Abstract
The use of an efficient frontier is considered within a problem of portfolio management. An aggregate portfolio is rebalanced annually to restore the percent weights of its strategic asset allocation; its annual total returns are assumed to be independent and lognormally distributed. Expanding on a previous paper, it is shown how a minimum-variance set based on ordinary returns turns into a minimum-variance set based on logarithmic returns. Remarkably, both sets have a similar shape. Moreover, it is pointed out how both a long-term expected accumulation and its confidence interval can be determined by virtue of such a mapping. A case in point is provided by using the annual total returns of 3 US asset classes for the years 1926-1997 under the usual simplifying assumption that population moments are the same as historical moments. As the procedure is analytically tractable, it might be operationally useful, especially to financial advisors and institutional investors.