Econ 424/Amath 462
Introduction to Portfolio Theory
Eric Zivot
July 30, 2013
Introduction to Portfolio Theory
Investment in Two Risky Assets
= simple return on asset A
= simple return on asset B
0 = initial wealth
Assumptions
and are described by the C
Chapter 1
Probability Concepts
This chapter reviews basic probability concepts that are necessary for the
modeling and statistical analysis of nancial data.
1.1
Random Variables
We start with the basic denition of a random variable:
Denition 1 A Random va
Introduction to Computational Finance and
Financial Econometrics
Probability Theory Review: Part 2
Eric Zivot
July 7, 2014
Bivariate Probability Distribution
Example - Two discrete rvs and
Bivariate
0
%
0
1/8
2/8
1
1/8
2
0
3
Pr( ) 4/8
pdf
1 Pr()
0
1/8
1/
Introduction to Computational Finance and
Financial Econometrics
Probability Theory Review: Part 1
Eric Zivot
June 28, 2011
1
Univariate Random Variables
Defnition: A random variable (rv) X is a variable that can take on a given
set of values, called the
Econ 424/CFRM 462
Portfolio Risk Budgeting
Eric Zivot
August 14, 2014
Portfolio Risk Budgeting
Idea: Additively decompose a measure of portfolio risk into contributions from
the individual assets in the portfolio.
Show which assets are most responsible f
2 Exploratory Data Analysis
2.1 Introduction
This book is concerned with the analysis of financial markets data such as equity prices, foreign exchange rates, and interest rates. These quantities vary randomly thereby causing financial risk as well as the
Computing Efficient Portfolios in R
Eric Zivot November 11, 2008
Abstract This note describes the computation of mean-variance efficient portfolios using R.
1
Portfolio Analysis Functions
I have written a few R functions for computing Markowitz mean-varia
Comput Stat (2011) 26:443458
DOI 10.1007/s00180-010-0217-1
ORIGINAL PAPER
maxLik: A package for maximum likelihood estimation
in R
Arne Henningsen Ott Toomet
Received: 15 October 2009 / Accepted: 7 September 2010 / Published online: 22 September 2010
Spr
Econ 424
Lab 4 Suggested Solutions
Descriptive Statistics
I Historical VaR
Historical VaR is computed from empirical quantiles. If W0 is the initial wealth and qr
is the empirical quantile of continuously compounded returns then the historical VaR is
give
Eric Zivot
Econ 424
Summer 2016
Problem Set #2
Working with Random Variables and Probability Distributions
Suggested Solutions
Exercises
R code for solutions is in the file econ424lab2solutions.R on the class homework page.
1. Suppose X is a normally dist
Eric Zivot
Econ 424
Summer 2016
Problem Set #3
Matrix Algebra, Time Series Concepts, and Descriptive Statistics for Financial Data
Due: Tuesday 7/12/16 at 8 PM (PST) via Canvas
Readings
My book chapters on matrix algebra review, time series concepts, and
Eric Zivot
Econ 424
Fall 2014
Problem Set #2
Working with Random Variables and Probability Distributions
Due: Wednesday 10/8/14 at 8pm via Canvas
Readings
My lecture notes on review of probability theory and random variables.
A Beginners Guide to R, chapt
University of Washington
Department of Economics
Fall 2010
Eric Zivot
Economics 424
Midterm Exam Solutions
This is a closed book and closed note exam. However, you are allowed one page of notes
(double-sided). Answer all questions and write all answers in
University of Washington Department of Economics Economics 424 Midterm Exam Suggested Solutions
Fall 2006 Eric Zivot
This is a closed book and closed note exam. However, you are allowed one page of notes (double-sided). Answer all questions and write all
Econ 424/Amath 462
Constant Exected Return Model
Eric Zivot
July 18, 2013
Constant Expected Return (CER) Model
= cc return on asset in month
= 1 assets; = 1 months
Assumptions (normal distribution and covariance stationarity)
2
( ) for all and
= []
Econ 424/CFRM 462
Descriptive Statistics for Financial Time
Series
Eric Zivot
Updated; July 15, 2014
Covariance Stationarity
cfw_ 1 = cfw_
is a covariance stationary stochastic process, and each is identically distributed with unknown pdf ()
Recall,
[] =
ECON 424 Lab 1
Fall 2014
Solutions
September 22, 2014
Part I: Return calculations
Consider the following (actual) monthly adjusted closing price data for
Starbucks stock over the period December 2004 through December 2005
End of Month Price Data for Starb
# econ424lab4.r script file for amath 462/econ 424 lab4 calculations
#
# author: Eric Zivot
# created: October 20, 2003
# revised: January 29, 2015
#
# comments:
# Data for the lab are
# monthly continuously compounded returns on Vanguard long term bond