Constantinos Kardaras, Hyeng Keun Koo, Johannes Ruf
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.