Empirical log-optimal portfolio selections: a survey∗

In this paper the static portfolio and the dynamic log-optimal portfolio for memoryless and for stationary market processes are studied. We illustrate their performance (average annual yield) for NYSE data. 1 Notations Consider a market consisting of d assets. The evolution of the market in time is represented by a sequence of price vectors s1, s2, . . . ∈ R+, where sn = (s (1) n , . . . , s (d) n ) such that the j-th component s n of sn denotes the price of the j-th asset on the n-th trading period. In order to normalize, put s 0 = 1. {sn} has exponential trend: s n = e nW (j) n ≈ e (j) , with average growth rate (average yield) W (j) n := 1 n ln s n ∗The first author acknowledges the support of the Computer and Automation Research Institute of the Hungarian Academy of Sciences.