Asset Allocation with Nonnegative Weights and Lognormal Portfolio Returns

Luigi Buzzacchi and Luca Ghezzi

The stage of strategic asset allocation is the most important one in a process of portfolio management: asset classes are selected and target weights are set. Careful decision-making benefits from the computation of an efficient frontier. In this work, weights are nonnegative and rebalanced once a year; portfolio returns are time uncorrelated and lognormal. Anovel sufficient condition is obtained, whereby efficient portfolios based on linear returns may turn into efficient portfolios based on logarithmic returns. If that is met, the efficient frontier based on logarithmic returns is upward sloping, stretching from a corner portfolio with global minimum-variance to acorner portfolio with global maximum-variance. Such a complementary efficient frontier allows a decision maker to forecast the long-term portfolio value. The null hypothesis of lognormal portfolio returns is also tested by using two different data sets. It is always rejected in the latter; it is either accepted or rejected in the former, depending on the specific efficient portfolio.