Welcome to the Stochastic Portfolio Theory Reading Seminar, run by the students of Columbia University.
This summer (summer 2021) we studied Stochastic Portfolio Theory by the book Stochastic Portfolio Theory by R. Fernholz. See the schedule below!
If you would like to come to our next seminars or to be added on the mailing list, please email ggaitsgori@math.columbia.edu.
| Date and time | Speaker | Title and abstract |
|---|---|---|
| Monday, May 17, 2:00p.m. EDT | Georgy Gaitsgori | Introduction to Stochastic Portfolio Theory (SPT Ch. 1.1)
Today we will discuss the introduction to Stochastic Portfolio Theory and cover the first part of the first chapter of SPT book. We will introduce main definitions, discuss some motivation behind, and give an exact formula for the portfolio value process in integral form. |
| Monday, May 24, 2:00p.m. EDT | Richard Groenewald | Relative Covariance and Long Run Portfolio Behavior (SPT Ch. 1.2-2.1)
We will prove some basic results regarding the relative covariance process, introduce the market portfolio and explore some of the asymptotic properties of the portfolio value process. If time permits, we will define market diversity and discuss some of its implications on markets composed of stocks with common or constant growth rates. |
| Monday, May 31, 2:00p.m. EDT | Richard Groenewald | Market Diversity and Entropy (SPT Ch. 2)
We will pick up where we left off last week by introducing market diversity and discussing some of its implications. We will define market entropy, its relationship to the entropy weighted portfolio and prove some results relating these topics to diversity. |
| Monday, June 7, 2:00p.m. EDT | Georgy Gaitsgori | Introduction to functionally generated portfolios (SPT Ch. 3.1-3.2)
We will introduce and explore the notion of functionally generated portfolios. We will discuss the motivation behind the notion and describe which functions can generate a portfolio as well as which portfolios can be functionally generated. |
| Monday, June 14, 2:00p.m. EDT | Hindy Drillick | Relative Arbitrage (SPT Ch. 3.3-3.4)
I will discuss how a weakly diverse market can give rise to arbitrage opportunities and give some examples of this phenomenon. |
| Monday, June 21, 2:00p.m. EDT | Xiang Fang | Portfolios of stocks selected by rank (SPT Ch. 4.1)
We will introduce rank process and give it's dynamics using local times. |
| Monday, June 28, 2:00p.m. EDT | Xiang Fang | Portfolios of stocks selected by rank (SPT Ch. 4.2-4.3)
We will look into portfolios generated by functions of ranked market weights and give some examples where the theory can be applied (size effect, leakage, etc). |
| Monday, July 5, 2:00p.m. EDT | No seminar |
|
| Monday, July 12, 2:00p.m. EDT | Georgy Gaitsgori | Capitalization distribution curve and stable markets (SPT Ch. 5.1-5.3)
We will start discussing chapter 5 of SPT book. The main object of study here is the distribution of capital curve. We will define the curve and look on its empirical chart. Then we will define what is a stable market, provide some necessary mathematical results for its exploration and discuss some stable models of the distribution of capital. |
| Monday, July 19, 2:00p.m. EDT | No seminar |
|
| Monday, July 26, 2:00p.m. EDT | Richard Groenewald | The Capital Distribution in Some Example Markets and the "First Order" Model (SPT Ch. 5.3-5.5)
We give some toy examples of the methodology presented in sections 5.1-5.3, attempt to apply some of the text's analysis to modern data and introduce a "first order" approximation to the model of the capital distribution. |
| Monday, August 2, 2:00p.m. EDT | Georgy Gaitsgori | Performance of Functionally Generated Portfolios (SPT Ch. 6)
We will try to cover the sixth chapter of the SPT book. We will analyze the simulated behavior of the main functionally generated portfolios in the U.S. stock market during the time period 1939-1998. We will show that both entropy- and diversity-weighted portfolios outperform the market, and that the small-stock index outperforms the large-stock index. If time permits, we will also discuss how to handle the leakage issues present in all simulations. |
| Monday, August 9, 2:00p.m. EDT | Georgy Gaitsgori | Some Applications of Stochastic Portfolio Theory (SPT Ch. 7)
We will try to cover the seventh chapter of the SPT book. We will consider some applications of SPT, namely we will discuss a passive strategy based on a diversity-weighted version of the S&P 500 Index, we will discuss how manager performance is related to the change in market diversity, and finally we will show how the first-order model can be used in portfolio optimization. |