Friday, September 7, 2007
Drexel University's Program in Business & Entrepreneurship Law is presenting a faculty colloquium with Professor Thomas Brennan entitled "Impossible Frontiers" on Friday Sept. 28 at 10:30 a.m. (this is a change from a previously posted date). Here is the abstract of Professor Brennan's paper:
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.
More information is available at Drexel's website.