PORTFOLIO MANAGEMENT USING R SIMULATION AND ARMA STOCK RETURN PREDICTION ...

49 Pages·2017·1.29 MB·English

by  Ali Salhi

SCHOOL OF SCIENCE AND ENGINEERING

PORTFOLIO MANAGEMENT USING R SIMULATION
AND ARMA STOCK RETURN PREDICTION

Capstone Deign
March 2017
A. Salhi
Supervised by N. Rhiati

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_____________________________________________________
Capstone Student: Ali Salhi

Approved by the Supervisor

_____________________________________________________
SUPERVISOR: Nabil Rhiati

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Acknowledgments page

This project would not have been possible without the help and support of many individuals.
First I would like to thank my supervisor who has helped me throughout this semester mainly by
setting deadlines for me and helping me respect them to the best of his ability as well as by
looking at my project through the eyes of a demanding customer seeking perfection. I would also
like to thank Mr. Tahar Harkat who provided me with the financial expertise and guided me
through a big part of this project by telling me which calculations to make and by showing me
which results were relevant and which were not.
I am also grateful to anybody that I have interacted with and talk to about my project and that has
provided me with great feedback. A lot of times people who aren’t related to any of the areas of
expertise that are included in this project gave me the best feedback and helped me see things
from their perspectives.
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Contents

1. Abstract 6
2. Introduction 7
3. Methodology 9
4. Financial concepts 11
4.1 Portfolio Management 11
4.2 Efficient Frontier 12
4.3 Portfolio Covariance Matrix 14
5. Mathematical Concepts 15
5.1 Mathematical Modelling 15
5.2 The Data and Model in use 16
6. Technology Enablers 21
6.1 The “R” Programing Language 21
6.2 Why “R” 21
6.3 R Studio 22
6.4 Packages 22
6.5 Packages Used 23
6.5.1 Quantmod 23
6.5.1.1 GetSymbols 23
6.5.2 Portfolio Analytics 24
6.5.2.1 Portfolio.Spec 24
6.5.2.2 Add.Constraint 24
6.5.2.3 Random_Portfolios 25
6.5.2.4 Add.Objective 25
6.5.2.5 Optimize.Portfolio 25
6.5.3 Plotly 26
6.5.4 Forecast 27
6.5.4.1 ARIMA 27
6.5.4.2 Forecast 27
6.5.5 Stats 28
6.5.5.1 NA.omit 28
6.5.5.2 Predict 28
7 The Program sequence 29
8 The output file 31
9 Conclusion 33
10 References 34
11 Appendix 1 36
12 Appendix 2 49

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Table of Figures

Figure 1: Example of a stationary time series 18
Figure 2: Example of a non-stationary time series 19
Figure 3: Adjusted closing price of INFOSYS over 1 year 20
Figure 4: The R Studio interface 36
Figure 5: Opening the R script on R studio 37
Figure 6: Loading the libraries to the current session 38
Figure 7: Prompt for the number of assets to invest in 38
Figure 8: Prompt for the start and end date for data retrieval 39
Figure 9: Entering 5 stocks and their index 39
Figure 10: IBM OHCL data frame 40
Figure 11: Prompt for constraints to be added to the portfolio 40
Figure 12: Suggestions and warning messages from the program 41
Figure 13: Script to visualize the portfolios plot with Risk VS Return 41
Figure 14: Random portfolios plot 42
Figure 15: Script to visualize efficient frontier 42
Figure 16: Efficient frontier data frame 43
Figure 17: Weights of assets making up the efficient frontier 43
Figure 18: Data frame showing the weights of assets within specific portfolios 43
Figure 19: Script to retrieve weights of assets making up a specific portfolio 44
Figure 20: Results from single portfolio weights retrieval 44
Figure 21: Script for retrieving manually computed values for individual stocks 45
Figure 22: Values for the IBM stock 45
Figure 23: Script for retrieving the automatically generated summary for each stock 46
Figure 24: Summary for the IBM stock 46
Figure 25: Script to plot the historical return and the predicted ones 47
Figure 26: Plot of the historical returns and predicted ones 48
Figure 27: Accuracy measures of predicted VS actual returns 49

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1. Abstract
This report covers all the aspects of my capstone project. It is structured in such a way that a
person can understand all of the work that was done with no prior knowledge about the fields of
finance, computer science, and mathematics. The introduction talks about all the fields that are
involved in the making of this project with a preview of the workings and intent behind the work
performed, which is to help portfolio managers make better informed decisions using analytics
tools as well as a mathematical model. After that, and since this is a software project, a
methodology section introduces the software engineering methodology that was used to keep all
of the stakeholders involved throughout the development phase. A well detailed description of
the technology enablers used follows that. Towards the end there is a full description of the
whole code from the beginning to the end followed by a demo with screenshots and snippets of
code.
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2. Introduction
Data science is a fast-growing field where various methods and processes are applied to raw and
usually large sets of data to extract valuable information. Data science is not a discipline on its
own but rather an interdisciplinary field that merges techniques from mathematics, statistics, and
computer science. This large area of studies is further divided into four more detailed and
specialized subfields, namely: Decision Analytics, Descriptive Analytics, Predictive Analytics,
and Prescriptive Analytics. The two that will be used extensively in the project are prescriptive
as well as predictive analytics. The first will be used to make a recommendation to the user on
what their best option of investment is. The recommendation will be based on a simulation to
which we will apply optimization techniques. The second one will be used to predict future
returns of certain stocks. That will help the portfolio manager make financial projections and run
different scenarios. Now following this logic and using tools and techniques from prescriptive as
well as predictive analytics, the goal of this project is to provide portfolio managers with a tool
they can use to get insight form structured historical data about assets, mainly stocks, to make
better informed decisions when handling their client’s money. [1]

To be able to perform simulations and use historical stock prices to make decent decisions on
where to invest your money, you should have an extensive knowledge in the financial field as
well as some training on a statistical software. The problem is that these two prerequisites are not
within everybody’s reach, and they themselves require time, energy and money. The only other
two alternatives are to invest your money at your own risk without any insight or prior
knowledge of the market, or hire somebody to invest your money and take a cut.

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Now with that being said, this program’s main purpose is to be able, through an interactive
interface, to give some sort of guidance to people that want to create a portfolio of assets to
invest in, maximize their returns, and make some money in the process. The user doesn’t
necessarily need to be an expert in the fields of computer science or finance to be able to use it.

My knowledge about the fields of data science and finance at the beginning of the project was
trivial. I was exposed to some of the technologies used in analytics by pure chance while
researching it online, as in for finance, I learned about it in one class I took while studying
abroad. I took this project as an opportunity to learn and absorb as much knowledge as possible
about these two fields because Business and Financial Services Analytics are fields that I am
highly interested in for my future career.

This report will contain all the information that relates to the project whether that be detailed
technical information or methodologies used and organization followed to conduct the whole
project and take it from the design stages to the concrete realization and testing. The report will
be complemented by screenshots of its workings to better illustrate the descriptions given and
provide the reader with a visual idea of the final product.

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3. Methodology
The main goal behind this capstone project being the development of a computer program I
relayed heavily on the methodologies I have learned in my two software engineering classes.
These methodologies are there to ensure smooth execution of the project and a good flow
throughout the progress towards the final and desired result. After a review of the many
methodologies available I judged the best fit for the size and nature of this project to be the
“Agile Scrum Methodology”.

Agile methods were created due to the continuous problems caused by the huge amounts of
overhead involved in the design of new software. Agile methodologies favor small steps and
incremental development with the minimal necessary planning over long-term unnecessary
planning that might be subject to change because of the nature of the fast-paced environment that
we live in. Following these methodologies guarantees frequent delivery of new functionalities
that are added with every new increment. Agile also favors face to face communication over
written documents to avoid any ambiguity and misunderstandings. The main principles of Agile
methodologies are best illustrated through the Agile manifesto:

Individuals and interactions over processes and tools
Working software over comprehensive documentation
Customer collaboration over contract negotiation
Responding to change over following a plan
(Agile manifesto)[2]

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Agile methodologies have their limitations as well. Some of the ones that were faced during the
development of this project are the difficulty to keep all the stakeholders interested in the project
as well as maintaining simplicity. The first one is because most of the stakeholders don’t have a
background in computer science and get bored fast when programing technicalities and
difficulties are discussed. The second one is because there is a constant need to cope with change
and that entails adding or deleting parts of the program which doesn’t help keep it simple and
straightforward. [3]

The Agile Scrum methodology is the closest to what was adopted during the development of this
process. The term closest is used because this project was developed with only one programmer
and not a team. The main goal of the scrum is to provide a process that favors iterative
development and continuous customer involvement. The first phase of the Scrum is where the
general outline and objectives of the project are determined with the participation of the
programmer and the customer. This phase is what gave birth to the project specification
document. The second phase is the longest since it’s the one of the development which happen in
small increments. These are called sprint cycles with each sprint resulting in an increment to the
program. The third and final phase of the scrum is the one that completes the required
documentation, does an assessment of the project and performance of the time and completes
.
anything that is left other than code [3]

The sprint being the main component of the Scrum process, it is divided into four distinct phases
that are followed daily to make sure that everything is in order. These phases are:
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