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Although originally called the "appraisal ratio" by Treynor and Black, the information ratio is the ratio of relative return to relative risk (known as "tracking error"). Whereas the Sharpe ratio looks at returns relative to a riskless asset, the information ratio is based on returns relative to a risky benchmark which is known colloquially as a "bogey." Given an asset or portfolio of assets with random returns designated by Asset and a benchmark with random returns designated by Benchmark, the information ratio has the form:
Mean(Asset - Benchmark) / Sigma (Asset - Benchmark)
Here Mean(Asset - Benchmark) is the mean of Asset minus Benchmark returns, and Sigma(Asset - Benchmark) is the standard deviation of Asset minus Benchmark returns. A higher information ratio is considered better than a lower information ratio. For more information, see inforatio.
To calculate the information ratio using the example data, the mean return of the market series is used as the return of the benchmark. Thus, given asset return data and the riskless asset return, compute the information ratio with
load FundMarketCash
Returns = tick2ret(TestData);
Benchmark = Returns(:,2);
InfoRatio = inforatio(Returns, Benchmark)
which gives the following result:
InfoRatio = 0.0432 NaN -0.0315
Since the market series has no risk relative to itself, the information ratio for the second series is undefined (which is represented as NaN in MATLAB^{®} software). Its standard deviation of relative returns in the denominator is 0.