Book Image

Introduction to R for Quantitative Finance

By : Gergely Daróczi, Michael Puhle, Edina Berlinger (EURO), Daniel Daniel Havran, Kata Váradi, Agnes Vidovics-Dancs, Agnes Vidovics Dancs, Michael Phule, Zsolt Tulassay, Peter Csoka, Marton Michaletzky, Edina Berlinger (EURO), Varadi Kata
Book Image

Introduction to R for Quantitative Finance

By: Gergely Daróczi, Michael Puhle, Edina Berlinger (EURO), Daniel Daniel Havran, Kata Váradi, Agnes Vidovics-Dancs, Agnes Vidovics Dancs, Michael Phule, Zsolt Tulassay, Peter Csoka, Marton Michaletzky, Edina Berlinger (EURO), Varadi Kata

Overview of this book

Introduction to R for Quantitative Finance will show you how to solve real-world quantitative fi nance problems using the statistical computing language R. The book covers diverse topics ranging from time series analysis to fi nancial networks. Each chapter briefl y presents the theory behind specific concepts and deals with solving a diverse range of problems using R with the help of practical examples.This book will be your guide on how to use and master R in order to solve quantitative finance problems. This book covers the essentials of quantitative finance, taking you through a number of clear and practical examples in R that will not only help you to understand the theory, but how to effectively deal with your own real-life problems.Starting with time series analysis, you will also learn how to optimize portfolios and how asset pricing models work. The book then covers fixed income securities and derivatives such as credit risk management.
Table of Contents (17 chapters)
Introduction to R for Quantitative Finance
Credits
About the Authors
About the Reviewers
www.PacktPub.com
Preface
Index

Arbitrage Pricing Theory


The Arbitrage Pricing Theory (APT) of Ross (1977) is also used in finance to determine the return of different securities. The APT states that, in equilibrium, no arbitrage opportunity can exist and, also, that the expected return of an asset is the linear combination of multiple random factors (Wilmott 2007). These factors can be various macro-economic factors or market indices. In this model, each factor has a specific beta coefficient:

αi is a constant denoting security i; βij is the sensitivity of security i to factor j; Fj is the systematic factor; while ei is the security's unsystematic risk, with zero mean.

A central notion of the APT is the factorportfolio. A factorportfolio is a well-diversified portfolio which reacts to only one of the factors, so it has zero beta for all other factors, and a beta of 1 to that specified factor. Assuming the existence of the factorportfolios, it can be shown using the arbitrage argument that any well-diversified portfolio...