I. INTRODUCTION The common practice in the investment management industry is to impose a limit on the volatility of the deviation of the active portfolio from the benchmark, namely on the tracking error volatility (TEV). The pioneer of this approach is Roll (1992), who noted that the active portfolio had not only a systematically higher risk than the benchmark, but also a beta greater than one and it is not optimal. These problems have been further pointed out by Bertrand, Prigent and Sobotka (2001), Jorion (2003) and Bertrand (2010), who have studied several alternatives of portfolio optimization program. This setup leads naturally to the use of information ratios(IR), as a performance measure, defined as the ratios of the portfolio excess return over his benchmark to its TEV. Bertrand (2005, 2010) proves, by defining the IR as a forward-looking measure, that the information ratio is constant across all TEV efficient portfolios. Thus, it is the appropriate measure for the risk adjusted performance of an active portfolio with a TEV constraint against a benchmark. Indeed, it ranks all the TEV efficient portfolios in the same way. Traditionally, the IR has been computed as an ex-post performance measure. As such, it is commonly used to compare investment managers. But, the IR must be estimated in a certain way and on a given sample. Thus, estimation errors arise, raising the following question: how accurately is the IR computed? In a recent paper, Lo (2002) derives the explicit expressions for the statistical distribution of the Sharpe ratio using the standard asymptotic theory under several sets of assumptions for the return-generating process. Since Sharpe ratios must be estimated, they are also subject to estimation error. In this paper, we have extended his work to the information ratio (IR). We assume that each return generating process is i.i.d., allowing however for cross-correlation. First of all, 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. Then, we derive the analytic expression for the asymptotic variance of the IR in the Gaussian i.i.d. case. Finally, we conduct some simulations in order to highlight the behavior of the asymptotic variance of the IR. II. ASYMPTOTIC VARIANCE OF THE INFORMATION RATIO Recall that Lo (2002) has established that the standard error for the Sharpe ratio (SR) in the i.i.d. case estimator is given by: [sigma](SR) = [square root of (1 + 1/2 [SR.sup.2])/T] where the Sharpe ratio is define as: SR = [[mu].sub.P] - [R.sub.f]/[sigma]([R.sub.P] The information Ratio is defined as: IR [equivalent to] [[mu].sub.P] - [[mu].sub.B]/[sigma]([R.sub.P] - [R.sub.B]) Let [R.sub.P] and [R.sub.B] denote the one-period return of an active portfolio and of its associated benchmark. The risk less interest rate is denoted [R.sub.f]. The mean returns are denoted [[mu].sub.p] and [[mu].sub.B], and the variances [[sigma].sub.P] and [[sigma].sub.B] . The term [sigma]([R.sub.p] - [R.sub.B]) is the tracking error volatility and is defined as (1): [[sigma].sup.2]([R.sub.p] - [R.sub.B] [equivalent to] [[sigma].sup.2.sub.P] + [[sigma].sup.2.sub.B] - 2[[sigma].sub.PB] = [[sigma].sup.2.sub.P] + [[sigma].sup.2.sub.B] - 2[rho][[sigma].sub.p][[sigma].sub.B] The quantities [[mu].sub.P] , [[mu].sub.B], [[sigma].sub.P], [[sigma].sub.B] and [[sigma].sub.PB] (or [rho]) are the population moments of the joint distribution of [R.sub.P] and [R.sub.B]. These are unobservable and must be estimated using historical data. Given a sample of historical returns (([R.sub.P1], [R.sub.B1]), ([R.sub.P2], [R.sub.B2]),...,([R.sub.PT], [R.sub.BT])), the estimator of the IR is given by: IR [equivalent to] [[mu]. …