The document summarizes a capstone project analyzing volatility patterns of stock prices. It discusses: 1) The team conducting the project and their industry collaboration with Agrud, a FinTech company. 2) The dataset used, which contains OHLC data from 2012-2017 for Apple, Amazon, Google, and American Airlines. 3) Tools and techniques used in the analysis, including ARIMA, GARCH models, and Excel, R, and SAS software. 4) Key findings that GARCH more accurately predicted volatility over the next month compared to ARIMA.

1. Prediction & Analysis of
Volatility Patterns
Capstone Project
Group 2 - PGP-BABI, Jan 2017

2. The Team
Anirban Dey
Soumojit Bose Krishna BV
Manish Kathait

3. Industry Collaboration
• Agrud (http://www.agrudadvisors.com/) is a Singapore
based FinTech company that specializes in financial
analytics & contributes mostly in Ultra-HNI wealth
management.
• Global Financial Advisory: Agrud provides a global
financial advisory with focus on Strategic & Tactical
Asset Allocation, Manager Selection and Direct
Investment.
• Corporate Advisory: Focused on helping family
businesses on their corporate finance needs which can
include M&A, borrowings, restructurings etc.

4. Dataset
• An open-high-low-close (also known as OHLC) is a type of data typically
used to illustrate movements in the price of a financial instrument over
time.
• Used OHLC data from Jan 1st, 2012 till 31st May,
2017.
• Stocks selected: Apple, American Airlines,
Amazon & Google
• NASDAQ Ticker Symbol (in above order): AAPL,
AAL, AMZN, GOOGL

5. What is Volatility?
• In finance, volatility (symbol σ) is the degree of variation of a trading
price series over time as measured by the standard deviation of
logarithmic returns.
• Realized Volatility: Also referred to
as the historical volatility.
• Key benefits of the study –
• Estimate the value of market risk.
• Pricing financial derivatives.
• General portfolio management

6. Exploratory Data Analysis
How’s volatility measured?

7. Tools & Techniques Used
Models Used
Tools Used
• Autoregressive Integrated Moving Average (ARIMA)
• Generalized Autoregressive Conditional Heteroskedasticity (GARCH)
• MS-Excel
• R
• SAS
• Tableau

8. ARIMA
• Test of Stationarity using Augmented Dickey Fuller Test
• Differencing
• ACF & PACF – In order to identify the orders of AR and MA
• ARIMA(p, d, q)
• Forecast using ARIMA
• Validation
Steps:

9. Stationary Time Series:
Statistical Properties such as Mean, Variance are constant over time

10. RV Visualization:

11. Augmented Dickey Fuller Test:
A unit root test is a statistical test for the proposition that in a
autoregressive statistical model of a time series, the autoregressive
parameter is one. In a data series y(t), where ‘t’ is a whole number,
modelled by:
y(t+1) = ay(t) + other terms
where ‘a’ is an unknown constant. A unit root test would be a test of the
hypothesis that a=1, usually against the alternative that |a| is less than 1.

12. ADF Test Results:
Stocks p-values
Apple .07477
Amazon .02167*
Google .1392
American Airlines .04703

13. ADF Test Results(after differencing):
Stocks p-value p-value
Apple .07477 .01*
Amazon .02167*
Google .1392 .01*
American Airlines .04703 .01*

14. ACF Vs PACF Plot:

15. Forecasting:

16. Forecasting(Contd..):

17. Validation:
ME RMSE MPE MAPE
Apple .002140 0.0126676 17.10188 157.2353
Amazon -5.265094e-05 0.0114969 -11.50538 28.66192
Google -0.007271 0.0577223 100 100
American
Airlines
-0.000390 0.0061836 -181.4209 280.358

18. GARCH
• GARCH (1,1) Model : The Equation –
• We are calculating variance as a function of three factors –
1. Weighted long run average variance (Marked in Yellow)
2. Weighted lagged squared return (Coefficient denoted as alpha)
3. Weighted lagged variance (Coefficient denoted as beta)

19. GARCH
Fitted the GARCH (1,1) model for further analysis:

20. Findings from the study
• We have done a comparative study using both ARIMA & GARCH to predict the volatility for
next one month for one particular stock(AAL).
• When compared with ARIMA, it is quite evident that using GARCH we could predict
volatility more accurately for next one month.
• Prediction for American Airlines –

21. Future Scope
• More detailed analysis using GARCH model to predict volatility more accurately.
• Analyze social media data to understand market sentiment and include the factor while
predicting the volatility.
• Working on implied volatility using VIX data and comparative study of patterns.

22. Gratitude
We are extremely grateful to these people for the enormous support –
• Mr. Manjunatha Bhaskar Gummaraju (our Mentor)
• Dr. P K Viswanathan
• Dr. R L Shankar
• Dr. Bappaditya M
& of course…
• Mr Sarath Krishnan

23. Thank You!