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Abstract:
We use stochastic Taylor series matrix methods to explain the poor
out-of-sample performance of mean-variance optimized investment
portfolios,
developing theoretical bias adjustments for the effects of estimation
risk
by asymptotically expanding future returns of portfolios formed with
estimated weights. We provide closed-form adjustments of classical
estimates
of portfolio mean and standard deviation. The adjustments
significantly
reduce bias in international equity portfolios, increase economic
gains, and
are robust to sample size and to non-normality. Dominant terms grow
linearly
with the number of assets and decline inversely with the number of
past time
periods in the data set. Under suitable conditions, optimized
portfolios
become more diversified. Using these approximation methods it may be
possible to assess, before investing, the effect of statistical
estimation
error on portfolio performance.
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