Mathematical Portfolio Theory

By Prof. Siddhartha Pratim Chakrabarty | IIT Guwahati

Learners enrolled: 658

This course will give an introduction to the mathematical approaches used for 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 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 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).

PREREQUISITES : Basic probability theory at undergraduate level.

INDUSTRIES SUPPORT : This course would be useful to finance industry, particularly companies involved in asset management.

Summary

Course Status :	Completed
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Postgraduate
Start Date :	14 Sep 2020
End Date :	04 Dec 2020
Enrollment Ends :	25 Sep 2020
Exam Date :	20 Dec 2020 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

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 (gBm) asset pricing models

Week 3: Mean-Variance Portfolio Theory:Return and risk; Expected return and risk; Multi-asset portfolio; Efficient frontier

Week 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

Thanks to the support from MathWorks, enrolled students have access to MATLAB for the duration of the course.

Books and references

1. S. Roman. Introduction to the mathematics of finance: from risk management to options pricing. Springer Science & Business Media, 2004.

2. J. C. Francis and D. Kim. Modern portfolio theory: Foundations, analysis, and new developments. John Wiley & Sons, 2013.

3. J. Cvitanic and F. Zapatero. Introduction to the economics and mathematics of financial markets. MIT Press, 2004.

4. O.D.L. Grandville. Bond pricing and portfolio analysis. Cambridge, 2001.

5. M.J. Capinski and E. Kopp. Portfolio Theory and Risk Management. Cambridge University Press, 2014.

6. John C. Hull. Risk management and financial institutions. John Wiley & Sons, 2012.
7. M. Capinski and T. Zastawniak. Mathematics for finance: An Introduction to financial engineering. Springer, 2010.

Instructor bio

Prof. Siddhartha Pratim Chakrabarty

IIT Guwahati

Prof. Chakrabarty has more than ten years of teaching experience (in addition to research experience) in the areas of financial engineering, computational finance, portfolio theory and financial risk management and has offered several courses to the B.Tech. (Mathematics and Computing) and M.Sc. (Mathematics and Computing) students of IIT Guwahati.

Course certificate

•The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
•The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
• Date and Time of Exams: 20 December 2020, Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
•Registration url: Announcements will be made when the registration form is open for registrations.
• The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
•Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE:
• Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
• Exam score = 75% of the proctored certification exam score out of 100
•Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75.
•If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
• Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Guwahati. It will be e-verifiable at nptel.ac.in/noc
•Only the e-certificate will be made available. Hard copies will not be dispatched.

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