Ir vs sharpe_ratio
- 1. INVESTMENT PERFORMANCE MEASUREMENT BY DEBORAH KIDD, CFA The Sharpe Ratio and the Information Ratio The Sharpe ratio and the information ratio are routinely used in performance assessment; they are the original risk-adjusted performance measures. Though they are simple metrics, practitioners should take care not to use them naively. This article highlights shortcomings of the two ratios and provides a framework for evaluating each ratio each within the appropriate context. P erhaps nothing has revolutionized the performance portfolio could be expected to generate per unit of port- measurement industry more than the introduction folio return variability. Sharpe’s original version assumed of the Sharpe ratio in 1966. Building upon his own that borrowing at the risk-free rate would finance the groundbreaking work as one of the originators of the investment in the risky asset, a zero-investment strategy. capital asset pricing model (CAPM), William Sharpe Throughout the years, users of the metric referred to designed the first performance metric to isolate excess it as the Sharpe measure or Sharpe ratio and began to return per unit of risk taken. Performance evaluation has employ it for measuring investment decisions ex post. The since evolved to include the analysis of such risks as ex post, or historical, Sharpe ratio uses actual instead of disaggregating idiosyncratic and systematic risk and the expected returns and is calculated as evaluation of higher moments and downside risk associ- ated with tail loss. This article is the first in a series that Rp − rf defines and reviews various performance measurement SR = . σp metrics and provides guidance to the practitioner on their proper use and interpretation. We begin with the two best- R p represents the average return of the portfolio and known and most widely used metrics: the Sharpe ratio and r f is the average return of the risk-free rate for the time the information ratio. These relatively simple tools can period under evaluation. The average standard deviation yield valuable performance information, yet they can be of the portfolio is represented by p. The Sharpe ratio ˆ misleading if misinterpreted, misused, or manipulated. tells an investor what portion of a portfolio’s performance SHARPE RATIO is associated with risk taking. It measures a portfolio’s The Sharpe ratio is the industry standard for measuring added value relative to its total risk. A portfolio of risk- risk-adjusted return. Sharpe originally developed this free assets or one with an excess return of zero would have ratio as a single-period forecasting tool and named it a Sharpe ratio of zero. the reward-to-variability ratio. The Sharpe ratio was As useful as the Sharpe ratio is, it has real limitations. designed as an ex ante, or forward-looking, ratio for deter- It is based on the Markowitz mean–variance portfolio mining what reward an investor could expect for investing theory, which proposes that a portfolio can be described by in a risky asset versus a risk-free asset. The numerator of just two measures: its mean and its standard deviation of the ratio is the expected portfolio return less the risk-free returns. The Sharpe ratio measures only one dimension of rate, and the denominator is the portfolio’s expected vol- risk: the variance. Thus, the Sharpe ratio is designed to be atility or standard deviation of returns (less that of the applied to investment strategies that have normal expected risk-free asset’s standard deviation, which is zero). The return distributions; it is not suitable for measuring invest- resulting ratio isolates the expected excess return that the ments that are expected to have asymmetric returns. ©2011 cfa institute ᭜ 1
- 2. Even within a framework of normally distributed The variable R p represents the return of the portfolio investment returns, the Sharpe ratio cannot tell an investor for the time period under measurement and R B represents whether a high standard deviation is due to large upside the return of the benchmark. The term P B is the ˆ deviations or downside deviations; the Sharpe ratio penal- standard deviation of the difference in returns between izes both equally. Negative Sharpe ratios—such as those the portfolio and its benchmark. The portfolio’s excess arising during portfolio underperformance, which often return is also known as its active return, and the variability occurs during bear markets—are also uninformative. of the excess return is also referred to as active risk, Although some users advocate squaring the returns to tracking risk, or tracking error. A second form of the generate a positive number, Sharpe himself dislikes this information ratio measures residual return to residual approach. He differentiates this as a separate ratio, called risk; it measures the components of performance that the “Sharpe ratio squared,” and believes it obscures impor- come from manager bets unrelated to the benchmark, tant negative information (Sharpe 1994). An alternative such as idiosyncratic risk. Although the active return/ approach is to turn to another performance metric. active risk ratio is the more commonly used version, investors need to understand which version is being used Expanding the time series gives rise to another con- because the two forms can yield very different results sideration when evaluating a Sharpe ratio. An investor (Terhaar 2009). must consider the length of the time period used in the The information ratio, like the Sharpe ratio, is based measurement; longer time periods tend to result in lower on the Markowitz mean–variance paradigm and is appli- volatility measures. Spurgin (2001) showed that the cable to portfolios with normal expected return distribu- annualized standard deviation of returns tends to be tions. An information ratio can tell whether a manager higher for shorter periods: Daily returns have higher outperformed his or her benchmark on a risk-adjusted standard deviations than weekly returns, which have basis, but it cannot tell specifically how the outperformance higher standard deviations than monthly returns. He was achieved. Was it due to the manager’s strategy (skill) concluded that lengthening the measurement period can or an unexpected surprise (luck)? Was it based on persistent be a way to manipulate the Sharpe ratio. Sharpe recom- small gains versus the benchmark or on one extreme, mended using short periods (for example, monthly) to positive event? Moreover, is this the outcome the investor measure risks and returns and then annualizing the data expected given the strategy and market conditions? (Sharpe 1994). He believed using multiperiod returns Investors should be aware that the information ratio complicates the ratio because of compounding or poten- is highly dependent on the time period under measure- tial serial correlation. ment and the chosen benchmark index. Favorable IRs can be generated by manipulating the measurement period to INFORMATION RATIO include or exclude certain performance periods. Market The information ratio (IR) is often referred to as a vari- conditions during the time period under evaluation ation or generalized version of the Sharpe ratio. It evolved should also be considered. Were market returns domi- as users of the Sharpe ratio began substituting passive nated by a value or growth style or by cap size? Does the benchmarks for the risk-free rate. The information ratio investor believe the style—and the manager’s strategy in tells an investor how much excess return is generated from relation to it—will continue? the amount of excess risk taken relative to the benchmark. The choice of benchmark index will likely have a It is frequently used by investors to set portfolio con- significant effect on the ratio. Goodwin (2009) showed straints or objectives for their managers, such as tracking that managers who were benchmarked against the S&P risk limits or attaining a minimum information ratio. 500 Index as a proxy for the broad market index had lower The information ratio is calculated by dividing the information ratios than those benchmarked against the portfolio’s mean excess return relative to its benchmark Russell 1000 Index. Similarly, managers who used the by the variability of that excess return: Russell 2500 as a proxy for the small-cap universe had notably poorer information ratios than managers mea- Rp − RB IRP = . sured against the Russell 2000. Roll (1978) also showed σP − B that even a small change in the market portfolio used as 2 ᭜ www.cfainstitute.org
- 3. a benchmark can yield vastly different measurement good,” and .50 as “good.” Goodwin (2009) measured IRs results. Additionally, investors should consider that over a 10-year period and found that even among consis- benchmark indices lack transaction costs, so in a sense, tently outperforming long-only managers, very few are the IR will be understated to the degree that transaction able to sustain an IR of .50 or higher, suggesting that the costs matter. ranking criteria may be too high. Goodwin further sug- gested that IRs are most useful when comparing manag- COMPARING THE TWO RATIOS ers within their own style universe rather than among The Sharpe ratio and the information ratio are valuable styles. A general consensus among the investment pro- tools when used correctly; used naively, they can be mis- fession is that an IR of .20 or .30 is superior. leading or uninformative at best. Both ratios are most useful Investors should be mindful that very long time for evaluating portfolios with normal expected return dis- periods may reduce a portfolio’s Sharpe ratio due to lower tributions and are not applicable to such asymmetric return volatility for longer periods. In contrast, information strategies as those frequently used by hedge funds. ratios based on longer periods are more valuable; they The Sharpe ratio measures a portfolio’s excess return indicate persistence in manager skill. A final caveat is to its total risk; it answers the question of how much an that performance metrics are based on historical data; investor was compensated for investing in a risky asset one cannot assume the future will bear close resemblance versus a risk-free asset. All portfolios measured with the to the past. ᭜ Sharpe ratio, then, have the same benchmark: the risk- free asset. The information ratio measures a portfolio’s R E FE R E N C E S excess return relative to its benchmark tracking error. It Bailey, Jeffery V., Thomas M. Richards, and David E. Tierney. 2009. answers the question of how much reward a manager “Evaluating Portfolio Performance.” In Investment Performance Measurement: Evaluation and Presenting Results. Edited by Philip generated in relation to the risks he or she took deviating Lawton and Todd Jankowski. Hoboken, NJ: John Wiley & from the benchmark. The information ratio is used for Sons:11–80. Reprinted from Managing Investment Portfolios: A measuring active managers against a passive benchmark. Dynamic Process. 3rd ed. (Hoboken, NJ: John Wiley & Sons, 2007):717–780. Neither the Sharpe ratio nor the information ratio takes into account dynamic correlations between asset CFA Institute. 2010a. 2011 Level III CFA Program Curriculum. vol. 5, reading 36. Charlottesville, VA: CFA Institute:87, 267–268. classes. The Sharpe ratio should be used to evaluate indi- vidual portfolios or funds, whereas the information ratio ———. 2010b. 2011 Level III CFA Program Curriculum. vol. 6, reading 46. Charlottesville, VA: CFA Institute:171–176. can be used to measure the value of a multi-asset portfolio Reprinted from Jeffery V. Bailey, Thomas M. Richards, and or an investor’s total portfolio. Investors using the Sharpe David E. Tierney. Managing Investment Portfolios: A Dynamic ratio can rank or compare funds within their risk tolerance Process. 3rd ed. (Hoboken, NJ: John Wiley & Sons, 2007): 717–780. to see which funds have the best risk-adjusted returns. The ———. 2010c. 2011 Level III CFA Program Curriculum. vol. 6, information ratio, on the other hand, is best used by reading 46. Charlottesville, VA: CFA Institute:230–231. investors to measure or rank manager performance. It can DeFusco, Richard A., Dennis W. McLeavey, Jerald E. Pinto, and be used as an absolute measure of manager skill. David E. Runkle. 2004, 2007. Quantitative Investment Analysis. How does an investor know whether a Sharpe or Charlottesville, VA: Association for Investment Management and information ratio is “good”? A simple rule of thumb is Research:115–118, 496–505. that higher is better. Because the Sharpe ratio is best used Goodwin, Thomas H. 2009. “The Information Ratio.” In Investment on a relative basis, the investment with the higher Sharpe Performance Measurement: Evaluation and Presenting Results. Edited by Philip Lawton and Todd Jankowski. Hoboken, NJ: John Wiley ratio is the preferred investment. Evaluating the informa- & Sons:705–718. Reprinted from Financial Analysts Journal, vol. 54, tion ratio for portfolios is more challenging. Grinold and no. 4 (July/August 1998):34–43. Kahn (2000) contended that top-quartile active equity Grinold, Richard C., and Ronald N. Kahn. 1995. Active Portfolio managers generally have information ratios of .50 or Management. Chicago, IL: Richard D. Irwin. higher. In another work, Grinold and Kahn (1995) rated ———. 2000. Active Portfolio Management. 2nd Edition. New York: an information ratio of 1.0 as “exceptional,” .75 as “very McGraw-Hill. ©2011 cfa institute ᭜ 3
- 4. Lawton, Philip, and Todd Jankowski. 2009. Investment Performance Terhaar, Kevin. 2009. “Return, Risk, and Performance Attribution.” In Measurement: Evaluation and Presenting Results. Hoboken, NJ: Investment Performance Measurement: Evaluation and Presenting John Wiley & Sons. Results. Edited by Philip Lawton and Todd Jankowski. Hoboken, NJ: John Wiley & Sons:387–396. Reprinted from AIMR Conference Roll, Richard. 1978. “Ambiguity when Performance is Measured by the Proceedings: Benchmarks and Attribution Analysis, vol. 2001, no. 3 Securities Market Line.” Journal of Finance, vol. 33, no. 4:1051–1069. (June 2001):21–27. Sharpe, William F. 1994. “The Sharpe Ratio.” Journal of Portfolio Management, vol. 21, no. 1 (Fall):49–58. Deborah Kidd, CFA, is senior vice president, Boyd Watterson Asset Spurgin, R. 2001. “How to Game Your Sharpe Ratio.” Journal of Management, LLC. Alternative Investments, vol. 4, no. 3:38–46. 4 ᭜ www.cfainstitute.org