英文标题：
《Bounds on Portfolio Quality》
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作者：
Steven E. Pav
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最新提交年份：
2014
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英文摘要：
The signal-noise ratio of a portfolio of p assets, its expected return divided by its risk, is couched as an estimation problem on the sphere. When the portfolio is built using noisy data, the expected value of the signal-noise ratio is bounded from above via a Cramer-Rao bound, for the case of Gaussian returns. The bound holds for `biased\' estimators, thus there appears to be no bias-variance tradeoff for the problem of maximizing the signal-noise ratio. An approximate distribution of the signal-noise ratio for the Markowitz portfolio is given, and shown to be fairly accurate via Monte Carlo simulations, for Gaussian returns as well as more exotic returns distributions. These findings imply that if the maximal population signal-noise ratio grows slower than the universe size to the 1/4 power, there may be no diversification benefit, rather expected signal-noise ratio can decrease with additional assets. As a practical matter, this may explain why the Markowitz portfolio is typically applied to small asset universes. Finally, the theorem is expanded to cover more general models of returns and trading schemes, including the conditional expectation case where mean returns are linear in some observable features, subspace constraints (i.e., dimensionality reduction), and hedging constraints.
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中文摘要：
p资产组合的信噪比，其预期收益除以风险，被描述为球面上的一个估计问题。当使用噪声数据构建投资组合时，对于高斯回报的情况，信噪比的预期值通过Cramer-Rao界由上而下。“有偏”估计量的界成立，因此，对于最大化信噪比的问题，似乎不存在偏差-方差权衡。给出了Markowitz投资组合的信噪比的近似分布，并通过蒙特卡罗模拟证明，对于高斯收益以及更奇异的收益分布，该分布相当准确。这些发现意味着，如果最大总体信噪比的增长速度慢于宇宙大小的1/4次方，则可能没有多元化的好处，而预期的信噪比会随着额外资产的增加而降低。作为一个实际问题，这或许可以解释为什么马科维茨投资组合通常适用于小型资产领域。最后，该定理被扩展以涵盖更一般的收益和交易方案模型，包括条件期望情况，其中平均收益在一些可观察特征中是线性的，子空间约束（即维度缩减）和对冲约束。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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