Quantitative Applications in Finance

8/11/2019 Quantitative Applications in Finance

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Quantitative Applications in Finance

Project Report

Group7

2014-15

Indian Institute of Management

Lucknow

PGP ID Name Company

PGP29002 Pratik Mandhana Larsen & Toubro

PGP29041 Raghavendra Hindalco Industries

PGP29017 Waman Virgaonkar Ultratech Cement

PGP29057 Kirtesh Kumar Bank of Baroda

PGP29033 Srikanth Dasika Petronet LNG

PGP29334 Venkat Rajath Mahindra & Mahindra


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1.Companies

1.1. Ultratech CementUltraTech Cement Limited is engaged in the business of cement and cement related products. The

Company provides a range of products that cater to all the needs from laying the foundation to

delivering the final touches. The Company manufactures and provides ordinary Portland and

Portland Pozzolana Cement, Ready-Mix Concrete, and White Cement. White cement is

manufactured under Birla White brand, ready mix concretes under UltraTech Concrete brand and

new age building products under UltraTech Building Products Division. The retail outlets of the

Company operate under UltraTech Building Solutions. The Company is also an exporter of cement

clinker spanning export markets in countries across the Indian Ocean, Africa, Europe and the Middle

East. The Company conducts business activity in United Arab Emirates, Sri Lanka, Bahrain, and

Bangladesh.

2.Modelling of Returns

2.1.

Testing for Stationarity

2.1.1. Ultratech Cement

The returns of Ultratech Cement appear to be stationary as shown below by the ACF/PACF plots and

the ADF test.


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2.2.

Modelling of Returns


AR/MA

The ACF-PACF plots in the stationarity section shows a geometrically declining ACF and PACF with asingle spike. This gives an indication for an AR(1) model. The following is the R output for AR(1)

model:

Since the intercept term here is insignificant, we remodel the data without it:

Based on this model the final equation is:

yt= 0.097 * yt-1 + et

The diagnostics test for this model indicates that the returns are pure white noise:


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ARMA

The ARMA(1,1) model for the given data comes out to be insignificant as shown below:

ARMAX

The ARMAX(0,1) model based on the AR(1) model and using NIFTY Returns as external regressors

gives the following output:

Since the intercept and the AR(1) term are both insignificant, we remodel without them:


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The diagnostics test for this model indicates that the returns are not pure white noise as shown by

the Ljung-Box statistics:

This tells that the model is not a good one and hence cannot be considered.

ARIMA

The ACF-PACF plots of the first order difference are shown below:


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The PACF is geometrically declining, while the ACF has two spikes. This gives an indication for

ARIMA(0,1,2) model.

The equation of the model comes out to be:

yt-1= - 0.9113 * et-1 0.0887 * et-2 + et

The diagnostics test shows that the errors are pure white noise:


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The following table gives the summary of all the models that can be used for Ultratech Cement:

Model Equation

AR(1) yt= 0.097 * yt-1 + et

ARIMA(0,1,2) yt-1= - 0.9113 * et-1 0.0887 * et-2 + et

2.3.

Forecasts from models


The following table compares the return forecasts of all the suitable models for Ultratech Cement

with the actual returns for a period of 1 month:


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This shows that the AR(1)is clearly the best model for Ultratech.

3.Modeling of Volatility

3.1.

Testing for ARCH effect


The ACF-PACF plots of the residuals from the AR(1) model and the ARCH LM test shows that the datasuffers from an ARCH effect:

Forecasts Sign Direction Forecasts Sign Direction

02-06-2014 0.028587 0.002761 1 0.003511 1

03-06-2014 0.042117 0.004067 1 0 0.004436 1 0

04-06-2014 0.007186 0.000696 1 1 0.001252 1 1

05-06-2014 0.023582 0.0023 1 0 0.003009 1 0

06-06-2014 0.01603 0.001587 1 1 0.002217 1 1

09-06-2014 0.047127 0.004775 1 0 0.005173 1 0

10-06-2014 -0.00102 -0.0001 1 1 0.000523 0 1

11-06-2014 -0.00801 -0.00082 1 0 0.000297 0 0

12-06-2014 -0.00245 -0.00025 1 1 0.000786 0 1

13-06-2014 -0.00025 -2.55E-05 1 1 0.000928 0 1

16-06-2014 -0.00771 -0.00078 1 1 0.000236 0 0

17-06-2014 0.018295 0.001825 1 1 0.002688 1 1

18-06-2014 0.002932 0.000292 1 1 0.001093 1 1

19-06-2014 -0.01772 -0.00173 1 1 -0.00059 1 1

20-06-2014 -0.01014 -0.00096 1 1 0.000271 0 1

23-06-2014 -0.00594 -0.00056 1 1 0.000594 0 1

24-06-2014 -0.00203 -0.00019 1 1 0.000906 0 1

25-06-2014 0.00693 0.000651 1 1 0.001642 1 1

26-06-2014 -0.01448 -0.00135 1 1 -0.00025 1 1

27-06-2014 -0.0332 -0.00315 1 0 -0.00176 1 0

30-06-2014 -0.00152 -0.00014 1 1 0.001092 0 1

Accuracy 100.00% 75.00% 57.14% 70.00%

Date

Actual

Returns

AR(1) Model ARIMA(0,1,2) Model


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3.2. Volatility Models

3.2.1. Ultratech cement

The Skewness and the Kurtosis of the returns comes out to be as follows:

As we can see that these moments differ a lot from the normal distribution and hence we are using a

sged distribution for all the models of volatility.

SD & EVE

The following plot shows the Standard Deviation with close and other Extreme Value Estimators


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The Volatility equation for this model is:

ht= 0.065583 * residt-1 + 0.808354 * ht-1

The diagnostics of the model shows everything perfectly fine:


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eGARCH

The eGARCH model for the given data is as follows:


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log(ht)= 0.149852 * |residt-1/ht-1| + 0.913837 * log(ht-1) - 0.075339 * (residt-1/ht-1)



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gjrGARCH

The gjrGARCH model for Ultratech Cement is as follows:


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ht= 0.000024 + 0.850043 * ht-1 - 0.093782 * residt-1* It-1



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gjrGARCH-m

The gjrGARCH-in-Mean model for the given sample of data comes out to be as follows:


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The return and volatility equations for this model as are as follows:

yt= 0.046222 * yt-1 + 3.578019 * sigmat-1 + et

ht= 0.847886 * ht-1 - 0.086535 * residt-1* It-1

The diagnostics of this model are perfectly normal:


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Quantitative Applications in Finance