Mathematical Portfolio Theory

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.

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