## Using the Information Ratio

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.