Grand project for Financial Analytics

G GR

GRAND PROJECT OF BASIC FINANCIAL ANALYTICS

INVESCO INDIA GROWTH FUND UTI DYNAMIC BOND FUND

PGDM 2015-17

1011517068

STATISTICAL ANALYSIS AND REGRESSION MODEL FOR RETURN

OF MUTUAL FUNDS OF EQUITY AND DEBT MARKET Guided by: Professor Abhay Raja

Submitted by: Prakash Chandrashekar [email protected]

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Table of Contents INVESCO INDIA GROWTH FUND (G) ........................................................................................... 3

Objective of the scheme .................................................................................................................... 3

Details of the scheme ......................................................................................................................... 3

Asset Allocation of the scheme ......................................................................................................... 3

Objective of the Grand Project ........................................................................................................ 4

Identifying the variables ................................................................................................................... 4

Dependent variable ......................................................................................................................... 4

Independent variable ....................................................................................................................... 4

Reasons for choosing the independent variables ............................................................................ 4

Inflation ........................................................................................................................................... 4

Treasury Bills yield ......................................................................................................................... 4

Credit Deposit Ratio ....................................................................................................................... 5

Methodology ....................................................................................................................................... 5

Accrue Dataset ................................................................................................................................ 5

Assumptions of Classical Linear Regression Model ...................................................................... 5

Creation and Analysis of Regression model using E-views ........................................................... 6

Regression equation ........................................................................................................................ 6

Regression Model ........................................................................................................................... 6

Interpretation ................................................................................................................................... 6

Regression Model -2 ....................................................................................................................... 7

Interpretation ................................................................................................................................... 7

Testing the Assumptions of Classical Linear Regression Model (CLRM) .................................. 8

Conclusion of the model ................................................................................................................. 10

UTI DYNAMIC BOND FUND REGULAR GROWTH ................................................................. 11

Objective of the scheme .................................................................................................................. 11

Details of the scheme ....................................................................................................................... 11

Asset Allocation of the scheme ....................................................................................................... 11

Recommendations for the investors .............................................................................................. 11

Objective of the Grand Project ...................................................................................................... 12

Identifying the variables ................................................................................................................. 12

Dependent variable ....................................................................................................................... 12

Independent variable: .................................................................................................................... 12

Reasons for Choosing these Variables .......................................................................................... 12

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Inflation ......................................................................................................................................... 12

Foreign currency Assets ................................................................................................................ 12

10 year Bond yield ........................................................................................................................ 13

Accrue Dataset .............................................................................................................................. 13

Assumptions of Classical Linear Regression Model .................................................................... 13

Creation and Analysis of Regression model using E-views ............................................................. 14

Regression equation ...................................................................................................................... 14

Regression Model ......................................................................................................................... 14

Interpretation ................................................................................................................................. 14

Alternate Method to remove return of benchmark index using SPSS ....................................... 15

Interpretation ................................................................................................................................. 16

Regression Model -2 ..................................................................................................................... 16

Interpretation ................................................................................................................................. 17

Testing the Assumptions of Classical Linear Regression Model (CLRM) ................................ 17

Limitation for the model ................................................................................................................ 20

Conclusion of the model ................................................................................................................. 20

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INVESCO INDIA GROWTH FUND (G)

Objective of the scheme The scheme aims to generate long-term capital growth by investing predominantly in equity

and equity related securities following a bottom-up approach in selecting stocks depending on

their market-cap and sector.

Details of the scheme

Fund Type Open Ended

Investment Plan Growth

Launch Date July 19, 2007

Benchmark S&P BSE 100

Asset Size Rs. 126.72 Crores

Minimum Investment Rs. 5000

Major 2 competitors Reliance Dynamic Bond(G), IDFC Dynamic

bond (G)

Asset Allocation of the scheme

Debt Not Applicable

Equity 95.15%

Cash 4.85%

30.28%14.49%

13.22%5.77%

5.11%4.86%

4.25%3.75%

2.40%2.24%1.98%

1.62%1.57%1.50%1.24%

0.53%0.34%

4.85%

0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00%

Banking & Financial services

Automotive

Tobacco

Capital goods

Mining and Metal

Media & Entertainment

Telecommunication

Chemicals

Cement

Secotoral Allocation of Funds

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Objective of the Grand Project

To analyse and check if 91 day Treasury bill yield, Credit Deposit ratio, Consumer price

inflation index, returns of BSE Sensex, BSE S&P 100 benchmark indices are having

any impact in the returns of the Invesco India Growth mutual fund scheme and also to

remove one of the variable which is most affecting the returns of scheme moreover

remove one benchmark index whose return is most affecting the returns of scheme,

statistically.

Create a model and analyse if the remaining two variables from the above objective and

the entrusted Benchmark index best explains the returns of the scheme.

Identifying the variables Dependent variable: Return of mutual fund.

Independent variable: 91 day Treasury bill Yield (T bill), Credit Deposit Ratio (CDR),

Consumer price inflation index (CPI), returns of BSE Sensex (BSE Sensex) and Return

of BSE S&P 100 (BSE 100).

Reasons for choosing the independent variables

Inflation

Inflation has always been one of the most important macroeconomic factor affection the

country. It represents the general price level of the country’s inflation which has always

lowered the actual return from bank savings. The main problem with stocks and inflation is

that a company's returns tend to be overstated. In times of high inflation, a company may look

like it's prospering, when really inflation is the reason behind the growth. When analysing

financial statements, it's also important to remember that inflation can wreak destruction on

earnings depending on what technique the company is using to value inventory.

Treasury Bills yield

T-bills are the most marketable money market security. Their popularity is mainly due to their

simplicity. Essentially, T-bills are a way for the Indian government to raise money from the

public. T-bills are short-term securities that mature in one year or less from their issue date.

They are issued with three-month, six-month and one-year maturities. T-bills are purchased for

a price that is less than their face value when they mature, the government pays the holder the

full par value. If the return in T-bills are higher than the mutual funds, obviously investors will

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get lured to invest in T-bills which is the variable is chosen as it impacts the return of mutual

funds.

Credit Deposit Ratio

It is the ratio of how much a bank lends out of the deposits it has mobilised. It indicates how

much of a bank's core funds are being used for lending, the main banking activity. A higher

ratio indicates more reliance on deposits for lending and vice-versa. This will have an impact

on mutual funds because investor’s money will be there in the bank which indeed is used for

investing in the mutual fund and bank might use those amount in deposits for lending. So this

variable is chosen as independent variable.

Methodology

Accrue Dataset

Stockpiled monthly dataset for Net asset value (units in Rs.) of the Invesco India

Growth Fund scheme for the period December-2011 to August-2016, amassed 57

observations and calculated their returns.

Accumulated monthly close price dataset for the benchmark index of S&P BSE 100

and BSE Sensex for the period December-2011 to August-2016 and calculated their

returns.

Amassed dataset of T bill, Credit deposit ratio and consumer price inflation index for

the period December-2011 to August-2016, a total of 57 observations each.

Assembled all the collected information in a single excel file named “Prakash_bfa-gp”

sheet named “Invesco analysis”.

Assumptions of Classical Linear Regression Model

The classical linear regression equation y= a+b1X1+b2X2+b3X3+e

Mean of residuals is Zero

Correlation between Error and residuals are Zero.

They are normally distributed

Observation of errors are not correlated with each other (No Auto Correlation)

Variance of residuals is constant (Homoscedastic)

Independent variables are not correlated with each other (No multicollinearity)

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If 4 of the 6 assumptions are satisfied, then it can be said that the model is fit for use and used

for the further study.

Creation and Analysis of Regression model using E-views

Regression equation Return of Mutual Fund= 0.0886 -0.11944(CDR) +0.103078(Consumer price inflation)

+0.082609(T bill) +0.604167 (returns of BSE 100) +0.273017 (BSE Sensex).

Regression Model Dependent Variable: RETURN_OF_MF Method: Least Squares Date: 09/14/16 Time: 15:46 Sample (adjusted): 2012M01 2016M08 Included observations: 56 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C 0.088619 0.160408 0.552460 0.5831

CREDIT_DEPOSIT_RATIO -0.119448 0.221596 -0.539034 0.5923 _91_DAY_TREASURY_BILL__

P 0.082609 0.240125 0.344026 0.7323 CPI 0.103078 0.277426 0.371552 0.7118

S_P_BSE_100 0.604167 0.283714 2.129493 0.0382 S_P_BSE_SENSEX 0.273017 0.311505 0.876444 0.3850

R-squared 0.906456 Mean dependent var 0.014762

Adjusted R-squared 0.897101 S.D. dependent var 0.042416 S.E. of regression 0.013606 Akaike info criterion -5.655628 Sum squared resid 0.009256 Schwarz criterion -5.438626 Log likelihood 164.3576 Hannan-Quinn criter. -5.571497 F-statistic 96.90102 Durbin-Watson stat 2.328640 Prob(F-statistic) 0.000000

Table 1 CDR, Tbill, Cpi, bse100 & bsesnsx

Interpretation

Null Hypothesis: Variables are not significant.

Alternate Hypothesis: Variables are significant.

When we examine the independent variables of CPI, CDR and T-bill, it can be observed

that T-bill is most insignificant variable among the 3 as its probability is 0.7323 which

is highest. Hence T-bill variable can be removed as other two best explains the return

of mutual fund to meet the objective.

When we examine the benchmark indices, it is noticeable from the above table 1 that

returns of BSE Sensex is insignificant as their probability (p>0.05) which implies we

accept null hypothesis. As the objective demands to remove the least explaining

benchmark index which is return of BSE Sensex. Hence we can remove Return of BSE

Sensex from the above regression model.

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Regression Model -2

Apply general regression again after removing one least explaining variable and one

benchmark index.

Dependent Variable: RETURN_OF_MF Method: Least Squares Date: 09/14/16 Time: 20:22 Sample (adjusted): 2012M01 2016M08 Included observations: 56 after adjustments


CREDIT_DEPOSIT_RATIO -0.057359 0.191366 -0.299735 0.7656 CPI 0.095941 0.271106 0.353889 0.7249

S_P_BSE_100 0.850755 0.039184 21.71192 0.0000 R-squared 0.904541 Mean dependent var 0.014762


New Regression Equation

Return of Mutual fund= 0.048- 0.0573 (CDR) + 0.0959 (CPI) + 0.8507 (S&P BSE)

Interpretation

Null Hypothesis: Model is not significant.

Alternate Hypothesis: Model is significant.

According to F-statistics, F- significance tells us if the model (regression equation) is

significant or not.

Probability of F-stat = 0.000.

If probability< 0.05, we can reject null hypothesis and hence we can say that the model is

significant.

R-square tells us how confident we are with the model and Adjusted R-square tells us if chosen

independent variables best explains the dependent variable or not and ideally both these should

be more than 50%.

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But here, R square = 90.45% and Adjusted R square = 89.90% which means that the level of

confidence of the model is 90.45% and the level of confidence of independent variables

explaining dependent variables is 89.90%.

Degree of Freedom = n-k-1 = 56-3-1 =52 which means we are giving freedom for model to

commit errors.

Testing the Assumptions of Classical Linear Regression Model (CLRM) 1. Mean of residuals is Zero.

It is been tested in Excel file “Prakash_bfa_gp” sheet name “Invesco Analysis”.

This assumption is satisfied as mean of residuals is Zero.

2. Correlation of Independent variables and residuals is Zero.

It is been tested in the Excel file “Prakash_bfa_gp” sheet name “Invesco Analysis”.

This assumption is satisfied as all the correlations between independent variables and residuals

is Zero.

3. The variables should be normally distributed i.e., normality should be satisfied.

Null Hypothesis: Data is normally distributed i.e. series is normal

Alternate Hypothesis: Data is not normally distributed i.e. series is not normal.

If p<0.05, then we reject the null hypothesis perhaps in this case Probability is>0.05

and therefore we accept null hypothesis which is Series is normal.

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From Jarque-Bera probability test, we can say that the series is normal that is data is

normally distributed because Jarque-Bera probability = 0.76 which is greater than 0.05.

Further Kurtosis value is <3 which means there is no problem in the data statistically

but here the kurtosis =3.43 which is slightly greater than 3. So this can be ignored and

accepted.

4. Observations of errors are not correlated with each other (No Auto Correlation)

To test this, we use the serial correlation LM test.

Null Hypothesis: There is no Auto correlation.

Alternate Hypothesis: There is Auto correlation.

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 0.863326 Prob. F(2,50) 0.4279

Obs*R-squared 1.869297 Prob. Chi-Square(2) 0.3927

As probability is 0.3927>0.05, we accept the Null Hypothesis.

Hence this assumption is satisfied as there is no Auto correlation.

5. Variance of residuals is constant (Homoscedastic)

Null Hypothesis: There is no heteroscedasticity which is desirable.

Alternate Hypothesis: there is heteroscedasticity which is non desirable.

Heteroskedasticity Test: White



Scaled explained SS 4.615843 Prob. Chi-Square(9) 0.8664

As probability is 0.8838 >0.05, we accept the Null Hypothesis.

Hence this assumption is satisfied as there is no heteroscedasticity viz. homoscedastic

which is desirable.

6. Independent variables are not correlated with each other (No multicollinearity).

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There is negative correlation between CDR and S&P BSE 100.

Variance Inflation Factors

Date: 09/14/16 Time: 22:51

Sample: 2011M12 2016M08

Included observations: 56

Coefficient Uncentered Centered

Variable Variance VIF VIF

C 0.021255 6552.410 NA

CREDIT_DEPOSIT_RATIO 0.036621 6568.142 1.015203

CPI 0.073498 2.004835 1.049626

S_P_BSE_100 0.001535 1.101279 1.037706

As all the variables have centred VIF approximately 1, we can say that there is no

multicollinearity.

Hence this assumption is satisfied as independent variables are not correlated with each other.

Conclusion of the model

Return of Mutual fund= 0.048- 0.0573 (CDR) + 0.0959 (CPI) + 0.8507 (S&P BSE)

From the above equation, it is clearly evident that as Credit deposit ratio decreases, then

return on Invesco mutual fund increases.

As consumer price inflation increases, return on mutual fund increases.

As return on BSE 100 benchmark index increases, return on mutual fund also increases.

Further, as all 6 assumptions of classical linear regression model is satisfied, we can

rely on the model and it can be used for further study.

Further analysis can be carried by including few other variables as independent and

performing the same regression model in due course to increase the credibility and level

of confidence of the model.

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UTI DYNAMIC BOND FUND REGULAR GROWTH

Objective of the scheme

The scheme seeks to generate optimal returns with adequate liquidity through active

management of the portfolio, by investing in debt and money market instruments.

Details of the scheme

Fund Type Open Ended

Investment Plan Growth

Launch Date Jun 23, 2010

Benchmark Crisil Composite Bond Fund

Asset Size Rs. 712.54 crores

Minimum Investment Rs. 10000

Major 2 competitors Reliance Dynamic Bond(G), IDFC Dynamic

bond (G)

Asset Allocation of the scheme

Debt 17.51%

Money Market 80.47%

Cash 2.01% Table 2 Data as on 29th July 2016

Recommendations for the investors

Optimal returns with adequate liquidity over medium term.

Investment in debt market/money market.

Investors should consult their financial advisors if in doubt about whether this product

is suitable for them.

80%

17%

3%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

Government securities

NCD's

NCA

Government securities NCD's NCA

Series1 80% 17% 3%

Asset Allocation as on 31st July 2016

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Objective of the Grand Project

To analyse and check if 10 Year Bond Yield, Foreign currency assets, Consumer price

inflation index, returns of BSE Sensex, BSE S&P 100 benchmark indices are having

any impact in the returns of the UTI dynamic Bond mutual fund scheme and also to

remove one of the variable which is most affecting the returns of scheme moreover

remove one benchmark index whose return is most affecting the returns of scheme,

statistically.

Create a model and analyse if the remaining two variables from the above objective and

the entrusted Benchmark index best explains the returns of the scheme.

Identifying the variables Dependent variable: Return of mutual fund.

Independent variable: 10 Year Bond Yield (10yryld), Foreign currency assets (FCA),

Consumer price inflation index (CPI), returns of BSE Sensex (BSE Sensex) and Return of BSE

S&P 100 (BSE 100).

Reasons for Choosing these Variables

Inflation

Inflation has always been one of the most important macroeconomic factor affection the

country. It represents the general price level of the country’s inflation which has always

lowered the actual return from bank savings. The main problem with stocks and inflation is

that a company's returns tend to be overstated. In times of high inflation, a company may look

like it's prospering, when really inflation is the reason behind the growth. When analysing

financial statements, it's also important to remember that inflation can wreak destruction on

earnings depending on what technique the company is using to value inventory. Hence

Consumer price inflation has been chosen in this case.

Foreign currency Assets

We all know the impact of Brexit on International Mutual funds. It is known that addition of

currency in underlying securities and change in exchange rate is total return of the fund.

Consider a Canadian mutual fund that holds Indian stocks. Investors buy the fund using

Canadian dollars. The fund has to convert these Canadian dollars to INR in order to purchase

Indian stocks. If the INR rises relative to the Canadian dollar, any exchange-rate gain will add

to the fund’s total return. However, if the INR falls, any decline will reduce the fund’s total

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return. Even if all the fund’s underlying stocks were to remain unchanged in INR terms, the

fund would still change in value due to the effects of currency fluctuations because it is priced

in Canadian dollars. This is the reason Foreign currency asset is chosen as it might impact

return on mutual fund.

10 year Bond yield

Governments and Businesses raise capital by accessing the fixed income markets. To be able

to attract the buyers, the bond issuers have to give competitive yields on the fixed income

instruments. Such bonds issued by governments and businesses are not often open for

individuals. Mutual funds houses can buy these bonds. So essentially, a subscriber to a debt

mutual fund is indirectly investing in these bonds through the mutual fund house. The Net

Asset Value (NAV) of such mutual funds is calculated as a sum of price of the bond and coupon

payments (interest accrued). Since these funds are traded in secondary markets, the interest

accrued is calculated on a daily basis to realize the accurate NAV of the fund. The NAV of

debt funds varies with the prices of bonds they hold and interest being accrued on them. Since

the prices of the bonds are governed by the interest rates, a change in the interest rate is reflected

in the NAV of the debt fund. The NAVs of the debt mutual fund hold inverse relation with

Interest-rates. Hence this yield is chosen in this scheme as it is a bond (debt scheme).

Methodology

Accrue Dataset

Stockpiled monthly dataset for Net asset value (units in Rs.) of the UTI Dynamic Bond

Fund Growth scheme for the period December-2011 to August-2016, amassed 57

observations and calculated their returns.

Accumulated monthly close price dataset for the benchmark index of S&P BSE 100

and BSE Sensex for the period December-2011 to August-2016 and calculated their

returns.

Amassed dataset of 10 year bond yield, foreign currency assets and consumer price

inflation index for the period December-2011 to August-2016, a total of 57 observations

each.

Assembled all the collected information in a single excel file named “Prakash_bfa-gp”

sheet named “uti analysis”.

Assumptions of Classical Linear Regression Model

The classical linear regression equation y= a+b1X1+b2X2+b3X3+e

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Mean of residuals is Zero

Correlation between Error and residuals are Zero.

They are normally distributed

Observation of errors are not correlated with each other (No Auto Correlation)


Independent variables are not correlated with each other (No multicollinearity)

If 4 of the 6 assumptions are satisfied, then it can be said that the model is fit for use and used

for further study.

Creation and Analysis of Regression model using E-views

Regression equation Return of Mutual Fund= 0.04 -0.404(10 Year Bond Yield) +0.028671(Consumer price

inflation) -0.000000422(Foreign currency assets) +0.3634(returns of BSE 100) -0.3196(BSE

Sensex).

Regression Model Dependent Variable: RETURN_OF_MF Method: Least Squares Date: 09/14/16 Time: 15:36 Sample (adjusted): 2012M01 2016M08 Included observations: 56 after adjustments


_10YRYIELD -0.404798 0.220422 -1.836465 0.0722 CPI 0.028671 0.131986 0.217225 0.8289 FCA -4.22E-07 3.36E-07 -1.254801 0.2154

BSE100 0.363416 0.132699 2.738638 0.0085 BSESENSX -0.319613 0.146251 -2.185377 0.0336

R-squared 0.339271 Mean dependent var 0.008472


Table 3: UTI Return with CPI, FCA, 10yr yield, Bse100, Bsesensx

Interpretation

Null Hypothesis: Variables are not significant.

Alternate Hypothesis: Variables are significant.

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1. When we examine the independent variables of CPI, FCA and 10yryield it can be

observed that CPI is most insignificant variable among the 3 as its probability is 0.8289

which is highest. Hence CPI variable can be removed as other two best explains the

return of mutual fund to meet the objective.

2. When we examine the benchmark indices, it is noticeable from the above table 2 that

returns of BSE Sensex and BSE 100 are significant as their probability (p<0.05) which

implies we reject null hypothesis. Although both the benchmark indices are significant,

the objective demands to remove the least explaining benchmark index which is return

of BSE Sensex in this case is 96.64% significance level but return of BSE 100 is 99.15%

significance level. Hence we can remove Return of BSE Sensex from the above

regression model.

Alternate Method to remove return of benchmark index using SPSS This method is used to validate the above interpretation using another software and a parameter

called “change in R-square” would be used to authenticate, which parameter is least important

to be removed.

Dependent variable: Return of mutual fund

Independent variable: Return of BSE 100, Return of BSE Sensex

Regression output using SPSS

Variables Entered/Removeda

Model

Variables

Entered

Variables

Removed Method

1 bse100b . Enter

2 bsesensxb . Enter

a. Dependent Variable: ReturnMf b. All requested variables entered.

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Variables Entered/Removeda

Model

Variables

Entered

Variables

Removed Method

1 bsesensxb . Enter

2 bse100b . Enter

a. Dependent Variable: ReturnMf

b. All requested variables entered.

Interpretation

R-Sq of BSE 100 R-Sq change of BSE Sensex

Return of Mutual Fund 0.239 0.025

R-Sq of BSE Sensex R-Sq change of BSE 100

Return of Mutual Fund 0.206 0.058

From the above table, it can be said that when we introduce Return of BSE 100 first,

there is 23.9% R-Square when compared to Return of BSE Sensex first (20.6%). Hence

BSE 100 is more important which means BSE Sensex is least explanatory and it should

be removed.

From the above table, it can also be said that there is 5.8% change in R-square when

we introduce BSE 100 along with BSE Sensex when compared 2.5% of change in R-

Square when we introduce BSE Sensex along with BSE 100. Hence BSE Sensex is

least explaining the return of mutual fund which should be eliminated from further

analysis to meet our objective.

Regression Model -2 Dependent Variable: RETURN_OF_MF Method: Least Squares Date: 09/14/16 Time: 15:38 Sample (adjusted): 2012M01 2016M08 Included observations: 56 after adjustments


_10YRYIELD -0.474779 0.220613 -2.152094 0.0361 FCA -3.97E-07 3.35E-07 -1.184211 0.2417

BSE100 0.076735 0.018929 4.053791 0.0002

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R-squared 0.275992 Mean dependent var 0.008472 Adjusted R-squared 0.234222 S.D. dependent var 0.007525 S.E. of regression 0.006585 Akaike info criterion -7.139208 Sum squared resid 0.002255 Schwarz criterion -6.994540 Log likelihood 203.8978 Hannan-Quinn criter. -7.083121 F-statistic 6.607469 Durbin-Watson stat 1.477874 Prob(F-statistic) 0.000724

New Regression Equation

After eliminating the least explaining benchmark index (BSE Sensex) as well as least

explaining variable (CPI), the new regression Equation is as follows:-

Return of UTI mutual fund= 0.05299-0.000000397 (FCA) -0.4747 (10 year yield) + 0.076735 (BSE 100).

Interpretation

Null Hypothesis: Model is not significant.

Alternate Hypothesis: Model is significant.

According to F-statistics, F- significance tells us if the model (regression equation) is

significant or not.

Probability of F-stat = 0.000724.

If probability< 0.05, we can reject null hypothesis and hence we can say that the model is

significant.

R-square tells us how confident we are with the model and Adjusted R-square tells us if chosen

independent variables best explains the dependent variable or not and ideally both these should

be more than 50%.

But here, R square = 27.5% and Adjusted R square = 23.4% which is a major concern for the

level of confidence of the model. Hence there are certain limitations which is an area of advance

study which will be covered in limitations of the project.

Degree of Freedom = n-k-1 = 56-3-1 =52 which means we are giving freedom for model to

commit errors.

Testing the Assumptions of Classical Linear Regression Model (CLRM)

Mean of residuals is Zero.

It is been tested in Excel file “Prakash_bfa_gp” sheet name “UTI Analysis”.

This assumption is satisfied as mean of residuals is Zero.

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Correlation of Independent variables and residuals is Zero.

It is been tested in the Excel file “Prakash_bfa_gp” sheet name “UTI Analysis”.

This assumption is satisfied as all the correlations between independent variables and

residuals is Zero.

The variables should be normally distributed i.e., normality should be satisfied.

Null Hypothesis: Data is normally distributed i.e. series is normal

Alternate Hypothesis: Data is not normally distributed i.e. series is not normal.

If p<0.05, then we reject the null hypothesis perhaps in this case Probability is>0.05

and therefore we accept null hypothesis which is Series is normal.

From Jarque-Bera probability test, we can say that the series is normal that is data is

normally distributed because Jarque-Bera probability = 0.96 which is greater than 0.05.

Further Kurtosis value is <3 which means there is no problem in the data statistically.

Observations of errors are not correlated with each other (No Auto Correlation)

To test this, we use the serial correlation LM test.

Null Hypothesis: There is no Auto correlation.

Alternate Hypothesis: There is Auto correlation.

Breusch-Godfrey Serial Correlation LM Test:


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Hence this assumption is satisfied as there is no Auto correlation.


Null Hypothesis: There is no heteroscedasticity which is desirable.

Alternate Hypothesis: there is heteroscedasticity which is non desirable.

Heteroskedasticity Test: White



Scaled explained SS 8.683502 Prob. Chi-Square(9) 0.4670


Hence this assumption is satisfied as there is no heteroscedasticity viz. homoscedastic

which is desirable.

Independent variables are not correlated with each other (No multicollinearity).

There is negative correlation between FCA and other two variables (10 year yield &

BSE 100).

Variance Inflation Factors

Date: 09/14/16 Time: 02:03

Sample: 2011M12 2016M08

Included observations: 56

Coefficient Uncentered Centered

Variable Variance VIF VIF

C 0.000474 612.3729 NA

FCA 1.13E-13 46.42875 1.496035

_10YRYIELD 4.87E-06 413.1884 1.505800

BSE100 0.000358 1.076570 1.014423

20 | P a g e PGDM 2015-17 1011517068

As all the variables have centred VIF approximately 1, we can say that there is no

multicollinearity.

Hence this assumption is satisfied as independent variables are not correlated with each other.

Limitation for the model The main limitation of the model is that its R--square is around 27.5% and its adjusted R-

Square is around 23% which questions the level of confidence of the model which is an area

of concern. This happened mainly because of benchmark index i.e. Bombay Stock Exchange.

The level of confidence of the model is <50% which says that statistically, we cannot rely on

the model.

Another limitation of the project is that we had restricted the number of independent variables

to 3 which can be another major cause for the R-Square to be <50%. It might happen that there

are few other variables which are majorly impacting the return on UTI bond which is neglected

in this project as it is out of scope of the project to include more number of variables.

Conclusion of the model Return of UTI mutual fund= 0.05299-0.000000397 (FCA) -0.004748 (10 year yield) + 0.076735 (BSE

100).

From the above equation, it is clearly evident that as 10 year bond yield decreases, then

return on UTI mutual fund increases.

As Foreign Currency Assets decreases, return on mutual fund increases.

As return on BSE 100 benchmark index increases, return on mutual fund also increases.

Further, as all 6 assumptions of classical linear regression model is satisfied, we can

rely on the model and it can be used for further study.

Keeping the limitation in view, further analysis can be carried by including few other

variables as independent and performing the same regression model in due course to

increase the credibility and level of confidence of the model.

Data & Analytics

Grand project for Financial Analytics