Impossible Frontiers
43 Pages Posted: 24 Nov 2008 Last revised: 10 Sep 2009
There are 2 versions of this paper
Impossible Frontiers
Impossible Frontiers
Date Written: November 23, 2008
Abstract
A key result of the Capital Asset Pricing Model (CAPM) is that the market portfolio - the portfolio of all assets in which each asset's weight is proportional to its total market capitalization - lies on the mean-variance efficient frontier, the set of portfolios having mean-variance characteristics that cannot be improved upon. Therefore, the CAPM cannot be consistent with efficient frontiers for which every frontier portfolio has at least one negative weight or short position. We call such efficient frontiers 'impossible', and derive conditions on asset-return means, variances, and covariances that yield impossible frontiers. With the exception of the two-asset case, we show that impossible frontiers are difficult to avoid. Moreover, as the number of assets n grows, we prove that the probability that a generically chosen frontier is impossible tends to one at a geometric rate. In fact, for one natural class of distributions, nearly one-eighth of all assets on a frontier is expected to have negative weights for 'every' portfolio on the frontier. We also show that the expected minimum amount of short selling across frontier portfolios grows linearly with n, and even when short sales are constrained to some finite level, an impossible frontier remains impossible. Using daily and monthly U.S. stock returns, we document the impossibility of efficient frontiers in the data.
Keywords: Shortselling, Long/Short, Portfolio Optimization, Mean-Variance Analysis, CAPM, 130/30
JEL Classification: G12
Suggested Citation: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
Portfolio Selection and Asset Pricing Models
By Lubos Pastor
-
A Test for the Number of Factors in an Approximate Factor Model
-
Comparing Asset Pricing Models: an Investment Perspective
By Lubos Pastor and Robert F. Stambaugh
-
Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps
By Tongshu Ma and Ravi Jagannathan
-
On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model
By Louis K.c. Chan, Jason J. Karceski, ...
-
Honey, I Shrunk the Sample Covariance Matrix
By Olivier Ledoit and Michael Wolf
-
Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach
By Lorenzo Garlappi, Tan Wang, ...
-
Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach
By Lorenzo Garlappi, Tan Wang, ...
-
Portfolio Constraints and the Fundamental Law of Active Management