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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
2.2.1. Ultratech Cement
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
2.3.1. Ultratech Cement
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
3.1.1. Ultratech Cement
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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The Volatility equation for this model is:
log(ht)= 0.149852 * |residt-1/ht-1| + 0.913837 * log(ht-1) - 0.075339 * (residt-1/ht-1)
The diagnostics of the model shows everything perfectly fine:
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gjrGARCH
The gjrGARCH model for Ultratech Cement is as follows:
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The Volatility equation for this model is:
ht= 0.000024 + 0.850043 * ht-1 - 0.093782 * residt-1* It-1
The diagnostics of the model shows everything perfectly fine:
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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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