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Course11110313739 lectures

Mathematical Portfolio Theory

Prof. Siddhartha Pratim Chakrabarty · IIT Guwahati

Start with lecture 1 At NPTEL

Lectures

Week 1: Basics of Probability Theory

  1. Lecture 1: Probability space and their properties, Random variables Video
  2. Lecture 2: Mean, variance, covariance and their properties Video
  3. Lecture 3:Â Linear regression; Binomial and normal distribution; Central Limit Theorem Video

Module 2: Basics of Financial Markets

  1. Lecture 4 :Â Financial markets Video
  2. Lecture 5 :Â Bonds and stocks Video
  3. Lecture 6 : Binomial and geometric Brownian motion (gBm) asset pricing models Video

Module 3: Mean-Variance Portfolio Theory-I

  1. Lecture 7 :Â Expected return, risk and covariance of returns Video
  2. Lecture 8 : Expected return and risk of a portfolio; Minimum variance portfolio Video
  3. Lecture 9 : Multi-asset portfolio and Efficient frontier Video

Module 4: Mean-Variance Portfolio Theory-II

  1. Lecture 10 : Capital Market Line and Derivation of efficient frontier Video
  2. Lecture 11 : Capital Asset Pricing Model and Single index model Video
  3. Lecture 12 : Portfolio performance analysis Video

Module 5: Non-Mean-Variance Portfolio Theory-I

  1. Lecture 13 : Utility functions and expected utility Video
  2. Lecture 14 :Â Risk preferences of investors Video
  3. Lecture 15 : Absolute Risk Aversion and Relative Risk Aversion Video

Module 6: Non-Mean-Variance Portfolio Theory-II

  1. Lecture 16 :Â Portfolio theory with utility functions Video
  2. Lecture 17 : Geometric Mean Return and Roy's Safety-First Criterion Video
  3. Lecture 18 :Â Kataoka's Safety-First Criterion and Telser's Safety-First Criterion Video

Module 7: Non-Mean-Variance Portfolio Theory-III

  1. Lecture 19 : Semi-variance framework Video
  2. Lecture 20 : Stochastic dominance; First order stochastic dominance Video
  3. Lecture 21 : Second order stochastic dominance and Third order stochastic dominance Video

Module 8: Optimal Portfolio and Consumption-I

  1. Lecture 22 : Discrete time model and utility function Video
  2. Lecture 23 : Optimal portfolio for single-period discrete time model Video
  3. Lecture 24 : Optimal portfolio for multi-period discrete time model; Discrete Dynamic Programming Video

Module 9: Optimal Portfolio and Consumption-II

  1. Lecture 25 : Continuous time model; Hamilton-Jacobi-Bellman PDE Video
  2. Lecture 26 : Hamilton-Jacobi-Bellman PDE; Duality/Martingale Approach Video
  3. Lecture 27 : Duality/Martingale Approach in Discrete and Continuous Time Video

Module 10: Bond Portfolio Management

  1. Lecture 28 : Interest rates and bonds; Duration Video
  2. Lecture 29 : Duration; Immunization Video
  3. Lecture 30 : Convexity; Hedging and Immunization Video

Module 11: Risk Management

  1. Lecture 31: Quantiles and their properties Video
  2. Lecture 32:Â Value-at-Risk and its properties Video
  3. Lecture 33: Average Value-at-Risk and its properties Video

Module 12: Applications with market data

  1. Lecture 34: Asset allocation Video
  2. Lecture 35: Portfolio optimization Video
  3. Lecture 36: Portfolio optimization with constraints, Value-at-Risk: Estimation and backtesting Video

Live Session

  1. Live Session 07-10-2020 Video
  2. Live Session 10-11-2020 Video
  3. Live Session 01-12-2020 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Guwahati
Department
Mathematics
Teacher
Prof. Siddhartha Pratim Chakrabarty
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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