BRM Individual Assignment

Submitted By:

Nilotpal Ray

PGP-12-198

Division C

PGDM: Operations

2012-2014

Table of Contents:

Sl. No. Topic Page No.

1.1 Management Research Problem

Statement

1

1.2 Business Research Problem Statement 1

2.1 Methodology & Decoding the Business

Problem

2

2.2 The Research problem: Part I 2

2.3 The Research Problem: Part II 2

2.4 Final Objective 2

3.1 Collection of Data 3

4.1 The Multiple Discriminant Analysis Model 3

4.2 Interpretation of SPSS Output 9

4.3 Test of the MDA Function 15

5.1 The CAPM-SML Equation 16

6.1 Comparing CAPM-SML with MDA

Function

17

7.1 Final Conclusion & Recommendation 17

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BRM Assignment:

Name: Nilotpal Ray (Div-C, Operations)

Group: 38

Domain: Power (Central Sector)

Organization Chosen: National Thermal Power Corporation (NTPC)

Limited

1.1 Management Research Problem:

To study the risk & return towards investments in NTPC Limited Stocks in the Indian Stock

Market (NSE).

1.2 Business Research Problem:

To calculate the predicted return over NTPC Stocks as per the Capital Asset Pricing

Model (CAPM) Security Market Lien taking CNX Nifty 50 as a basis of market yield and

comparing it with a Multiple Discriminant Analysis Model based on historic returns on

NTPC Stocks to address the following research problems:

1) To design a MDA model to predict the nature of return on stocks of NTPC Ltd.

which is dependent on changes in macroeconomic and industry scenario

like Coal Prices, Exchange Rates, IIP Index (electricity), GDP at factor cost,

BV/MV ratio etc.

2) Comparing the MDA model with the CAPM Model for predicting the nature

of returns on NTPC stocks.

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2.1 Methodology & Decoding the Business Problem:

National Thermal Power Corporation Limited (NTPC Ltd.) is a public sector undertaking

(PSU) by the Government of India. The company is responsible for catering to the

electricity distribution all across India through various grids of capacities upto 750 KV.

Being in the sector of power & electricity generation, the following factors have been

identified, which is primarily assumed to influence the risk & return of the NTPC Ltd.

stocks in the National Stock Exchange.

Industry Variables Macroeconomic Variables

1. IIP Index (Electricity): X1 1. GDP at Factor Cost: X4

2. WPI (Coal): X2 2. Exchange Rates (USD vs. INR): X5

3. (Book Value/Market Value) Ratio: X3

2.2 The Research Problem: Part I:

In the first part, the research tries to formulate a Multiple Discriminant Analysis Model as

per the following structure:

Return on NTPC Stocks (Y: +1,-1) = f (X1, X2, X3, X4, X5)

Y = C1X1+C2X2+C3X3+C4X4+C5X5+ C6 +ei Where, C1, C2…C6= Constants, ei = Error

With this MDA Model, an attempt has been made to forecast the nature future returns

on the NTPC Stocks.

2.3 The Research Problem: Part II:

In the second part of the research, an attempt has been made to calculate the historic

returns of NTPC Stocks w.r.t the CNX Nifty 50 Portfolio as per the Capital Asset Pricing

Model (CAPM) and thereby calculate the risk coefficient (β) of the Security Market Line:

E(Rj) = Rf + β [E(Rm) –Rf]

2.4 Final Objective: Combining Part I & Part II:

The final objective of this research is to see how efficient is the MDA Model in predicting

the movement of the stocks of NTPC Ltd. for certain changes in macroeconomic &

industrial variables i.e. to get a comparative scenario between the interpretations of the

MDA Model and the CAPM Security Market Line for predicting the returns on NTPC stock

in the Indian Equity Market.

E(Rj) = Expected return on NTPC Stocks

Rf = Risk free return

β = risk coefficient

E(Rm) = Market return on portfolio

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3.1 Collection of Data:

Data required for the research were collected from reliable secondary sources. The

following provides a list of them:

Data Source

Monthly Quotes for NTPC Stocks Yahoo Finance Website

Monthly Quotes for CNX Nifty 50 -do-

10 yr yield on GOI Bonds Economic Times

IIP Index (Electricity) RBI Database on current statistics

WPI Coal -do-

Book Value/Market Value Yahoo Finance Website

GDP at factor cost RBI Database on current statistics

Exchange Rates -do-

Excel sheets having the Data are attached with the report for reference.

4.1 The Multiple Discriminant Analysis Model:

The Multiple Discriminant Analysis Model goes per the following structure:

Return on NTPC Stocks (Y: +1,-1) = f (X1, X2, X3, X4, X5)

Y = C1X1+C2X2+C3X3+C4X4+C5X5+ C6 +ei Where, C1, C2…C6= Constants, ei = Error

With the obtained values of Y (+1,-1) we are trying to predict the nature of return for

investments in NTPC Stocks:

Y= +1: Returns are Positive

Y= -1: Returns are Negative

To test the model, we do a Trendline plot for each of the variables X1 to X5. From the

Trendline plot we calculate data for next three periods and test our MDA Model with

the actual returns.

Next part of the research goes with formulating the SML as per the CAPM stipulations,

taking into account the historic returns of NTPC stocks w.r.t CNX Nifty 50 returns. Again

we do the same test for the next three periods to test the strength of SML Regression

Equation.

Finally we present a comparative picture of the two outcomes.

Y= +1 will imply that investments in NTPC Stocks will yield a positive return.

Y= -1 will imply that investments in NTPC Stocks will yield a negative return.

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y = -0.5629x + 153.54

R² = 0.9027

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

IIP Electricity

IIP Electricity

Linear (IIP Electricity)

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y = 0.0093x2 - 1.9647x + 214.01

R² = 0.9472

0.0

50.0

100.0

150.0

200.0

250.0

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

WPI Coal

WPI Coal

Poly. (WPI Coal)

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y = 3E-07x3 + 7E-05x2 - 0.0093x + 0.587

R² = 0.7868

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

BV/MV Ratio

BV/MV Ratio

Poly. (BV/MV Ratio)

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y = -1.0333x + 257.3

R² = 0.982

0.00

50.00

100.00

150.00

200.00

250.00

300.00

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

GDP Factor Cost

GDP Factor Cost

Linear (GDP Factor Cost)

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y = -2E-05x3 + 0.0057x2 - 0.4191x + 53.969

R² = 0.5058

0

10

20

30

40

50

60

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Exchange Rates

Exchange Rates

Poly. (Exchange Rates)

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Forecasted Values:

X1 X2 X3 X4 X5

P1 (Oct’12) 153.54 214.01 0.587 257.30 53.97

P2 (Nov’12) 154.10 215.98 0.596 258.33 54.43

P3 (Dec’12) 154.66 217.97 0.606 259.37 54.96

Actual Values:

X1 X2 X3 X4 X5

P1 (Oct’12) 150.24 210.3 0.537 256.67 54.78

P2 (Nov’12) 153.67 210.3 0.547 257.42 55.52

P3 (Dec’12) 155.18 210.3 0.580 260.71 55.38

Percentage Deviation:

X1 X2 X3 X4 X5

P1 (Oct’12) 2.20% 1.76% 9.31% 0.25% -1.48%

P2 (Nov’12) 0.28% 2.70% 8.96% 0.35% -1.96%

P3 (Dec’12) -0.34% 3.65% 4.48% -0.51% -0.76%

Hence we see that our trendline models can be accepted. So next we will form the

MDA Function and apply these values on it.

4.2 Interpretation of the MDA Function from SPSS Output:

4.2.1 Analysis Case Processing Summary

Unweighted Cases N Percent

Valid 95 100.0

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 95 100.0

This implies that all observations provided in the data is valid and there are no missing

values. The minimum ratio of valid cases (i.e., observations) to independent variables for

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discriminant analysis is 5 to 1, with a preferred ratio of 20 to 1. In this analysis, there are

95 valid cases and 5 independent variables. The ratio of cases to independent

variables is 19 to 1, which satisfies the near maximum requirement.

4.2.2 Group Statistics

Y Mean Std. Deviation Valid N (listwise)

Unweighted Weighted Unweighted Weighted

-1 X1 123.05957

44680851

0

16.2064756189

89550 47 47.000

X2 142.36595

74468085

0

30.5429866467

32500 47 47.000

X3 .44219340

211095

.087737812510

647 47 47.000

X4 202.17276

59574468

0

28.5169291979

13630 47 47.000

X5 45.835720

14061590

3.93080367697

3489 47 47.000

1 X1 129.90208

33333333

0

15.8998526633

52250 48 48.000

X2 153.51458

33333333

0

31.0555370030

22440 48 48.000

X3 .41797318

568094

.085467481693

121 48 48.000

X4 213.12416

66666666

0

28.2152790080

75290 48 48.000

X5 45.725302

56283070

3.50176989556

1275 48 48.000

Total X1 126.51684

21052631

0

16.3328389516

17850 95 95.000

X2 147.99894

73684211

0

31.1470072833

64390 95 95.000

X3 .42995581

907263

.086992026845

304 95 95.000

X4 207.70610

52631579

0

28.7455438653

79390 95 95.000

X5 45.779930

20657700

3.70074457563

8813 95 95.000

This gives the distribution of the two test groups with a prior division of 0.5 randomly.

Studying the group means can reveal some discriminant loadings across the groups.

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4.2.3 Tests of Equality of Group Means

Wilks'

Lambda F df1 df2 Sig.

X1 .956 4.315 1 93 .041

X2 .968 3.111 1 93 .081

X3 .980 1.858 1 93 .176

X4 .963 3.540 1 93 .063

X5 1.000 .021 1 93 .885

This table gives the results of hypothesis testing that the two group means are equal and

there is no discriminancy between the two groups. The table applies the test to the

contribution of each IV. Here we see that X1, X2, X4 rejects the null hypothesis at 10%

level of significance. But, X3 & X5 fails to reject the null hypothesis. This discrepancy may

be due to the fact that we are handling macroeconomic data and they are highly

influenced by a lot of social and behavioral aspects. Hence, an absolute fit of

macroeconomic variable in a statistical model is very rare.

4.2.4 Pooled Within-Groups Matrices

X1 X2 X3 X4 X5

Correlation X1 1.000 .924 .100 .952 .589

X2 .924 1.000 .211 .940 .702

X3 .100 .211 1.000 -.032 .416

X4 .952 .940 -.032 1.000 .582

X5 .589 .702 .416 .582 1.000

This table gives the correlation coefficients between the IV’s. We see X1 is closely

related to X2, X4 and X5.

4.2.5 Test Results

Box's M 8.240

F Approx. .518

df1 15

df2 34789.162

Sig. .933

Tests null hypothesis of equal population covariance matrices.

Homogeneity of variances of the independent variables across the groups of the

dependent variable is tested by Box's M. The null hypothesis is that the group variance-

covariance matrices are equal. If we fail to reject the null hypothesis and conclude that

the variances between groups are equal, it would imply that there is strong

homogeneity, across groups. This, in turn, implies that the independent variables have

failed to discriminate the groups formed by the dependent variable. Put differently,

MDA is unsuccessful. In our case though it may seem that the null hypothesis is failed to

be rejected, this discrepancy may be due to the fact that we are handling

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macroeconomic data and they are highly influenced by a lot of social and behavioral

aspects. Hence, an absolute fit of macroeconomic variable in a statistical model is very

rare. Hence, we move ahead with our MDA and finally we would like to check what

percentage of the total observations is correctly classified by the MDA Function.

4.2.6 Eigenvalues

Function Eigenvalue

% of

Variance Cumulative %

Canonical

Correlation

1 .122(a) 100.0 100.0 .330

a. First 1 canonical discriminant functions were used in the analysis.

This table explains how efficient is the MDA Function to discriminate the DV as a

function of the IV’s. Here the value of (Canonical Correlation) 2 goes as 11%. So literally

only 11% of the discrimination can be explained by the discriminant function. But, finally

we would like to check what percentage of the total observations is correctly classified

by the MDA Function.

4.2.7 Wilks' Lambda

Test of Function(s)

Wilks'

Lambda Chi-square df Sig.

1 .891 10.428 5 .064

Wilk's Lambda captures the within group variability, as compared to the total variability.

Total variability can be of two types: within group and between groups. Wilk's Lambda

is represented as WSS/TSS = Within Group Sum of Squares / Total Sum of Squares. For

MDA to make sense within group variability should be minimized and between groups

variability should be high. Hence, a low Wilk's Lambda value is preferred. The null hyp is

this case is high within group variability, i.e., high WSS. If the null hyp is strongly rejected,

we conclude that the indep variables have been able to successfully discriminate the

two groups of the dep vairable (i.e., satisfied and dissatisfied customers). However, this

is an overall study and does not give any idea about the discriminatory power of each

and every independent variable. Here, though we are able to reject the null hypothesis

at a significance level of 10%, but we have a high Wilk’s Lambda. This may be due to

the fact that we are dealing with macroeconomic variables which have a lot of social

and behavioral aspects linked to it. Finally, we are interested in knowing what

percentage of the total observations is explained by the MDA Function.

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4.2.8 Structure Matrix

Function

1

X1 -.616

X4 -.558

X2 -.523

X3 .404

X5 .043

Pooled within-groups correlations between discriminating variables and standardized canonical

discriminant functions .Variables ordered by absolute size of correlation within function.

The structure matrix table shows the correlations of each variable with each

discriminate function. These Pearson coefficients are structure coefficients or

discriminant loadings. They serve like factor loadings in factor analysis. By identifying the

largest loadings for each discriminate function the researcher gains insight into how to

name each function. Here, we see that X1, X2, X3, and X4 are substantially loaded in

the Discriminant Function.

4.2.9 Canonical Discriminant Function Coefficients

Function

1

X1 -.105

X2 -.069

X3 10.110

X4 .097

X5 .153

(Constant) -7.967

Unstandardized coefficients

This defines the Multiple Discriminant Function:

Y = 0.153 (X5) + 0.097 (X4) + 10.110 (X3) - 0.069 (X2) - 0.105 (X1) -7.967

The discriminant function coefficients b or standardized form beta both indicate the

partial contribution of each variable to the discriminate function controlling for all other

variables in the equation. They can be used to assess each IV’s unique contribution to

the discriminate function and therefore provide information on the relative importance

of each variable. If there are any dummy variables, as in regression, individual beta

weights cannot be used and dummy variables must be assessed as a group through

hierarchical DA running the analysis, first without the dummy variables then with them.

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The difference in squared canonical correlation indicates the explanatory effect of the

set of dummy variables.

4.2.10 Functions at Group Centroids

Y

Function

1

-1 .349

1 -.342

Unstandardized canonical discriminant functions evaluated at group means

The group centroids table gives us the basis of discriminating Y = +1 from Y = -1.

By substituting the values of IV’s X1 to X5, we will get a value for Y. Closer the value of Y

to a group centroid, closer is the classification to that group.

4.2.11 Classification Results (a)

Y

Predicted Group Membership Total

-1 1 -1

Original Count -1 29 18 47

1 18 30 48

% -1 61.7 38.3 100.0

1 37.5 62.5 100.0

a 62.1% of original grouped cases correctly classified.

The classification table, also called a ‘confusion table’ gives us an estimate of the final

power of the MDA Function. Here we see that we are able to classify 62.1% of the

original grouped cases. Considering the variability of macroeconomic data (social,

political, behavioral etc.) this is a good hit percentage. The independent variables

could be characterized as useful predictors of membership in the groups defined by

the dependent variable if the cross-validated classification accuracy rate was

significantly higher than the accuracy attainable by chance alone, called the

Proportional Chance Criterion.

Operationally, the classification achieved by MDA, including the cross-validated

classification accuracy rate should be 25% or more high than the proportional by

chance accuracy rate.

The proportional by chance accuracy rate was computed by squaring and summing

the proportion of cases in each group from the table of prior probabilities for groups

(0.5² + 0.5² = 0.5). The criteria (thumb-rule) for a useful model is 25% greater than the by

chance accuracy rate (1.25 x 50% = 62.5%). Here we are just near to that stipulated

value. Hence, we can conclude that our MDA Function has been able to classify the

dataset satisfactorily.

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4.3 Test of the MDA Function:

We have devised the MDA Function as follows:

Y = 0.153 (X5) + 0.097 (X4) + 10.110 (X3) - 0.069 (X2) - 0.105 (X1) -7.967

The Group Centroids are:

Y Function

1

-1 .349

1 -.342

Testing Independent Variables are as follows:

X1 X2 X3 X4 X5

P1 (Oct’12) 153.54 214.01 0.587 257.30 53.97

P2 (Nov’12) 154.10 215.98 0.596 258.33 54.43

P3 (Dec’12) 154.66 217.97 0.606 259.37 54.96

Test Results goes as follows:

X1 X2 X3 X4 X5

Y

Classification

P1 (Oct’12) 153.54 214.01 0.587 257.30 53.97

0.294

-1

P2 (Nov’12) 154.10 215.98 0.596 258.33 54.43

0.361

-1

P3 (Dec’12) 154.66 217.97 0.606 259.37 54.96

0.448

-1

Interpretation of results goes as follows:

Y

Classification

Interpretation

Actual

Returns

Verdict

P1 (Oct’12)

0.294

-1

Returns are negative

-1.18%

Pass

P2 (Nov’12)

0.361

-1

Returns are negative

0.37%

Fail

P3 (Dec’12)

0.448

-1

Returns are negative

-3.55%

Pass

Hence, our model gives correct results in 66.67% of the cases.

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y = -0.7491x + 0.0061

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

Y (Security)

Y (Security)

Linear (Y (Security))

5.1 The CAPM-SML (Security Market Line) Equation:

The CAPM Model derives the equation of the Security Market Line as follows:

E(Rj) = Rf + β [E(Rm) –Rf]

The steps of calculating WACC and Growth Rate from the CAPM Model are

enumerated as below:

Step 1: Calculating Historic Returns of Shopper’s Stop:

This was done by taking historic data (monthly) from Yahoo Finance and thereby

applying the formula (see attached excel sheet):

% Return = (Present Month closing value of stock) – (Previous Month closing value of stock)

Step 2: Calculating Historic Returns of a portfolio:

This was done by taking the CNX Nifty 50 as a indicator of the Market. The historic

returns were calculated upto year 2002 (see attached excel sheet):

% Return = (Present Month closing value of Nifty 50) – (Prev. Month closing value of Nifty 50)

Step3: Calculating β (Risk Coefficient):β, the risk coefficient was calculated by plotting

the Market Returns on X axis and Stock Returns on Y Axis and then taking the slope of

the best fit straight line:

E(Rj) = Expected return on Shoppers Stop Stocks

Rf = Risk free return

β = risk coefficient

E(Rm) = Market return on portfolio

Previous Month closing value of Stock

Previous Month closing value of Nifty 50

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Step 4: Calculating Expected Rate of Return on Equity:

6.1 Comparing CAPM-SML with MDA Function:

The outcomes from the MDA Function and from CAPM Equation and a comparative

picture between them are enumerated as below:

MDA(Y)

Classification

MDA

Interpretation

SML

Returns

Verdict

P1 (Oct’12)

0.294

-1

Returns are

negative

-1.11%

Pass

P2 (Nov’12)

0.361

-1

Returns are

negative

1.11%

Pass

P3 (Dec’12)

0.448

-1

Returns are

negative

-1.11%

Pass

7.1 Final Conclusion:

Hence we see that our MDA Model is successfully able to classify the nature of returns

from the NTPC Stocks. The securities of NTPC have historically generated negative

returns as we see from the SML Equation. For this reason, it has a negative beta (β) and

inspite of being a low risk security, no shareholder will like to keep NTPC Stocks as a part

of his/her portfolio. Recommendations for Management:

I. Deleverage the capital structure of the firm with more equity and less debt.

II. Invest in safe havens and generate higher returns for shareholders.

III. Devise a proper dividend distribution policy to generate shareholder interest.

The hit ratio of our MDA Function though stands at 62.1%, it is able to predict the nature

of returns from NTPC stocks based on some very volatile macroeconomic factors such

as IIP Electricity, WPI Coal, BV/MV Ratio, GDP at Factor Cost and Exchange Rates. Since

macroeconomic factors are influenced heavily by social, political and behavioral

aspects, it is very difficult to fit them in a rigid statistical model. Keeping that in view, a

62.1% hit ratio is decent enough.

Risk free rate (Yeild on 10yr GOI Bond) 8.18% As per Economic Times 13.12.2012

Beta -0.74907

Return on Market 20.59%

Equity Risk Premium = (Return on Market - Risk Free Rate) 12.41%

Expected Return on Equity -1.11%

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