final project report- portfolio analysis

8/10/2019 Final Project Report- Portfolio Analysis

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Portfolio Analysis

Joanna Pimento

5/16/2013


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1.Executive Summary

The Project analyzes the various factors affecting the Exchange Traded Funds offered by Motilal

Oswal Asset Management Company. The aim of this project was to develop a model using

Regression Analysis that would explain the correlation between various variables and the ETFs.

The analysis mainly tested the significance of interest rates, GDP, Inflation and equity Indices on

the ETFs.

ETF NAVs, Daily Returns on the underlying Indices and the Index Values were used as

dependant variables in individual regression models. The CRISIL G10 Values, CCIMIBOR,

Inflation and GDP were the main predictors. The regression results focused on comparing R-

Square, Adjusted R-Square, and P-Values of the regression coefficients.

Using Microsoft Office Excel and Minitab, the analysis began with simple linear regression

models, then added and modified variables into multiple regression models and finally

concluded with Lagged Distributed regression models.


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Contents

1. Executive Summary. 2

2. Analysis of ETF NAVs.. 4

2.1.

Most Shares M50 4

3. Analysis of Index Values Of the Benchmark Index 5

3.1. NIFTY INDEX Analysis 5

4. Analysis of Daily Returns on the Benchmark Index. 6

4.1. NIFTY Daily Returns.. 6

4.2. CNXMCAP Daily returns. 7

4.3. NASDAQ Daily Returns 7

4.4. Gold Daily returns.. 7

5. Lagged Distributed Models. 8

6. Time Series Plots.. 10

6.1. NIFTY v/s CCIMIBOR without Time Lag. 10

6.2. NIFTY v/s CCIMIBOR with Time Lag. 11

7. Autoregressive Models 12

7.1. NIFTY Daily Returns. 12

7.2. CNXMCAP Daily Returns. 12

8. Comparison of Regression Models. 13

9. Conclusion. 15

10.References 16


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2.Analysis of ETF NAVs

Objective:To determine the significance of interest rates, inflation, GDP and Gold Commodity

on the Net Asset Values of Most Shares M50.

Methodology:

Data for a period of 2 years is collected and suitably interpolated for missing values.

Using Excel, the NAV Values of the ETF is independently regressed with the above

mentioned variables.

The Level Of significance is set at 0.05.

If the P-values of the regression coefficients are lower than 0.05 we reject the null

hypothesis that the coefficient is zero, thus concluding our coefficient is statistically

significant.

Most Shares M50

Period: March 2011- Feb2013

Response Variable: M50 NAVs

Predictor Variables: CCIMIBOR, CRISIL G10 INDEX, CRISIL G10 RETURNS, MONTHLY INFLATION, GDP,

GOLD Commodity.

Results

Predictors Correlation R square Intercept P-Values Coefficient/slope P-Values

CCIMIBOR 45.06% 20.30% 103.38 9.83E-153 -3.63 4.02E-26

CRISIL G10 INDEX 46.27% 21.41% 16.24 0.001 0.03 1.25E-27

INFLATION 14.86% 2.21% 79.88 5.49E-09 -0.73 4.88E-01

GDP 3.56% 0.13% 69.77 0.13 0.0002 0.94

GOLD Commodity 11.99% 1.44% 79.78 1.54E-138 -7.23E-05 0.007

CRISIL G10 INDEX has the highest correlation with M50 NAVS.

The Highest R-Square value suggests that the regression model using CRISIL G10 INDEX is better

suited for the analysis when compared with the other variables.

The intercept column gives the predicted value of M50 NAVS, if the predicted variables were

forecasted to be zero.

From the P-values we conclude that excluding GDP all other variables are statistically significant.

Inflation and CCIMIBOR have a negative relationship withM50 NAVs, while the other variables

will positively influence on M50 NAVs.

The slope column gives values of M50 NAVs when the predictor variable changes by one unit.

Again the P-values indicate that excluding GDP all other variables are statistically significant.


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3.Analysis of the Index Values


on the Values of the benchmark Index.

Methodology:


Using Excel, the Index values itself is independently regressed with the above





significant.

NIFTY Index


Response Variable: NIFTY Index

Predictor Variables: CCIMIBOR, CRISIL G10 INDEX, CRISIL G10 RETURNS, MONTHLY INFLATION, GDP,

GOLD Commodity.

Results


CCIMIBOR 19.71% 3.88% 4451.68 2.59E-12 74.58 2.59E-12

CRISIL G10 INDEX 39.66% 15.73% 659.58 0.02 2.16 6.27E-48

CRISIL G10 Returns 3.26% 0.11% 4942.80 0.00 -6183.73 0.25

INFLATION 35.86% 12.86% 4152.78 4.81E-21 101.97 0.005

GDP 63.73% 40.61% -159.21 0.92 0.42 0.003

Gold Commodity 56.25% 31.64% 3369.46 3.20E-292 0.03 2.71E-104

GDP has the highest correlation with NIFTY INDEX.

The Highest R-Square value suggests that the regression model using GDP is better suited for theanalysis when compared with the other variables.

The intercept column gives the predicted value of the NIFTY INDEX, if the predicted variables

were forecasted to be zero.

The zero P-values for CCIMIBOR, CRISIL G10 Returns, CRISIL G10 INDEX, INFATION and GOLD

suggest that the intercept values are statistically significant.

However the GOLD Commodity slope coefficient is most significant in the analysis.


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4. Analysis of Daily Returns on the underlying Index


on the Daily returns on the benchmark Index.

Methodology:


Using Excel, the daily returns on each Index are independently regressed with the above





significant.

i) NIFTY Daily Returns


Response Variable: Daily Returns on NIFTY

Predictor Variables: CCIMIBOR, CRISIL G10 INDEX, CRISIL G10 RETURNS, WPI MONTHLY INFLATION, GDP

(Quarterly), GOLD Commodity

Results:


CCIMIBOR 5.00% 0.25% 0.26% 0.09 -0.04% 0.08

CRISIL G10 INDEX 4.40% 0.19% -0.95% 0.13 0.0005% 0.12

CRISIL G10 Returns 3.87% 0.15% 0.00% 0.94 14.67% 0.17

INFLATION 34.12% 11.64% 0.35% 0.02 -0.05% 0.01

GDP 10.95% 1.20% -0.25% 0.66 0.000021% 0.66

GOLD Commodity 0.22% 0.0005% 0.02% 0.63 5.197E-10 0.94

4. Inflation has the highest correlation with NIFTY daily Returns.

5. The Highest R-Square value suggests that the regression model using inflation is better suited for the

analysis when compared with the other variables.

6.

The intercept column gives the predicted value of the daily returns on NIFTY, if the predictedvariables were forecasted to be zero.

7. From the P-values we conclude that only inflation is statistically significant in our analysis.

8. Inflation and CCIMIBOR have a negative relationship with NIFTY daily returns, while the other

variables will positively influence NIFTY returns.

9. The slope column gives the change in NIFTY returns when the predictor variable changes by one

unit. Again the P-values indicate only inflation to be statistically significant.


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ii.

CNXMCAP Returns

Response Variable: Daily Returns on CNXMCAP

Results:


CCIMIBOR 10.24% 1.05% 0.005 0.0006 -0.07% 0.0003

CRISIL G10 INDEX 5.02% 0.25% -0.010 0.080 0.0005% 0.078

CRISIL G10 Returns 5.41% 0.29% 0.000 0.98 18.36% 0.06

INFLATION 38.06% 14.48% 0.005 0.006 -0.06% 0.003

GDP 7.63% 0.58% -0.002 0.78 0.000018% 0.76

iii.

NASDAQ Returns

Response Variable: Daily Returns on NASDAQ

Results:


CCIMIBOR 4.35% 0.19% 0.003 0.06 -0.03% 0.13

CRISIL G10 INDEX 1.57% 0.02% -0.003 0.65 0.0002% 0.58

CRISIL G10 Returns 2.68% 0.07% 0.001 0.18 -9.80% 0.35

INFLATION 28.42% 8.07% 0.002 0.01 -0.02% 0.03

GDP 27.34% 7.47% -0.004 0.33 0.000035% 0.26

iv.

Gold Returns

Response Variable: Daily Returns on NASDAQ

Results:


CCIMIBOR 4.36% 0.19% 0.002 0.05 -0.03% 0.13

CRISIL G10 INDEX 0.12% 0.0001% 0.000 0.93 0.00001% 0.97

CRISIL G10 Returns 3.21% 0.10% 0.001 0.08 -9.50% 0.26

INFLATION 5.77% 0.33% 0.000 0.86 0.01% 0.66

GDP 6.48% 0.42% 0.001 0.52 -0.000004% 0.79


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5. Lagged Distributed Models

Objective: To study the relationship between timed lagged values of the variables in

consideration.

Methodology:

NIFTY daily Returns are regressed with lagged values of CCIMIBOR.

Each CCIMIBOR Lag Value is treated as an independent Variable.

The first Model consisted of 16 independent variables regressed with NIFTY daily returns.

The r egressi on equat i on i s

NI FTY = 0. 00424 + 0. 00320 Lag 1 + 0. 00137 Lag 2 - 0. 00180 Lag 3 - 0. 00170Lag 4- 0. 00171 Lag 5 + 0. 00290 Lag 6 + 0. 000261 Lag 7 - 0. 00162 Lag8-0. 000778 Lag 9 - 0. 00290 Lag 10 + 0. 00112 Lag 11 + 0. 00149 Lag 12- 0. 00202 Lag 13 + 0. 00155 Lag 14 - 0. 000599 Lag 15 + 0. 000615 Lag16

The adjusted R-Square, P Values of the Maximum Lag term Coefficient, The Akaike informationcriteria and the Schwartz information criteria are used to analyze the model.

If the model was found to be inadequate, the Lag (q) was reduced by 1 and a new model consisting

of q-1 variables is then tested until the lowest p-value was obtained.

Results

*AIC: Akaike Information Criteria

SIC: Schwarz Information Criteria

LAG (q Days) R-SQUARE Adjusted R-Square P-Value Of q Co-

efficient

AIC* SIC*

LAG 16 8.1% 6.9% 0.382 0.000271 0.000291

LAG 15 8.1% 6.9% 0.713 0.000271 0.000289LAG 14 8.1% 7.0% 0.033 0.000270 0.000288

LAG 13 7.7% 6.7% 0.108 0.000273 0.000289


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Inference:

From the table above the P-value of the 16th

coefficient is greater than 0.05. Hence we cannot

reject the null hypothesis and the variable is dropped from the model.

In a similar way by the above tabulated results, the regression model with 15 lagged variables

is also rejected. The best suited regression model consists of 14 lagged variables giving a r-Square of 8.1% .The

increase in the adjusted R-Square value suggests that the dropping the LAG 15 and LAG 16 is

better suited for the analysis.

The r egressi on equat i on i s

NI FTY = 0. 00429 + 0. 00308 Lag 1 + 0. 00149 Lag 2 - 0. 00185 Lag 3 - 0. 00169Lag4- 0. 00169 Lag 5 + 0. 00291 Lag 6 + 0. 000270 Lag 7 - 0. 00164 Lag 8- 0. 000772Lag 9 - 0. 00285 Lag 10 + 0. 00117 Lag 11 + 0. 00144 Lag 12- 0. 00199 Lag 13 +0. 00148 Lag 14

Since the P-Value of the 14th

coefficient is less than 0.05 we keep the variable in the model.

If the Lag 14 variable was dropped, the adjusted R-Square of the LAG 13 Model decreasessuggesting that the dropped variable reduced the efficiency of the model.

Lastly comparing the AIC and SIC the LAG 14 model having lowest AIC and SIC is best suited for

the analysis.

Calculations:

AIC=

SIC= /

Model RSS

Total Obs

(n)

Regressors

(K) 2K/N RSS/N AIC K/N N^(K/N) SIC

LAG 16 0.322324 1222 17 0.02782324 0.00026 0.000271 0.013912 1.103942 0.000291

LAG 15 0.322549 1223 16 0.02616517 0.00026 0.000271 0.013083 1.097467 0.000289LAG 14 0.322644 1224 15 0.0245098 0.00026 0.000270 0.012255 1.091039 0.000288

LAG 13 0.326837 1225 14 0.02285714 0.00027 0.000273 0.011429 1.084658 0.000289


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6. Time-Series Plots

Objective:To compare models Time lagged Models with Simple Linear models with the help of Time

Series Plots.

1.

NIFTY Daily Returns Regressed with CCIMIBOR (NO TIME LAG)

R-Square: 0.25%

Known NIFTY returns plotted along with Predicted NIFTY Returns obtained from the

regression model using CCIMIBOR (without lag) as the independent variable.

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NIFTY Returns

Predicted NIF TY Returns

Variable

Time Series Plot of NIFTY Returns, Predicted NIFTY Returns

NIFTY Daily Returns predicted from the regression model do not follow the same trend as the known

NIFTY Returns. This Model is not suitable for the analysis.


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2.

NIFTY daily Returns Regressed with CCIMIBOR (LAG 14 Model)

R-Square: 8.1%

Known NIFTY returns plotted along with Predicted NIFTY Returns obtained from the

regression model using CCIMIBOR (with a 14 day lag) as the independent variable.

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NIFTY Returns

Predicted NIFTY Returns

Variable

Time Series Plot of NIFTY, Predicted NIFTY

In comparison to the earlier Time series Plot (with no time lag), NIFTY Returns predicted from

the Lag 14 Model are closer to the known NIFTY Returns.

Conclusion:

The Regression model using a 14 day lag period for the CCIMIBOR values as independent

variables is better suited for the analysis on NIFTY Returns as compared to a model with no time

lag.


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7.Autoregressive Models

Objective: To determine the significance of lagged values of the dependant variable in the regression

equation.

Methodology:

Lagged values of the dependant variable ranging from lag 1 to lag 15 are added to the Regression

equations obtained above.

Results:

Dependant Variable: NIFTY Daily Returns

Independent Variables R-Square Adjusted R-Square

CCIMIBOR Lag 7, CRISIL G10 Lag 14 0.80% 0.60%

CCIMIBOR Lag 7, CRISIL G10 Lag 14, NIFTY Lag 1 0.90% 0.70%

CCIMIBOR Lag 7, CRISIL G10 Lag 14, NIFTY Lag 1, NIFTY Lag 2 1.00% 0.70%CCIMIBOR Lag 7, CRISIL G10 Lag 14, NIFTY Lag 1, NIFTY Lag 2,Nifty Lag 3 1.00% 0.60%

Dependant Variable: CNXMCAP Daily Returns


CCIMIBOR LAG 10,CRISIL G10 LAG 14 2. 8% 2. 6%

CCIMIBOR LAG 10, CRISIL G10 LAG 14,CNXMCAP LAG 1 2. 9% 2. 7%

CCIMIBOR LAG 10, CRISIL G10 LAG 14,CNXMCAP LAG 1-LAG2 3. 0% 2. 6%

CCIMIBOR LAG 10, CRISIL G10 LAG 14,CNXMCAP LAG 1-LAG3 3. 0% 2. 6%

Based on all of the above analysis using linear, multiple and lagged distribute models the following

models are setup in conclusion


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1. Comparison of Regression Models

Model 1:Dependant Variable: CNXMCAP Daily Returns

Independent Variable: Lagged NIFTY Daily Returns

Table 8.1

Independent Variables R-Square Adjusted R-SquareNifty Lag 1- Nifty Lag 15, Lag 30, Lag 60 5.40% 4.00%

Nifty Lag 1- Nifty Lag 15, Lag 30 5.40% 4.20%

Nifty Lag 1- Nifty Lag 15 5.40% 4.20%







Nifty Lag 1- Nifty Lag 8 4.60% 4.00%Nifty Lag 1- Nifty Lag 7 4.20% 3.70%





Nifty Lag 1-Nifty Lag 2 3.30% 3.10%

Nifty Lag 1 2.80% 2.80%

Compare the colored models from table 8.1 with the corresponding models in table8.2.

Table 8.2


NIFTY Daily Returns (No lag) 75.10% 75.10%

NIFTY (No Lag), Nifty Lag1- Nifty Lag 14 78.50% 78.20%

NIFTY (No lag),Nifty Lag 1- Nifty Lag 10 78.50% 78.30%

Nifty No Lag, Nifty Lag 1- Nifty Lag 3 78.30% 78.20%

Nifty No Lag, Nifty Lag 1- Nifty Lag 2 77.50% 77.40%

Inference: The NIFTY Daily Returns without any Time LAG are largely significant in the analysis.


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Model 2


Independent Variable: NIFTY, CCIMIBOR LAG 10, CRISIL G10 LAG 14

Model 3


Independent Variable: NIFTY, CCIMIBOR, CRISIL G10

R-Sq = 75.5%

R-Sq(adj) = 75.5%

Model 4

Dependant Variable: NIFTY Daily Returns

Independent Variable: CNXMCAP, CCIMIBOR LAG 14, CRISIL G10 LAG 7

The regression equation is

CNXMCAP = 0.00083 + 0.759 Nifty - 0.000308 CCIMIBOR LAG 10+ 0.000001 CRISIL G10 LAG 14

R-Sq = 75.3%

R-Sq(adj) = 75.3%


CNXMCAP = - 0.00122 + 0.772 Nifty - 0.000419 CCILMIBOR + 0.000002 CRISIL G10 INDEX


NIFTY = - 0.00274 + 0.000200 CCIMIBOR LAG 14 + 0.000001 CRISIL G10 LAG 7+0.986CNXMCAP

R-Sq = 0.8%

R-Sq(adj) = 0.6%


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9. Conclusion

The R-Square values obtained in the analysis were relatively low until another equity index was added to

the regression model. The linear models explained at the start attained a maximum R-Square of 21%

when the NAVs of the ETFs were used as dependant variable. When the Daily Returns on the underlyingindex were regressed the maximum R-square value was 15% and using the Index values itself as the

dependant variable explained 40% influence of the predictors.

However when time lagged values of the predictors were used in the regression, model efficiency

increased by approximately 8%. A 14day Lag in CCIMIBOR influenced NIFTY Returns to a larger extent

than CCIMIBOR without lag. Autoregressive models did not approach a R-Square greater than 5%

indicating lagging the dependant variable was not significant.

Finally when NIFTY Returns were added to the model having CNXMCAP as the dependent variable an

R-Square of 75% was obtained clearly indicating a strong relation of the two indices. Lagging the values

of NIFTY Returns in the model is not appropriate for the analysis as indicated by Model 1. As model 3

suggest lagging values of interest rates has a negligible change in model efficiency suggesting the central

parameter is the NIFTY index to explain variation in CNXMCAP Returns.

In conclusion Interest rates, GDP, inflation do not have a very strong influence on Index Returns. A

regression model consisting of these parameters is not efficient to understand factors affecting ETFs.

Variation in CXMCAP Daily Returns is most efficiently explained by NIFTY Daily Returns.


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10. References

Books:

Gujarati, Damodar N: Basic Econometrics, 4th

Edition, Tata McGraw Hill

Koop, Gary: Analysis of Economic Data, 3rdEdition.

Abner, David J.: The ETF Handbook: How to Value Exchange Traded Funds, Wiley Finance

Google Scholar:

1. Pricing Efficiency of Exchange Traded Funds- Pavel Prusevic

2. The pricing Of China region ETFs- An empirical Analysis-

-Yao Zheng- University of New Orleans

-Eric Osmer-University of New Orleans

3. A Cost-Performance Analysis of Exchange Traded Funds: Evidence from iShares

By Gerasimos G. Rompotis_

Websites:

Motilal Oswal Asset Management Company.

http://www.motilaloswal.com/Asset-Management

http://www.mostshares.com

Wikipedia

http://en.wikipedia.org/wiki/Bayesian_information_criterion

http://en.wikipedia.org/wiki/Akaike _information_criterion

Pearson Education

http://www.aw-bc.com/info/studenmund/Chapter6.pdf

Office of the Economic Advisor

http://eaindustry.nic.in/Key_Economic_Indicators/Key_Economic_Indicators.pdf

Investopedia

http://www.investopedia.com/university/advancedbond/advancedbond5.asp

CRISIL

http://crisil.com/capital-markets/10yr-gilt-index.html

Data Source:

Office of the Economic Advisor:http://eaindustry.nic.in/

RBIs Database Warehouse:http://dbie.rbi.org.in
http://www.motilaloswal.com/Asset-Managementhttp://www.motilaloswal.com/Asset-Managementhttp://www.mostshares.com/http://www.mostshares.com/http://en.wikipedia.org/wiki/Bayesian_information_criterionhttp://en.wikipedia.org/wiki/Bayesian_information_criterionhttp://en.wikipedia.org/wiki/Akaike%20_information_criterionhttp://en.wikipedia.org/wiki/Akaike%20_information_criterionhttp://www.aw-bc.com/info/studenmund/Chapter6.pdfhttp://www.aw-bc.com/info/studenmund/Chapter6.pdfhttp://eaindustry.nic.in/Key_Economic_Indicators/Key_Economic_Indicators.pdfhttp://eaindustry.nic.in/Key_Economic_Indicators/Key_Economic_Indicators.pdfhttp://www.investopedia.com/university/advancedbond/advancedbond5.asphttp://www.investopedia.com/university/advancedbond/advancedbond5.asphttp://crisil.com/capital-markets/10yr-gilt-index.htmlhttp://crisil.com/capital-markets/10yr-gilt-index.htmlhttp://eaindustry.nic.in/http://eaindustry.nic.in/http://eaindustry.nic.in/http://dbie.rbi.org.in/http://dbie.rbi.org.in/http://dbie.rbi.org.in/http://dbie.rbi.org.in/http://eaindustry.nic.in/http://crisil.com/capital-markets/10yr-gilt-index.htmlhttp://www.investopedia.com/university/advancedbond/advancedbond5.asphttp://eaindustry.nic.in/Key_Economic_Indicators/Key_Economic_Indicators.pdfhttp://www.aw-bc.com/info/studenmund/Chapter6.pdfhttp://en.wikipedia.org/wiki/Akaike%20_information_criterionhttp://en.wikipedia.org/wiki/Bayesian_information_criterionhttp://www.mostshares.com/http://www.motilaloswal.com/Asset-Management

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