Drexel University College of Law Program in Business & Entrepreneurship Law

A Faculty Colloquium:

Professor Thomas Brennan *

will discuss his paper (co-authored with Andrew Lo †) entitled

“Impossible Frontiers”
    Friday, September 28th, starting at 10:30 a.m.

The Capital Asset Pricing Model (CAPM) is an idea that defines a point of intersection between finance and law. In proffering a theory of how prices are determined for assets such as stocks, CAPM has become a foundational tenet of corporate law and securities regulation. But finance theory has moved on from its initial conclusions on asset pricing, perhaps leaving the law behind with a now naïve conception as its justification for various rules and policies.

The goals for our discussion are two. First, Professor Brennan is seeking to engage others working in finance theory in a discussion of his methodology and findings and their implications for finance theory. Second, in furtherance of the Program in Business & Entrepreneurship Law’s agenda to promote interdisciplinary scholarship in law and business, we are hoping to engage also in a broader discussion of the implications for law and public policy of the growing critique of traditional theories of capital asset pricing. If, for example, Brennan & Lo’s findings are correct, do they suggest an explanation for the differing valuation perspectives that some see as explaining private equity activity? Do these findings also support recent work by Bill Sharpe and others questioning the value of portfolio management practices premised on assumptions of commonly-held (and smooth) utility functions? And if so, what does this mean for securities regulation and the larger debate we see raging around the role financial markets play in determining social welfare. We hope to provide a venue for a vigorous discussion that brings together both hard quantitative analysis and an understanding of the public policy context in which these issues could play out.

The abstract of the paper states:

“A key concept of the Capital Asset Pricing Model is the Mean-Variance Efficient Frontier, the collection of portfolios of n assets having mean-variance characteristics that cannot be improved upon. We study Mean-Variance Efficient Frontiers for which every portfolio on the frontier has at least one negative weight, i.e., for every portfolio, at least one asset is sold short. We call such a frontier an "impossible frontier" because the CAPM requires that the market portfolio—the portfolio of all n assets where the weight of each asset is proportional to that asset’s market capitalization—lie somewhere on the efficient frontier. Whether a frontier is impossible depends upon the particular values of the set of expected returns and covariances of the assets. In the two-asset case, we find that impossible frontiers occur only under certain unusual circumstances. However, for three assets or more, we find impossible frontiers in more common situations. Moreover, as the number of assets grows, we show that the probability that a generically chosen frontier is impossible tends to one. In fact, we find that for large n, nearly a quarter of all assets on a frontier are expected to have negative weights for every portfolio on the frontier. We also show that the expected minimum amount of short selling across points on frontiers grows linearly with n. Finally, we find that an impossible frontier remains impossible even if constraints are placed on the amount of short selling allowed in each portfolio.”

A copy of the current draft will be available by request to karl.okamoto@drexel.edu. The Colloquium will be held on Friday, September 28th, starting at 10:30am. We will meet in Room 420 at the Earle Mack School of Law, 3320 Market Street, Philadelphia, PA 19104. Please register your intent to attend and address any questions to karl.okamoto@drexel.edu. Or contact Karl Okamoto, Director, Program in Business & Entrepreneurship Law at (215) 571-4761.

* Assistant Professor of Law, Earle Mack School of Law. A.B., summa cum laude, Princeton University; J.D., cum laude, Harvard University; A.M. (mathematics) Harvard University; Ph.D. (mathematics) Harvard University.
† Harris & Harris Group Professor, MIT Sloan School of Management and Director of the MIT Laboratory for Financial Engineering