The logarithm of the estimated next-day wealth return is approximated by k terms of its Taylor series. The resulting Type k universal portfolio generated by the f-divergence is obtained. An implicit form of the portfolio is also obtained by exploiting the mean-value theorem. An empirical study of the performance of the portfolio is focused on the Type 2 Helmbold universal portfolio. A few generalizations of the Helmbold universal portfolio have recently been studied, namely the reverse Helmbold and the parametric Helmbold portfolios. This new type of portfolio can be regarded a contribution to the inventory of Helmbold related universal portfolios. It is verified experimentally that an investor's wealth can be significantly increased by using the Type 2 Helmbold portfolio in investment.
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