A convex polynomial with a non-integer degree is used to generate a Bregman- divergence universal portfolio together with an application of a first-order binomial expansion of the multiplicative update. The next-day portfolio is a weighted combination of the present- day portfolio and a power of the present-day portfolio, where the weights are depending on functions of the present-day stock price relatives. A parameter delta is introduced in the portfolio with aims to find the parameter that exhibiting the best performance locally. The portfolio is run over five stock data sets selected from the local stock exchange to study and to compare its empirical performance. The empirical results are compared with the results obtained by using the reverse Helmbold universal portfolio. Better performance is demonstrated for the portfolio introduced in this paper with respect to certain values of the parameters used on three data sets. There is promising evidence that this portfolio can increase the investment wealth significantly with the proper choice of the portfolio parameters.