The Statistics of The Information Ratio

15 Pages Posted: 30 Sep 2015

See all articles by Philippe Bertrand

Philippe Bertrand

AMGSM-IAE Aix-en-Provence, Aix Marseille University, CERGAM; KEDGE Business School

Protopopescu Protopopescu Costin

Aix-Marseille University

Date Written: April 10, 2007

Abstract

In a recent paper, Lo (2002) derives the asymptotic distribution of the Sharpe ratio under several sets of assumptions for the return-generating process. In this paper, we extend his work to the information ratio (IR), the ratio of the excess return of a portfolio over his benchmark to its tracking-error volatility. We assume that each return generating process is i.i.d., allowing however for cross-correlation.

First, given the cross-dependency between the portfolio and the benchmark returns, we derive the analytic expression of the asymptotic variance of the IR and we show explicitly how the higher order covariance influence the precision of the variance estimation. On the other hand we study the partial derivatives of the asymptotic variance of the IR with respect to the different moments of the returns.

Second, we conduct some simulations in order to highlight the behavior of the IR’s asymptotic variance.

Keywords: Information ratio, Asymptotic distribution

JEL Classification: G11, G12, G13

Suggested Citation

Bertrand, Philippe and Protopopescu Costin, Protopopescu, The Statistics of The Information Ratio (April 10, 2007). International Journal of Business, Vol. 15, No. 1, 2010, Available at SSRN: https://ssrn.com/abstract=2666519 or http://dx.doi.org/10.2139/ssrn.2666519

Philippe Bertrand (Contact Author)

AMGSM-IAE Aix-en-Provence, Aix Marseille University, CERGAM ( email )

Chemin de la Quille - Puyricard
Aix en Provence, 13089
France

KEDGE Business School ( email )

Domaine de Luminy - BP 921
BP 921
Marseille, PACA 13288
France

Protopopescu Protopopescu Costin

Aix-Marseille University ( email )

3 Avenue Robert Schuman
3 Avenue Robert Schuman,
Aix-en-Provence, 13628
France

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