About the Course
Learn mathematical, programming and statistical tools used in the real world analysis and modeling of financial data. Apply these tools to model asset returns, measure risk, and construct optimized portfolios using the open source R programming language and Microsoft Excel. Learn how to build probability models for asset returns, to apply statistical techniques to evaluate if asset returns are normally distributed, to use Monte Carlo simulation and bootstrapping techniques to evaluate statistical models, and to use optimization methods to construct efficient portfolios.
Course Syllabus
Topics covered include:
Computing asset returns
Univariate random variables and distributions
Characteristics of distributions, the normal distribution, linear function of random variables, quantiles of a distribution, Value-at-Risk
Bivariate distributions
Covariance, correlation, autocorrelation, linear combinations of random variables
Time Series concepts
Covariance stationarity, autocorrelations, MA(1) and AR(1) models
Matrix algebra
Descriptive statistics
histograms, sample means, variances, covariances and autocorrelations
The constant expected return model
Monte Carlo simulation, standard errors of estimates, confidence intervals, bootstrapping standard errors and confidence intervals, hypothesis testing , Maximum likelihood estimation, review of unconstrained optimization methods
Introduction to portfolio theory
Portfolio theory with matrix algebra
Review of constrained optimization methods, Markowitz algorithm, Markowitz Algorithm using the solver and matrix algebra
Statistical Analysis of Efficient Portfolios
Risk budgeting
Euler’s theorem, asset contributions to volatility, beta as a measure of portfolio risk
The Single Index Model
Estimation using simple linear regression
Suggested Readings
(The first 4 texts are highly recommended)
Introduction to Computational Finance and Financial Econometrics, Eric Zivot and R. Douglas Martin.
Manuscript under preparation
Statistics and Data Analysis for Financial Engineering by David Ruppert, Springer-Verlag.
Beginner's Guide to R by Alain Zuur, Elena Ieno and Erik Meesters, Springer-Verlag.
R Cookbook by Paul Teetor, O'Reilly.
Other books for further reference:
Introductory Statistics with R, Second Edition (Statistics and Computing, Paperback), by Peter Dalgaard, Springer-Verlag, New York.
Modern Portfolio Theory and Investment Analysis, by E.J. Elton et al., Wiley, New York.
Financial Modeling, by Simon Benninga. MIT Press.
Statistical Analysis of Financial data in S-PLUS, by Rene Carmona, Springer-Verlag, 2004.