A Mean-Variance Analysis of Self-Financing Portfolios

Abstract

This paper develops the analytics and geometry of the investment opportunity set (IOS) and the test statistics for self-financing portfolios. A self-financing portfolio is a set of long and short investments such that the sum of their investment weights, or net investment, is zero. This contrasts with a standard portfolio that has investment weights summing to one. Examples of self-financing portfolios are hedges, overlays, arbitrage portfolios, swaps, and long/short portfolios. A standard portfolio plus the IOS of self-financing portfolios form a restricted IOS hyperbola with restricted efficient set constants that differ from the usual constants. The restrictions affect statistical tests of portfolio efficiency, which are developed for the self-financing restrictions. As an application, we consider the self-financing portfolios formed by Fama and French (1992, 1993, 1995), based on market capitalization and value. In contrast to Fama and French (1992, 1993, 1995), we find that their restricted IOS is significantly different from the unrestricted IOS with the implication that the Fama-French tests are misspecified.Investment opportunity set, Long/short portfolios, Spanning, Intersection

Management Science, Economics and Finance: A Connection

“…Bai, Liu, and Wong extend the work of Markowitz [35], Korkie and Turtle [36] and others by proving that the traditional estimate for the optimal return of self-financing portfolios always over-estimates its theoretical value. In order to circumvent the problem, they develop a bootstrap estimate for the optimal return of self-financing portfolios, and prove that this estimate is consistent with its counterpart parameter.…”

Portfolio Optimization Under Tracking Error and Weights Constraints

“…where y ≡ x -b is a self-financing portfolio 5 (sum of the weights equal to zero), and the benchmark b is the "host portfolio" as defined in Korkie and Turtle (2002). In the sequel, self financing portfolios are referred as SF, are underlined.…”

“…Their solution for the constrained optimal portfolio can be expressed as the sum of the optimal portfolio in absence of the tracking error constraint plus a "self-financing" portfolio as defined in Korkie and Turtle (2002).…”

Portfolio Optimization Under Tracking Error and Weights Constraints

“…In particular, Roll (1992) and Jorion (2003) examine the deformation of the efficient frontier because of these TE constraints. Their solution for the constrained optimal portfolio can be expressed as the sum of the optimal portfolio in absence of the TE constraint plus a self‐financing portfolio as defined in Korkie and Turtle (2002).…”