Creation of Regression Model to predict the returns of 2 mutual funds (Invesco and UTI) Validating both the models by testing the assumptions of CLRM

1. G GR
GRAND PROJECT OF BASIC FINANCIAL ANALYTICS
INVESCO INDIA GROWTH FUND UTI DYNAMIC BOND FUND
PGDM 2015-17
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STATISTICAL ANALYSIS AND REGRESSION MODEL FOR RETURN
OF MUTUAL FUNDS OF EQUITY AND DEBT MARKET
Guided by: Professor Abhay Raja
Submitted by: Prakash Chandrashekar
Prakash.c15@shantibschool.edu.in

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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
Variable Coefficient Std. Error t-Statistic Prob.
C 0.048027 0.145790 0.329425 0.7432
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
Adjusted R-squared 0.899033 S.D. dependent var 0.042416
S.E. of regression 0.013478 Akaike info criterion -5.706793
Sum squared resid 0.009446 Schwarz criterion -5.562125
Log likelihood 163.7902 Hannan-Quinn criter. -5.650706
F-statistic 164.2448 Durbin-Watson stat 2.312064
Prob(F-statistic) 0.000000
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
F-statistic 0.434889 Prob. F(9,46) 0.9091
Obs*R-squared 4.391237 Prob. Chi-Square(9) 0.8838
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)
 Variance of residuals is constant (Homoscedastic)
 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
Variable Coefficient Std. Error t-Statistic Prob.
C 0.047578 0.021977 2.164933 0.0352
_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
Adjusted R-squared 0.273198 S.D. dependent var 0.007525
S.E. of regression 0.006416 Akaike info criterion -7.159239
Sum squared resid 0.002058 Schwarz criterion -6.942237
Log likelihood 206.4587 Hannan-Quinn criter. -7.075108
F-statistic 5.134806 Durbin-Watson stat 1.663076
Prob(F-statistic) 0.000707
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
Variable Coefficient Std. Error t-Statistic Prob.
C 0.052994 0.021777 2.433535 0.0184
_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:
F-statistic 1.802171 Prob. F(2,50) 0.1755

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Obs*R-squared 3.765425 Prob. Chi-Square(2) 0.1522
As probability is 0.1522 >0.05, we accept the Null Hypothesis.
Hence this assumption is satisfied as there is no Auto correlation.
 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
F-statistic 1.200321 Prob. F(9,46) 0.3179
Obs*R-squared 10.65019 Prob. Chi-Square(9) 0.3005
Scaled explained SS 8.683502 Prob. Chi-Square(9) 0.4670
As probability is 0.3005 >0.05, we accept the Null Hypothesis.
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

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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.