Mathematical Portfolio Theory
This Mathematical Portfolio Theory course will give an introduction to the mathematical approaches used for the 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 the 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 the 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).
What Will I Learn?
- Week 1:Basics of Probability Theory: Probability space and their properties; Random variables; Mean, variance, covariance and their properties; Binomial and normal distribution; Linear regression
- Week 2:Basics of Financial Markets: Financial markets; Bonds and Stocks; Binomial and geometric Brownian motion (gym) asset pricing models
- Week 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 investors
- Week 6:Non-Mean-Variance Portfolio Theory: Portfolio theory with utility functions; Safety-first criterion
- Week 7:Non-Mean-Variance Portfolio Theory: Semi-variance framework; Stochastic dominance
- Week 8:Optimal portfolio and consumption: Discrete-time model; Dynamic programming
- Week 9:Optimal portfolio and consumption: Continuous-time model; Hamilton-Jacobi-Bellman partial differential equation
- Week 10:Bond Portfolio Management: Interest rates and bonds; Duration and Convexity; Immunization
- Week 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