Statistical Analysis of the Log Returns of Financial Assets
Statistical Analysis of the Log Returns of Financial Assets
Leo Quigley Student ID Number: 0442372 BSc in Financial Mathematics Supervisor: Dr. Volkert Paulsen Second Reader: Dr. David Ramsey
April 9, 2008
Abstract
In many models of financial mathematics, such as the mean-variance model for portfolio selection and asset pricing models, the independence and identical normal distribution of the asset returns is the cornerstone assumption on which these are built. Empirical studies have shown that the returns of an asset don't actually follow a normal distribution but in fact they have fatter tails than the normal can capture. There is evidence that the asset returns not only display this so-called heavy tailed behaviour but are also possibly skewed in their distributions. Empirical research has also found that returns display alternating periods of high and low volatility contradicting the idea of independent and identical distribution.
Acknowledgments I would like to thank my family for all of their support throughout my time in college.
Thanks to everyone who I have become friends with in college who have made this the best four years of my life.
I would also like to thank my supervisor, Dr. Volkert Paulsen, for both suggesting this topic and assisting me throughout.
Contents
1 Introduction
3
1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Outline of Paper . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Overview of Returns of Financial Assets
6
2.1 Properties of Stock Prices . . . . . . . . . . . . . . . . . . . . 6
2.2 Defining a Financial Asset Return . . . . . . . . . . . . . . . . 9
2.3 Statistical Properties of Returns . . . . . . . . . . . . . . . . . 13
3 Random Walk Approach and Normality of Returns
16
3.1 Random Walk Hypothesis . . . . . . . . . . . . . . . . . . . . 16
3.1.1 Market Efficiency . . . . . . . . . . . . . . . . . . . . . 17
3.1.2 Definition of a Random Walk . . . . . . . . . . . . . . 19
3.1.3 Applying the Hypothesis to Financial Series Data . . . 19
3.2 Testing for Normality . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Overview of Normality in Returns . . . . . . . . . . . . 21
3.2.2 Exploratory Data Analysis . . . . . . . . . . . . . . . . 24
1
CONTENTS
2
3.2.3 Statistical Tests of Normality . . . . . . . . . . . . . . 47
4 Extreme Value Theory Approach
66
4.1 Extreme Value Theory . . . . . . . . . . . . . . . . . . . . . . 66
4.1.1 Fisher-Tippett Theorem . . . . . . . . . . . . . . . . . 68
4.1.2 Generalisalized Extreme Value Distribution . . . . . . 70
4.1.3 General Pareto Distribution . . . . . . . . . . . . . . . 70
4.2 Peak Over Threshold Method . . . . . . . . . . . . . . . . . . 71
4.2.1 Introduction to Peak Over Threshold . . . . . . . . . . 71
4.2.2 Pickands-Balkema-De Hann Theorem . . . . . . . . . . 72
4.2.3 POT Using GPD Approach . . . . . . . . . . . . . . . 73
4.2.4 Application of POT to the Tails . . . . . . . . . . . . . 75
5 Time Series Approach
89
5.1 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2 Correlation and Autocorrelation. . . . . . . . . . . . . . . . . 91
6 Conclusions
97
6.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- package stocks r
- trusted in depth market data for historical quotes
- statistical analysis of the log returns of financial assets
- retrieving historical spot future prices for commodities
- 8 129 10 at 1 42pm et co race trade free for e trade
- section 15 prices census
- stock index futures spread trading
- exhibit no exhibit 67 witness paul moul date of request
- microsoft excel assignment 1 city college of san francisco
- guide thomson one excel université de sherbrooke
Related searches
- department of the treasury bureau of fiscal
- copy of the nasw code of ethics
- assess the impacts of the french policy of assimilation on africans
- examples of the first law of motion
- names of the periodic table of elements
- history of the nasw code of ethics
- examples of the second law of motion
- equation of the tangent line of 2sinxcosx
- office of the navy chief of information
- office of the joint chiefs of staff
- examples of the universal law of gravitation
- chairman of the joint chiefs of staff