No abstract uploaded!

This article introduces the large portfolio selection using gross-exposure constraints. It shows that with gross-exposure constraints, the empirically selected optimal portfolios based on estimated covariance matrices have similar performance to the theoretical optimal ones and there is no error accumulation effect from estimation of vast covariance matrices. This gives theoretical justification to the empirical results by Jagannathan and Ma. It also shows that the no-short-sale portfolio can be improved by allowing some short positions. The applications to portfolio selection, tracking, and improvements are also addressed. The utility of our new approach is illustrated by simulation and empirical studies on the 100 FamaFrench industrial portfolios and the 600 stocks randomly selected from Russell 3000.

It is a great honor for me to be invited by Tsinghua University to talk today. Tsinghua has, in its history, made many contributions to mathematics. The two most famous mathematicians in modern Chinese history have both been closely related to Tsinghua University. One is Professor Hua Lo-Keng, the other is Prof essor Chern Shiing-Sheng. Especially since Professor Chern is my teacher, I feel proud to be able to say some words in the opening ceremony for the Center for Advanced Study. I chose the title of my talk also for this reason. Due to my critical comments, I have decided to spend most of my time in giving a general talk in English. The remainder of the talk will be in Chinese.

No abstract uploaded!

No abstract uploaded!