Mathematical Portfolio Theory (English)

   Thursday, March 28, 2024   

Starting a new Lecture Notes Series on Mathematical Portfolio Theory

Youtube Lecture Playlist Credits 

Channel Name: NPTEL IIT Guwahati

So Let Us Start to This Journey of Learning 

Mathematical Portfolio Theory By Lecture Notes together!

Lecture 1: Mathematical Portfolio Theory

Lecture 2: Lec 1: Probability space and their properties, Random variables

Lecture 3: Lec 2: Mean, variance, covariance and their properties

Lecture 4: Lec 3: Linear regression; Binomial and normal distribution; Central Limit Theorem

Lecture 5: Lec 4: Financial markets

Lecture 6: Lec 5: Bonds and stocks

Lecture 7: Lec 6: Binomial and geometric Brownian motion (gBm) asset pricing models

Lecture 8: Lec 7: Expected return, risk and covariance of returns

Lecture 9: Lec 8: Expected return and risk of a portfolio; Minimum variance portfolio

Lecture 10: Lec 9: Multi-asset portfolio and Efficient frontier

Lecture 11: Lec 10 : Capital Market Line and Derivation of efficient frontier

Lecture 12: Lec 11 : Capital Asset Pricing Model and Single index model

Lecture 13: Lec 12: Portfolio performance analysis

Lecture 14: Lec 13: Utility functions and expected utility

Lecture 15: Lec 14: Risk preferences of investors

Lecture 16: Lec 15: Absolute Risk Aversion and Relative Risk Aversion

Lecture 17: Lec 16 : Portfolio theory with utility functions

Lecture 18: Lec 17: Geometric Mean Return and Roy's Safety-First Criterion

Lecture 19: Lec 18: Kataoka's Safety-First Criterion and Telser's Safety-First Criterion

Lecture 20: Lec 19: Semi-variance framework

Lecture 21: Lec 20: Stochastic dominance; First order stochastic dominance

Lecture 22: Lec 21: Second order stochastic dominance and Third order stochastic dominance

Lecture 23: Lec 22: Discrete time model and utility function

Lecture 24: Lec 23: Optimal portfolio for single-period discrete time model

Lecture 25: Lec 24: Optimal portfolio for multi-period discrete time model; Discrete Dynamic Programming

Lecture 26: Lec 25: Continuous time model; Hamilton-Jacobi-Bellman PDE

Lecture 27: Lec 26: Hamilton-Jacobi-Bellman PDE; Duality/Martingale Approach

Lecture 28: Lec 27: Duality/Martingale Approach in Discrete and Continuous Time

Lecture 29: Lec 28: Interest rates and bonds; Duration

Lecture 30: Lec 29: Duration; Immunization

Lecture 31: Lec 30: Convexity; Hedging and Immunization

Lecture 32: Lec 31: Quantiles and their properties

Lecture 33: Lec 32: Value - at - Risk and its properties

Lecture 34: Lec 33: Average Value-at-Risk and its properties

Lecture 35: Lec 34: Asset allocation

Lecture 36: Lec 35: Portfolio optimization

Lecture 37: Lec 36: Portfolio optimization with constraints, Value-at-Risk: Estimation and backtesting