A study of principal eigenportfolios for US equities

This will be an introductory talk on a problem in financial mathematics that involves data analysis. Background material and terminology used will be provided and explained.

It is well known empirically that principal eigenportfolios are a good proxy for the market portfolio. I will describe how to quantify this property through a large-dimensional asymptotic analysis of a spike model, which is comprised of a rank-1matrix and a random matrix. Historical returns data supports this analytical explanation for the correspondence between the top eigenportfolio and the market portfolio. I will also describe how alternative data structures can be used to construct proxies for the market portfolio as well as an application to option portfolios. I will end with a brief description of some related problems in this area.