1.3 Traditional Risk and Risk-Adjusted Return Measures .1 Volatility.1Volatility
1.3.8 Information Ratio
• Annualized benchmark returnrBmp:a:in cellC 20:
13:02% D fPRODUCT.1C.C 2WC19//^.12=18/1g
• Annualized portfolio volatilityPfp:a:in cellB21: 16:49% D SQRT.12/STDEV:S.B2WB19/
• Annualized benchmark volatilityBmp:a:in cellC 21: 17:02% D SQRT.12/STDEV:S.C 2WC19/
• Sharpe ratio of portfolioSRPf in cellB22: 0:96 D B20=B21
• Sharpe ratio of benchmarkSRBmin cellC 22: 0:76 D C 20=C 21
The portfolio has a higher Sharpe ratio than the benchmark, i.e., for one unit of risk (volatility) the investor in the portfolio receives a higher additional return than when passively investing in the index.
End of Example 10 1.3.7.3 Conclusion
The Sharpe ratio is a key ratio when evaluating a portfolio. It is an absolute risk- adjusted return measure as it does not look at portfolio returns versus a benchmark, but rather at the portfolio returns by themselves. In order to calculate the Sharpe ratio, either the portfolio’s percentage return or the return premium (return minus risk-free rate) can be used. The associated risk is always volatility. In practice, the risk-free rate should be omitted to avoid questions on the choice of the risk-free rate or its computation. For benchmark-oriented portfolios, the Sharpe ratio should be calculated both for the portfolio and the benchmark in order to find out if the portfolio or the benchmark delivers a better risk-adjusted return in absolute terms.
However, what risk-adjusted return measure would we need to analyze a portfolio versus the benchmark performance? In principle, a relative risk-adjusted return measureis very similar to theabsolute risk-adjusted return measureSharpe ratio.
We only need to replace the absolute return by the relative return (alpha) and the absolute risk measure (volatility) by the relative risk measure (tracking error). This new risk-adjusted return measure is calledinformation ratio.
Definition: Information Ratio
Let Œ0; T with T 1 year be the analyzed historical time period. The information ratio IR measures the annualized relative return (alpha) of a portfolio generated per unit of annualized relative risk (tracking error) for a portfolio that is managed against a benchmark49:
IRDIRp:a: D ˛p:a:
TEp:a: D rPfp:a:rBmp:a:
TEp:a: : (1.76)
Hereby:
rPfp:a: D annualized portfolio return using data from time periodŒ0; T ;
rBmp:a: D annualized benchmark return using data from time periodŒ0; T ;
˛p:a: D annualized excess return of portfolio over its benchmark, using data from time periodŒ0; T ;
TEp:a: D annualized tracking error of the portfolio vs. its benchmark, using data from time periodŒ0; T :
Ideally, a high information ratio is achieved by having a high positive alpha and a low tracking error.
1.3.8.1 Note
Since at least 1 year of performance data is needed to calculate tracking error, the calculation of the information ratio for time periods below 1 year is meaningless.
When using monthly return data, ideally 3 years of data should be available to get a meaningful value. Tracking error and alpha have to be annualized. For the calculation of the information ratio it is important to use the same underlying return data, especially, with the same data frequency (for example, monthly or daily).
1.3.8.2 Interpretation
For example, a typical actively managed equity fund, the information ratio can (based on practical experience) broadly be categorized in the following way, if the underlying time series is sufficiently long (ideally five or more years):
• IR1:5and higher: top portfolio
• IR0:81: very good portfolio
• IR0:5: average portfolio
49Lhabitant (2004, p. 67).
• IR0:2: poor portfolio
• IRnegative: bad portfolio since it has a negative alpha
This interpretation is only valid using gross-of-fee return data, (i.e., without considering fees for management, which can be substantial, for example, for portfolios of emerging markets equity). Therefore, it would be more precise to talk about a gross-of-fee information ratio. In contrast, if the fees were already subtracted from the return (net-of-fee), the interpretation for such a net-of-fee information ratiowould look slightly different and depend on the charged fees. The information ratio istherisk-adjusted return measure for actively managed portfolios irrespective of if the investment approach is fundamental, quantitative or a hybrid of both.
Example 11
Table1.16is an extension of Table1.7to calculate the information ratio. Use the following Excelrformulas to obtain the information ratio:
Table 1.16 Example 11: Calculation of a portfolio’s information ratio
A B C D
Monthly portfolio Monthly benchmark Monthly alpha
1 Month performance (%) performance (%) (%)
2 07/2012 6.10 % 6.01 % 0.09 %
3 08/2012 5.50 % 5.45 % 0.05 %
4 09/2012 4.70 % 4.63 % 0.07 %
5 10/2012 5.00 % 6.99 % 1.99 %
6 11/2012 5.10 % 4.16 % 0.94 %
7 12/2012 6.70 % 7.07 % 0.37 %
8 01/2013 6.03 % 5.97 % 0.06 %
9 02/2013 3.23 % 2.95 % 0.28 %
10 03/2013 5.12 % 4.66 % 0.46 %
11 04/2013 5.21 % 4.91 % 0.30 %
12 05/2013 4.10 % 4.01 % 0.09 %
13 06/2013 4.50 % 3.87 % 0.63 %
14 07/2013 1.75 % 2.95 % 4.70 %
15 08/2013 3.71 % 4.52 % 0.81 %
16 09/2013 4.20 % 3.93 % 0.27 %
17 10/2013 4.26 % 4.99 % 0.73 %
18 11/2013 4.00 % 3.84 % 0.16 %
19 12/2013 5.10 % 4.99 % 0.11 %
20 TEmonthlyD 1.29 %
21 TEp:a:D 4.48 %
22 rPfp:a:D 15.79 % rBmp:a:D 13.02 %
23 IRD 0.62
Source: Own, for illustrative purposes only
• Annualized portfolio returnrPfp:a:in cellB22:
15:79% D f.PRODUCT.1CB2WB19//^.12=18/1g
• Annualized benchmark returnrBmp:a:in cellD22:
13:02% D f.PRODUCT.1CC 2WC19//^.12=18/1g
• Monthly tracking errorTEmonthlyin cellD20: 1:29% D STDEV:S.D2WD19/
• Annualized tracking errorTEp:a:in cellD21 4:48% D SQRT.12/STDEV:S.D2WD19/
• Information ratioIRof the portfolio in cellB23: 0:62 D .B22D22/=D21
An information ratio of0:62is rather average. However, a meaningful inter- pretation of this value is difficult as only 18months of performance data are available.
End of Example 11 1.3.8.3 Conclusion
The information ratio is used to evaluate the added value (alpha) of an actively managed portfolio and, thereby, the quality of its portfolio manager on a risk- adjusted basis. The higher the information ratio, the better. In the long run, an information ratio of1is very good: It indicates that for each additional percentage of tracking error the active manager can generate an additional percentage point of alpha.