Fund models are statistical descriptions of markets where all asset returns are spanned by the returns of a lower-dimensional collection of funds, modulo orthogonal noise. Equivalently, they may be characterised as models where the global growth-optimal portfolio only involves investment in the aforementioned funds. The loss of growth due to estimation error in fund models under local frequentist estimation is determined entirely by the number of funds. Furthermore, under a general filtering framework for Bayesian estimation, the loss of growth increases as the investment universe does. A shrinkage method that targets maximal growth with the least amount of deviation is proposed. Empirical evidence suggests that shrinkage gives a stable estimate that more closely follows growth potential than an unrestricted Bayesian estimate.
翻译:基金模式是市场统计描述,所有资产收益都以较低维度集资的回报率(modulo orthogoal 噪声)为范围。同样,它们也可以被描述为全球增长最佳投资组合只涉及对上述基金投资的模型。根据当地常客估计的基金模型估计错误造成的增长损失完全取决于资金数量。此外,根据巴伊西亚估算的一般过滤框架,增长损失随着投资领域的变化而增加。提出了一种收缩方法,以最大增长为目标,而偏离幅度最小。经验证据表明,萎缩提供了一种稳定的估计,即比无限制的贝伊斯估计更接近增长潜力。