Abstract
The stage of strategic asset allocationisthe most important one in a process of portfolio management. Asset classes are to be selected and percent target weights are to be set. Careful decision-making benefits from the computation of an efficient frontier. In this work, a single investment is considered with all coupons and dividends being reinvested. Percent weights are supposed to be nonnegative and subject to annual rebalancing. Portfolio returns are assumed to be time uncorrelated and lognormal. Linear quadratic optimization is complemented with a lognormal mapping, resulting in a rigorous procedure, where by efficient portfolios based on linear returns may turn into efficient portfolios based on logarithmic returns. Two data sets are used by way of illustration under the tentative yet usual assumption that forecast moments are the same as historical moments. The former data set includes the annual total returns of three US asset classes for the years 1872-2012. The latter includes the annual total returns offour equity or equity-like asset classes for the years 1972-2017. The efficient frontier based on logarithmic returns is upward sloping in both instances, stretching from a portfolio with global minimum-variance to a portfolio with global maximum-variance. Nonetheless, if short selling and hence negative weights were allowed, the efficient frontier based on logarithmic returns wouldn't be upward sloping in the latter instance. The null hypothesis of lognormal returns is tested. It is always rejected in the latter data set; it is either provisionally accepted or rejected in the former data set, depending on the specific efficient portfolio. An interpretation of the statistical evidence is provided.