Empirical Bayes stock market portfolios

Authors:
Thomas M Cover;David H Gluss
Affiliations:
Department of Statistics, Stanford University, Stanford, California 94305 USA;Stanford University, Department of Statistics and Electrical Engineering USA and Stanford University USA
Venue:
Advances in Applied Mathematics
Year:
1986

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Abstract

We exhibit a compound sequential Bayes portfolio selection algorithm based solely on the past which not only lives off market fluctuations but follows the drift as well. In fact, this sequential portfolio performs as well (up to first order terms in the exponent) as the optimal portfolio based on advance knowledge of the n-period empirical distribution of the market. Moreover, to first order in the exponent, the capital resulting from this portfolio will be no less than the best of the available stocks. This is a result that holds for every sample sequence. Thus bull markets and bear markets can not fool the investor into over-committing or under-committing his capital to the risky alternatives available to him. The goal is accomplished by a choice of portfolio which is robust with respect to futures that may differ drastically from the past.