

= (37 x -1.173) + (41 x 1.059) ___________________________ 37 + 41

= 0.018 _____ 78 = 0.000231

The decision rule classification will be as under: -

Predict and classify as Low Performer if

-1.173 < Z < 0.000231

Predict and classify as High Performer if

0.000231 < Z < 1.059

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SPSS Output :

Classification Processing Summary

Processed 78

Excluded Missing or out-of-range group codes 0

At least one missing discriminating variable 0

Used in Output 78

The classification processing summary gives us the summary the total cases

that have been processed successfully based on the analysis. Incase, any

observation is not processed the reason for the same is highlighted here. In

the present research all the 78 observations have been processed

successfully.

SPSS Output :

Prior Probabilities for Groups

PERFORMANCE Prior Cases Used in Analysis

Unweighted Weighted Unweighted

High Performer .500 41 41.000

Low Performer .500 37 37.000

Total 1.000 78 78.000

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The prior probabilities give us the number of observations used in the analysis

and the distribution of the observations into groups used as a starting point in

the analysis. It gives the weighted value, which is further used in the

calculation of the centriod value.

Developing and Analysing the Confusion Matrix

For verifying the predictive capacity of the discriminant Function, the equation

is subjected to the data collected on the four dependent variables. The values

from the original data collected is substituted in the unstandardised

discriminant function and the decision rule is used to classify the performance.

The predicted group membership in the below classification results gives the

predicted frequencies of groups from the analysis. The number of

observations given in this column indicates how many have been correctly

and incorrectly classified. The original gives the frequencies of the groups in

the data. The count gives the number of observations falling into the given

category and the %u gives the percentage of observations in a given group.

The discriminant function thus developed was subjected to predict how many

of these schemes were low performer or high performer. The prediction,

based on this discriminant function, was compared with the actual information

from the data collected. If the original value was the same as that of value

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used in the data collected then there is no error. In other cases, the model

has led to an error on classification.

SPSS Output :

Classification Results(a)

PERFORMANCE Predicted Group

Membership Total

1 2 1

Original Count High Performer 41 0 41

Low Performer 2 35 37

% High Performer 100.0 .0 100.0

Low Performer 5.4 94.6 100.0

a 97.4% of original grouped cases correctly classified.

It has been observed that 97.4% of data was correctly classified as High

Performer and Low Performer of the scheme by the discriminant function. It

has also been noticed that out of the 78 schemes, 41 schemes have been

correctly classified as High Performing Schemes. Out of the 37 Low

Performing schemes, 35 schemes have been correctly classified as Low

Performing schemes whereas 2 schemes have been wrongly classified as

High Performing schemes. The accuracy of the model may hence be

considered adequate.

This indicates a very good predictive capacity of the discriminant function. It

has the capacity to predict whether a scheme would be a potential high

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performer or a low performer based on the Treynor & Mazuy’s alpha

coefficient, Treynor Index, the Mean Return and the Geometric Mean of the

Excess Return over the Benchmark.

Example 1:

ABN ABRO Equity Fund had a NAV of Rs 10.38 as on 1st October, 2004 and

Rs 35.37 as on 30th September, 2007. The mean return of the scheme over

the period was 33.25%. The model will predict if the scheme is a potential

high performer or low performer as mentioned below: -

Z = -2.544 + 0.002(Stock Selection & Timing) + 0.080(Existing Return of

the Scheme) + .078(Excess Return over the Benchmark)

Stock Selection & Timing = -25.23

Existing Mean Return = 33.25

Excess Return over the Benchmark = 5.45

Substituting the values in the above model -

Z = -2.544 + (0.002 * -25.23) + (0.080 * 33.25) + (0.78 * 5.45)

Z = 0.49064

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The decision rule for classification is

Predict and classify as Low Performer if

-1.173 < Z < 0.000231

Predict and classify as High Performer if

0.000231 < Z < 1.059

Based on the Z computed value is 0.49064, thus the scheme is a potential

high performer scheme.

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Chapter 10 Summary & Conclusion

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CHAPTER 10

SUMMARY AND CONCLUSIONS

The Indian Mutual Fund Segment is the fastest growing sector in the Financial

Sector. Many more Investors are investing in the Mutual Fund Schemes due

to the perceived features of Liquidity, Returns, Professional Management, Tax

Benefit and various other factors, which make them more attractive in

comparison to direct investment. Moreover, in the period covered in this

study, the returns given by the Open Ended Equity schemes are surprisingly

high, considering the fact that more and more schemes are beating the

Benchmark.

An Investor is concerned about risk as well as returns. It is axiomatic to say

that the higher the returns, higher the risk. However, in exception to the

same, some Mutual Funds have given higher returns as compared to the risk

involved in investing, in the open-ended equity schemes. The Fund Manager

puts in rigorous efforts to ensure that his schemes give higher returns as

compared to the risk involved in investing in securities and the Investors is

also keen to know which are potential high performing schemes. Considering

the same, the current research had focused on the performance of the Open

Ended Equity Schemes.

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There has been an explosive amount of literature on the performance of

Mutual Fund. For a long time, Sharpe Ratio, Treynor Index, Jenson Model

and Fama Model have been and continue to serve as measure of Portfolio

Performance. The position here is ex-post (After the period elapsed).

This thesis strives to determine the factors that drive the portfolio Fund

Manager's performance ex-ante. Assuming these factors are taken into

consideration at the start of the Investment period, the Fund Manager should

be in a better position to attain performance better than the benchmark.

In this connection, the literature survey showed that a study was conducted by

Pendaraki et al on Greek Mutual Fund. This research identified factors

affecting superior performance applicable to Greek Markets. The findings

were based on UTIDAS. This is a recent study completed in year 2003. The

Mutual Fund sector in India is only in its 35th Year, quite young in comparison

to US counter parts. Mutual Fund investing is at its nascent stage. It is all the

more important that Fund Managers handle the portfolios in a responsible

manner. In this context, this study addressed the literature gap on Indian

Mutual Fund by taking the Pendaraki's approach but only as a starting point.

This being the first model developed on the factors affecting the performance

of the Indian Mutual Fund Industry, is a new contribution to the Indian Mutual

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Fund Industry. The model was tested successfully and results discussed in

Chapter 9 (page 183).

The Key research results from the above analysis have been summarized as

under: -

The four core factors that influence the performance of the Open ended equity

schemes are Stock Selection & Timing, Risk Management, Existing Returns

of the scheme and Excess Returns over the Benchmark. These four core

factors have been extracted out of the total 18 criteria, which were used to

evaluate the Mutual Fund performance on the three years data.

A similar type of study was conducted by Pendaraki, Doumpos and

Zopounidis on Greek Mutual Funds. As per this study four core factors

accounting for 88.5% of the total variance were evolved. These were (1) Past

Returns of the Mutual Fund (2) Forecasting Ability of the Mutual Fund

Manager (3) Market Timing ability of the Mutual Fund Manager and (4)

Systematic Risk of the Mutual Funds.

The outcome of the present research on the Indian Mutual Fund Industry is

nearly similar to the earlier research done on the Greek Mutual Fund.

However, there are some exceptions in the final criteria used for evaluation of

the four core factors.

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Firstly, in the Indian context, the Mean Return has been the criterion for

evaluating the returns of the Mutual Fund scheme, whereas in the Greek

Mutual Fund study, it was the return in the 3 year period of the Mutual Fund

scheme. Hendricks et al, Brown and Goetzman in their studies have found

evidence supporting the idea that past performance is related to future

performance. Thus, the first core factor viz mean returns over the period of 3

years considered in this research is supported by the above findings.

Secondly, in the forecasting ability and the stock selection ability, the criterion

used is the Treynor & Mazuy's α Coefficient. In the Greek Mutual Fund study,

the Hendriksson-Merton α Coefficient and the Treynor & Black appraisal ratio

were the two management evaluation criteria measuring the efficiency of the

Mutual Fund Managers. Treynor & Mazuy in their research titled 'Can Mutual

Funds Outguess the Market' have found that a positive gamma will indicate

that timing activities have added value to portfolio performance. Comparing

the gammas of different funds will indicate the relative importance of timing

activities in their investment policies. A study was conducted by Nalini Prava

Tripathy, in their research titled 'Market timing abilities and Mutual Fund

Performance - An Empirical Investigation into Equity Linked Saving Schemes'

for examining the market timing abilities of the Fund Managers to reward

higher return to the Investors. The study was for testing the performance

evaluation of the Indian Mutual Funds. As per the study there was only one

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scheme where market timing ability of the Fund Managers was to some

extend exhibited.

Thirdly, in the Indian scenario, it was the Treynor Index as the criterion to

measure the portfolio’s excess return per unit of risk. In the Greek Study, the

systematic risk of the Mutual Fund was the Beta Coefficient in the Greek

Mutual Fund evaluation Model. Ibrahim M M in his study 'Performance

Evaluation of the Mutual Fund Industry in Nigeria :- 1990 - 2002' has

emphasized that Treynor Index sums up the risk and return of the portfolio in

a single number while categorizing the performance of the portfolio. The

Sharpe and Treynor indices yielded similar results in actual empirical tests

(Fischer et al. 1997).

Finally, apart from the above, the Geometric Mean of the excess returns over

the Benchmark, which gives the central tendency, which is calculated by

multiplying the set of numbers and taking the nth root, where n is the number

of returns was the additional factor affecting the performance of the Indian

Mutual Fund Industry. The Geometric means of the excess returns over the

benchmark, also helps the Investors to assess how well the fund manager

has performed as compared to some benchmark indices. The Geometric

Means of the excess returns over the Benchmark shows how well the Fund

Manager was able to pick stock (Pendaraki et al)

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Thus, the present research appears to hold good in the Indian Mutual Fund

Industry upto a certain extent.

A basic model was developed to identify the potential high performer and the

low performer, based on the above four factors identified by the Factor

Analysis. The model has classified 97.4 % of the groups correctly. This gives

extremely high result of the model to come out with correct classifications of

the high performer and the low performer. The model has used only three

variables viz Stock Selection and Timing, Existing Returns of the Schemes

and Excess Return over the Benchmark. Adding more variables to this model

will further refine the model and could further improve the predictive ability of

the model.

The model developed in the present research, is considered to be a major

innovation and supportive to the Mutual Fund Managers and the Investors.

The present model would be handy to the Mutual Fund Managers and

Investors in the Mutual Fund Open Ended Equity schemes. The main use of

the said model to the Investors would be for selection of appropriate Mutual

Fund Open Ended Equity scheme for investing over a medium to a long-term

period. Also the said model will be very useful to the Mutual Fund Managers

to monitor the performance of their schemes and to come out with appropriate

vital strategies to align their portfolio and ensure high performance of their

schemes in the future.

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Limitation of the Study

The present study has been done only on the Open Ended Equity Schemes

and therefore may not hold good in case of Closed Ended Equity schemes or

a Balance or Liquid Scheme. The findings of the present research cannot be

generalized to all the segments of Mutual Fund Schemes.

The stock market is very dynamic, due, to which the above research findings

may not be the same in the very long run and need to be reviewed

periodically.

In the Factor Analysis, the results of three-fourth of the influencing variables

has been explained by the primary data collection. The impact of the one-

fourth has not been identified in the study.

Recommendation for Future Research

A similar type of research has been done on the Greek Mutual Fund and the

Indian Mutual Fund Industry. The research can be carried out on other

International Mutual Funds to analyse whether the findings are the same or

there are differences in the core factors affecting the performance of Mutual

Fund Schemes.

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In the Indian Scenario, the BSE Sensex containing 30 scrips has been

selected as the proxy for the Benchmark. However, at present there are

broader indices available like the NIFTY, BSE 100 etc.