Efficient Frontier, Lognormal Returns, and Shortfall Constraint

19 Pages Posted: 27 Jun 2015

See all articles by Luca Ghezzi

Luca Ghezzi

Università Carlo Cattaneo (LIUC)

Giancarlo Giudici

Polytechnic University of Milan - Dipartimento di Ingegneria Gestionale

Date Written: June 26, 2015

Abstract

An efficient frontier model is derived within a problem of passive 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 independently and lognormally distributed. Expanding on previous theoretical results, we show how a minimum-variance set based on ordinary returns turns into a minimum-variance set based on logarithmic returns. According to our theoretical results, which have a general validity, inefficient portfolios based on ordinary returns cannot turn into efficient portfolios based on logarithmic returns, whereas efficient portfolios based on ordinary returns can also turn into inefficient portfolios based on logarithmic returns. In the latter instance, there can be two different qualitative patterns, both of which are portrayed by using historical data. Moreover, the shortfall constraint approach is extended to the case of lognormal portfolio returns. Each threshold return can be turned into a threshold accumulation that has the same shortfall probability; coeteris paribus, the more distant the time horizon, the smaller the shortfall probability. As our procedure is analytically tractable, it might be operationally useful, especially to financial advisors and institutional investors.

Keywords: Portfolio management, passive management, efficient frontier, lognormal returns, shortfall constraint

JEL Classification: G11

Suggested Citation

Ghezzi, Luca and Giudici, Giancarlo, Efficient Frontier, Lognormal Returns, and Shortfall Constraint (June 26, 2015). Available at SSRN: https://ssrn.com/abstract=2623492 or http://dx.doi.org/10.2139/ssrn.2623492

Luca Ghezzi

Università Carlo Cattaneo (LIUC) ( email )

Corso Matteotti, 22
21053 Castellanza (VA)
Italy

Giancarlo Giudici (Contact Author)

Polytechnic University of Milan - Dipartimento di Ingegneria Gestionale ( email )

Via Lambruschini 4
Milan, 20156
Italy

Register to save articles to
your library

Register

Paper statistics

Downloads
43
Abstract Views
515
PlumX Metrics