Kachapova Farida. Mathematical Models in Portfolio Analysis

Bookboon, 2013. — 110 p. — ISBN: 978-87-403-0370-4.This book explains portfolio modelling in financial mathematics as a consistent mathematical theory with all steps justified. The topics include mean-variance portfolio analysis and capital market theory. The book contains many examples with solutions. Linear algebra rather than calculus is used as foundation for portfolio analysis; this approach is more conceptual and helps to avoid tedious calculations. The reader does not need much previous mathematical knowledge, only interest in mathematics and its financial applications because the book provides a general mathematical introduction.Part Mathematical Introduction
Matrices and Applications
Terminology
Matrix Operations
Determinants
Systems of Linear Equations
Positive Definite Matrices
Hyperbola
Orthogonal Projection
Orthogonal Projection onto a Subspace
Orthogonal Projection onto a Vector
Minimal Property of Orthogonal Projection
Random Variables
Numerical Characteristics of a Random Variable
Covariance and Correlation Coefficient
Covariance Matrix
Regression
Euclidean Space of Random Variables
Regression
Regression to a Constant
Simple Linear Regression
Part Portfolio Analysis
Portfolio Modelling
Terminology
Short Sales
Minimizing Risk
Statistical Parameters of an N-Asset Portfolio
Envelope of Financial Assets
Mean-Variance Analysis
Principle of Two Fund Separation
Efficient Frontier
Mean-Variance Relation
Mean-Variance Relation for 2-Asset Portfolios
Capital Market Theory
Risk-Free Asset
Tangency Portfolio
Market Portfolio. Capital Market Line
Finding Market Portfolio and CML Equation
Regression in Finance. Beta Coefficient
Capital Asset Pricing Model and Security Market Line.