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.

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估计基金模型的增长

基金模型是市场的统计描述，其中所有资产收益都由低维基金集合的收益（模正交噪声）跨越。同样，它们可以被描述为全球增长最优投资组合仅涉及对上述基金的投资的模型。局部频繁估计下的基金模型估计误差导致的增长损失完全取决于基金的数量。此外，在贝叶斯估计的一般过滤框架下，增长损失随着投资范围的增加而增加。提出了一种以最小偏差量最大增长为目标的收缩方法。经验证据表明，与不受限制的贝叶斯估计相比，收缩给出了更接近增长潜力的稳定估计。