New York Quantitative Finance Seminar

****RSVP here: http://www.cfe.columbia.edu/misc-pages/RSVP-NYQF.html ****

The Center for Financial Engineering at Columbia University is pleased to invite you to the forthcoming New York Quantitative Finance Seminar

http://www.cfe.columbia.edu/seminars/NY_Quantitative_Finance/

on Thursday, February 28, 2008, 5.30 PM-7:00 PM . for a presentation by Dr Robert FERNHOLZ, INTECH on " Modeling equity market behavior'

http://www.cfe.columbia.edu/seminars/NY_Quantitative_Finance/

Abstract stock markets are stochastic models that exhibit some of the properties of real stock markets. In these markets, the stock capitalizations are modeled by Brownian motions with drift and variance processes that depend on the market weights or the ranks of the stocks. We assume that the stocks pay no dividends, and that there are no splits or mergers. We study a number of market properties, including long-term stability, the existence of arbitrage, and the distribution of capital.

The simplest market models, those that appear in classical finance, have constant drift and variance parameters. While these models can be useful for studying short-term phenomena, they are unstable over the long term, and, hence, unsuitable for long-term analysis. In fact, in a market of stocks with constant drift and variance parameters, after the passage of time virtually all the market capital will become concentrated into single stocks. For long-term stability, variable drift and variance processes are needed, and we consider abstract markets that are stabilized either by volatility or by the use of parameters that are based on rank.

Volatility-stabilized markets are abstract markets in which the variance of the stocks is greater for smaller stocks. This property holds for real stock markets, and we show that it results in a form of long-term stability. In some of these markets, the greater volatility of the smaller stocks can be exploited by portfolios that systematically overweight these stocks, and this creates an opportunity for arbitrage.

Markets of stocks with drift and variance parameters that depend on rank can also be stable over the long term. Roughly speaking, if the lower-ranked stocks drift upward faster than the larger stocks, then the market will be stable over the long term. We can create markets of this type that have stable capital distributions similar to the capital distributions of real stock markets, however, the dynamic behavior of these markets is likely to be quite complicated, and there are many open questions regarding them.

VENUE:  BlackRock Auditorium, Park Avenue Plaza, 55 East 52nd Street, 11th floor. An ID will be needed to access the auditorium (lower level). A cocktail will be served after the seminar.

About the speaker: Dr. Robert Fernholz is founder and Co-Chief Investment Officer of INTECH, an institutional equity manager and subsidiary of the Janus Capital Group that has used mathematical investment strategies since 1987.  Dr. Fernholz received his Ph.D. in Mathematics from Columbia University, and has served on the faculty of Princeton University and the City University of New York. In 2002 Dr. Fernholz published the research monograph "Stochastic Portfolio Theory" (Springer-Verlag), which provides a general mathematical framework for equity investment.

The New York Quantitative Finance Seminar is a forum for discussion of new results and insights coming from quantitative modeling in finance and risk management, for the New York quantitative finance community. The New York Quantitative Finance Seminar  is organized by The Center for Financial Engineering, Columbia University and NYU Courant Institute of Mathematical Sciences and sponsored by: Blackrock, JP Morgan, Standard and Poor's, Finance Concepts, Europlace Institute of Finance.

Organizing committee: Andrew ABRAHAMS ( JP Morgan ), Marco AVELLANEDA ( NYU Courant Institute) Rama CONT ( Columbia University ) Emanuel DERMAN ( Columbia University ) Craig FRIEDMAN ( Standard and Poor's) Bernard LEE (BlackRock)

The New York Quantitative Finance Seminar

http://www.cfe.columbia.edu/seminars/NY_Quantitative_Finance/