# Mathematical Portfolio Theory

- Institution: IIT Guwahati
- Department: Mathematics
- Teacher: Prof. Siddhartha Pratim Chakrabarty
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111103137)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111103137)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1: Probability space and their properties, Random variables](https://invisiblenetwork.ai/learn/nptel/111103137/279adfb8311e) (Video)
2. [Lecture 2: Mean, variance, covariance and their properties](https://invisiblenetwork.ai/learn/nptel/111103137/a1aee4bd0e94) (Video)
3. [Lecture 3:Â Linear regression; Binomial and normal distribution; Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/111103137/0ddad3c0bcb6) (Video)
4. [Lecture 4 :Â Financial markets](https://invisiblenetwork.ai/learn/nptel/111103137/3f5c1e46990c) (Video)
5. [Lecture 5 :Â Bonds and stocks](https://invisiblenetwork.ai/learn/nptel/111103137/67187dd5d3bb) (Video)
6. [Lecture 6 : Binomial and geometric Brownian motion (gBm) asset pricing models](https://invisiblenetwork.ai/learn/nptel/111103137/30dd98eff5f9) (Video)
7. [Lecture 7 :Â Expected return, risk and covariance of returns](https://invisiblenetwork.ai/learn/nptel/111103137/6538932d4fb2) (Video)
8. [Lecture 8 : Expected return and risk of a portfolio; Minimum variance portfolio](https://invisiblenetwork.ai/learn/nptel/111103137/a5a19cb91380) (Video)
9. [Lecture 9 : Multi-asset portfolio and Efficient frontier](https://invisiblenetwork.ai/learn/nptel/111103137/a62706e08cac) (Video)
10. [Lecture 10 : Capital Market Line and Derivation of efficient frontier](https://invisiblenetwork.ai/learn/nptel/111103137/d5cfb98484cb) (Video)
11. [Lecture 11 : Capital Asset Pricing Model and Single index model](https://invisiblenetwork.ai/learn/nptel/111103137/2285201bfe09) (Video)
12. [Lecture 12 : Portfolio performance analysis](https://invisiblenetwork.ai/learn/nptel/111103137/cbd5ee319397) (Video)
13. [Lecture 13 : Utility functions and expected utility](https://invisiblenetwork.ai/learn/nptel/111103137/5ebc94c69b68) (Video)
14. [Lecture 14 :Â Risk preferences of investors](https://invisiblenetwork.ai/learn/nptel/111103137/36e84385c585) (Video)
15. [Lecture 15 : Absolute Risk Aversion and Relative Risk Aversion](https://invisiblenetwork.ai/learn/nptel/111103137/822971f1c3f4) (Video)
16. [Lecture 16 :Â Portfolio theory with utility functions](https://invisiblenetwork.ai/learn/nptel/111103137/d6ee98f29796) (Video)
17. [Lecture 17 : Geometric Mean Return and Roy's Safety-First Criterion](https://invisiblenetwork.ai/learn/nptel/111103137/7c6269f1e713) (Video)
18. [Lecture 18 :Â Kataoka's Safety-First Criterion and Telser's Safety-First Criterion](https://invisiblenetwork.ai/learn/nptel/111103137/3c926235e23b) (Video)
19. [Lecture 19 : Semi-variance framework](https://invisiblenetwork.ai/learn/nptel/111103137/d3e95f7455ca) (Video)
20. [Lecture 20 : Stochastic dominance; First order stochastic dominance](https://invisiblenetwork.ai/learn/nptel/111103137/8aded88a923d) (Video)
21. [Lecture 21 : Second order stochastic dominance and Third order stochastic dominance](https://invisiblenetwork.ai/learn/nptel/111103137/1e081d6e20bb) (Video)
22. [Lecture 22 : Discrete time model and utility function](https://invisiblenetwork.ai/learn/nptel/111103137/cc3c6461fce0) (Video)
23. [Lecture 23 : Optimal portfolio for single-period discrete time model](https://invisiblenetwork.ai/learn/nptel/111103137/85eeb14159b0) (Video)
24. [Lecture 24 : Optimal portfolio for multi-period discrete time model; Discrete Dynamic Programming](https://invisiblenetwork.ai/learn/nptel/111103137/e0791ebe051e) (Video)
25. [Lecture 25 : Continuous time model; Hamilton-Jacobi-Bellman PDE](https://invisiblenetwork.ai/learn/nptel/111103137/fa5561db3ba2) (Video)
26. [Lecture 26 : Hamilton-Jacobi-Bellman PDE; Duality/Martingale Approach](https://invisiblenetwork.ai/learn/nptel/111103137/f626725afbf0) (Video)
27. [Lecture 27 : Duality/Martingale Approach in Discrete and Continuous Time](https://invisiblenetwork.ai/learn/nptel/111103137/77d29b4d2574) (Video)
28. [Lecture 28 : Interest rates and bonds; Duration](https://invisiblenetwork.ai/learn/nptel/111103137/653a2595d5e7) (Video)
29. [Lecture 29 : Duration; Immunization](https://invisiblenetwork.ai/learn/nptel/111103137/53190ab0eeb4) (Video)
30. [Lecture 30 : Convexity; Hedging and Immunization](https://invisiblenetwork.ai/learn/nptel/111103137/59b684d22a83) (Video)
31. [Lecture 31: Quantiles and their properties](https://invisiblenetwork.ai/learn/nptel/111103137/34843a1fca3a) (Video)
32. [Lecture 32:Â Value-at-Risk and its properties](https://invisiblenetwork.ai/learn/nptel/111103137/a7076dadd7a7) (Video)
33. [Lecture 33: Average Value-at-Risk and its properties](https://invisiblenetwork.ai/learn/nptel/111103137/9fe6d7bfeeb9) (Video)
34. [Lecture 34: Asset allocation](https://invisiblenetwork.ai/learn/nptel/111103137/cee8250a8731) (Video)
35. [Lecture 35: Portfolio optimization](https://invisiblenetwork.ai/learn/nptel/111103137/1e2b13d8d598) (Video)
36. [Lecture 36: Portfolio optimization with constraints, Value-at-Risk: Estimation and backtesting](https://invisiblenetwork.ai/learn/nptel/111103137/436246ff91c5) (Video)
37. [Live Session 07-10-2020](https://invisiblenetwork.ai/learn/nptel/111103137/279adfb8311e-2) (Video)
38. [Live Session 10-11-2020](https://invisiblenetwork.ai/learn/nptel/111103137/a1aee4bd0e94-2) (Video)
39. [Live Session 01-12-2020](https://invisiblenetwork.ai/learn/nptel/111103137/0ddad3c0bcb6-2) (Video)