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Tracking Error and the Information Ratio

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Tracking Error and the Information Ratio It Is More Than]ust Performance: TRACKING ERROR AND THE INFORMATION RATIO By Jay L. Shein, Ph.D., ClMA, CFP ONE OF OUR MOST POPULAR CONTRIBUTORS REVIEWS SOME QUANTITATIVE TECHNIQUES THAT CAN ASSIST THE CONSULTANT IN MANAGER SELECTIONS AND IN ASSET ALLOCATION DESIGN. Introduction properly these statistical measures can be dentifying and selecting the most appropri­ useful tools. ate mutual fund or money manager to use Tracking error was defined by Tobe (1999) as in an investor's portfolio are major aspects the percentage difference in total return between of the investment consultants responsibili­ an index fund and the benchmark index the fund ties. This is true for both active and passive was designed to replicate. This definition of track­ money manager searches and selection. ing error is best used for evaluation of a passive When searching for and selecting money man­ manager such as an index fund. Tracking error agers, consultants and investment advisors typical­ used in the context of active manager evaluation is ly look at both qualitative and quantitative infor­ better defined as active manager risk. For purpos­ mation before making their recommendations. The es of this commentary, tracking error is defined as investment consultant knows that items such as the standard deviation between two return series philosophy, process, people, and strategic business written as: 1 plans are important, if not sometimes more impor­ tant than historical performance. Even though the qualitative side is important, the investment con­ TE= i-I sultant will ultimately use some quantitative mea­ N-l sure such as a ratio, statistic, risk-adjusted measure of performance, and/or absolute performance to Where: validate the qualitative component of money man­ IE = Tracking Error ager search and selection. Rp = Return of Manager or Fund Two of the most important quantitative tools RB = Return of Benchmark the investment consultant can use are tracking N = Number of Return Periods error and the selection Sharpe ratio. When used 18 THE]OURNAL OF INVESTMENT CONSULTING © 2000 Investment Management Consultants Association Inc. Reprint with permission only. Tracking Error Significance strategy from meeting its objectives. The strategic he sophisticated investor or plan sponsor passive asset allocation is the determinant of the is concerned with both relative and active portfolio tracking error. Any asset classes' absolute performance. A tool such as contribution to a portfolio will be a factor of the tracking error can be used to provide an asset classes' weight in the strategic portfolio, its acceptable range of relative performance when correlation with the other asset classes and its evaluating a manager. High tracking error may be tracking error. caused by style bets, security selection, transaction costs, and fees. When consultants look for man­ agers to outperform a benchmark, should they look for high or low tracking error? Does high tracking error imply a higher probability that a HEN SEARCHING manager will generate positive alpha? And does tracking error correlate with consistent manager FOR AND SELECTING outperformance? According to Gupta, Prajogi, and Stubbs (1999), the number of quarters that man­ MONEY MANAGERS, agers outperformed their benchmarks was uncor­ related with tracking error for most asset classes, except for emerging market equity and interna­ CONSULTANTS AND tional fixed income managers. Because of the dis­ parity of results, it appears that high tracking error INVESTMENT ADVISORS does not indicate a manager's ability to generate consistent positive alpha. TYPICALLY LOOK FOR For managers to consistently generate positive alpha they will have some tracking error. Managers who strive to maximize their alpha will most like­ BOTH QUALITATIVE AND ly have a high tracking error. Gupta, Prajogi, and Stubbs (1999) suggest that to maximize informa­ QUANTITATIVE INFORMATION tion ratios, tracking error for U.S. fixed income, international fixed income, U.S. small-cap and BEFORE MAKING THEIR international developed eqUity should be between 2 percent and 4 percent. A tracking error of 1 per­ cent to 2 percent is indicated for U.S. large-cap RECOMMENDATIONS. equity to maximize the information ratio. Emerging market equity managers maximize infor­ The consultant can consider tracking error mation ratios in the 6 percent to 12 percent range relative to a passive benchmark or a returns-based with the best results at the high and low end of the style benchmark. The consultant using a passive range. When multiple managers are considered for benchmark such as an index will need an index a portfolio the consultant may want to budget this that is a good fit for the managers style for the active manager risk by setting a maximum tracking tracking error to be of greatest value. Because of error budget for the overall portfolio of multiple the uniqueness of each active manager, a Returns­ managers. Investment consultants assist in the Based Style Analysis (RSBA) or Portfolio design of the allocation of various asset classes Opportunity Distributions (PODs) approach contained in the investor or plan sponsor's portfo­ would give a more accurate benchmark for lio. Budgeting of total overall portfolio tracking developing tracking error constraints. An out-of­ error will help keep the asset allocation strategy on sample analysis may also give an indication of the track. Too much total active variance from the tracking error consistency. portfolio's total tracking error budget may keep the Continued on page 20 VOL. 2, NO.2, JUNE 2000 19 © 2000 Investment Management Consultants Association Inc. Reprint with permission only. Continued from page 19 Tracking Error Illustration ssume that an investor~ benchmark for IR = -,=~R~p~-==R~B= the U.S. equity component of the portfo­ I.(Rp- RBr lio was an index such as the Wilshire ;=1 5000. The investor wants to outperform N-l this benchmark but does not want to underper­ form the benchmark by more than 2 percent. The Where: investment consultant would want to use a IR = Information Ratio manager or group of managers that, when Rp = Manager or Fund Return combined, would have a low total tracking error to R = Return of Benchmark the benchmark. B N = Number of Return Periods What if the investor was comfortable with a The only difference in the numerator of the return of 5 percent or more below the benchmark Sharpe ratio and the selection Sharpe ratio is the with the opportunity to outperform the bench­ choice of benchmarks. The Sharpe ratio uses a mark by 5 percent or more? In this case the invest­ risk-free asset such as Treasury bills, and the selec­ ment consultant would assemble a manager or tion Sharpe ratio uses a style benchmark, equity group of managers that had a much higher track­ index, or fixed income index. I will refer to the ing error relative to the benchmark. selection Sharpe ratio as the information ratio for The Information Ratio the balance of this commentary. The information ratio is considered a risk­ o with tracking error in mind, what is a adjusted measure of performance focusing on good predictor of consistency of perfor­ residual (active) return relative to residual (active) mance? The selection Sharpe ratio known risk. This is a useful ratio for comparing skill across by investment consultants as the informa­ managers. It can provide a measure of a manager~ tion ratio, and sometimes referred to as the performance above that attributed to investment appraisal ratio, has shown some correlation with style. Gupta, Prajogi, and Stubbs (1999) maintain consistency of outperforming a benchmark. The that the information ratio is a significant indicator Sharpe ratio and the selection Sharpe ratio are both of the persistence of manager performance. It has excellent risk-adjusted measures of performance been suggested by Sharpe (1994) that for this to be developed by the Nobel Laureate William F a very useful ratio, long and short positions must be Sharpe. The Sharpe ratio represents th~ manager's available with a resulting zero-investment strategy. returns per unit of total risk. It is sometimes It is very important to use the appropriate referred to as the excess return Sharpe ratio or the benchmark in order to have a reliable comparison Sharpe performance index. 2 between managers. This is particularly important when you have a portfolio made up of SR = -r==R~p=-:;';,R~F= multiple managers. When evaluating money managers, the invest­ ment consultant should seek managers with the N-l highest information ratios for a given level of risk. How well a money manager takes advantage of the Where: opportunities available is reflected in the informa­ SR = Sharpe Ratio .tion ratio. An active manager may make style, sec­ R = Manager or Fund Return p tor, and/or security selection bets. A higher Rp = Risk Free Rate Information Ratio indicates that the manager effec­ RA = Manager or Fund Arithmetic Mean Return tively selected the correct style, sector, or security N = Number of Return Periods for a portfolio. The active manager is essentially I ' ! The selection Sharpe ratio also known as the making an ex post or an ex ante forecast regarding information ratio is a measure of active (residual) style, sector, or the securities they select. or selection return per unit of active (residual) risk. 3 The information ratio can be used as a manager~ 20 THE JOURNAL OF INVESTMENT CONSULTING © 2000 Investment Management Consultants Association Inc. Reprint with permission only. skill for ex post (historical skill) or ex ante (an Excel Spreadsheet assessment of forecasted skill). Remember that even Simple spreadsheet can be prepared to though many evaluation tools used by the invest­ calculate the information ratio. The his­ ment consultant are used for ex ante purposes, nei­ torical returns on a monthly or quarter­ ther past performance nor historical ratios are a 1y basis for the money manager or fund guarantee or indication of future performance.
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