Mathematical Portfolio Theory

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).

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

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Lec 13: Utility functions and expected utility

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Lec 14: Risk preferences of investors

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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

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Lec 30: Convexity; Hedging and Immunization

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Lec 31: Quantiles and their properties

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Lec 32: Value – at – Risk and its properties

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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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About Course

This Mathematical Portfolio Theory course will give an introduction to the mathematical approaches used for the design and analysis of financial portfolios.

What Will You Learn?

Course Content

Mathematical Portfolio Theory

Mathematical Portfolio Theory [Intro Video]

Lec 1: Probability space and their properties, Random variables

Lec 2: Mean, variance, covariance and their properties

Lec 3: Linear regression; Binomial and normal distribution; Central Limit Theorem

Lec 4: Financial markets

Lec 5: Bonds and stocks

Lec 6: Binomial and geometric Brownian motion (gBm) asset pricing models

Lec 7: Expected return, risk and covariance of returns

Lec 8: Expected return and risk of a portfolio; Minimum variance portfolio

Lec 9: Multi-asset portfolio and Efficient frontier

Lec 10 : Capital Market Line and Derivation of efficient frontier

Lec 11 : Capital Asset Pricing Model and Single index model

Lec 12: Portfolio performance analysis

Lec 13: Utility functions and expected utility

Lec 14: Risk preferences of investors

Lec 15: Absolute Risk Aversion and Relative Risk Aversion

Lec 16 : Portfolio theory with utility functions

Lec 17: Geometric Mean Return and Roy’s Safety-First Criterion

Lec 18: Kataoka’s Safety-First Criterion and Telser’s Safety-First Criterion

Lec 19: Semi-variance framework

Lec 20: Stochastic dominance; First order stochastic dominance

Lec 21: Second order stochastic dominance and Third order stochastic dominance

Lec 22: Discrete time model and utility function

Lec 23: Optimal portfolio for single-period discrete time model

Lec 24: Optimal portfolio for multi-period discrete time model; Discrete Dynamic Programming

Lec 25: Continuous time model; Hamilton-Jacobi-Bellman PDE

Lec 26: Hamilton-Jacobi-Bellman PDE; Duality/Martingale Approach

Lec 27: Duality/Martingale Approach in Discrete and Continuous Time

Lec 28: Interest rates and bonds; Duration

Lec 29: Duration; Immunization

Lec 30: Convexity; Hedging and Immunization

Lec 31: Quantiles and their properties

Lec 32: Value – at – Risk and its properties

Lec 33: Average Value-at-Risk and its properties

Lec 34: Asset allocation

Lec 35: Portfolio optimization

Lec 36: Portfolio optimization with constraints, Value-at-Risk: Estimation and backtesting

Student Ratings & Reviews