Mathematical Portfolio Theory

  • Course level: Beginner
  • Categories C-Science
  • Last Update 23/06/2021


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

Topics for this course

37 Lessons

Mathematical Portfolio Theory

Mathematical Portfolio Theory [Intro Video]00:00:00
Lec 1: Probability space and their properties, Random variables00:00:00
Lec 2: Mean, variance, covariance and their properties00:00:00
Lec 3: Linear regression; Binomial and normal distribution; Central Limit Theorem00:00:00
Lec 4: Financial markets00:00:00
Lec 5: Bonds and stocks00:00:00
Lec 6: Binomial and geometric Brownian motion (gBm) asset pricing models00:00:00
Lec 7: Expected return, risk and covariance of returns00:00:00
Lec 8: Expected return and risk of a portfolio; Minimum variance portfolio00:00:00
Lec 9: Multi-asset portfolio and Efficient frontier00:00:00
Lec 10 : Capital Market Line and Derivation of efficient frontier00:00:00
Lec 11 : Capital Asset Pricing Model and Single index model00:00:00
Lec 12: Portfolio performance analysis00:00:00
Lec 13: Utility functions and expected utility00:00:00
Lec 14: Risk preferences of investors00:00:00
Lec 15: Absolute Risk Aversion and Relative Risk Aversion00:00:00
Lec 16 : Portfolio theory with utility functions00:00:00
Lec 17: Geometric Mean Return and Roy’s Safety-First Criterion00:00:00
Lec 18: Kataoka’s Safety-First Criterion and Telser’s Safety-First Criterion00:00:00
Lec 19: Semi-variance framework00:00:00
Lec 20: Stochastic dominance; First order stochastic dominance00:00:00
Lec 21: Second order stochastic dominance and Third order stochastic dominance00:00:00
Lec 22: Discrete time model and utility function00:00:00
Lec 23: Optimal portfolio for single-period discrete time model00:00:00
Lec 24: Optimal portfolio for multi-period discrete time model; Discrete Dynamic Programming00:00:00
Lec 25: Continuous time model; Hamilton-Jacobi-Bellman PDE00:00:00
Lec 26: Hamilton-Jacobi-Bellman PDE; Duality/Martingale Approach00:00:00
Lec 27: Duality/Martingale Approach in Discrete and Continuous Time00:00:00
Lec 28: Interest rates and bonds; Duration00:00:00
Lec 29: Duration; Immunization00:00:00
Lec 30: Convexity; Hedging and Immunization00:00:00
Lec 31: Quantiles and their properties00:00:00
Lec 32: Value – at – Risk and its properties00:00:00
Lec 33: Average Value-at-Risk and its properties00:00:00
Lec 34: Asset allocation00:00:00
Lec 35: Portfolio optimization00:00:00
Lec 36: Portfolio optimization with constraints, Value-at-Risk: Estimation and backtesting00:00:00
Mathematical Portfolio

Enrolment validity: Lifetime


  • Basic probability theory at the undergraduate level.