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Impossible Frontiers

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  • Thomas J. Brennan
  • Andrew W. Lo

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 shortselling across frontier portfolios grows linearly with n, and even when shortsales 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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14525.

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Date of creation: Dec 2008
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Handle: RePEc:nbr:nberwo:14525

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  1. Brito, Ney O, 1978. "Portfolio Selection in an Economy with Marketability and Short Sales Restrictions," Journal of Finance, American Finance Association, vol. 33(2), pages 589-601, May.
  2. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 293-305, September.
  3. Dybvig, Philip H, 1984. " Short Sales Restrictions and Kinks on the Mean Variance Frontier," Journal of Finance, American Finance Association, vol. 39(1), pages 239-44, March.
  4. Duffie, Darrell & Garleanu, Nicolae & Pedersen, Lasse Heje, 2002. "Securities lending, shorting, and pricing," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 307-339.
  5. Merton, Robert C., 1972. "An Analytic Derivation of the Efficient Portfolio Frontier," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(04), pages 1851-1872, September.
  6. Garlappi, Lorenzo & Uppal, Raman & Wang, Tan, 2005. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," CEPR Discussion Papers 5041, C.E.P.R. Discussion Papers.
  7. Tu, Jun & Zhou, Guofu, 2004. "Data-generating process uncertainty: What difference does it make in portfolio decisions?," Journal of Financial Economics, Elsevier, vol. 72(2), pages 385-421, May.
  8. Sun, Wan Gui & Wang, Chun Feng, 2006. "The mean-variance investment problem in a constrained financial market," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 885-895, November.
  9. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
  10. Pogue, G A, 1970. "An Extension of the Markowitz Portfolio Selection Model to Include Variable Transactions' Costs, Short Sales, Leverage Policies and Taxes," Journal of Finance, American Finance Association, vol. 25(5), pages 1005-27, December.
  11. Best, Michael J. & Grauer, Robert R., 1990. "The efficient set mathematics when mean-variance problems are subject to general linear constraints," Journal of Economics and Business, Elsevier, vol. 42(2), pages 105-120, May.
  12. Tu, Jun & Zhou, Guofu, 2010. "Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(04), pages 959-986, August.
  13. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  14. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(03), pages 621-656, September.
  15. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-87, June.
  16. Diamond, Douglas W. & Verrecchia, Robert E., 1987. "Constraints on short-selling and asset price adjustment to private information," Journal of Financial Economics, Elsevier, vol. 18(2), pages 277-311, June.
  17. Jarrow, Robert A, 1980. " Heterogeneous Expectations, Restrictions on Short Sales, and Equilibrium Asset Prices," Journal of Finance, American Finance Association, vol. 35(5), pages 1105-13, December.
  18. Jérôme B. Detemple & Shashidhar Murthy, 1997. "Equilibrium Asset Prices and No-Arbitrage with Portfolio Constraints," CIRANO Working Papers 97s-12, CIRANO.
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Cited by:
  1. Levy, Haim & Levy, Moshe, 2014. "The benefits of differential variance-based constraints in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 372-381.

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