Impossible Frontiers
Impossible Frontiers
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不可能的边界
DOI：
10.2139/ssrn.1306185
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
A. Lo
中科院分区：
文献类型：
--
作者：
T. J. Brennan;A. Lo
资本资产定价模型（CAPM）的一个关键结果是，市场投资组合-所有资产的投资组合，其中每种资产的权重与其总市值成比例-位于均值-方差-有效边界上，这组投资组合具有无法改进的均值-方差特征。因此，资本资产定价模型不能与有效边界一致，因为每个边界投资组合至少有一个负权重或空头头寸。我们称这种有效边界为“不可能”，并表明不可能边界是难以避免的。特别是，作为资产的数量，n，增长，我们证明了一个一般选择的边界是不可能的概率趋于一个几何速率。事实上，对于一个自然分布类别，边界上所有资产的近八分之一预计对边界上的每个投资组合都具有负权重。我们还表明，预期的最小数量的卖空整个前沿投资组合的增长与n线性，即使卖空限制到一定的有限水平，一个不可能的前沿仍然是不可能的。使用每日和每月的美国股票收益率，我们记录了数据中有效边界的不可能性。
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 show that impossible frontiers are difficult to avoid. In particular, 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.