Speaker: Edward Qian
Title: On Conditional Distribution and Portfolio Optimization.
Affiliation: Putnam Investments, Vice-President.
Date: Friday, January 28.
Place and Time: Room 101 - Love Building, 3:35-4:35 pm.
Refreshments: Room 204 - Love Building, 3:00 pm.

Abstract. Diversification is one of the central themes in modern portfolio theory. Yet, mean-variance optimization, which plays a fundamental role in the theory, often gives rise to portfolios that are overwhelmingly concentrated in just a few assets. The reason for this is that mean-variance optimization is notoriously sensitive to its inputs, which are expected returns and covariance matrix.

The Black-Litterman method was developed to alleviate the input sensitivity problem. It combines the market equilibrium expected returns, which are obtained by solving an inverse problem, with conditional distribution theory, which adjusts the mean vector to reflect an investor's personal forecast of a few expected returns. In this talk, we outline the background and approach behind their method. We then present a new unified method that extends the results by Black-Litterman. The motivation for the method is to obtain conditional mean vector as well as conditional covariance matrix given an investor's view, which embraces forecasts not only of expected returns but also of volatilities and correlations. Our method is based on a simple application of conditional distribution but it does not requires a Bayesian approach as in the Black-Litterman method. Finally, we discuss its application to asset allocation problems and certain risk management issues.