Mathematical Portfolio Theory

Overview

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This course will give an introduction to the mathematical approaches used for design and analysis of financial portfolios. It would be useful to participants who want to get a basic insight into mathematical portfolio theory, as well as those who are looking at a career in finance industry, particularly as asset managers. The course would be accessible to a broad spectrum of students of Mathematics, Statistics, Engineering and Management (with the requisite background in Mathematics). Further, practitioners in finance industry would also find the course useful from a professional point of view.
INTENDED AUDIENCE :Advanced undergraduate as well as postgraduate students in Mathematics, Statistics, Engineering and Management (with requisite background in Mathematics).PREREQUISITES : Basic probability theory at undergraduate level.INDUSTRIES SUPPORT :This course would be useful to finance industry, particularly companies involved in asset management.

Syllabus

COURSE LAYOUT

Week 1:Basics of Probability Theory:Probability space and their properties; Random variables; Mean, variance, covariance and their properties; Binomial and normal distribution; Linear regressionWeek 2:Basics of Financial Markets:Financial markets; Bonds and Stocks; Binomial and geometric Brownian motion (gBm) asset pricing modelsWeek 3:Mean-Variance Portfolio Theory:Return and risk; Expected return and risk; Multi-asset portfolio; Efficient frontierWeek 4: Mean-Variance Portfolio Theory: Capital Asset Pricing Model; Capital Market Line and Security Market Line; Portfolio performance analysis
Week 5:Non-Mean-Variance Portfolio Theory:Utility functions and expected utility; Risk preferences of investorsWeek 6:Non-Mean-Variance Portfolio Theory: Portfolio theory with utility functions; Safety-first criterionWeek 7:Non-Mean-Variance Portfolio Theory: Semi-variance framework; Stochastic dominanceWeek 8:Optimal portfolio and consumption: Discrete time model; Dynamic programmingWeek 9:Optimal portfolio and consumption: Continuous time model; Hamilton-Jacobi-Bellman partial differential equationWeek 10:Bond Portfolio Management:Interest rates and bonds; Duration and Convexity; ImmunizationWeek 11:Risk Management:Value-at-Risk (VaR); Conditional Value-at-Risk (CVaR); Methods of calculating VaR and CVaR Week 12:Applications based on actual stock market data: Applications of mean-variance portfolio theory; Applications of non-mean-variance portfolio theory; Applications of VaR and CVaR