Mathematical Portfolio Theory

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About Course

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).

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What Will You 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

Course Content

Mathematical Portfolio Theory

  • Mathematical Portfolio Theory [Intro Video]
    00:00
  • Lec 1: Probability space and their properties, Random variables
    00:00
  • Lec 2: Mean, variance, covariance and their properties
    00:00
  • Lec 3: Linear regression; Binomial and normal distribution; Central Limit Theorem
    00:00
  • Lec 4: Financial markets
    00:00
  • Lec 5: Bonds and stocks
    00:00
  • Lec 6: Binomial and geometric Brownian motion (gBm) asset pricing models
    00:00
  • Lec 7: Expected return, risk and covariance of returns
    00:00
  • Lec 8: Expected return and risk of a portfolio; Minimum variance portfolio
    00:00
  • Lec 9: Multi-asset portfolio and Efficient frontier
    00:00
  • Lec 10 : Capital Market Line and Derivation of efficient frontier
    00:00
  • Lec 11 : Capital Asset Pricing Model and Single index model
    00:00
  • Lec 12: Portfolio performance analysis
    00:00
  • Lec 13: Utility functions and expected utility
    00:00
  • Lec 14: Risk preferences of investors
    00:00
  • Lec 15: Absolute Risk Aversion and Relative Risk Aversion
    00:00
  • Lec 16 : Portfolio theory with utility functions
    00:00
  • Lec 17: Geometric Mean Return and Roy’s Safety-First Criterion
    00:00
  • Lec 18: Kataoka’s Safety-First Criterion and Telser’s Safety-First Criterion
    00:00
  • Lec 19: Semi-variance framework
    00:00
  • Lec 20: Stochastic dominance; First order stochastic dominance
    00:00
  • Lec 21: Second order stochastic dominance and Third order stochastic dominance
    00:00
  • Lec 22: Discrete time model and utility function
    00:00
  • Lec 23: Optimal portfolio for single-period discrete time model
    00:00
  • Lec 24: Optimal portfolio for multi-period discrete time model; Discrete Dynamic Programming
    00:00
  • Lec 25: Continuous time model; Hamilton-Jacobi-Bellman PDE
    00:00
  • Lec 26: Hamilton-Jacobi-Bellman PDE; Duality/Martingale Approach
    00:00
  • Lec 27: Duality/Martingale Approach in Discrete and Continuous Time
    00:00
  • Lec 28: Interest rates and bonds; Duration
    00:00
  • Lec 29: Duration; Immunization
    00:00
  • Lec 30: Convexity; Hedging and Immunization
    00:00
  • Lec 31: Quantiles and their properties
    00:00
  • Lec 32: Value – at – Risk and its properties
    00:00
  • Lec 33: Average Value-at-Risk and its properties
    00:00
  • Lec 34: Asset allocation
    00:00
  • Lec 35: Portfolio optimization
    00:00
  • Lec 36: Portfolio optimization with constraints, Value-at-Risk: Estimation and backtesting
    00:00

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